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Investigation of hybrid organic-inorganic lead
halide perovskites by modulated surface
photovoltage spectroscopy
Vorgelegt von
M.Sc.
Celline Awino Omondi
Geb. in Siaya (Kenia)
Von der Fakultät IV Elektrotechnik und Informatik
der Technischen Universität Berlin
zur Erlangung des akademischen Grades
Doktor der Naturwissenschaften
Dr. rer. nat.
genehmigte Dissertation
Promotionsausschuss:
Vorsitzender: Prof. Dr. Bernd Szyszka
Gutachter: Prof. Dr. Bernd Rech (TUB)
Prof. Dr. Roland Scheer (Martin Luther Universität, Halle)
PD Dr. Thomas Dittrich (TUB / HZB)
Tag der wissenschaftlichen Aussprache: 05. Juli 2018
Berlin 2018
2
Abstract
Hybrid organic-inorganic metal halide perovskites (called here perovskites) have emerged as
a new group of materials for highly efficient solar cells (SCs) based on earth abundant
elements which can be processed from solutions at low temperature. CH3NH3Pb(I1-xBrx)3
perovskite films were studied in the thesis since it belongs to the materials which are of great
interest for top SCs in tandem SCs with c-Si bottom SCs due to its tunable band gap. Electronic
properties of CH3NH3Pb(I1-xBrx)3 perovskite films sensitively depend on crystallization and
defect formation and are crucial for the performance and stability of SCs. The band gap (Eg),
exponential tail states (Et) and the diffusion length (L) are decisive parameters for absorbers
in SCs since they give principle limitations for photo-generation and Fermi-level splitting. In
CH3NH3Pb(I1-xBrx)3 perovskites, Eg, Et and L are not necessarily constant and can depend, for
example, on the preparation conditions and degradation. Therefore, Eg, Et and L of
CH3NH3Pb(I1-xBrx)3 perovskites were studied with respect to stoichiometry, interfaces,
degradation and temperature. Modulated surface photovoltage (SPV) spectroscopy was used
as the main characterization technique. Modulated SPV spectroscopy allows for the
contactless and very sensitive characterization of Eg, Et, direction of charge separation and L
(after Goodman) without the requirement of the preparation of contacts after or during different
stages of layer preparation, light soaking etc. Vegard’s law was applied to obtain the
composition of CH3NH3Pb(I1-xBrx)3 films. The Eg of CH3NH3Pb(I1-xBrx)3 films varied between
1.59 eV to 2.30 eV depending on the stoichiometry whereas the bowing parameter was 0.36
eV. The influence of the substrate on Eg and Et of CH3NH3PbI3 films was investigated. It has
been found, for example, that Eg and Et of CH3NH3PbBr3 sensitively depend on the substrate
and on soaking in nitrogen atmosphere and that light soaking has strong influence on the
direction of modulated charge separation. CH3NH3PbI3 deposited on double layers of TiO2-
PCBM and SnO2-PCBM showed a constant band gap of 1.58 eV and a low scatter in Et. This
was attributed to the modification of the TiO2 or SnO2/CH3NH3PbI3 interfaces by PCBM allowing
for efficient charge separation and transfer and well reproducible conditions for the layer
formation. A decrease of L with light soaking was observed and can be attributed to light
induced degradation due to charging and discharging of trap states and formation of defects
at the TiO2/ CH3NH3PbI3 interface. Furthermore, Eg and Et of CH3NH3PbI3 stabilized with
PMMA increased with increasing temperature, i.e. thermal expansion gives the predominant
contribution to the temperature dependence of Eg of CH3NH3PbI3 whereas dynamic disorder
was limited by phonons. A jump-like increase of Eg in the region of phase transition was
attributed to the phase transition from the tetragonal to the cubic phases.
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Zusammenfassung
Hybride organisch-anorganische Metallhalidperovskite (hier kurz Perovskite genannt) sind
eine neue Materialgruppe für hocheffiziente Solarzellen, welche auf in der Erdkruste reich
verfügbaren Elementen basieren und welche bei niedrigen Temperaturen aus Lösungen
hergestellt werden können. Perovskitschichten aus CH3NH3Pb(I1-xBrx)3 wurden in der
Doktorarbeit untersucht, da diese für Anwendungen als Topzellen in Tandemsolarzellen mit c-
Si-Bottomzellen aufgrund der einstellbaren Bandlücke von großem Interesse sind. Die
elektronischen Eigenschaften von Perovskitschichten aus CH3NH3Pb(I1-xBrx)3 hängen
empfindlich von der Kristallisation und der Bildung von Defekten ab und sind kritisch für die
Leistung und Stabilität von Solarzellen. Die Bandlücke (Eg), die exponentiellen Bandausläufer
(Et) und die Diffusionslänge (L) sind entscheidend für Absorber in Solarzellen, da sie die
Photogeneration und die Aufspaltung der Fermi-Niveaus limitieren. Eg, Et und L sind in
Perovskitschichten aus CH3NH3Pb(I1-xBrx)3 nicht zwingend konstant und hängen z.B von der
Präparation und der Degradierung ab. Deshalb wurden Eg, Et und L mit Hinblick auf die
Stöchiometrie, Grenzflächen, Degradierung und Temperatur untersucht. Als
Hauptuntersuchungsmethode wurde die modulierte Oberflächenphotospannungs-
spektroskopie (SPV) eingesetzt. Die SPV erlaubt eine kontaktlose und außerordentlich
empfindliche Bestimmung von Eg, Et, Richtung der Ladungstrennung und L (nach Goodman)
nach oder während verschiedener Schritte der Präparation oder Degradierung, z.B. unter
Beleuchtung. Anhand des Vegard’schen Gesetzes wurde die Stöchiometrie von CH3NH3Pb(I1-
xBrx)3 ermittelt. Eg von CH3NH3Pb(I1-xBrx)3 variierte zwischen 1.59 und 2.30 eV, wobei der
Bowingparameter 0.36 eV betrug. Starke Einflüsse des Substrates und der Lagerung in
Stickstoffatmosphäre auf Eg, Et und die Richtung der modulierten Ladungstrennung wurden
u.a. in CH3NH3PbBr3 festgestellt. Eg betrug für auf TiO2/PCBM oder SnO2/PCBM
abgeschiedenes CH3NH3PbI3 1.58 eV und Et zeigte nur geringfügige Variationen, PCBM hat
also kaum Einfluss auf Eg und Et. und trägt sehr zur effizienten Ladungstrennung und zur gut
reproduzierbaren Herstellung von Perovskitschichten bei. Die beobachtete Abnahme von L in
CH3NH3PbI3 unter Beleuchtung kann der Umladung von Defekten sowie der Generation
zusätzlicher Defekte besonders im Bereich der Grenzfläche zwischen TiO2 und CH3NH3PbI3
zugeordnet werden. Eg und Et stiegen mit steigender Temperatur für mit PMMA stabilisiertes
CH3NH3PbI3 an, was auf den dominanten Einfluss der thermischen Ausdehnung und der
Limitierung der dynamischen Unordnung durch Phononen zurückzuführen ist. Ein
sprunghafter Anstieg von Eg bei etwas höheren Temperaturen wurde dem Übergang der
tetragonalen Phase von CH3NH3PbI3 in die kubische Phase von CH3NH3PbI3 zugeordnet.
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Contents
CHAPTER 1 ............................................................................................................................. 6
Introduction ............................................................................................................................ 6
CHAPTER 2 ........................................................................................................................... 11
Fundamentals of perovskites .............................................................................................. 11
2.1. Perovskite structure ............................................................................................... 11
2.2. Band gap of hybrid organic-inorganic metal halide perovskites ....................... 15
2.3. Electronic and optical properties of hybrid organic-inorganic lead halide
perovskites ........................................................................................................................ 27
2.4. Solar cells based on hybrid organic-inorganic lead halide perovskite ............. 31
2.5. Stability of hybrid organic-inorganic lead halide perovskite ............................. 37
CHAPTER 3 ........................................................................................................................... 44
Modulated surface photovoltage (SPV) spectroscopy ..................................................... 44
3.1 Principle of modulated surface photovoltage spectroscopy ............................. 44
3.2 Components for modulated SPV spectroscopy measurements ........................ 47
3.3 Determination of the band gap and exponential tails by SPV ............................ 49
3.4 Measurement of the diffusion length after Goodman ......................................... 52
CHAPTER 4 ........................................................................................................................... 54
Experimental and characterization methods ..................................................................... 54
4.1. Preparation of substrates and of hybrid organic-inorganic lead halide
perovskites ........................................................................................................................ 54
4.2 Morphology and architecture of hybrid organic-inorganic lead halide
perovskites ........................................................................................................................ 60
4.3 Phase analysis by grazing incidence X-ray diffraction (GIXRD) ........................ 64
4.4 Ultraviolet-visible light spectroscopy (UV-vis) .................................................... 67
4.5 Photothermal deflection spectroscopy (PDS) ..................................................... 69
4.6 Experiments with modulated surface photovoltage (SPV) spectroscopy ........ 71
CHAPTER 5 ........................................................................................................................... 74
Properties of CH3NH3Pb(I, Br)3 and their dependence on aging and light soaking ....... 74
5.1. Mixed lead halide perovskite: CH3NH3Pb(I1-XBrX)3 ............................................... 74
5.2. The role of storage and light soaking on the degradation of CH3NH3PbBr3
coated with PMMA ............................................................................................................ 85
5.3. Influence of the substrate on the electronic properties of the CH3NH3 PbI3 films
................................................................................................................................. 88
5.4. Effects of light soaking on the transport length of CH3NH3PbI3 ........................ 97
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5.5. Summary ............................................................................................................... 101
CHAPTER 6 ......................................................................................................................... 103
Temperature dependent, modulated surface photovoltage measurements on stabilized
CH3NH3PbI3 layers .............................................................................................................. 103
6.1. Stabilization of CH3NH3PbI3 with PMMA for temperature-dependent
measurements ................................................................................................................ 103
6.2. Temperature dependent measurements of the modulated surface
photovoltage for the band gap of CH3NH3PbI3 stabilized with PMMA ....................... 116
6.3. Summary ............................................................................................................... 127
CHAPTER 7 ......................................................................................................................... 128
Summary and Outlook ....................................................................................................... 128
References .......................................................................................................................... 131
Publications ........................................................................................................................ 152
List of abbreviations and symbols ................................................................................... 153
Acknowledgments .............................................................................................................. 157
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CHAPTER 1
Introduction
With growing population, there is an unprecedented sharp rise in the energy demand of
mankind. The increasing energy demand leads to the depletion of fossil fuels. Furthermore,
the adverse climatic changes coupled with global warming due to the emission of greenhouse
gases from fossil fuels are growing. Therefore, the societies are faced with challenges to
develop and incorporate energy technologies based on renewable energy sources that can
replace fossil fuels. The sun is the largest source of energy with about 3.9 x 1024 J of solar
energy annually reaching the earth’s surface [1]. This qualifies solar energy as the most viable
candidate that can supply and meet the energy demand required by the growing population.
Photovoltaic or solar cells (SCs) convert solar light directly into electricity. Earth abundant
materials are key for the development and sustainable production of reliable and efficient solar
cells. Material concepts for SCs can be classified as large silicon crystals (wafer based
crystalline silicon), epitaxial layer systems of group III - V compounds, thin films on foreign
substrates and nanocomposites. The PV market is dominated by crystalline silicon (c-Si),
based on p-n junctions and account for more than 90% of the PV module production [2]. Silicon
is naturally abundant, reliable and c-Si solar cells are very stable with a life span of more than
25 years [3]. c-Si solar cells have record power conversion efficiencies of up to 26.7 % [4]. A
disadvantage with silicon based wafer technology is the relatively high energy demand for the
production of very pure silicon crystals.
The absolutely highest power conversion efficiency was reached under concentrated
sunlight for SCs based on epitaxial layers of group III V compounds (46% for multi-junction
SCs) [5]. Despite high efficiencies, the use of SCs based on group III-V semiconductors is
limited to space applications, and concentrator SCs due to the high cost of production [2]. Thin
film technologies are developed to reduce manufacturing costs and material usage. Thin
absorber layers are deposited on foreign substrates. However, disadvantages with thin film
SCs are, for example, a low efficiency for amorphous silicon (a-Si:H) and material scarcity
(tellurium in cadmium telluride and indium in copper gallium indium diselenide SCs) [6].
Nanocomposites are materials with interpenetrating different phases which are combined
together to achieve a desired combination of properties. Dye-sensitized solar cells [7] are the
most prominent nanocomposite SCs. However, the use of a liquid electrolyte prevented a
broad penetration of this technology.
For the further strong improvement of the efficiency of c-Si solar cells, their implementation
into tandem and other multi-junction SCs will be necessary. The Shockley-Queisser limit is 33
% [8] for single junction SCs and the efficiency is limited to 44 % [5] for tandem SCs at air
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mass 1.5 global (AM 1.5G).Therefore, there is the need to produce tandem solar cells with a
large band gap material (Eg about 1.7 eV) for the top cell and c-Si (Eg = 1.1 eV) for the bottom
cell. The top cell absorbs photons with high energies and transmits photons with low energies
to the bottom cell.
Quite recently, hybrid organic - inorganic metal halide perovskites (in this thesis also called
perovskites) emerged as a new group of materials for highly efficient SCs based on earth
abundant materials which can be processed at low temperature. The material has emerged as
a potential low cost alternative for top cells due to its flexibility, tunable band gap and it can be
deposited from solution processes with high efficiency.
A perovskite has a ABX3 structure, where A can be, for example, methyl ammonium
(CH3NH3+) (MA+) or formamidinium [HC(NH2)2+] (FA+) or cesium (Cs+) cation; B is commonly
a lead (Pb2+) or tin (Sn2+) cation and X is a halide anion (Cl-, Br-, or I-) [9]. The material
combines properties of both organic and inorganic materials and can be deposited from
solution processes leading to opto- electronic properties of perovskites well reliable for SCs.
In 1990s, Mitzi et al. [10] studied the semiconducting properties of hybrid organic-inorganic
halide perovskite in field effect transistors. The 3-D CH3NH3SnI3 perovskite revealed a low
charge carrier density with a Hall mobility of 50 cm2/V.s at 300 K [11]. In 2009, Kojima et al.
studied the photovoltaic function of CH3NH3PbI3 and CH3NH3PbBr3 on TiO2 as a light sensitizer
in photo electrochemical cells and realized a power conversion efficiency of 3.81 and 3.13%,
respectively [12]. Since then, lead halide perovskites have attracted increasing attention and
present a very promising technology for further development of SCs.
Perovskite material poses excellent absorption properties [13], an intrinsic material with
moderate charge carrier mobilities [14], large carrier diffusion length of more than 1 µm [15],
shallow defect levels [16] and a direct band gap resulting in high efficiencies up to 22.1 % [5].
Furthermore, perovskite materials have a band gap that can be tuned between 1.17 [17] and
2.3 eV [18] by varying the composition of ions (mixed cations and mixed anions) [9,19].
Perovskites undergo degradation when exposed to moisture, light and heat. A stabilized
power conversion efficiency (PCE) of about 21.1 % has been realized on mixed perovskite
based on the so-called triple cations (contains Cs+, MA+ and FA+) and upon light soaking for
250 h, PCE decreased to about 18% [9]. Formation of light induced traps and halide
segregation for CH3NH3Pb(I, Br)3 films upon light soaking has also been observed [20]. For
comparison, c-Si SCs are very stable (degradation rates are about 0.5 0.7 %) [21].Therefore,
the stability of perovskite SCs has to be further improved. Based on this, there are open
questions that need to be addressed to increase the understanding of the fundamental
properties of perovskite.
What is the nature of band structure of perovskite?
How do interfaces influence disorder in the bulk of perovskite materials?
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What are the mechanisms behind stabilization of perovskites?
The band gap (Eg), exponential tail states (characterized by Et, the tail energy, or Eu, the
so called Urbach energy which is obtained from absorption spectra) and the diffusion length
(L) are decisive parameters for absorbers for SCs since they give the principle limitations for
photo-generation and Fermi level splitting. In perovskites, Eg, Et (u) and L are not necessarily
constant and can depend, for example, on preparation and degradation. Therefore, Eg, Et and
L are studied in this work with respect to stoichiometry, interfaces, degradation and
temperature. For example, Eg is an important parameter that reflects on the nature of chemical
bonding of a material, Et gives information about the disorder in a material whereas L gives
information about photo-generation of charge carriers in SCs. Furthermore, light induced
defects are important because photo-generated electrons can change the chemical bonds.
Also, knowledge of the transport length of photo-generated charge carriers and their
dependence on light soaking is of interest for the development of efficient and stable solar
cells.
In order to study the Eg, Et and L, a sensitive method that depends on photo-generation,
charge transport and separation is needed for characterization. Modulated surface
photovoltage (SPV) spectroscopy was used as the main characterization technique. SPV is
the difference between the surface potential of a semiconductor material under illumination
and in the dark [22]. SPV signals are generated whenever photo-induced charge carriers are
separated in space [23]. The technique is contactless, non-destructive and surface sensitive.
Modulated SPV allows for the characterization of electronic properties related to the band gap
(Eg), exponential tail states close to the band edges (Et), deep defect states and transport or
diffusion length (L). Furthermore, SPV analysis does not require the preparation of contacts
and can be performed after different stages of layer preparation, light soaking etc.
The reproducibility of perovskites depends very much on the preparation conditions. For
example, the bandgap (Eg) for CH3NH3PbI3 perovskite can vary between 1.5 to 1.6 eV
[19,24,25] depending on the conditions of preparation. Furthermore, the prototypical
perovskite, i.e. CH3NH3PbI3, undergoes a phase transition from tetragonal to cubic at a
temperature of about 55° C [26] which can affect the performance and stability of perovskite
based devices. Depending on annealing time, CH3NH3PbI3 layers can be p-type or n-type
doped [27]. The excess of CH3NH3 and iodine (I) leads to p-type doping of CH3NH3PbI3 layers,
whereas the deficiency of CH3NH3 and I leads to the formation of the PbI2 phase on the surface
of CH3NH3PbI3 films and to n-type doping. Reduced disorder has been observed when a small
amount of ammonium valeric acid iodide (AVAI) is added into solution containing PbCl2 and
CH3NH3I [28]. This caused the formation of a stabilized precipitate of CH3NH3PbCl3 that
supported controlled crystallization of CH3NH3PbI3 which further led to a reduction of disorder.
Perovskite is known to be unstable when exposed to moisture, oxygen, continuous illumination
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and high temperature. Degradation of CH3NH3PbI3 leads to the formation of other phases such
as PbI2 [29]. The resulting PbI2 can form a passivating layer on the CH3NH3PbI3/PbI2 interface
during moderate heating which is beneficial for solar cells [29].
The temperature dependence of the band gap of CH3NH3PbI3 perovskite layers gives
information about the nature of the semiconductor, i.e. whether it is dominated by electron-
phonon interaction or by thermal expansion. For example, for conventional semiconductors
such as silicon, Eg decreases monotonically with temperature whereas for perovskites, Eg,
increases linearly with temperature [30,31] . The monotonic decrease of Eg with temperature
is due to dominant contribution of electron- phonon interaction [30] whereas the linear increase
of Eg with temperature is due to the dominant contribution of thermal expansion of the lattice
[31]. Furthermore, under operating conditions, the temperature of a solar cell can vary over a
relatively wide range up to 70° C. Temperature fluctuations affect the efficiency of perovskite
based solar cells. Therefore, the precise knowledge of the temperature dependence of the
band gap for methyl ammonium lead iodide and related perovskites is essential for deeper
understanding of the temperature dependence of solar cells and origins behind.
This thesis is divided into 7 chapters where chapter 1 and chapter 7 are the introduction
and summary, respectively. Chapter 2 covers the fundamentals of perovskite and its electronic,
optical and structural properties. Models of temperature variation of the band gap of
semiconductors are explained and the temperature dependence of the band gap of selected
semiconductors are compared. Stoichiometry of perovskites in relation to Vegard’s law is
described. A systematic description of different charge selective contacts with various
chemical, electric and transport properties is presented. Issues of stability under moisture,
oxygen, heat, light soaking, ultra violet (UV) illumination and charge selective contacts are
discussed.
Chapter 3 describes the fundamentals of modulated surface photovoltage (SPV)
spectroscopy. The principle of modulated SPV is explained. Modulated SPV signals such as
in-phase signals, phase shifted by 90° signals, amplitude and phase angles are explained and
the components of set-ups for modulated SPV spectroscopy measurements are described.
The chapter explains how the parameters Eg, Et and L were obtained. Eg, for example, was
analyzed as an onset energy (Eon), as energy of inflexion point (Eg-ip) and as a Tauc gap (Eg-
Tauc) for direct semiconductors.
The experimental methods are described in chapter 4. This includes substrate and sample
preparation, characterization and analysis methods. The fabrication method for CH3NH3PbI3,
CH3NH3PbBr3, stoichiometric variations of CH3NH3Pb(I1-XBrX)3 layers as well as preparation of
various charge selective contacts are explained. The chapter explains how Eg, Et, as well as L
after Goodman [32] were analyzed. Supporting methods such as UV-vis spectroscopy,
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photothermal deflection spectroscopy (PDS) and grazing incidence x-ray diffraction (GIXRD)
are also described in the chapter.
Chapter 5 gives the results on the properties of CH3NH3Pb(I, Br)3 and their dependence
on aging and light soaking. The band gap of CH3NH3Pb(I1-XBrX)3 films was tuned from 1.59 eV
to 2.30 eV by varying the stoichiometry of the perovskite. Vegard’s law was used to obtain the
composition of CH3NH3Pb(I1-X BrX)3 films. The lattice constant decreased linearly with
increasing CH3NH3Pb(I1-X)BrX)3 composition. Furthermore, the bowing parameter of 0.36 eV in
CH3NH3Pb(I1-X BrX)3 perovskite films measured by SPV correlated well with the values of 0.33
and 0.29 eV obtained by Noh et al. [19] and Jacobsson et al. [33] respectively.
The values of Eu and Et were observed to be lower for pure tri-iodide and tri-bromide
perovskite but higher for mixed perovskites. The influence of the substrate on Eg and Et of the
CH3NH3PbI3 films was investigated. CH3NH3PbI3 deposited on double layers of TiO2-PCBM
and SnO2-PCBM showed a constant band gap of 1.58 eV and low scatter in the value of Et.
This was attributed to the modification of theTiO2 or SnO2/CH3NH3PbI3 interfaces by the PCBM,
to allow for efficient charge separation and transfer [34]. Effects of light soaking on the transport
length of CH3NH3PbI3 were studied using SPV. A decrease in the transport length with light
soaking time was observed. The decrease in the value of transport length was attributed to
light induced degradation which arises due to trap states and charging- discharging effect at
TiO2/ CH3NH3PbI3 interface.
Chapter 6 covers the results of the temperature dependence of the band gap of
CH3NH3PbI3 perovskite layers measured by modulated SPV. In order to avoid degradation in
vacuum during temperature dependent SPV measurement, a poly (methyl methacrylate)
(PMMA) layer has been deposited on CH3NH3PbI3 films and optimized in order to stabilize
CH3NH3PbI3. The temperature dependence of Eg and Et were investigated using modulated
SPV spectroscopy. Eg and Et of CH3NH3PbI3 increased with increasing temperature. The
results showed that thermal expansion gives the predominant contribution to the temperature
dependence of the band gap of CH3NH3PbI3 whereas dynamic disorder is limited by phonons.
A jump in the value of Eg near the region of phase transition has been observed and was
related to the phase transition from the tetragonal to the cubic phases. The temperature
dependence of Et was fitted with a model taking into account phonon-induced disorder and
phonon energy Eph of 150 ± 40 was obtained.
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CHAPTER 2
Fundamentals of perovskites
2.1. Perovskite structure
The term perovskite is related to the structure of the mineral called calcium titanate oxide
(CaTiO3). It was collected in the Ural Mountains of Russia by Perovski and described for the
first time by Gustav Rose in 1839. He named the mineral as ‘Perovskite’ in honor of Russian
mineralogist Lev Alekseevich Perovski (1792-1852). The structure of hybrid organic-inorganic
perovskite family is ABX3, where A is a monovalent cation such as CH3NH3+ (methylamonium
cation), HC(NH2)2+ (formamidium cation), Rb+, Cs+; B is the inorganic component usually
divalent metal cation such as Mg2+, Ca2+, Sr2+, Ba2+, Sn2+, Pb2+ and X is anion such as O2- Cl-,
I-, Br- [9,35,36,37].
Figure 2.1: ABX3 perovskite structure.
The size of cation A has a strong influence on the structure of perovskite. Furthermore,
cation A compensates the charge within the lattice and has only minor influence on the
electronic properties of the perovskite. The size of cation A can cause distortion in the B-X
bonds, thereby affecting the symmetry [38]. Assuming a rigid sphere model for all ions,
Goldschmidt’s equation [39] can be used to calculate a tolerance factor (TF) for hybrid
perovskites from the effective radii of ions.
𝑇𝑇𝑇𝑇2(𝑟𝑟𝐵𝐵+𝑟𝑟𝑋𝑋)=𝑟𝑟𝐴𝐴+𝑟𝑟𝑋𝑋 2.1
where TF is tolerance factor, rA, rB and rX are the radii of the ions A, B and X respectively. It is
assumed that the values rA+rX and rB+rX are the approximate distances of between the anion
X and the cations A and B, respectively. For an ideal cubic perovskite structure, TF is equal to
unity. For TF > 1, the structure distorts towards the tetragonal structure. For TF < 1, the
structure distorts towards the bulk of the octahedral structure [40]. Therefore physical
properties such as magnetic, electronic and dielectric ones depend highly on distortions. For
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12
instance, the CH3NH3+ cation has a permanent electric dipole moment which changes the
dynamic orientations of these ions thereby contributing to the dielectric properties [41].
A hybrid organic-inorganic lead halide perovskite, such as CH3NH3PbX3, consists of a
divalent inorganic cation, a monovalent organic cation and halide anion. If the size of the
organic cation is too large, then the 3-D network is broken and a 2-D network is formed (see
figure 2.2). TF is equal to 1 for a perfect 3-D network. In reality, as found empirically, TF varies
between 0.8 and 1.0 for most of the cubic perovskite structures [42]. This implies that a small
organic cation consisting of two or three atoms with one carbon atom and one nitrogen atom
can fit into the space provided between nearest neighbours of the anion X [41,43]. On the other
hand, for a 2-D network, cation A is too large to fit into the space provided by the nearest
neighbours of the anion X within the inorganic sheet resulting in the distortion of the cubic
structure resulting in TF > 1. In such a situation, the organic cation is kept away from the
inorganic sheets by a spacer such as alkyl chains. A commonly used structure of a 2D
perovskite, given by (R-NH3)2BX4, is shown in figure 2.2 (b), where cation A is an organic
component of (R-NH3)2 with R being an aromatic ammonium or aliphatic cation. The layers of
the relatively large organic cations form barriers whereas the inorganic structures (BX4) form
wells for charge carriers so that the whole network form a self-organized quantum well
structure [43].
Figure 2.2: Schematics of (a) the 3-D octahedral and (b) the 2-D perovskite structures.
The 3-D crystal structure of hybrid organic-inorganic lead halide perovskites is of primary
interest for reaching very high efficiencies in SCs. This work is focused on methylammonium
lead iodide (CH3NH3PbI3), methylammonium lead bromide (CH3NH3PbBr3) and stoichiometric
variations of CH3NH3Pb(I1-XBrX)3 layers. Perovskites with mixed cations can result in higher
efficiencies. Perovskites with three different A cations can also be called triple cation, for
13
example, [Cs0.05(FA0.83MA0.17)0.95]Pb(I0.83Br0.17)3 where Cs, FA (CH3(NH2)2 and MA (CH3NH3)
stand for cesium, formamidium and methylammonium cations, respectively.
Early crystallographic studies identified three phases of CH3NH3PbI3: orthorhombic,
tetragonal and cubic phases [41]. X-ray diffraction (XRD) and calorimetric measurements have
confirmed two phase transitions of CH3NH3PbI3 at 162 K (orthorhombic / tetragonal) and 327
K (tetragonal / cubic) [44].
The orthorhombic phase of CH3NH3PbI3 occurs at temperature of about 160 K [45]. The
initial space group of orthorhombic phase was pna21 which was later reclassified into pnma by
neutron powder diffraction [46]. In the pnma space group, CH3NH3+ cations are fixed with
rotation restricted along the C-N axis. Furthermore, the CH3NH3+ cations are fully ordered
whereas the PbI6 octahedra are slightly distorted. The behaviour makes the average Pb-I-Pb
bond angle to be 154.5°, with the individual bond angle of Pb-I1-Pb being 161.94° along the b
axis and Pb-I2-Pb = 150.72° along both the a- and c- axes. These tilts enable iodide ions to
move towards the NH3 end of the CH3NH3+ cations and away from the CH3 end of the unit
cell [47]. On the other hand, the orthorhombic phase of CH3NH3PbBr3 exists at temperatures
below 144.5 K having a space group of pna21 with the lattice parameters of a= 7.979 Å, b =
8.58 Å and c = 11.849 Å. The unit cell occupies a volume of 811 ų [41] . In the pna21 space
group, the CH3NH3+ cation is highly ordered because the ions are in a frozen state by
mechanical strain or electric field [48]. As a remark, the orthorhombic phase of both
CH3NH3PbI3 and CH3NH3PbBr3 perovskite crystals possesses ferroelectric and anti-
ferroelectric properties because the symmetry of the unit cell changes from a centrosymmetric
to an acentric system making the ions within the lattice to be off-centred due to the rotation of
CH3NH3+ cation within the unit cell [41].
The tetragonal phase of CH3NH3PbI3 occurs at temperatures between 162.2 K and 327.4
K [41]. In the tetragonal structure, NH3+ moves closer to iodide (I-) thus lowering the
electrostatic energy due to rotation of the PbI6 octahedron along the c-axis. In addition, the
super lattice reflection increases in the tetragonal phase most probably due to ordering and
disordering of CH3NH3+ cations and I- anions. The CH3NH3PbBr3 perovskite has two tetragonal
phases, i.e. the beta (β) and the gamma (γ) phases. At temperatures between 155.1 and 236.9
K, the β phase of the CH3NH3PbBr3 tetragonal structure has the space group of I 4/mcm. In
this phase, the unit cell has the following lattice parameters: a = 8.322 and c = 11.83 . The
γ phase of CH3NH3PbBr3 occurs at temperatures between 149.5 and 155.1 K, has a space
group of P4/mmm and the following lattice parameters: a= 5.894 and c= 5,861 . The unit
cell of the tetragonal phase of CH3NH3PbBr3 possess the largest volume of 819 3 [41].
The cubic phase of CH3NH3PbI3 occurs at temperature above 327.4 K and has a space
group of pm3m with the lattice constant of the unit cell of a = b = c = 6.3285 . The unit cell of
the cubic phase of CH3NH3PbI3 occupies a volume of 253.5 3 [41]. In the cubic phase, the
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14
orientation of the CH3NH3+ cation is highly disordered in order to satisfy the cube symmetry.
Furthermore, CH3NH3+ poses two forms of orientational disorder whereby the first one involves
motion of the cation along the C-N axis with respect to the crystal axis whereas the second
one involves rotation of the cation around the C-N axis [44].
CH3NH3PbBr3 has a cubic structure at temperatures above 239.6 K with a space group of
pm3m. In this space group, the positions of CH3NH3+ cations are not fixed but possess an
eightfold disordered state in order to preserve the cubic symmetry of the lattice. The lattice
parameters in the cubic phase are as follows: a = 5.901 with the unit cell occupying a volume
of 260 [41], implying that in the cubic phase, there is rapid re-orientation of CH3NH3+ cation
along the C-N axis.
The lattice constant is a fundamental parameter of any crystalline material. The lattice
constant can help to identify a particular material and to provide information about the structural
properties of a material. Vegard’s law can be used to give an empirical relation between the
lattice constant and the composition of constituent elements. Vegard’s law states that the
crystallographic lattice parameters of a continuous solid solution vary linearly with composition
at a fixed temperature for constituent phases having the same bonding [49]. This means that,
when the influence of electronic effects is negligible, the lattice parameters of a unit cell in an
alloy shall vary linearly with the composition of a solid solution. The atoms or ions in the solid
solution are randomly distributed in order to substitute for each other. The relative size of the
atoms or ionic species controls the crystallographic lattice parameters making the law valid for
ionic compounds. In a binary solid solution of the compounds A and B, Vegard’s law can be
expressed as:
a = aA (1−x) + aB (x) 2.2
where x is the mole fraction of compound B and aA and aB are the lattice constants of the pure
compounds A and B, respectively.
Figure 2.3 shows the dependence of the lattice constant of pseudo-cubic CH3NH3Pb (I1-
xBrx)3 as a function of the content of bromide. The data points were acquired after Noh et al.
2013 [19]. The lattice constant decreased with an increase of the content of bromide in the
solution. According to Vegard’s law, the lattice constant in the alloy varies linearly with
composition at constant temperature and negligible electronic effects. Therefore, the linear
dependence of the lattice constant on x indicates the formation of a pseudo-cubic
CH3NH3Pb(I1-xBrx)3 compound in the complete range of 0 x 1 by a simple solution process.
Therefore, vice versa, the measurement of the lattice constant can be used for a precise
determination of x in CH3NH3Pb(I1-xBrx)3 compounds.
15
Figure 2.3: Dependence of the lattice constant of pseudo-cubic CH3NH3Pb(I1-xBrx)3 as a function of
bromide composition (x). Data point were taken after Noh et al. [19].
2.2. Band gap of hybrid organic-inorganic metal halide perovskites
2.2.1. Formation and origin of the band gap
The band gap (Eg) of a semiconductor is the difference between the valence band
maximum and conduction band minimum. A free electron is generated by exciting a valence
electron with energy equal or larger than Eg. An electron excited from the valence into the
conduction band leaves a mobile hole in the valence band. According to a periodic potential,
energy levels of free electrons and holes are arranged in bands.
The origin of Eg has been explained by different theories. In general, Eg originates from
the difference between bonding and anti-bonding states of hybrid orbitals. In the free electron
model, electrons move freely within the lattice, experiencing only potential barriers at the
boundaries [50]. Figure 2.4 (a) shows the energy of free electrons as a function of the electron
wave number. In the free electron model, all values of energy are allowed. On the other hand,
an electron travelling through a crystal lattice experiences periodic variation of potential
energy. This periodic variation of potential energy affects the behavior of conduction electrons.
The Bloch wave-function can be used to describe the periodic nature of an electron passing
through a periodic lattice. Electrons are considered as plane waves of the form exp(ikr)
travelling through a periodic lattice with the solution of the form
𝜑𝜑(𝐫𝐫)=𝑉𝑉𝑘𝑘(𝐫𝐫)exp(𝑖𝑖𝐤𝐤𝐫𝐫) 2.3
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16
where 𝑉𝑉𝑘𝑘(𝐫𝐫) has the periodicity of the lattice [50]. The wave functions of the form of equation
2.3 are called Bloch functions [50].
Figure 2.4 (b) shows the energy of electrons in a lattice as a function of the wave number.
Forbidden band gaps are those regions where solutions representing electrons passing
through a crystal lattice do not exist whereas allowed bands are the regions where electrons
can exist. For example, in the first Brillion zone, the allowed energy gap is between 𝜋𝜋
a<
𝐤𝐤<𝜋𝜋
a. Therefore the allowed energy bands can be represented by the wavenumber k within
the Brillion zone such that k =
a , where a, is the atomic spacing and n = ± 1, ± 2… which
can be seen as an overlap of atomic states. On the other hand, a forbidden band gap is
obtained where propagating waves are absent (see figure 2.4(b)).
Figure 2.4: Energy as a function of wave number for a free electron (a) and for an electron in a
periodic potential (b).
2.2.2. Direct and indirect band gap of hybrid organic-inorganic perovskite
Direct band gap semiconductors are those materials in which an electron is excited by a
photon of energy larger than the band gap to make transition from valence band maximum to
conduction band minimum (see figure 2.5 a). In such transitions, the crystal momentum or k-
vector is the same in both the valence band maximum and conduction band minimum. On the
other hand, indirect transition occurs when the energy of valence band maximum and
conduction band minimum takes place at different values of crystal momentum (see figure 2.5
b). In such transitions, a phonon is needed to supply the crystal momentum equal to the
difference between the minimum of the conduction band and valence band maximum.
It has been reported that CH3NH3PbI3 behaves like a direct band gap semiconductor since
a photon is needed in the absorption and emission processes via allowed transitions [51]. This
behaviour differs from indirect transitions in silicon in which absorption and recombination
processes involve a photon as well as a phonon. This explains why perovskite has high
17
absorption coefficients with slower recombination rates in comparison to silicon [52]. However,
theoretical calculations have also revealed the indirect nature of the CH3NH3PbI3 perovskite
absorber materials in which the conduction band minimum is slightly shifted relative to valence
band maximum [53]. The indirect nature is proposed to be due to Rashba splitting of the bands
due to electron phonon coupling which lead to the formation of spin allowed and spin
forbidden transitions. Spin forbidden transition results in a reduced recombination rate due to
momentum and spin mismatch while searching for phonon with the required momentum
[54].The reduced recombination results into longer lifetime for enhanced photovoltaic
performance.
Figure 2.5: Schematic illustration of (a) direct and (b) indirect band gap semiconductors.
2.2.3. Band gap of perovskite as a function of lattice constant and stoichiometry
The band gap of hybrid organic-inorganic halide perovskite materials can feasibly be tuned
by chemical substitution of alloys, enabling a wide range of parameters to be explored.
Comparing reported experimental values suggests that the band gap of perovskites can
feasibly be tuned from 1.17 eV for CH3NH3(SnxPb1-x)I3 [17] about 2.3 eV [55] for CH3NH3PbBr3
and even higher energies for chloride containing compounds [56]. However, the experimental
data sets obtained by different researchers are quite diverging suggesting the existence of
thermodynamic instability as well as miscibility gap for halide based compounds [57].Therefore
the band gap of perovskite based compound can be tuned following Vegard’s law.
Figure 2.6 (a) shows the dependence of band gap Eg as a function of lattice parameter of
pseudo-cubic CH3NH3Pb(I1-X BrX)3. The data points were acquired from the publication of Noh
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18
et al. [19]. Eg decreases with increasing lattice parameter suggesting a lattice contraction due
to increase in potential energy of the electrons in the orbitals of an atom.
Figure 2.6: Dependence of the band gap (a) on the lattice constant of pseudo-cubic CH3NH3Pb(I1-X
BrX)3 (data points acquired after Noh et al. [19]) and (b) on the bromide composition for pseudo-cubic
MAPb(I1-X BrX)3 [19] and FA0.16MA0.84Pb(I1-XBrx)3 [33].
Figure 2.6 (b) relates the reported band gap as a function of bromide composition for
CH3NH3Pb(I1-X BrX)3 and FA0.16MA0.84Pb(I1-XBrx)3 with data points acquired from Noh et al [19]
and Jacobsson et al. [33]. The non-linear variation of band gap as a function of bromide (Br)
composition can be obtained using the relation:
Eg [CH3NH3Pb(I1-x Brx)3]= Eg [CH3NH3PbI3] + Eg ([CH3NH3PbBr3] -[CH3NH3PbI3]- c)
+cx2 2.4
where c is the bowing parameter [58] which measures the degree of non-linear deviations
arising from the anisotropy in the binding energy. After substitution of the bowing parameter of
0.33 according to [19], equation 2.4 reduces to quadratic equation of the form:
Eg = 1.57 +0.39 x+0.33 x2 2.5
where x is the bromide concentration
Jacobson et al. [33] also applied equation 2.4 for band gap tuning of FA0.16MA0.84Pb(I1-
XBrX)3 and CH3NH3Pb(I1-XBrX)3 as a function of bromide concentration in the range between 0
x 1. A non-linear increase of Eg with increasing content of bromide has been observed.
The change in Eg with x did not significantly depend on the ratio between FA and MA cations
due to the fact that the organic cations have a small influence on the band gap because of a
negligible density of states near the band gap.
19
2.2.4. Band gap as a function of temperature
The band gap is a fundamental parameter of any semiconductor in relation to its electrical
and optical properties. It reflects the bond energies such that an increase in temperature affects
the chemical bonding when electrons are excited from the top of the valence band to bottom
of the conduction band [59]. The first experimental and theoretical work on electronic band gap
dated back to the dawn of the semiconductor era. Both the theoretical and experimental studies
have over many decades, successfully explained the normal behavior of the temperature
dependence of band gap for various types of semiconductors such as silicon (Si) [60],
germanium (Ge), gallium arsenide (GaAs) [61], indium phosphide (InP) [62], cadmium selenide
(CdSe) etc. In the conventional semiconductors, the band gap decreases monotonically with
increasing temperature, with the behavior being non-linear at low temperatures and linear at
higher temperatures [30]. For the inorganic semiconductors, the contribution of electron-
phonon interaction to the band gap change with temperature is more dominant in comparison
to dilation of the lattice [63,64]. However, there are some exceptional semiconductors with
unusual temperature behaviors where the band gap decreases with decreasing temperature.
An early example was PbTe in which a blue shift in energy gap was reported in the temperature
range between 50 and 300 K [65]. Recently, a similar unusual behavior has been observed for
lead sulphide (PbS) in which there is a strong increase in band gap energy with increase in
temperature, a behavior opposite to what is observed in most common semiconductors .The
increase was attributed to isotopic effect of the mass of sulphur which led to the cancellation
of the zero point motion of lead and sulphur [66]. CsSnI3 perovskite is another semiconductor
with the anomalous behavior of the band gap with temperature. A strong linear increase of the
band gap energy with increasing temperature in CsSnI3 perovskite was attributed to thermal
expansion contribution which dominates over electron-phonon interaction [31].
Several models have been reported in literature to describe temperature variation with
band gap energy. The first model was reported by Varshni in which he reported on empirical
model for the temperature dependent of the band gap energy in semiconductors [30]. The
proposed Varshni relation is of the form:
𝐸𝐸𝑔𝑔(𝑇𝑇)=𝐸𝐸𝑔𝑔(0)𝐴𝐴𝑇𝑇2
𝐵𝐵+𝑇𝑇 2.6
where 𝐸𝐸𝑔𝑔(𝑇𝑇) is the band gap energy as a function of temperature and the gap may be direct
or indirect, 𝐸𝐸𝑔𝑔(0) is the band gap at 0 K, 𝐴𝐴 is a constant whereas 𝐵𝐵 is fitting parameter related
to Debye temperature 𝜃𝜃𝐷𝐷 .Theoretical treatment of equation 2.6 leads to the form:
At 𝑇𝑇𝜃𝜃𝐷𝐷; ∆𝐸𝐸𝑔𝑔(𝑇𝑇)𝑇𝑇2 and 𝑇𝑇𝜃𝜃𝐷𝐷, ∆𝐸𝐸𝑔𝑔(𝑇𝑇)𝑇𝑇 2.7
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where ∆𝐸𝐸𝑔𝑔(𝑇𝑇) is the change in band gap as a function of temperature.
Expression 2.7 shows that the variation of band gap is non-linear at low temperatures and
linear at higher temperatures. At lower temperatures, the expression 2.7 indicates that there is
a quadratic temperature dependent which makes the fitting parameter 𝐵𝐵 negative for some
semiconductors such as diamond and hydrogenated silicon (6H SiC) [67]. The quadratic
behavior at low temperature contradicts with the experimental findings which showed an
approximate temperature independence of the band gap hence the inadequacy of the Varshni
model. This led to the development of The Bose-Einstein (BE) model which relates the shift
in the temperature dependent of energy gap with the Debye energy [68, 69]. Therefore, BE
model considers the contribution of both lattice dilation as well as electron –phonon vibrations.
According to this model, the change in band gap energy with temperature can be obtained
from the relation 2.8:
𝐸𝐸𝑔𝑔(𝑇𝑇)=𝐸𝐸𝑔𝑔(0)𝛼𝛼𝐸𝐸1 + 2
𝑒𝑒𝐸𝐸
𝑇𝑇 −1 2.8
where 𝛼𝛼𝐸𝐸 is parameter related to the strength of electron phonon interactions in the crystal
lattice; 𝐸𝐸 is Einstein characteristic temperature of interacting phonons within the system and
is related to the Debye temperature through the relation: 𝜃𝜃𝐷𝐷= 1.33 𝐸𝐸 [70].
Bose Einstein model has been used to obtain a better fit for Cu2ZnSnS4(CZTS) absorber
material with the experimental data [71]. The results suggested that a small shift of atoms or
ion arising due to lattice vibration would damage lattice periodic field which in turn affect
chemical bond length and energy of the band gap. In addition, temperature increase promotes
more active phonon population modes which results to more electron-phonon interaction
leading to shrinkage of the band gap [71]. However, the BE model could only be conceived in
rather low temperature regime and this led to the development of a model which is most
commonly used; the Pässler model.
Pässler model [72, 73] describes the variation of band gap with temperature based on the
dominant contribution of electron- phonon interaction. The model can be represented by the
following equation 2.9:
𝐸𝐸𝑔𝑔(𝑇𝑇)=𝐸𝐸𝑔𝑔(0)𝛼𝛼𝛼𝛼
2��1 + 2𝑇𝑇
𝛼𝛼𝑥𝑥
𝑥𝑥1 2.9
Where 𝐸𝐸𝑔𝑔(𝑇𝑇) and 𝐸𝐸𝑔𝑔(0) are the energy gaps at temperature T and 0 K, respectively.
As 𝑇𝑇, 𝛼𝛼=𝑑𝑑𝐸𝐸𝑔𝑔(𝑇𝑇)
𝑑𝑑𝑇𝑇 2.10
21
𝜃𝜃 is the temperature of phonon specific to a particular material whereas 𝑥𝑥 is empirical
parameter which is related to the shape of electron-phonon function usually confined to a range
of 𝑥𝑥> 2 [73].
In general the Varshni model presents three parameters whereas the Pässler model
presents 4 parameters that can be adjusted to fit the experimental data. Both models assume
that the dominant factor in the temperature dependent of the band gap is due to electron-
phonon interaction. However, the Varshni model shows some deviations in the low
temperature region with the experimental data in which the model predicts quadratic (T2)
behavior in the low temperature region and does not produce T4 temperature dependence
behavior observed in bulk silicon [74]. On the other hand, the Pässler model considers the
contributions of phonons with various energies. However, it ignores the contributions from the
thermal dilation of the lattice causing a significant deviations at higher temperatures. BE model
has been shown to fit in very well with the observed experimental trends at all temperatures
since it involves both the lattice dilation and electron-phonon interactions.
The contribution of the lattice dilation on the shift of band gap can be described by thermal
expansion based on the so called quasi harmonic approximation which assumes a harmonic
interatomic potential but takes into consideration zero point effects [31]. The periodic lattice
dilation of the temperature dependence of the energy band gap is given by the relation:
(𝑑𝑑𝐸𝐸𝑔𝑔
𝑑𝑑𝑇𝑇)𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑒𝑒 =(𝜕𝜕𝐸𝐸𝑔𝑔
𝜕𝜕𝜕𝜕)𝐵𝐵𝑜𝑜∆𝑉𝑉(𝑇𝑇)
𝑉𝑉𝑜𝑜 2.11
where 𝜕𝜕𝐸𝐸𝑔𝑔
𝜕𝜕𝜕𝜕 is pressure dependent at constant volume but independent of temperature, ∆𝑉𝑉(𝑇𝑇),
volume expansion term of the quasi harmonic approximation including zero-point effect. 𝑉𝑉𝑜𝑜 is
the volume of the lattice at temperature T and 𝐵𝐵𝑜𝑜 is the bulk modulus. The strongest
temperature variation appears through the term ∆𝑉𝑉(𝑇𝑇)
𝑉𝑉𝑜𝑜.
Therefore, at 𝑇𝑇<< 𝜃𝜃𝐷𝐷
∆𝑉𝑉(𝑇𝑇)
𝑉𝑉𝑜𝑜=𝑉𝑉(𝑇𝑇)−𝑉𝑉(0)
𝑉𝑉𝑜𝑜=𝑙𝑙𝑉𝑉𝛾𝛾𝐺𝐺
𝐵𝐵𝑜𝑜𝑇𝑇 2.12
where 𝑐𝑐𝑉𝑉 and 𝛾𝛾𝐺𝐺 are the specific heat capacity and Grüneisen parameter respectively [75]. On
the other hand, at 𝑇𝑇𝜃𝜃𝐷𝐷
∆𝑉𝑉(𝑇𝑇)
𝑉𝑉𝑜𝑜=𝑉𝑉(𝑇𝑇)−𝑉𝑉(0)
𝑉𝑉𝑜𝑜=𝑙𝑙𝑉𝑉𝛾𝛾′𝐺𝐺
4𝐵𝐵𝑜𝑜𝑇𝑇 2.13
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22
where 𝛾𝛾′𝐺𝐺 is an average of the Grüneisen parameters for the three branches of acoustic
phonons.
Generally, in most common semiconductors such as Si, GaAS, electron-phonon
interaction is the dominant factor that contributes to the shift in band gap with respect to
temperature. In these semiconductors, an increase in temperature promotes more phonon
population modes which increases more electron-phonon interaction leading to shrinkage of
the band gap. However, this is not the case for hybrid organic inorganic lead halide perovskite
which shows a reversed behaviour. The reports investigated in the literature indicate that the
contribution of direct electron-phonon interaction is negligible and the variation of band gap
with temperature is dominated by the thermal expansion contribution [31]. Thermal expansion
effects produces unusual signs which causes the anomalous behaviour in the energy band
gap with temperature. The unusual behaviour was first observed in PbTe and was attributed
to the interplay between lattice dilation and electron-phonon interaction in which the former
was thought to produce anomalous sign and contributed to half of the temperature dependence
of the band gap [76].
Figure 2.7 shows the dependence of the band gap energy with temperature. For common
semiconductors such as Si, GaAs, InP, the band gap decreases monotonically with increase
in temperature. The behavior is observed to be linear at higher temperatures and becomes
non-linear at low temperatures. However, CsSnI3 exhibited an exceptionally opposite behavior
in which the band gap increases monotonically with increasing temperature. For the former,
the major contributor to the variation of band gap with respect to temperature has been
reported to be mainly due to electron-phonon interaction with thermal expansion accounting
only for a small fraction of the total variation energy gap with temperature [30]. In contrast, for
the latter, the major contribution to variation of energy gap with temperature is mainly due to
lattice dilation as a result of thermal expansion of the lattice brought about by the anomalous
large electron effective mass [31]. In summary, the temperature variation of energy band gap
in semiconductors is mainly due to periodic lattice dilation [77] and electron-phonon interaction
[30].The dominant contribution in most semiconductors comes from electron-phonon
interaction which accounts for almost 80-90% of the shift in energy gap with temperature. This
is because lattice phonons have extremely small energies which make them readily excited in
large numbers at moderate temperature [59] and results into the shrinkage of the band gap
with increasing temperature.
23
Figure 2.7: Energy band gaps as a function of temperature for silicon (Si), gallium arsenide (GaAS),
indium phosphide (InP) and caesium tin iodide (CsSnI3) (red circles). The data for Si is obtained after
[60], GaAs [61], InP [62] and CsSnI3 [31]
Table 2.1 summarises some of the most commonly used parameters for different
compounds. The second column shows the ratio of electron effective mass to the rest mass
for Si, Ge, GaAS, InP, CdSe, CdTe and CH3NH3PbI3. Table 2.1 shows that GaAs has the
lowest effective mass whereas CsSnI3 compound has the largest value of electron effective
mass. The unusually large effective mass of CsSnI3 explain the unusual behaviour in the
temperature dependence of the band gap. Moreover, the temperature coefficient is of
significant importance since it enables the quantification of the temperature sensitivity of the
photovoltaic devices. As can be seen from table 2.1, dEg/dT is negative for common
semiconductors and positive for CH3NH3PbI3 and CsSnI3 semiconductors. The negative value
of dEg/dT for common semiconductors is due to strong electron-phonon interaction which
dominates over the thermal lattice dilation. On the other hand, for ionic semiconductors such
as CH3NH3PbI3 and CsSnI3, lattice dilation due to thermal expansion and intra-band interaction
is the dominant interaction in the temperature dependent of the band gap resulting into dEg/dT
< 0.
Figure 2.8 shows band gap energy and the slope of the linear approximation of the band
gap (dEg/dT) at 300 K for various semiconductors. For common semiconductors such as Ge,
Si, GaAs, CdTe, InP and CdSe, dEg/dT is negative. This is because for these semiconductors,
the electron-phonon interaction is stronger than intra-band interaction and thermal expansion
of the lattice resulting into dEg/dT < 0. On the other hand, for ionic semiconductors such as
CH3NH3PbI3 and CsSnI3, intra-band interaction and lattice dilation are the dominant
parameters responsible for positive temperature coefficient. It has also been reported in
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24
literature that band gap of CH3NH3PbI3 increases with increasing temperature due to reverse
band ordering of the electronic states such that the valence band maximum is constituted of
p-like states whereas the conduction band minimum is constituted of s-like states [78]. This
reverse ordering of band edge states are the main reason for the anomalous behavior of the
band gap with temperature CH3NH3PbI3 perovskite materials and hence the positive
temperature coefficient. Yu et al reported that the anomalous behavior of the temperature
dependence of the band gap of CsSnI3 perovskite was dominated by thermal expansion
contribution with negligible contribution from electron- phonon interaction due to unusually
large electron effective mass (0.734 mo) [31].
compounds
𝑚𝑚𝑒𝑒
𝑚𝑚
0
Band gap
(
𝐸𝐸
𝑔𝑔) (eV)
at 300 K
Temperature
Coefficient
𝑑𝑑𝐸𝐸𝑔𝑔
𝑑𝑑𝑇𝑇
×10
−4
eV/°K
References
Si
0.19
1.12
-4.73
[60,79, 80]
Ge
0.082
0.66
-4.4
[79, 81]
GaAS
0.067
1.424
-4.45
[82, 83, 84, 85]
InP
0.077
1.347
-2.88
[86, 87, 88]
CdSe
0.13
1.7
-3.3
[89, 90, 91]
CdTe
0.11
1.529
-4.3
[92, 81]
CH3NH3PbI3
0.32
1.55
3.2
[93, 17, 94]
CsSnI3
0.74
1.316
3.5
[31]
Table 2.1: Electron effective masses, band gaps at room temperature and values of temperature
coefficient (𝑑𝑑𝐸𝐸𝑔𝑔
𝑑𝑑𝑇𝑇) from a linear fit at 300 K.
Figure 2.8: Dependence of the temperature coefficient of band gap (dEg/dT) as a function of band gap
energy at 300 K for various semiconductors. See table 2.1 for references.
25
2.2.5. Influence of distortions in a lattice on absorption spectra near the band gap
A periodic lattice potential can be distorted by lattice vibrations and/or distortions in bond
lengths and bond angles due to defects such as lattice defects, impurities and dislocations.
Distortions in the periodic lattice potential cause fluctuations in the edges of the valence and
conduction bands and therefore of the band gap. In disordered semiconductors, such as
amorphous silicon (a-Si: H), local variations of bond lengths and bond angles are so strong
that the translation symmetry is lost. Furthermore, bond configurations change abruptly near
interfaces and surfaces of a semiconductor leading often to disorder in interface regions.
Fluctuations in the band gap result in a deviation of absorption spectra from those of ideal
direct or indirect semiconductors. These deviations are described by an exponential increase
of the absorption coefficient (α) with increasing photon energy near the band gap. The
exponential increase of α is characterized by the energy parameter Et (t stands for tails) or Eu
(u stands for Urbach who described the exponential absorption tails in semiconductors and
insulators for the first time [95]).
αexp(𝐸𝐸𝐸𝐸𝑜𝑜)/𝐸𝐸𝑙𝑙(𝑢𝑢) 2.14
Eu is also called the Urbach energy and is obtained by measuring the absorption spectrum.
Et(u) characterizes the degree of fluctuations or disorder in a semiconductor due to the
structure, composition and temperature. Compositional disorder can be due to variations in
stoichiometry, doping, hydrogenation, etc.
The characteristic energy describing the exponential increase of α with increasing
photon energy, i.e. Et(u), depends on temperature and structural disorder and is described by
the relation 2.15: 1
𝐸𝐸𝑡𝑡(𝑢𝑢)
=𝜎𝜎
𝐾𝐾𝐵𝐵𝑇𝑇 2.15
where 𝜎𝜎 is the steepness parameter of the absorption edge (depends on the nature of the
material), T is absolute temperature and KB is the Boltzmann constant. As an example, figure
2.9 shows the influence of temperature on Eu for a-Si:H. The values of Eu increase with
increasing temperature from about 55 meV at -150° C to about 67 meV at 60° C.
Figure 2.10 shows a typical absorption spectrum of a CH3NH3PbBr3 layer in the range near
the band gap. Three regions (A, B and C) can be distinguished in the absorption spectrum. At
lower photon energies, the absorption is caused by relatively deep defects states in the band
gap of CH3NH3PbBr3 films (region A). At photon energies between 2.24 and 2.3 eV (region B),
α shows an exponential absorption tail energy described by the relation 2.16: [96]
𝛼𝛼(𝐸𝐸,𝑇𝑇)=𝛼𝛼𝑜𝑜exp 𝐸𝐸−𝐸𝐸𝑜𝑜
𝐸𝐸𝑡𝑡(𝑢𝑢)
= 𝛼𝛼𝑜𝑜exp 𝜎𝜎(𝐸𝐸−𝐸𝐸𝑜𝑜)
𝐾𝐾𝐵𝐵𝑇𝑇 2.16
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26
Where Eo, is the optical band gap and 𝛼𝛼𝑜𝑜 is the convergence point of the Urbach bundle.
Figure 2.9: Example for the temperature dependence of the Urbach energy of a-Si:H (data points
after Cody et al. [63]).
At higher photon energies, α is directly proportional to the square root of the photon energy.
This region of absorption spectrum marks the direct optical band gap of CH3NH3PbBr3
perovskites at about 2.3 eV (region C).
Figure 2.10: Schematic of absorption spectrum of CH3NH3PbBr3.
27
2.3. Electronic and optical properties of hybrid organic-inorganic lead
halide perovskites
2.3.1. Transport length
The transport length is one of the most important properties of any absorber material for
solar cells. For a high short-circuit current, photo-generated charge carriers should be able to
travel to the charge-selective contact over a distance longer than the absorption length before
recombination takes place. Photo-generated charge carriers can travel by diffusion or drift.
Therefore, the diffusion length or the drift length should be longer than the absorption length.
The transport length corresponds to the dominating transport mechanism, i.e. the drift or
diffusion length. In case of very thin absorber layers, such as CH3NH3PbI3 with a typical
thickness between 200 and 300 nm [97, 98] the transport length should be as long as the layer
thickness in order to achieve a very high efficiency. This means, in the case of drift, there is an
electric field across the absorber layer. The electric field can be caused, for example, by a p-i-
n structure like in amorphous silicon (a-Si:H) solar cells [99].
The diffusion length is defined as the square root of the product of the lifetime and diffusion
constant 𝐿𝐿=𝜏𝜏𝜏𝜏 [15, 100].The diffusion constant and the lifetime can be obtained from the
measurement of the mobility 𝜏𝜏=𝜇𝜇𝐾𝐾𝐵𝐵𝑇𝑇
𝑞𝑞 and of the decays of photocurrent or
photoluminescence transients [15], respectively. However, this is an indirect method to obtain
the diffusion length. A direct method to measure the diffusion length is related to the
dependence of the illumination intensity on the absorption length at a constant surface
photovoltage. As remark, this method gives the drift length in case of very thin absorber layers
with a homogeneous electric field.
In CH3NH3PbI3, most studies have been done on the measurement of the diffusion length
by the indirect method based on lifetime and mobility measurements of charge carriers with
values of transport length up to 175 µm [101] and 1 µm [15] having been reported for single
crystals as well as thin films of perovskites. However, there is relatively little literature on direct
method of measurement of diffusion length after Goodman [32] for perovskite based devices.
So far, only Dittrich et al. have reported on the direct method of the determination of the
transport length after Goodman using surface photovoltage (SPV) and obtained values ranging
between 200 nm to tenths of µm for perovskite layers and powders respectively [102]. In order
to apply the Goodman method to measure transport length of perovskite layers, accurate and
precise knowledge of absorption coefficient and hence absorption length need to be known.
The preceding section will discuss briefly the absorption coefficient of some semiconductors
determined using different methods of measurement.
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28
2.3.2. Absorption coefficient
For measurement of transport length, the absorption length of the material at different
wavelengths need to be accurately known. The absorption coefficient is the reciprocal of
absorption length. De Wolf et al. [13] determined effective absorption coefficient of CH3NH3PbI3
films at room temperature and compared this with other semiconductor photovoltaic materials
such as CdTe, CIGS, GaAS and c-Si. They found out that CH3NH3PbI3 had an unusually sharp
shoulder appearing at 1.57 eV with no presence of deep states. They used photothermal
deflection spectroscopy (PDS) as well as Fourier transform photocurrent spectroscopy (FTPS)
to obtain an absorptance spectrum featuring an exponential increase for CH3NH3PbI3 layers.
FTPS enabled measurement to be done without the contribution of the substrate as opposed
to PDS. Xing et al [103] measured the absorption coefficient of CH3NH3PbI3 films based on
optical reflectance and transmittance method on quartz substrate. However, this technique
does not allow separation of band to band absorption from parasitic absorption. Barugkin et al
[104] used spectrally resolved PL measurements to determine band to band absorption
coefficient of CH3NH3PbI3 films in the wavelength range between 675-1400 nm. Absorption
coefficients as low as 10−14 cm-1 were obtained at room temperature for long wavelengths.
Figure 2.11: Absorption coefficient of CH3NH3PbI3 from ellipsometry measurements by Löper et al
[105] (red stars), spectrally resolved PL by Barugkin [104] (olive spheres). For comparison absorption
coefficient of c-Si (blue line) obtained by Green et al. [106]. All measurements were obtained at room
temperature.
In the wavelength region close to the band gap, the absorption coefficient of CH3NH3PbI3
decays exponentially suggesting high structural order and low density of deep defect states.
29
In this region, the absorption coefficient of CH3NH3PbI3 films obtained by PL and ellipsometry
methods matches very well (see figure 2.11). Furthermore the absorption coefficient obtained
by spectrally resolved PL technology can extend to longer wavelengths up to 1400 nm. For
comparison, the absorption coefficient of c-Si with data points acquired from Green et al. [106]
is included (blue line in figure 2.11). It should be noted that close to the sub band gap region
of CH3NH3PbI3 layers, both spectra show a sharp absorption edge with steep slopes in
comparison to that of c-Si.
2.3.3. Mobility and doping of hybrid organic-inorganic lead halide perovskites
Considerable attention has been drawn in the past towards the development of
photovoltaic technology which can be determined by controlled doping. The intentional doping
techniques has been widely used in inorganic semiconductors such as silicon [107] as well as
in the organic semiconductors [108]. For example, p-n junction has been reported to be formed
via boron diffusion into the n-type silicon wafer to enhance charge separation and carrier
collection efficiencies in the solar cell. Doping in semiconductors are beneficial since they
directly alter the electrical properties such as conductivity, mobility, rate of charge carrier
recombination, charge carrier diffusion length, interface energy barrier and contact resistance.
For example, doping can help shift the position of the fermi level towards transport states that
can help reduce ohmic losses and ease charge carrier injection to the contacts thereby
improving device performance. Unlike, inorganic semiconductors, hybrid organic-inorganic
perovskite semiconductors are usually processed in un-doped form. However, controlled and
stable doping is favorable for high efficient devices.
Recently hybrid organic inorganic lead halide perovskite in particular CH3NH3PbI3 has been
reported to be self-doped through defect engineering. CH3NH3PbI3 can either be p-type or n-
type self-doped, depending on the ratio of CH3NH3I to PbI2 during the formation process of
perovskite in the precursor solution. CH3NH3PbI3 rich in CH3NH3I were found to be p-type self-
doped whereas those films rich in PbI2 were n-type doped [109].Annealing can help transform
p-type doped perovskite into n-type doped perovskite by removing excess CH3NH3I. Naikaew
et al. demonstrated self-doping on the CH3NH3PbI3 perovskite film using modulated surface
photovoltage (SPV) technique [27]. They demonstrated that as-deposited samples annealed
under nitrogen conditions inside a glovebox at 15, 30 and 45 minutes were p-type doped
whereas perovskite samples annealed at 60 and 90 minutes showed n-type doping. The
appearance of PbI2 marked the transition from p to n-type doping [27].
First principle density functional theory (DFT) calculations also revealed that electrical
conductivity of CH3NH3PbI3 layers could be tuned from p-type to n-type doping by proper
choice of precursor composition during fabrication process [16]. For example, CH3NH3I and
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30
PbI2 form Schottky defects which do not create traps states within the band gap. However,
Frenkel defects such as Pb, I and CH3NH3 vacancies form shallow states near the band gap
and causes un-intentional doping [16]. Furthermore, CH3NH3PbI3 possess unusual defect
physics with the dominant defects being p-typed doped lead vacancies and n-type doped
CH3NH3I interstitials. The defects with low formation energies create shallow defects whereas
those with high formation energies create deep defects. The unusual defect physics could be
due to strong lead lone pair of s orbital and iodine p-orbital which form anti-bonding states and
ionic property of CH3NH3PbI3 layers [110].
Electronic transport properties of conventional semiconductor materials usually have a
high “μτ”product which is defined at the product of the charge carrier mobility, μ, and carrier
lifetime τ. The relation is closely related to the diffusion length L, given by L = (Dτ), where D is
the charge carrier diffusion coefficient given as D = (μkBT/q), with q being the electronic charge,
kB is the Boltzmann constant, and T is the absolute temperature. Long charge carrier lifetimes
could imply slow charge carrier recombination with low trapping probabilities, however that
does not automatically imply high mobility’s, which are limited by scattering. Charge carrier
mobilities in hybrid organic-inorganic lead halide perovskite are often moderate and
comparable to those of organic semiconductors but lower by several orders of magnitudes to
Si, GaAS and some other inorganic semiconductors like CdTe as indicated in table 2.2.
semiconductor
Effective mass
Electron
mobility
(cm2/VS)
(cm2/VS)
References
Silicon
0.19
1500
[60, 111]
GaAS
0.067
8000
[82, 111]
CdTe
0.11
≤ 1000
[92, 111]
Rubrene
0.77
≤0.1
[110, 112]
CH
3
NH
3
PbI
3
0.32
800
[93, 113]
[101]
CH
3
NH
3
PbBr
3
≤ 100
[114]
CH
3
NH
3
SnI
3
[114]
Table 2.2: Electron effective masses, electron and hole mobilities at room temperatures of selected
semiconductor materials used as photovoltaic absorbers.
As a remark, mobility is usually proportional to charge carrier lifetime and indirectly
proportional to carrier effective mass. If effective masses of perovskite are indeed comparable
31
to those of inorganic semiconductors (see table 2.2), then it means that the mobility of
perovskite is limited by the scattering of acoustic phonons [115] and polaronic effects [116].
Polarons are quasi particles in which a phonon could screen charge carriers from conducting
thereby lowering their mobilities. Therefore, the observation of a long carrier lifetime coupled
with the indirect power dependence of mobility with temperature, suggest that there is
negligible scattering from impurity and defects at room temperature but the main scattering are
caused by phonons. This therefore, imply that the origin of polaronic effect may be due to
mechanical and vibrational properties of perovskite material as a ‘soft material’, given a very
small bulk and young modulus.
2.4. Solar cells based on hybrid organic-inorganic lead halide
perovskite
Unlike silicon solar cells, perovskite-based solar cells are usually not doped hence there
is no p-n junction in such devices. Since there is no p-n junction in perovskite solar cells, there
is a need for electron transporting material (ETM) and hole transporting material (HTM) to
transport charge carriers from absorber material to the ohmic contacts. Therefore this section
will discuss the solar spectrum and work-function of different charge selective contacts and
their role in charge carrier transport in perovskite based devices.
2.4.1. Solar spectrum
Solar energy is one of the inexhaustible renewable energy source with a large potential
on the surface of the earth. Approximately 1.08x1018 KWh of the solar energy strike the earth’s
surface per year [1]. Practically about 600 TW of global terrestrial solar energy is provided with
about 30% being reflected by the earth’s atmosphere. In comparison, the annual global
electricity consumption in 2016 was estimated as 22000 TWh indicating the average power
consumption of around 2.4 TW [117]. Therefore, photovoltaic solar energy received on the
earth’s surface is significantly able to fully cover the electricity demand around the globe.
Engineering efficient photovoltaic devices comprising of absorber materials with different
band gap energies is of crucial importance for making efficient multi-junction based devices
which can match the solar spectrum. One way to realize high efficiencies is to make a multi-
junction solar cells, whereby multiple absorber layers are used to divide the solar spectrum
into different parts. This allows multi-junction solar cells to reach high efficiencies which cannot
be achieved by a single junction based technologies.
The solar irradiance is standardized by the American society for testing of materials
(ASTM). Therefore, the solar irradiance reaching the earth’ surface is described by the ASTM-
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32
173-03 standard designated by AM 1.5G [118].This standard correspond to the hemispherical
global irradiance that consist of both direct and diffuse reflections. Figure 2.12 shows the
normalized solar spectrum as a function of photon energy for the air mass of 1.5 global (AM
1.5 G) corresponding to the angle of incidence of 48°.19°. AM 1.5 G is the most commonly
used solar spectrum with the irradiance normalized to an integrated power density of 1000
Wm-2 in order to calibrate and characterize solar cells [119]. The ultra-violet and visible
irradiance roughly covers the spectral region from about 4.4 to about 1.6 eV and near infra-red
roughly denotes the spectral region from 1.6 - 0.89 eV hence most spectral regions of solar
spectrum is fully covered. Therefore the spectral regions match the optimal absorption region
for a solar cell devices. The blue arrows in the figure 2.12 shows the band gap of Si, GaAS
and CH3NH3PbI3 perovskite absorber materials to be about 1.12 eV [60], 1.42 [84] and 1.55
eV [17] respectively. Therefore tandem solar cells comprising silicon as bottom cells with
perovskite or GaAS as top cell can have potential to exceed the state of the art high efficiency
single junction solar cells.
Figure 2.12: Solar spectrum with irradiance normalized to an integrated power density of 1000 Wm-2
(AM 1.5G). The arrows indicate the band gap of Si, GaAS, CH3NH3PbI3 and tandem solar cells
relevant for photovoltaic applications [120].
2.4.2. ETM and HTM layers used in perovskite solar cells
The electronic levels such as work function (Φ), fermi levels (EF), vacuum level (Evac),
ionization energy (IE) and activation energy (AE) are fundamental parameters for controlling
charge transport properties across different material interfaces. These electronic levels are
sensitive to the structure, morphology and chemical compositions of a material. For example,
a small amount of impurity on the surface of a metal or a semiconductor can significantly
33
change the work function and position of vacuum level [121].
The work function (Φ) can be defined as the minimum amount of energy required to
remove an electron originally at EF deep into the material and place it at vacuum level (Evac)
[121]. Therefore for a metal surface, Φ corresponds to energy difference between Fermi-
energy (EF) and vacuum level (Evac) (see figure 2.13 (a)). Figure 2.13 (a) shows schematic
energy diagram of a metal in which the valence band is filled with electrons up to the Fermi-
energy (EF). Φ is equal to energy difference between EF and Evac which is also similar to the
difference between the ionization energy (IE) and electron affinity (EA) of a metallic material.
IE can be defined as the work done in removing an electron at zero temperature or in the case
of a molecule, IE can be defined as the standard enthalpy of ionization at 0 K [122].
Figure 2.13: Schematic energy diagram of (a) metal with valence band (VB) filled with electrons up to
the Fermi energy (EF), vacuum level Evac and work function (Ф) (b) in-organic and organic
semiconductors with the band edges EV, Ec and LUMO, HOMO respectively. EV and Ec are the
energies of the valence band maximum and conduction band minimum respectively, whereas LUMO
and HOMO are the lowest unoccupied and highest occupied molecular orbitals of organic
semiconductors. Vacuum level Evac, work function (Ф), energy gap (Eg), ionization energy (IE), and
electron affinity (EA) are as defined.
Figure 2.13 (b) shows schematic energy levels of inorganic and organic semiconductors.
For inorganic semiconductors, Φ depends directly on EF and position of the Evac such that Φ =
Evac - EF. Ionization energy IE = Evac EV, whereas electron affinity (EA) can be given by the
relation: energy EA = Evac – Ec. The band gap energy Eg is the energy difference between the
energy of conduction band minimum (Ec) and valance band maximum (Ev), i.e. Eg = Ec Ev.
The energy levels of organic semiconductors are described by the lowest unoccupied
molecular orbitals (LUMO) and highest occupied molecular orbital (HOMO) for a neutral
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34
molecule in a ground state energy. The band gap Eg is equivalent to the difference in Energy
between the LUMO and HOMO levels I.e. Eg = LUMO-HOMO.
Figure 2.14: Energies of the conduction and valence band edges (a) different electron selective
contacts, perovskite and transparent conductive oxides and (b) hole selective contacts and
perovskites. The band gap with corresponding references are as shown in table 2.3.
The work function of charge transport layers has a strong influence on device performance
(see table 2.3). This is because it significantly affects the open circuit voltage (Voc) of perovskite
based solar cells. It has been shown that Voc of regular (n-i-p) structure is higher than that of
inverted structure (p-i-n). The band gap of inorganic metal oxides used as electron selective
materials (ETL) is very wide. For example, for SnO2 the band gap is 3.5 eV, that ofTiO2 (3.2
eV) and for ZnO: Al (3.3-3.7 eV). These wide band gaps enable ETLs to absorb higher photon
energies without themselves contributing to photocurrents thus minimizing ETL induced
current losses. As can be seen in figure 2.14 (a) for metal oxide ETLs, SnO2 has the highest
(a)
(b)
35
band gap. This implies that it possesses a favourable band alignment with perovskite
photoactive layer hence reduced current losses than TiO2 and ZnO : Al. Furthermore, these
wide band gap metal oxide have ionization energies of about 2 eV larger then perovskite active
layers. This property enables for distinct hole extraction barrier at the interface with perovskite
active layer. In contrast, fullerene derivatives used in the thesis as ETLs, have 1 eV lower
ionization energies than inorganic metal oxide hence substantially have an increased hole
blocking capability (see figure 2.14 (a)).
substrate
Work function (eV)
Band gap (eV)
FTO
4.4
3.2 [123]
ITO
4.4 [124]
4.2 [125]
PEDOT:PSS
4.9 [126]
1.4 - 2.5 [127]
TiO
2
4.2
3.2 [128]
SnO
2
4.75
3.5 [129]
C
60
4.7
2.0 [130]
PCBM
4.3 [131]
2.0 [130]
ZnO: Al
4.62 [132]
3.32 - 3.77 [133]
ICMA
4.3
2.1 [134]
MoO
3
6.9
3.2 [135]
PTAA
5.1
1.95 - 3.3 [136, 137]
BCP
6.7 [138]
3.5 [130, 139]
MAPbI
3
4.8 [140]
1.6 [130]
MAPbBr
3
4.0 [141]
2.3 [136]
Triple cation
1.61 [142]
Table 2.3: work function and band gap of various substrates and perovskite absorber materials
In this thesis, the Spiro-OmeTAD was used as hole transporting material (HTM) in the n-
i-p structure whereas PEDOT: PSS and PTAA were employed in inverted structure. The work
function of PEDOT: PSS is 4.9 eV (see table 2.3) and from the energy level diagram (figure
2.14 (b)), the highest molecular orbital (HOMO) level was higher in comparison to perovskite
material. This implied that low work function coupled with high HOMO level make PEDOT:
PSS energetically unfavourable for efficient charge carrier transport with perovskite absorber
materials. Poly-triarylamine (PTAA) is another HTL used in the study with a work function of
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36
5.1 eV slightly higher than PEDOT: PSS (see table 2.3). The favourable band alignment
between PTAA and perovskite absorber material may lead to improvement in the open circuit
voltage of perovskite-based solar cells.
2.4.3. Tandem solar cells
Tandem solar cells are double junction solar cells with an optimum combination of band
gap values. The device consists of a low band gap bottom cell and a higher band gap top cell.
In ideal case, the bottom cell absorbs all the light transmitted by the top cell [143]. Studies have
shown through device modelling that for efficient tandem device, the top cell should have a
band gap between 1.7 eV to 1.9 eV whereas for bottom cell, the band gap should range
between 0.9 eV to 1.2 eV [144]. Halide perovskite based on tin (Sn) and lead (Pb) demonstrate
excellent band gap tenability across the solar spectrum. For example, Pb- perovskite based
on mixed iodide and bromide cover a band gap range from 1.5 eV [145] for pure iodide to 2.3
eV [19] for pure bromide. On the other hand, mixed Pb and Sn perovskites based on iodide
can cover a band gap range of 1.17 [17] for 50% Sn and 50% Pb to 1.5 eV [145] for pure Pb.
This makes Pb perovskite based on mixed halide suitable as a top cell whereas mixed Pb and
Sn perovskite based on iodide as a bottom cell for tandem solar cells. Furthermore, both the
low band gap and wide band gap halide perovskites can be fabricated via low temperature
processing thus preventing undesirable damage during fabrication of tandem devices [143].
Albrecht et al. [143] fabricated a monolithic tandem solar cells based on silicon as bottom
cell and perovskite as top cell and realized a power conversion efficiency of 18%. The
monolithic integration was realized via low temperature processing of perovskite absorber
layer, electron selective contacts (SnO2) and hole transporting material (spiro-OMeTAD). The
low temperature processing of the top cell ensured that optical and transport properties of
bottom cell (silicon) was not damaged [143]. Zhao et al. fabricated an all metal halide
perovskite 4-terminal tandem solar cells with a low band gap (1.25 eV) bottom cell based on
mixed Sn and Pb halide perovskite and demonstrated a high power conversion efficiency
(PCE) of 17.6 % and PCE of 21% when stacked together with wide band gap (1.58 eV) top
cell [146]. Eperon et al. [147] reported on the 2 and 4 terminal all perovskite tandem solar cells
[147]. For the two terminal tandem device, a low band gap (1.2 eV) bottom cell was used
which consisted of FA0.75Cs0.25Sn0.5Pb0.5I3 and demonstrated a PCE of 14.8% with Voc greater
than 1.65 eV and PCE of 17% when stacked with a wide band gap (1.8 eV) top cell.
Figure 2.15 shows energy level diagram of a two terminal tandem solar cell. Light travels
through ITO and spiro-OMeTAD layer before being absorbed in the perovskite layer. The
perovskite layer transmits a large proportion of near infra-red light (NIR) to generate high
37
photocurrent in the silicon bottom cell which can absorb near infra -red light. ITO/SnO2 is used
as a recombination/interfacial layer for electrical contact between the cells. However, ITO acts
as a transparent layer as well as an intermediate reflector so as to significantly decrease the
light that is passed to the bottom silicon solar. SnO2 is used as electron selective contact given
that it has a favourable energy level aligned with the conduction band of perovskite [143].
Hybrid Organic-inorganic lead halide perovskite has evolved rapidly over the years with
power conversion efficiency reaching 22.1% [5] in a span of less than 10 years. However the
stability issue remains a challenge for commercial utilization. Long term operational stability of
perovskite-based devices is important for practical applications. There have been remarkable
improvements in the stability of halide perovskite with some studies having recorded
measurements in thousands of hours. This improvements have been realized through interface
engineering [34], device architecture & optimization [148] and using mixed halide perovskite
[33, 19].
Figure 2.15: Energy level diagram of a 2-terminal solar cell
2.5. Stability of hybrid organic-inorganic lead halide perovskite
Stability studies are required in order to gain a deeper understanding of the reasons for
degradation of devices and possible ways to enhance the long-term stability of solar cells
based on hybrid organic-inorganic lead halide perovskites. For instance, chemical interaction
between a perovskite and an electrode could lead to device instability as well as photo-induced
degradation. Metals such as aluminium, silver and gold may react or induce chemical reactions
with perovskite film under humid conditions resulting into degradation of perovskite absorber
layer. Furthermore, metals can also diffuse into charge-selective contact layers, which gives
additional reasons for the degradation of solar cells. For example, aluminium can diffuse into
PCBM layers during evaporation causing local shunts [149].
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2.5.1. Stability under moisture and oxygen
Humidity is regarded as one of the major causes of degradation in perovskite, however
humidity alone is not the main degradation component but rather the quantity of photons in
combination with humidity triggers instability. Leijtens et al. established that by applying a weak
field of 600 Vcm-1 near gold electrodes coated with perovskite film in the presence of moisture
led to irreversible degradation [150]. The irreversible degradation in the presence of moisture
was attributed to the ion movement in the electric field [150]. Furthermore, trap charges also
play a significant role in the irreversible degradation of perovskite films under moisture [151]
by causing the deprotonation of the CH3NH3+ cation. The deprotonation of the CH3NH3+ cation
induces local electric fields that distort the structure of the perovskite when octahedral PbI6
interacts with CH3NH3+ and water.
Although most reports indicate that moisture causes degradation of perovskite films, it has
been revealed that mild moisture could have a positive impact on the perovskite film formation.
Due to the hygroscopic nature of methyl ammonium iodide, exposing the precursor solution of
perovskite to moisture during film formation could lead to accumulation of moisture in the grain
boundaries causing grain- boundary creep that could lead to a merger of corresponding grain
boundaries. The effect increases the size of the grains and subsequent reduction of pin-holes.
In addition, mild moisture levels (35% ±5%) could also result into a significant enhancement in
perovskite device performance with a power conversion efficiency of 17.1% and fill factor of
80% with an intense and sharp XRD diffraction [152].
De Wolf investigated moisture induced degradation of methyl ammonium lead iodide using
photothermal deflection spectroscopy (PDS) [13]. A sharp onset of the absorption spectrum of
methyl ammonium lead iodide perovskite at 1.5 eV has been observed during the initial state
suggesting a low density of deep defect states. However, with exposure to a relatively high
humidity in the range of 30-40 %, there was a significant drop in the absorptance spectrum
towards high energy at about 2.3 eV corresponding to the band gap of PbI2 [153].
2.5.2. Stability of perovskite in UV- light and light soaking
Ultra violet (UV) illumination can reduce the performance of devices based on perovskite
due to the generation of defects by different mechanisms. In contact with TiO2, degradation
induced by UV-light can be explained by chemical reactions activated by photo-generation at
the surface of TiO2. Oxygen vacancies, the concentration of which can be high at the surface
of TiO2, act as efficient electron donating deep sites. The electrons from such deep sites
interact with oxygen from the atmosphere, which in-turn adsorbs to the oxygen vacancy sites
forming a charge transfer complex [154].
39
Figure 2.16: Mechanism for ultraviolet (UV) induced degradation [154]. Band diagram of TiO2
surrounded by oxygen (O2) from atmosphere; upon UV absorption electron-hole pair is created in
which the photo-generated electrons from TiO2 react with O2 to generate oxygen radical called
superoxide (O2-). The holes in the valence band of TiO2 recombine with electrons present at the
oxygen adsorbed site thereby desorbing the oxygen (a). Excitation of the perovskite absorber material
sandwiched between TiO2 (ETM) and spiro-MeOTAD (HTM), electrons are injected into the
conduction band (CB) of TiO2 for where they become deeply trapped while holes are attracted to the
valence band (VB) of HTM (b).
Photo-generation of electron-hole pairs under UV illumination leads to recombination of
holes from the valence band of TiO2 with electrons trapped at adsorbed oxygen. As
consequence of recombination, oxygen is desorbed (figure 2.16 a). This means that free
electrons in the conduction band of TiO2 as well as unfilled positively charged oxygen
vacancies are left on the surface of TiO2. Upon excitation of the perovskite absorber material,
electrons are injected into the conduction band of TiO2 from where they are deeply trapped
whereas holes in the absorber are attracted towards hole transporting material e.g. spiro-
OMETAD (see figure 2.16 b).Therefore, by considering perovskite absorber material
sandwiched between TiO2 (ETM) and spiro-OMeTAD (HTM), excess holes in the spiro-
OMeTAD will recombine with trapped electrons from TiO2 leading to device degradation.
Chemical models of photo-induced degradation
Light induced degradation of CH3NH3PbI3 in dry air can be initiated when an iodide anion
undergoes oxidation and donates an electron to the surrounding oxygen. In the presence of
light, the surrounding oxygen forms a free radical of superoxide (O2-) which deprotonates the
methyl ammonium cation to form a highly volatile methylamine molecule that escapes from the
surface of perovskite leaving behind lead iodide. The transformation equation is shown in 2.17
and 2.18:
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40
CH3NH3PbI3 CH3NH3I +PbI2 2.17
2CH3NH3I +1/2 O2 2CH3NH2 + H2O +I2 2.18
Recent similar reports show that illumination of CH3NH3PbI3 films with or without the
presence of oxygen results into dissociation of methyl ammonium (CH3NH3+) cations into
methylamine (CH3NH2) and molecular hydrogen which at room temperature can easily diffuse
out of the perovskite sample [155]. Illumination of CH3NH3PbI3 layers with a photon energy
greater than the band gap of perovskite in the presence of oxygen leads to the creation of
electron-hole pairs. The free electron in the conduction band of CH3NH3PbI3 could easily be
captured by an oxygen molecule forming a superoxide (O2-) (equation 2.19). The superoxide
formed reacts with a CH3NH3+ cation and forms methylamine (CH3NH2) and hydroperoxyl
(HO2) (see equation 2.20). Because CH3NH2 has a low boiling point of -6.7 °C [156], it
evaporates easily from the sample surface resulting in the breakdown of the CH3NH3PbI3
lattice. The unstable hydroperoxyl dissociates into oxygen and hydrogen gas as shown in
equation 2.21 [155].
O2 light O2- 2.19
CH3NH3+ + O2- HO2 + CH3NH2 2.20
2HO2 2O2 + H2 2.21
Perovskite also degrades rapidly in the presence of light. For example, the air stability of
pure CH3NH3PbI3 and CH3NH3PbI3 embedded on poly-vinylpyrrolidone (PVP) both deposited
on mesoporous TiO2 were compared. Minor degradation was observed for the film stored in
the dark and humid environment, but rapid degradation was found for films exposed to light in
the presence of humidity. This was attributed to surface defects at the TiO2/CH3NH3PbI3
interface which were initiated by the light and caused charge imbalance in the perovskite films
[157].
A reversible red shift of the photoluminescence (PL) spectrum (peak at 1.68 eV) as well
as a splitting of X-ray diffraction peaks for CH3NH3Pb(BrxI1-x)3 films upon light soaking have
been recently demonstrated [20]. This finding was ascribed to photoexcitation that induces
migration of halides. The migration of halides causes phase separation into domains of iodide
(lower band gap) and bromide (higher band gap). The iodide precipitates act as traps for holes
from the valence band offset. The electrons trapped in the conduction band at the Br- site and
the holes in the valence band of the I- site recombine and the energy of the emitted photons
corresponds to the difference between [valence band edge of iodine and the conduction band
edge of bromine. The increased recombination resulted also in a reduced splitting of the quasi
Fermi levels and therefore to a reduced Voc [20].
41
It has also been reported that UV illumination of the Pb-X bond could generate halogen
free radicals that break down the perovskite structure resulting in the irreversible formation of
PbX2 [20]. Christian et al. [158] suggested that after light soaking of perovskite films, organic
cations, such as CH3NH3+, may become less tightly bound to the PbI64- octahedra due to weak
hydrogen bonds. Furthermore, light soaking of perovskite films in the presence of moisture
induced irreversible degradation. As main reasons for this irreversible degradation, reduced
hydrogen bonding that occur after photo-excitation and trapping of charge carriers along grain
boundaries were suggested [158].
Grain boundaries act as accumulation sites for trapped charges and provide pathways for
infiltration of water molecules [151]. The formation of hydrates (for example,
(CH3NH3)4PbI6.2H20), which may be triggered by trapped charge carriers, was suggested as a
further scenario for irreversible decomposition of perovskite films [158]. The PbX6 octahedra
within the hydrated perovskite interact with both organic cations and water causing trapped
charges at the defect site, which induce local electric fields and deprotonate organic cations.
Such a deprotonation process in the presence of water molecules yields volatile molecules
that can evaporate at room temperature [151]. The deprotonation takes place via the following
reaction 2.22:
2CH3NH3+ + 2e 2CH3NH2 + H2 2.22
The two molecules formed (i.e. methylamine and molecular hydrogen are highly volatile hence
diffuse easily outside the sample surface leading to breakdown of the perovskite lattice.
2.5.3 Thermal stability
Supasai et al. [29] used SPV and GIXRD to characterize CH3NH3PbI3 layers annealed
under vacuum conditions to temperatures up to 160°C. GIXRD showed no PbI2 diffraction
peaks for CH3NH3PbI3 layers annealed at 100°C. However, the impurity peak of PbI2 was
observed for CH3NH3PbI3 layers annealed inside a glovebox under nitrogen conditions at 140
°C and 160° C. SPV spectra showed a change of sign in the in-phase and phase shifted by
90° signal for CH3NH3PbI3 layers annealed at 100° C and above. The change of sign was
correlated to the onset of defect states at the surface of CH3NH3PbI3 layers which changes the
electronic properties of the perovskite layers. Furthermore, there was a strong change of SPV
signals at photon energies of 2.36 eV after annealing at 140°C corresponding to PbI2 phase,
which was in agreement with GIXRD measurements indicating onset of degradation process
[29].
Recently Zhang et al. [159] studied photovoltaic behaviour of CH3NH3PbI3 perovskite solar
cells over a wide temperature range from 80-360 K and observed a maximum open circuit
voltage of about 1.15 V at 200 K close to phase transition from tetragonal to orthorhombic
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symmetry. On the contrary, the photocurrent was remarkably stable from 360-240 K but drops
abruptly below 220 K indicating that there is inefficient charge generation in the orthorhombic
perovskite structure [159]. Habisreutinger et al. [160] subjected CH3NH3PbI3-xClx to a
temperature of 80° C in air and observed fast degradation in the perovskite films, characterized
by color change from dark brown to yellow indicating degradation to PbI2.
GIXRD diffraction peak at 12.65° was observed for CH3NH3PbI3 layers annealed in
nitrogen filled atmosphere in a glovebox at 100° C for 60 min, with the intensity of the diffraction
peak increasing strongly at 90 min. The diffraction peak at 12.65° was attributed to appearance
of PbI2 which was the onset of degradation of CH3NH3PbI3 films [27]. Kim et al. [161] also
employed in-situ synchrotron radiation analysis to monitor thermal degradation of perovskite
solar cells. CH3NH3PbI3 films changed to intermediate phase before it degrades to CH3I, NH3
and PbI2 after short exposure to heat stress for 20 min at 100° C and after longer exposure to
heat stress at 80°C for more than one hour.
2.5.4. Role of interfaces for stability
Hybrid organic inorganic perovskite are susceptible to degradation under moisture,
oxygen, heat and light due to their low formation energies. In this respect, charge selective
contacts play an important role in protective perovskite absorber layers from such
environmental exposure. Therefore charge selective layers are crucial for energy level
matching, charge transport and for high stability. You et al [149] reported on solution processed
CH3NH3PbI3 solar cells with p - i - n structure, employing NiOx and ZnO as hole & electron
transporting material respectively. The solar cell had improved stability against degradation
from water and oxygen given that ZnO separates perovskite and Al layers thus preventing
infiltration of Al layers into perovskite films.
Perovskite solar cells with planar TiO2 as electron transporting material (ETM) have been
demonstrated to exhibit un-stabilized power conversion efficiencies (PCE) with high hysteresis.
The anomalous hysteresis in the I-V curves may be due to large contact resistance for electron
transfer between TiO2 and perovskite interface [162]. Hysteresis-free perovskite solar cells
have also been reported using SnO2 as ETM, attaining PCE of above [163]. SnO2 has been
chosen because it has favorable conduction band alignment with perovskite as compared to
TiO2 which showed energy band mismatch with perovskite. Furthermore, SnO2 has a deeper
conduction band and can be fabricated via low temperature processing conditions hence can
facilitate the realization of long term air stability devices with enhanced hysteric behavior.
Electron injection dynamic behavior from CH3NH3PbI3 into TiO2 and SnO2 based devices has
also been studied with SnO2 exhibiting better electron extraction property in comparison to
TiO2 indicating a favorable energetic band alignment for the former [163].
43
Anaraki et al. [164] reported on planar perovskite-based solar cell on SnO2 ETM prepared
by simple, low temperature deposition process through a combination of spin coating and
chemical bath techniques; attaining PCE of 20.7% at stabilized maximum power point tracking
after storage in the dark under aging conditions. Their work demonstrated the importance of
electron selective contacts as a means of achieving high efficiency and stability in perovskite
based devices. In the p - i - n structure, the ETM is the topmost layer exposed to ambient air if
metal electrode is excluded. For example, PCBM could absorb water or oxygen onto its surface
resulting into the formation of dipole moment and high resistance that lead to decomposition
of the perovskite photoactive layer [149].
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CHAPTER 3
Modulated surface photovoltage (SPV) spectroscopy
3.1 Principle of modulated surface photovoltage spectroscopy
Modulated surface photovoltage (SPV) spectroscopy is a contactless non-destructive
technique for investigating semiconductors and semiconductor surfaces by examining
modulated illumination that induces changes in the surface potential [22]. The SPV is defined
as the difference between the surface potentials of a semiconductor under illumination and in
the dark [165]. A nonzero SPV implies that photogenerated free charges are redistributed in
the space [22].
SPV signals are measured between two electrodes, the sample and the reference
electrodes (figure 3.1 (a)). For modulated SPV measurements, both electrodes are electrically
connected via a very high resistance. Electrons flow from the electrode with lower work function
to the electrode with the higher work function until equilibrium of the Fermi-level (EF) is
achieved. The difference in the work functions of the reference and sample electrodes is called
the contact potential difference (CPD). The sample electrode is covered with the
semiconductor. Under illumination of the semiconductor (figure 3.1 (b)), free charge carriers
are photogenerated. The separation of photogenerated charge carriers in space results in the
change of the surface dipole and leads to the change of the semiconductor work function
(∆CPD). The SPV is defined as the negative change of the CPD, i.e. - ∆CPD.
Figure 3.1: Energy schemes of a sample electrode with a surface layer and reference
electrode in the dark (a) and under illumination (b). Both the electrodes are connected with a
measurement resistance. The reference electrode is connected to a high impedance buffer. The work
functions of the sample and reference electrodes are χs and χref, respectively. The contact potential
difference (CPD), the light induced change of the CPD (ΔCPD) and the light induced voltage between
the electrodes (Vs) are indicated.
(a)
(b)
45
The change in the surface work function induces a current flow through the very high
measurement resistance (Rm) between the sample and reference electrodes until the Fermi-
levels are re-aligned. In modulated SPV measurements, the measurement capacitance (Cm)
between the sample and reference electrodes is fixed (fixed capacitor arrangement, figure 3.2).
Therefore, the Fermi-levels re-align within the RmCm time constant. If RmCm is much longer
than the modulation period, the CPD is preserved and a positive voltage corresponding to a
lower electron potential is obtained. On the other hand, if the measurement time is longer than
RmCm, the potential at the external contacts drops to zero voltage due to discharging of the
capacitor with respect to ΔCPD [166, 167].
Figure 3.2: Schematic of the fixed capacitor arrangement for modulated SPV measurements
(a) and a photo of a given reference electrode with a sample and a mica spacer (b).
The sign of modulated SPV signals gives the direction of modulated charge separation. A
positive SPV signal is obtained when electrons are separated towards the sample electrode
(equivalent to charge separation in the surface space charge region of an n-type doped
semiconductor in depletion), whereas a negative SPV signal is measured for separation of
electrons towards the surface of the sample (equivalent to charge separation in the surface
space charge region of a p-type doped semiconductor in depletion).
In modulated SPV measurements with a double phase lock-in amplifier, the in-phase (also
called x-signals) and phase-shifted by 90° (also called y-signals) signals are distinguished
(figure 3.3). The x- and y-signals correspond to the sine or cosine components of the
modulated signals (in figure 3.3, the coefficients mx and my are used for explanation). For a
positive increasing (light on) and decreasing (light off) signals, the x- and y-signals are positive
and negative, respectively (on dominating mechanism of charge separation). Therefore, the
in-phase signal gives the information about the direction of charge separation.
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The x- and y-signals correspond to the fast and slow response in relation to the
modulation period, i.e. the y-signal is zero if the increase and the decay of the signal is much
faster than the modulation period and the x-signal is zero if the increase and the decay of the
signal is much slower than the modulation period [28].
Figure 3.3: Example of modulated signal (a), coefficients for analyzing the in-phase and phase shifted
by 90° signals (mx and my, (b) and (c) respectively) and the products of the modulated signal with mx
and my ((d) and (e), respectively). The in-phase and phase shifted by 90° signals are indicated.
The amplitude of modulated SPV signals (R) is defined as the square root of the sum of
the squared x- and y-signals:
𝑅𝑅=𝑥𝑥2+𝑦𝑦2 3.1
The tangent of the phase angle (ϕ) is defined as
𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡=𝑦𝑦
𝑥𝑥 3.2
Modulated SPV spectroscopy is an ideal method for the characterization of electronic
properties of hybrid organic-inorganic lead halide perovskites since it does not require the
preparation of contacts and since it can be performed after every step of layer preparation,
light soaking etc. For example, the passivating behavior [29] and hole blocking [168] of the
CH3NH3PbI3 / PbI2 interface, the dependence of the electronic properties of the CH3NH3PbI3 /
TiO2 interface on the presence [28] and thickness of amino valeric acid (AVAI) during
47
deposition [169], the role of phase composition of electronic states in CH3NH3PbI3 prepared
from CH3NH3I/PbCl2 solution [27], the determination of the transport length (L) of CH3NH3PbI3
after Goodman in layers and powders [102], dependence of L on light soaking of CH3NH3PbI3
powders [170] and its dependence on the grain size in CH3NH3PbI3 layers [171] and the
modulated charge transfer at interfaces between carboxylated multi-walled carbon nanotubes
and CH3NH3PbI3 [172] were investigated by modulated SPV spectroscopy. In this thesis,
modulated SPV spectroscopy is applied in order to investigate the behavior of the band gap
(Eg), exponential tail states close to the band edges (Et), deep defect states, charge separation
and transport or diffusion length (L).
3.2 Components for modulated SPV spectroscopy measurements
Figure 3.4 shows the block scheme for measurements by modulated SPV spectroscopy.
A lamp with a monochromator is used for spectral-dependent illumination. The light passes an
optical chopper for modulation and is directed onto the sample and reference electrodes
(measurement capacitor). The impedance of the measurement capacitor is matched with the
input impedance of the lock-in amplifier by a high-impedance buffer. The SPV signal passes
the high impedance buffer and is measured with the double-phase lock-in amplifier. A personal
computer is used for adjusting the wavelength via the stepper driver control unit and for
measuring the modulated SPV spectra.
A quartz prism monochromator was used for measuring SPV spectra from the near
infrared to the ultraviolet range without the need for changing order filters and gratings, i.e.
without breaking points in the spectra. Incidentally, SPV spectra measured over a wide spectral
range cannot be simply normalized to the photon flux as is be done, for example, for the
measurement of the quantum efficiency.
Figure 3.4: Block diagram of the set-up for measurement by modulated SPV spectroscopy.
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Figure 3.5 (a) shows a measurement capacitor connected directly with a lock-in-amplifier.
The relatively low input resistance of the measurement device (kΩ to MΩ) acts as a shunt. As
a consequence, a current flow will be measured as a potential drop across the input resistance
of the measurement device, i.e. the measured signal is not directly related to the SPV.
Therefore, a device matching the impedance of the measurement capacitor with the
impedance of the measurement device is required (figure 3.5 b).This device is called a high-
impedance buffer because the input resistance of a high impedance buffer is extremely high
in order to match the impedance of the measurement capacitor. On the other side, the output
resistance of the high impedance buffer is usually 50 . For ideal high-impedance buffers, the
input resistance is infinitely high and the input capacitance is zero and the output resistance is
much lower than the input resistance of the measurement device so that the input potential is
equal to the output potential.
Figure 3.5: Equivalent circuits of a measurement capacitor connected directly with a measurement
device (a) and connected with a measurement device via an ideal (b) or real (c) high-impedance
buffer.
In real high impedance buffers, however, the input resistance cannot be infinitely high and
the input capacitance cannot be zero. This has consequences for the measurements of SPV
49
signals. Figure 3.5 (c) shows an equivalent circuit of a real high impedance buffer consisting
of an ideal high impedance buffer connected in parallel with an input resistance (Ri), input
capacitance (Ci )and a bias current source (Ibias) at the input and connected in series with an
output resistance (Rout) at the output. For the buffer used in our experiments, an operational
amplifier (OPA565) with Ibias equal to 2 fA and Ci of the order of 3-4 pF was used.
Both measurements capacitance Cm across the sample and input capacitance Ci form a
capacitive voltage divider which reduces the output voltage Uout.
Uout =CmCm+ Ci
Uin 3.3
The product of Ibias and Ri is high because Rin is very high (of the order of TΩ for OPA565).
Uin = Ibias. Ri 3.4
The high bias voltage (Uin) is reduced by implementing a measurement resistance (Rm),
which is of the order of GΩ. In addition, Ibias charges the Cm and a potential drift (Uib) appears:
𝑑𝑑 Uib
𝑑𝑑𝑙𝑙 =Ibias Cm
3.5
The measurement resistance Rm charges and discharges Cm with the time constant given by:
𝝉𝝉= RmCm 3.6
This has the consequence that SPV signals can be measured only at times significantly shorter
than the RmCm.Therefore, the modulation period of the chopped light should be significantly
shorter than RmCm [166]. For more detailed analysis, the response function of a given high-
impedance buffer shall be simulated (see, for example, [173]).
3.3 Determination of the band gap and exponential tails by SPV
Modulated SPV amplitudes may not be linked directly to the photon flux since different
processes may contribute to charge separation, for example, with opposite direction of charge
separation and/or with different dependencies on light intensity. Furthermore, SPV signals, in
analogy to the open circuit voltage of a solar cell, can depend logarithmically on the light
intensity (at high light intensity), can saturate at very high light intensity or can depend linearly
on the light intensity (at low light intensity, limitation by the shunt resistance). Therefore, SPV
signal may result into a non-linear response [174].
Measurements by modulated SPV spectroscopy are performed at low light intensities,
which are of the order of tens of µW/cm². Therefore, measurements are performed in the low
signal case, for which the response is linear if there is no change in the mechanisms of charge
separation and relaxation within the considered spectra range. The phase angle is very
sensitive to the change of the mechanisms of modulated charge separation and relaxation. As
a criterion, the spectra of the modulated SPV amplitudes can be analyzed in analogy to optical
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measurements if the phase angle is constant (or nearly constant) in the considered spectral
range. Incidentally, the value of Et obtained by SPV is not necessarily equal to the value of Eu
obtained by UV-vis spectroscopy because charge carriers excited into localized states do not
participate in charge transport and do therefore not contribute to the SPV signal. This is shown
schematically in figure 3.6 for fundamental absorption (process A), for which both the
photogenerated electron and hole are mobile, for excitation from a delocalized into a localized
state (process B), for which one of the photogenerated charge carriers is not mobile, and for
excitation from a localized into a localized state (process C), for which both photogenerated
charge carriers are not mobile.
Figure 3.6: Schematic of photogeneration in fundamental absorption (A), for excitation from a
delocalized into a localized state (B) and from a delocalized into a delocalized states (C).
If there is only one mechanism of charge separation and relaxation, the distribution of
exponential defect states below the band gap can be analyzed by dividing the SPV amplitude
by the photon flux (Φph). The value of Et was obtained by fitting the leading edge of the SPV
amplitude normalized Φph with an exponential function.
𝑅𝑅Φ𝑝𝑝ℎ
=𝐵𝐵 𝑒𝑒𝑥𝑥𝑒𝑒ℎ𝜐𝜐−𝐸𝐸𝑔𝑔
𝐸𝐸𝑡𝑡 3.7
where B is a proportionality factor, ℎ𝜐𝜐 is the photon energy, Eg denotes the band gap at the
onset energy.
SPV spectra of the amplitude or of the in-phase or phase-shifted by 90° signals can be
used to determine the approximate band gap of semiconductors. In most semiconductors,
there is a pronounced increase of the absorption coefficient closer to the band gap (Eg).
Therefore, SPV signals are directly proportional to the absorption coefficient of a
semiconductor as long as the absorption length, i.e. the reverse absorption coefficient, is
shorter than the diffusion length of minority charge carriers [22] an as long as there is only one
dominating process of charge separation and relaxation involved into the formation of the SPV
signals.
51
SPV or absorption spectra around the band gap of a thin semiconductor layer do often not
correspond to those of ideal semiconductors. There are different opportunities to define a band
gap or an onset energy for SPV spectra. The easiest way is to get the onset energy (Eon) of a
SPV spectrum (figure 3.7 (a)). The onset energy can be acquired from the spectra of the
modulated SPV amplitude by extrapolating the leading edge of the SPV signal to the photon
energy scale and reading out the photon energy at the point of intersection with photon energy
axis. For ordinary semiconductors, Eon of the SPV signal is depicted by the signature near the
band gap and corresponds to a strong increase in the magnitude of the SPV signal [175]. As
an example, Lagowski et al. [176] applied a similar method to define an onset energy in order
to study the SPV response of silicon-on-sapphire films.
Figure 3.7: Analysis of the band gap as the onset energy (a), energy in the inflection point (b) and
Tauc gap for a direct semiconductor (c).
Another way to define a band gap is the analysis of the inflection point of the spectrum
normalized to the photon flux (Eg-ip). In this case, the band gap is close to the maximum of the
spectrum of the first derivative as suggested by Lassabatere et al. [177] (figure 3.7 (b)). The
inflection point analysis is the most general approach, which does not depend on the nature of
the band gap and which does only weakly depend on the exponential tails. As an example,
Lassabatere et al. [177] used maximum derivative of wavelength dependent modulated SPV
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to determine the Eg-ip of GaAs films, which was in excellent agreement with Eg resulting from
conventional optical measurements [85].
The nature of the band gap is considered in the analysis of the so-called Tauc gap (Eg-
Tauc). This method of determining Eg-Tauc was introduced by Tauc [178] who demonstrated that
amorphous germanium has an indirect transition in its optical absorption spectrum. For a
semiconductor with a direct band gap, the Tauc gap is found from the extrapolation of the
linear region of the squared spectrum normalized to the photon flux to the axis of the photon
energy (figure 3.7 (c)).
3.4 Measurement of the diffusion length after Goodman
The diffusion or transport length (L) is the average distance over which excess charge
carriers can travel before they recombine. It can be measured by direct and indirect methods.
The direct method is related to the dependence of the intensity on the absorption length at a
constant SPV [32]. The indirect method, on the other hand, involves the dependence of L on
the lifetime (τ) and diffusion constant (D) [15] through the relation
𝐿𝐿=𝜏𝜏𝜏𝜏 3.8
The lifetime can be obtained from the measurement of the decays of photocurrent or
photoluminescence transient whereas D can be found from the mobility [15] by using the
Einstein equation:
𝜏𝜏=𝜇𝜇𝐾𝐾𝐵𝐵𝑇𝑇
𝑞𝑞 3.9
In order to measure the diffusion length after the method developed by Goodman [32], a
modulated SPV signal between an illuminated surface and a non-illuminated back surface is
kept constant at each wavelength by adjusting the light intensity. The constant SPV signal
provides a constant Fermi-level splitting during the measurement and therefore avoids an
influence of the spectral-dependent surface recombination velocity. By plotting the light
intensity versus the absorption length and extrapolating to zero light intensity, a straight line,
the negative intercept of which is equal to the diffusion length (L), is obtained (see figure 3.8).
Following the original equation of Goodman [32], the intensity is equal to a constant
multiplied by a functional dependence of the absorption coefficient α, such that,
𝐼𝐼0(𝜆𝜆)=𝑐𝑐𝑐𝑐𝑡𝑡𝑐𝑐𝑡𝑡. (𝛼𝛼(𝜆𝜆)−1+𝐿𝐿) 3.10
with the condition that
𝐿𝐿,𝛼𝛼−1 𝑑𝑑 3.11’
𝐿𝐿,𝛼𝛼−1 𝑡𝑡 3.11’’
53
∆𝑒𝑒𝑡𝑡0 3.11’’’
where α-1 is the absorption length, 𝑡𝑡 is the thickness of the absorber layer, 𝑑𝑑 is the depletion
width of the space charge region, 𝑡𝑡0 is the majority charge carrier density and ∆𝑒𝑒 the minority
charge carrier density. Equations (3.10 and 3.11) can be applied if a low level of charge
injection was considered, when trapping and recombination processes in the space charge
region was neglected and when there is only a small variation of the quantum efficiency and
of the reflectance with the wavelength.
Figure 3.8: So-called Goodman plot, which gives the dependence of the light intensity on the
absorption length by keeping SPV constant.
The knowledge of the precise absorption spectrum of the investigated semiconductor is
needed for a direct analysis of the diffusion length. In contrast to c-Si, precise data of
absorption spectrum for CH3NH3PbI3 and other perovskites are rare. In this thesis, the data of
Löper et al., which was obtained with from ellipsometry measurements [105], were fitted with
cubic spline function and used in the analysis of the transport length.
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CHAPTER 4
Experimental and characterization methods
Electronic, structural and optical properties of hybrid organic-inorganic lead halide
perovskite depend on the preparation conditions, crystallization methods and defect formation.
Solution based techniques are most commonly used. The formation of perovskites depends
on the solvents, additives, temperature and substrates. Furthermore, electronis properties
change as a function of time and additional factors such as light soaking, coating and
temperature treatments, which are important factors for the stability of perovskite solar cells.
Grazing incidence X-ray diffraction (GIXRD), surface photovoltage spectroscopy (SPV),
optical (UV-vis) spectroscopy and photothermal deflection spectroscopy (PDS) were used for
characterization. GIXRD gives information about the phase composition of perovskite whereas
SPV allows for the characterization of the exponential tail states (Et) close to the band edge,
the band gap (Eg), defects below the band gap and the diffusion length (L). UV-vis
spectroscopy allows for the characterization of the optical properties of the perovskite layer. In
this thesis, material properties related to degradation, stoichiometry, band gap (Eg), Et and L
were investigated.
By varying different halide compositions, the band gap of perovskite could be changed.
Similarly diffusion length after Goodman can provide a useful information about the lifetime of
solar cells. Furthermore, temperature dependent measurement of the band gap as well as
investigation of the role in interfaces in the evolution of defect states will be determined by
SPV. In the study of interfaces, different electron selective as well as hole selective contacts
will be varied and their influence on perovskite properties determined.
4.1. Preparation of substrates and of hybrid organic-inorganic lead
halide perovskites
4.1.1. Preparation of the substrates and preparation routes for deposition of hybrid
organic-inorganic lead halide perovskites
Substrates consisted of glass coated with bare transparent conductive oxides (TCOs) or
coated with a TCO and an electron or hole selective contact material. The substrates were
subsequently cleaned in acetone, 2% mucasol (detergent), deionized water and isopropanol
for 15 minutes each. After each step, the samples were dried with nitrogen and thereafter
55
treated with ozone (generated by UV light) for 20 minutes in order to activate the surface. The
TCOs were SnO2: In (indium doped tin oxide, ITO), SnO2: F (fluorine doped tin oxide, FTO),
MO3 (molybdenum oxide, MO), In2O3: H (hydrogen doped indium oxide, IOH). The used
electron selective contact materials were TiO2 (titanium oxide, sputtered), np-TiO2 (film of TiO2
nanoparticles spin coated from a suspension), np-SnO2 (film of SnO2 nanoparticles spin coated
from a suspension), np-ZnO:Al (aluminium doped zinc oxide nanoparticles spin coated from a
suspension), PCBM (Phenyl-C60-butyric acid methyl ester), C60 (Buckminster-fullerene) [179],
BCP (Bathocuproine) and indene C60-mono adduct (IC60MA). The used hole-selective contact
materials were PEDOT: PSS (poly (3, 4-ethylenedioxythiophene)polystyrene sulfonate) and
PTAA (poly (triaryl amine)).
The substrates (size 2.5x2.5 cm2) with ITO contacts (Lumtec) had the following
specification: LTG001 plane ITO glass with a resistivity of about 15 Ω/sq and LT-G001 PT,
patterned ITO with a resistivity of about 15 Ω/sq. The substrates (size 5x5 cm2, thickness 2.2
mm) with FTO contacts (Solaronix) had the following specification: co022-7/LI, resistivity of
7Ω/sq. The substrates were cut into pieces of 2.5x2.5 cm². The substrates coated with MO3
were provided from PVcomB (size: 10x10 cm²). The Mo substrates were cut into pieces of
2.35×2.35 cm2, which was suitable for spin coating (with another spin coater). IOH was
prepared by sputtering (TU Berlin) with the following sputter specification: A600V7 from
Leybold Optics, pulsed DC, from a ceramic target of 0.6 kW with a power ratings (P/A) of about
0.8 W/cm². The oxygen pressure during sputtering was maintained at about 3×10-4 Pa. The
obtained layers of IOH (thickness about 200 nm) were annealed in vacuum at 200°C for 1
hour.
Nanoparticles of TiO2 were prepared as reported elsewhere [180]. 0.25 ml of anhydrous
TiCl4 (99.9 %, Sigma-Aldrich) was added drop-wise while stirring in a vial containing 1 ml of
anhydrous ethanol (Sigma-Aldrich) and 5 ml of anhydrous benzyl alcohol (99.8 %, Sigma-
Aldrich). The solution was stirred for 9 h at a temperature of 80 °C. Thereafter, the solution
was cooled down to room temperature before being mixed in diethyl ether at a volume ratio of
1:9 in order to form precipitates of TiO2 nanoparticles. 10 ml of the precipitate was centrifuged
at 6000 rpm for 5 min, washed with acetone and then re-dispersed in 20 ml of anhydrous
ethanol. Lastly, 5 µl of Titanium diisopropoxide bis (acetylacetonate) (Tiacac) was directly
added for each 20 ml of the dispersion to form TiO2 nanoparticles. TiO2 nanoparticles were
spin coated twice over ITO glass substrate at 1000 rpm for 40 seconds in ambient air. For each
subsequent spin coating, the sample was thermally annealed at 150 °C for 30 min, before
repeating the procedure for a double final film thickness [34]. Nanoparticles of SnO2 were
prepared by dissolving 4 mg of SnCl2.2H2O (> 99.995% Sigma-Aldrich) in 1 ml of anhydrous
ethanol (sigma-Aldrich). The precursor solution was stirred at room temperature for 30 minutes
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and thereafter spin-coated on a pre-cleaned ITO substrate at 2000 rpm for 40 s and then
annealed for 1 hour at 180°C as reported by Ke et al. [181].
A PC60BM solution was prepared by dissolving phenyl-C60-butyric acid methyl ester
(PC60BM, 99.5% Solenne BV) into anhydrous chlorobenzene at a concentration of 10 mg/ml
and stirred in a glovebox overnight at 60° C. The solution was spin coated on a ITO substrate
at 2000 rpm for 30 s in a nitrogen filled glovebox [34].Indene C60- mono Adduct (AC60MA, >>
99 %, Lumtec) was dissolved in anhydrous chlorobenzene at a concentration of 10 mg/ml,
stirred overnight at 60° C and spin coated at 2000 rpm, 30 s in a nitrogen filled glovebox. C60
was thermally evaporated at a pressure of 1×10-6 mbar with crucible temperature maintained
at 385° C at an evaporation rate of 0.2 yielding a film which is 35 nm thick. Bathocuproine
(BCP), which acts as an exciton blocking layer [139], was deposited using thermal evaporation
as well as using solution spin coating method. For the case of thermally evaporated BCP, the
base pressure and deposition rate were 1×10-6 mbar and 1.0 /min. For BCP deposited from
a solution, 0.5 mg of BCP was dissolved in 1 ml of anhydrous ethanol at room temperature
while stirring. The solution was then spin coated onto a substrate in a nitrogen filled glovebox
at 4000 rpm for 60 s [182].
Commercially purchased PEDOT:PSS (Clevious AI 4083, Heraus) was spin coated on
UV-ozone treated ITO glass substrate at 3000 rpm for 60 sec and thereafter annealed at 135°C
for 20 minutes [183]. PTAA was dissolved in toluene at 15 mg/ml solution. 13.6 µl Li-
bis(trifluoromethanesulfonyl)imide (Li-TFSI) , 28.3 mg/ml of acetronile and 3.4 µl of 4-tert-
butylpyridine (TBT) were added to the solution and spin coated at 3000 rpm for 30 s [184].
Perovskites such as CH3NH3PbX3 (X = I, Cl, Br or mixed halides) can be prepared by
reaction of an organic halide precursor salt (for example, CH3NH3I) with an in-organic halide
precursor salt (for example, PbI2). Layers of CH3NH3PbI3 were prepared by different
techniques: the solution process technique [185], the two step sequential deposition [186] ,
two step inter-diffusion method [187] and the vapour assisted deposition [188].The solution
based process by single step preparation is the most commonly and widely used due to its
simplicity and short processing time. For the case of CH3NH3PbI3, one mole of CH3NH3I (159
mg) and one mole of PbI2 (461 mg) were dissolved in 700 µl of dimethylformamide (DMF) and
71 µl dimethyl sulfoxide (DMSO). The solution was dissolved overnight at 60° C in a nitrogen
filled glovebox. To prepare CH3NH3PbI3 films, the solution was spin coated onto a substrate
(2.5x 2.5 cm2).
A summary of different preparation routes used for the deposition of perovskite on different
substrates were as shown in figure 4.1. For example, in the temperature dependent
measurement of CH3NH3PbI3 by modulated surface photovoltage, the perovskite precursor
solution was deposited on a Mo substrate, annealed and thereafter coated with a thin layer of
poly methyl methacrylate (PMMA) as a capping layer on the surface of the perovskite films
57
(process 2). On the other hand, for transport/diffusion length measurements after Goodman,
perovskite films were deposited on electron selective contacts (ETM) such as SnO2 and TiO2
while PEDOT/PSS and PTAA were used for hole-selective contacts (HTM). The TCOs used
for this deposition were ITO (textured or plane) and IOH (Process 3). For studying the role of
interfaces on the evolution of defects during light soaking by SPV, perovskite was deposited
on either ETM or HTM with or without a capping layer (Process 3). Perovskite was also
deposited on ITO, FTO and Mo substrates and the properties were studied and compared
(Process 1). Electronic properties of a solar cell (without ohmic contacts) were studied by SPV
and results were compared with the device performance (process 4).
Figure 4.1: Perovskite preparation routes used in this work.
4.1.2. Single step preparation of hybrid organic-inorganic lead halide perovskites
Figure 4.2 shows a summary of a scheme illustrating some preparation routes of the active
perovskite layer. The precursor salts used in the synthesis of hybrid organic-inorganic lead
halide perovskites were: methyl ammonium iodide, CH3NH3I (MAI, Dyenamo); lead iodide,
(PbI2, 99.99 %, TCI), methyl ammonium bromide, CH3NH3Br (MABr, Dyenamo); lead bromide
(PbBr2, Alfa Aesar); formamidinium iodide, (FAI) and cesium bromide (CsBr). Different types
of salts were used for different perovskite compositions. For example, in the preparation of
pure methyl ammonium lead iodide, CH3NH3PbI3, the films were prepared according to the
modified procedure as reported by Jeon et al. [185]. The precursor solutions of CH3NH3PbI3
were prepared by dissolving 1 M MAI and 1M PbI2 in γ-butyrolactone (GBL, 99 %, Sigma
Aldrich) and dimethyl sulfoxide (DMSO, Sigma-Aldrich) at a volume ratio of 7:3. The precursor
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solutions were stirred at 60°C for 12 h in a nitrogen filled glovebox. Before perovskite
deposition, the temperature of the atmosphere in the glovebox was kept constant at around
28 C. Three consecutive steps of spin coating at 1000 rpm for 10 s, 2000 rpm for 20 s and
5000 rpm for 10 s were used to spin precursor solutions on the sample substrates with a final
dripping of 150 μl of toluene while spinning was continued (third or final stage). After that, the
CH3NH3PbI3 films were formed during annealing at 100°C for 10 min.
Similarly, CH3NH3PbBr3 films were prepared from a precursor solution containing 1M
MABr and 1M PbBr2 dissolved in DMSO and DMF at a volume ratio of 1:4. Before spin coating,
the solution was placed on a hot plate at a temperature of 60°C and stirred overnight in a
nitrogen filled glovebox. Perovskite precursor solutions were spin coated on pre-cleaned ITO
substrates at 4000 rpm, acceleration of 5 m s2 for 30 s [55]. During the spin coating process,
100 µl of chlorobenzene (Sigma Aldrich) was dripped on the spinning sample 10 s prior to the
end of the spinning program. Similarly, the spin coated film was left in the glovebox ground for
3-5 minutes before annealing at 100°C for 10 min [136] in the glovebox.
Figure 4.2: Parameter variation for single step preparation of perovskite
To prepare mixed perovskites based on iodide and chloride, precursors of PbCl2 and
CH3NH3I with a molar ratio of 1:3, respectively [189] were spin coated using a two-step spin
coating process at 2000 rpm for 10 s followed by 3000 rpm for 30 s onto the substrates and
the perovskite film was formed during annealing at 100°C for 60 min directly after the spin
coating. Finally, CH3NH3Pb(I1-xBrx)3 solutions were prepared by stoichiometric mixing of
synthesized solutions of CH3NH3PbI3 and CH3NH3PbBr3 at 60° C for 60 min as reported by
Noh et al. [19]. The solutions of CH3NH3Pb(I1-xBrx)3 were then spin coated on pre-cleaned ITO
59
substrates at 4000 rpm, acceleration of 5 m s2 for 30 s. 10 s prior to the end of the spinning
program, 100 µl of chlorobenzene (Sigma Aldrich) was dripped on the spinning sample. The
spin coated sample was annealed at 100° C for 10 min.
Spin coating is a rapid solution based process for depositing thin films on substrates. The
process involves the preparation of the solution with the desired concentration of the precursor
salt(s), applying a quantity of the solution to a substrate and then spinning the substrate. As
the solution spreads, it dries and leaves a film. Deposition parameters consist of choice of the
substrate, deposition temperature, solvent, and concentration of the hybrid in the solvent and
speed of spin [190]. Spin coating enables formation of highly oriented perovskite films on a
substrate while solvent evaporates off (see figure 4.3).
Figure 4.3: Scheme of spin coating and annealing with anti-solvent dripping for single step
preparation of perovskites.
In this thesis different spin coating parameters were used to spin coat hybrid organic-
inorganic metal halide perovskite. Layers of CH3NH3PbI3, based on PbI2 and CH3NH3I, three
consecutive spin coating steps of 1000 rpm for 10 s, 2000 rpm for 20 s and 5000 rpm for 10 s
were used to spin precursor solutions on the substrate with 150 μl of toluene dripped while
spinning in the third stage. Toluene was used as anti-solvent to aid in the formation of a
uniform, dense and homogeneous perovskite film thus controlling the morphology of the film.
In this sense, the toluene is used as a capping layer on top of a perovskite film since it does
not dissolve the perovskite material and miscible in DMF, DMSO and GBL which are solvents
commonly used in perovskite preparation [185]. During the spin coating process, the solvent
evaporates and self-orientation of the films occurs and induces the formation of a crystalline
perovskite layer due to ionic interaction between metal cations and halide anions. On the other
hand, mixed perovskite based on iodide and chloride, (precursors of PbCl2 and CH3NH3I),
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were spin coated using a two-step spin coating process at 2000 rpm for 10 s followed by 3000
rpm for 30 s. In this process, no anti-solvent was used.
Thermal annealing at 100°C for different times has been applied in various preparation
conditions of perovskite films in order to reach high solar energy conversion efficiencies [9, 34,
191] . In this thesis, CH3NH3PbI3, based on PbI2 and CH3NH3I was annealed at 100°C for 10
min, CH3NH3PbI3, based on PbCl2 and CH3NH3I was annealed at 100°C for 60 minutes, triple
cation of FA0.85 MA0.15 Cs0.17Pb (I0.83 Br0.17)3 was annealed at 100°C for 20 min and
CH3NH3PbBr3 annealed at 100°C for 10 min.
For some investigations, perovskite layers have been stabilized with a capping layer
(PMMA (Sigma Aldrich): poly methyl methacrylate). The capping layer can have different
functions, for example, it can avoid the penetration of moisture into the perovskite during the
transfer of samples out from the glovebox and it can slow down the decomposition of the
perovskite during temperature-dependent measurements. For this purpose, PMMA was
dissolved in butyleacetate (Sigma Aldrich) and heated to 60°C in a nitrogen filled glovebox.
The stability of the perovskite layer was optimized by varing the concentration of PMMA in the
butylacetate (0, 20, 40, 60, 80, and 100 mg/ml). After annealing of the perovskite, the hot
solution of PMMA and butylacetate was spin coated (2000 rpm for 60 s) onto the perovskite
layer as described by Yu et al. [192].
4.2 Morphology and architecture of hybrid organic-inorganic lead
halide perovskites
4.2.1. Morphology of TCOs (transparent conductive oxide)
Figure 4.4 shows SEM (secondary electron microscopy) micrographs of bare FTO (a), ITO
(b), IOH (c) and MO (d), substrates. The SEM images of FTO shows different facets of
crystallites on the surface. The facets are relatively large indicating that the FTO surface is
quite rough. FTO is known to be very rough with reported root mean square roughness of the
order of 70 90 nm [193]. The high roughness is beneficial for the enhancement of light
trapping in the solar cell. On the other hand, the Mo substrate poses elongated structures of
facets which are uniform and compact suggesting that the surface is also rough. However, the
surface roughness is smaller compared to FTO due to smaller grain sizes. The morphology of
ITO shows small grains in comparison to the FTO and MO substrates indicating the formation
of a smoother surface with smaller grains. IOH has the smoothest surface with very small
grains. In general, the roughness of the substrate can have a strong impact on the
homogeneity of perovskite films.
61
Figure 4.4: SEM micrographs of used substrates (FTO (a), ITO (b), IOH (c) and MO (d)
4.2.2. Morphology of hybrid organic-inorganic lead halide perovskites deposited on
transparent conductive oxides and electron and hole selective contact materials
Figure 4.5: SEM images of np-TiO2 (a) sputtered np-TiO2 (b), np-SnO2 (c), np-TiO2/ perovskite (d),
sputtered np-TiO2/, perovskite (e) and np-SnO2 /perovskite (f).
Figure 4.5 the SEM micrographs of np-TiO2 (a), sputtered TiO2 (b), np-SnO2 (c), np-TiO2/
perovskite (d), sputtered np-TiO2/ perovskite (e) and np-SnO2 /perovskite (f). The SEM top
views show that the sputtered TiO2 has a larger grain size than spin coated np-TiO2 and spin
coated np-SnO2 suggesting that perovskite films with larger grains can be formed on sputtered
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np-TiO2 in comparison to spin coated films. SEM images of annealed perovskite active layers
on np-TiO2 and np-SnO2 did not show major differences in grain sizes. The average grain size
of perovskite absorber layers was about 240 nm on spin coated substrates and about 470 nm
on sputtered substrates. Perovskite absorber layers with larger grain sizes are desirable for
longer diffusion length due to the reduced recombination rates at grain boundaries [102].
Figure 4.6 presents SEM micrographs of annealed perovskite active material on various
fullerenes; ICMA (a), PCBM (b), C60 (c) and a cross-section image of perovskite on C60. The
SEM micrograph of annealed perovskite active layers on various fullerenes did not show a
pronounced difference in the grain size which was of the order of 240 nm. Figure 4.6 (d)
illustrates a SEM cross section image of annealed perovskite active material deposited on C60.
The cross section image revealed remarkable appearance of horizontal grain boundaries in
the perovskite layer with an average thickness of about 350 nm.
Figure 4.6: SEM images of perovskite on fullerenes, ICMA (a) PCBM (b) C60 (c) and cross-section
image of perovskite on C60 (d)
Figure 4.7 shows SEM micrographs of PEDOT: PSS (a), PTAA (b), annealed perovskite
on (c) PEDOT: PSS and (d) PTAA respectively. The PEDOT: PSS layer on ITO substrate
showed a blurred morphology whereas for PTAA, the morphology of ITO was conserved at the
surface. This suggests that the layer of PEDOT: PSS on the ITO substrate was a significantly
thicker in comparison to the PTAA layer. The size of perovskite grains on both PEDOT: PSS
(c) and on PTAA (d) was of about 125 nm.
63
Figure 4.7: SEM images of PEDOT: PSS (a), PTAA (b), annealed perovskite on (c) PEDOT: PSS (d)
and PTAA, respectively.
4.2.3. Layer structures used for characterization
Figure 4.8 shows different layer structures of perovskite films used for the characterization.
For the investigation of material properties at room temperature, hybrid organic-inorganic lead
halide perovskite layers were deposited onto glass substrates coated with a TCO (usually ITO)
layer (figure 4.8 a).
Figure 4.8: Layer structures of investigated perovskite samples. Glass / TCO / perovskite (a) Glass /
TCO / perovskite / capping layer (b); Glass / TCO / HTM or ETM / perovskite (c) and Glass / TCO /
HTM / Perovskite / ETM (d).
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For the investigation of the temperature dependence of the band gap of CH3NH3PbI3 by
SPV, the layer architecture glass/Mo/perovskite/PMMA (figure 4.8 b) was used. In order to
investigate the influence of charge-selective contacts on charge separation, different hole- or
electron-selective contacts were deposited onto the TCO layer before the perovskite layer was
deposited (glass/ITO/HTM/perovskite or glass/ITO/ETM/perovskite, (figure 4.8 c). For some
SPV measurements, the perovskite layer was sandwiched between an HTM (PEDOT: PSS or
PTAA) bottom and an ETM (double layers of PCBM/BCP, C60/BCP and IPH/C60) top layers
(glass/ITO/HTM/Perovskite/ ETM (see figure 4.8 d)).
4.3 Phase analysis by grazing incidence X-ray diffraction (GIXRD)
Grazing incidence x-ray diffraction (GIXRD) is a powerful and non-destructive technique
for characterizing films with thicknesses of a few atomic layers [194]. The method was originally
developed in 1979 by Marra et al. for studying ordered interfaces and surface phenomena for
atomic layers of Al and GaAs [195]. In this technique, the detector was placed horizontal to the
plane parallel to the surface of the film in order to record diffraction patterns from lattice planes
that are perpendicular to the film surface. At an angle of incidence near or above the critical
angle, total internal reflection occurs, giving rise to x-rays with highly enhanced intensities and
a small penetration depth [196].
Figure 4.9 shows a schematic diagram of GIXRD geometry in which the incident x-ray
beam of the wave vector 𝐤𝐤𝐢𝐢 impinges on the film surface at a glancing angle of 𝛼𝛼𝑙𝑙<. The
diffracted wave vector 𝐤𝐤𝐬𝐬 was detected at an angle αs with respect to the sample surface and
at an angle of 2𝜃𝜃 with respect to the transmitted beam. The investigated sample rotates around
its surface in a so-called ω scan (see figure 4.9).
α
i
α
s
2θ
k
i
k
s
Incident
ray
Scattered
ray
ω
Figure 4.9: Schematic diagram of GIXRD geometry
The GIXRD beam irradiates the sample surface in a grazing incidence with αi close to the
critical angle for total internal reflection to occur. The incident x-ray beam gives rise to a
diffracted beam from the lattice planes that are perpendicular to the surface. The diffracted
beam encloses an angle of which was fixed with respect to the detector and leaves the
65
surface at a grazing angle αs [194].The grazing incidence x-ray diffraction pattern was
measured by Bruker AXS (D8 Advance) for thin films analysis with a Cu radiation source
of wavelength 0.154065 nm. The instrument was equipped with a 9-fold sample changer. For
the investigation of the perovskite thin films, the angle was scanned from 10° to 70° using
a step size of 0.02° and acquisition time of 4 s deg-1.
The measured GIXRD patterns enabled to gain information about the phases in the layers
by comparing with the reference data. The international center for diffraction data base was
installed at the PC in the lab xlabd8bb, room PT006 of Helmholtz Zentrum Berlin. Bruker
diffraction EVA software version 4.1.1 in combination with free powder diffraction data base
(COD 7218931) was used for phase analysis and structure determination.
Figure 4.10 shows GIXRD patterns of CH3NH3PbI3 films for as-prepared, 7 and 43 days
of storage in air (a, b & c respectively). For the as-prepared sample (figure 4.10 (a)), the
GIXRD pattern showed diffraction peaks at 14.2°, 20.01°, 23.48°, 24.5°,28.5°, 31.89° and 43.5°
corresponding to the (110), (112),(211), (202), (220),(310) and (314) diffraction planes of the
tetragonal phase of CH3NH3PbI3 [12]. After 1 week of storage in air (figure 4.10 (b)),
CH3NH3PbI3 undergoes a phase change with the appearance of a new phase with an additional
peak at 12.67°. This new phase characterized by the appearance of the peak at 12.67°
corresponds to PbI2 [197] which did occur due to decomposition of CH3NH3PbI3 to its
constituent precursor compounds. After continuous storage in air for 43 days (figure 4.10 (c)),
the intensity of the PbI2 peak at 12.67° continued to increase whereas the intensity of the
CH3NH3PbI3 peak at 14.2 ° decreased strongly. Therefore, the CH3NH3PbI3 continued to
degrade to PbI2, due to evaporation of CH3NH3I from the surface of the sample [192].
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Figure 4.10: Grazing incidence x-ray diffractogram (GIXRD) of as-prepared CH3NH3PbI3 (a), and of
CH3NH3PbI3 after storage in air for 7 days (b) and after 43 days (c)
The GIXRD patterns of a CH3NH3PbI3 and CH3NH3PbBr3 thin films are compared in figure
4.11. A systematic shift in GIXRD peak patterns towards higher 2θ degrees was observed for
CH3NH3PbBr3 in comparison to CH3NH3PbI3 thin films. This was attributed to volume
contraction of the unit cell of CH3NH3PbBr3 layers [41] due to smaller ionic radius of bromide
ion which favors the formation of a cubic structure. The structural differences of CH3NH3PbI3
and CH3NH3PbBr3 thin films seem to originate from the ionic radius of iodine and bromide
anion which according to reported values in literature are 2.2 and 1.96 respectively [19].This
implies that smaller bromine atoms decreases the lattice spacing for CH3NH3PbBr3 perovskite
layer as compared to larger iodine atom in CH3NH3PbI3 film.
For the case of CH3NH3PbI3 layers deposited on an ITO substrate, two dominant peaks at
14.12° and 28.45° were observed. These peaks corresponded to (110) and (220) diffraction
planes of tetragonal lattice [12].The GIXRD analysis for CH3NH3PbBr3 thin films reveals
characteristic diffraction peaks of cubic perovskite phase with a preferential orientation at
14.98° corresponding to (100) plane of cubic perovskite [198]. Other peaks appear at 21.92°,
30.18°, 33.84°, 37.18°, 43.204° and 45.97° corresponding to (110), (200), (210) (112) (220)
and (300) planes respectively of crystalline cubic phase of perovskite [41]. Lattice constant
was calculated to be 5.93 Å and 6.32 Å for CH3NH3PbBr3 and CH3NH3PbI3, respectively, which
agrees well with previously reported value [12].
67
Figure 4.11: GIXRD of as- prepared CH3NH3PbI3 and CH3NH3PbBr3 (red and black lines,
respectively).
4.4 Ultraviolet-visible light spectroscopy (UV-vis)
Ultraviolet-visible (UV-vis) light spectroscopy is an optical method allowing for the
measurement of reflected and transmitted light. The intensity of the absorbed light is obtained
from the difference between the intensity of the incident light and of the intensities of the
transmitted and reflected light. For thin planar samples, the intensities of the reflected and
transmitted light can be simply measured by placing the detector in line with the reflected or
transmitted light beams (figure 4.12 (a)). However, perovskite layers are deposited onto
substrates containing additional layers, for example, for contacts and/or passivation.
Furthermore, perovskite layers consist of grains with different size so that the layer thickness
is not constant and light is partially scattered (figure 4.12 (b)). Therefore, perovskite layers are
not ideal for optical measurements and sophisticated optical models are needed for the
detailed analysis of transmission and reflectance spectra. This is out of the scope of this thesis.
Here, the measurement of the band gap and of the Urbach tails is desired for a large variety
of perovskite samples.
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Figure 4.12: Schematic of transmission and reflection of an ideal sample (a) and of a sample
with a layered structure and with partial light scattering (b); arrangement of the measurement of
transmitted (c) and reflected light with an Ulbricht or integrating sphere.
The completely transmitted and reflected light can be measured with an Ulbricht or
integrating sphere. In an ideal integrating sphere, light is not absorbed but scattered into all
directions with the same probability (white Lambertian surface). For this purpose, the internal
surface of an integrating sphere is coated with, for example, barium sulfate (BaSO4) or Teflon
(PTFE). For the measurement of the complete intensity of transmitted light, the sample is
placed at the entrance of the integrating sphere (figure 4.12 (c)). A baffle shields the detector
from direct incoming light so that only light which is scattered in the integrating sphere can be
detected. Therefore, the detector is sensitive to the complete intensity of transmitted light. For
the measurement of the complete reflected light, the sample is placed at the edge of the
opposite surface of the integrating sphere (figure 4.12 (d)). Again, a baffle shields the detector
from directly reflected light. UV-vis measurements are calibrated by measuring the spectra of
the incident light without placing a sample into the positions for the measurement of
transmission and reflection spectra.
As an example, figure 4.13 shows reflectance, transmittance and absorbance spectra of
CH3NH3PbBr3. The absorbance increases steeply in the range of the band gap. The values of
the band gap and of the Urbach tails were obtained from the absorbance spectra by applying
the analysis explained before.
69
Figure 4.13: Spectra of the reflectance, transmittance and absorbance (black, blue and red lines,
respectively) of a CH3NH3PbBr3 layer deposited on glass.
Absorbance spectra of hybrid organic-inorganic perovskite layers were measured with a
commercial UV-vis spectrometer (Perkin Elmer Lambda 1050 spectrophotometer) in the
spectral range from 175 nm to 3300 nm. In this spectrometer, a grating monochromator is
used. The spectrophotometer uses two detectors inside the integrating sphere. One detector
is a photomultiplier (PMT) in combination with InGaAs as a cathode covering the spectral range
between 860 to 1800 nm and wide band covering between 860-2500 nm. The second detector
is a PbS detector which is sensitive in the wavelength range between 1800/ 2500-3300 nm.
4.5 Photothermal deflection spectroscopy (PDS)
Photothermal deflection spectroscopy (PDS) is an optical technique allowing for the
characterization of the absorption spectrum near the band gap of a thin semiconductor layer
[199]. PDS is based on the absorption of a periodically modulated light beam (pump beam,
figure 4.16). The light from the pump beam (see figure 4.16) is absorbed by the sample and
transformed into heat [199]. This causes a small modulated increase of the temperature at the
surface of the sample. The sample surface is in contact with a liquid. Therefore, the liquid is
periodically heated by the heated surface of the sample and a modulated temperature gradient
arises in the liquid. The liquid is a material with a strong temperature dependence of the
refractive index (for example, tetradecafluorohexane, C6F14). The resulting change of the
gradient of the refractive index is detected by the deflection of a probe beam (usually a He-Ne
laser) which is aligned in parallel to the sample surface and perpendicular to the pump beam
[200]. The deflection of the probe beam is detected with a position-sensitive photodiode.
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Figure 4.16: Working principle of PDS.
By probing the gradient of the refractive index with a probe beam, its deflection can be
related to the optical absorption of the sample whereas the degree of deflection corresponds
to the optical absorption of the sample [201]. In order to increase the sensitivity, the sample is
immersed in a transparent liquid characterized by a relatively strong change of the refractive
index with small changes of the temperature so that tiny increments of the temperature can be
detected ( of 10-4 K) [202]. However, one has to keep in mind that the liquid should not interact
with the sample. This is the case for C6F14 in contact with perovskites.
A typical PDS set-up consists, as shown in figure 4.17, of a halogen lamp with a
monochromator and an optical chopper in order to create the wavelength-dependent
modulated pump beam, a He-Ne laser (probe beam) and a position-sensitive detector
(quadrant photodiode).
The deflection is detected with a lock-in amplifier (lock-in A) as the difference between the
photocurrents of the quadrants of the photodiode. An oscilloscope is used for the alignment of
the quadrant detector. The cuvette with the C6F14 and the sample is placed on a x-y-z-Φ stage
for alignment of the position and the orientation angle in relation to the He-Ne laser,
respectively. The position of the quadrant detector is aligned with a x-y stage. A part of the
pump beam is directed via a beam splitter onto a calibrated tandem detector for measuring the
intensity of the pump beam. The tandem detector consist, for example, of a silicon photodiode
and a lead sulfide (PbS) photoresistor (or a GaInAs photodiode). The intensity of the pump
beam is measured with a second lock-in amplifier (lock-in B).
PDS measurements were performed on selected samples (CH3NH3PbBr3) in the range
between 0.7 and 2.7 eV. For the measurements, a home-made set-up was used.
71
Figure 4.17: Set-up for PDS measurements.
4.6 Experiments with modulated surface photovoltage (SPV)
spectroscopy
Two setups were used for modulated SPV spectroscopy. In both setups, illumination was
performed with a halogen lamp (100 W) and quartz prism monochromator (SPM2). The
modulation frequency was usually 8 Hz. The reference electrodes consisted of a quartz
cylinder partially coated with conductive SnO2:F (band gap about 3.6 eV). The reference
electrode was gently pressed onto the sample surface with a cardanic spring whereas a thin
mica sheet (thickness 20 30 µm) was placed between the sample surface and the reference
electrode in order to form the measurement capacitor [203]. The capacitance of the
measurement capacitor was between 10 and 20 pF. The sample electrode was grounded.
The reference electrode was connected with the high-impedance buffer.
For temperature-dependent measurements, a home-made high vacuum chamber (figure
4.18, base pressure below 2 x 10-5 mbar) was used. The high-impedance buffer (Rm = 50 GΩ)
was placed outside the chamber (BNC feedthrough). A Pt100 placed directly underneath the
sample was used for temperature measurement. A temperature controller with a current
source was applied for regulating the temperature. For routine SPV measurements at very low
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noise levels, a second home-made chamber (figure 4.19), in which a battery powered high-
impedance buffer (Rm = 150 G) was placed inside the chamber, was used. The noise levels
were about 1 2 µV and 0.2 0.3 µV for the temperature-dependent and routine SPV
measurements, respectively, for standard measurement conditions (integrating time constant
300 and 500 ms, respectively; 10 averages). For routine SPV measurements, the chamber
was pumped to vacuum with a rotary pump (base pressure below 10-2 mbar) and filled with
nitrogen gas to a pressure of about 700 mbar. During SPV measurements with the routine
chamber, the pump was switched off. EG&G 5210 and EG&G 7260 lock-in amplifiers were
used in the set-ups for temperature-dependent and routine measurements, respectively.
The transfer of the sample from the glovebox to the chamber took about 2 min during
which the sample was exposed to air. Usually, SPV Spectra were measured in a wide range
(0.4 4.0 eV, step 50 meV) and in a narrow (around the band gap, step 10 meV) range. A
widths of the entrance and exit slits of the monochromators were set to 0.3 mm (spectral
resolution better than 10 meV).
For the measurement of the diffusion length after Goodman, the modulated SPV signals
were kept constant by keeping constant the output signal of the lock-in amplifier (lock-in A in
figure 4.19) with a power supply and an integrated feedback unit (Electronic Manufaktur
Mahlsdorf).
Figure 4.18: Scheme of the experimental set-up for temperature-dependent modulated SPV
spectroscopy.
73
Figure 4.19: Scheme of the experimental set-up for modulated SPV spectroscopy (routine
measurements and measurement of the diffusion length after Goodman).
The intensity was measured by coupling out a part of the light with a beam splitter and
using a photodetector (Elektronik Manufaktur, Mahlsdorf) and a second lock-in amplifier (lock-
in B in figure 4.19). The shape of the spectral response function of the detector was calibrated
separately with a pyrodetector.
For quasi in-situ monitoring of the degradation of perovskite films, a LED lamp (see figure
4.20) was used. For this purpose the parabolic mirror, which is used for focusing the light from
the monochromator onto the electrode, was moved out from the optical path and replaced by
a LED (separate red / green / blue, about 1 mW).
Figure 4.20: Chamber of SPV measurements during light soaking with a blue LED.
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CHAPTER 5
Properties of CH3NH3Pb(I, Br)3 and their dependence on
aging and light soaking
The investigation of electronic properties of CH3NH3Pb(I, Br)3 and their dependence on
aging and light soaking is important for better understanding of the stability of solar cells based
on related materials. Some of the results presented in this chapter were published in [34,
204].Modulated surface photovoltage spectroscopy (SPV) allows for ex-situ and quasi in-situ
characterization of the band gap, tail states, direction of charge separation and diffusion length.
In this thesis, material properties related to degradation, stoichiometry, the band gap (Eg),
exponential tail states (Et) and diffusion length (L) were investigated. By varying different halide
compositions, the band gap of perovskite was tuned. Similarly, the measurement of the
diffusion length after Goodman [32], can provide useful information in accordance to the
lifetime of minority charge carriers in solar cells. In the study of interfaces, different electron
selective as well as hole selective contacts were varied and their influence on perovskite
properties were determined. It has been found, for example, that the Tauc gap and energy of
exponential tail states sensitively depend on the substrate and on soaking in nitrogen
atmosphere and that light soaking has strong influence on the direction of modulated charge
separation. In this chapter, the effect of stoichiometry and light soaking on transport length,
exponential defects and Eg of CH3NH3Pb(I1-X)BrX)3 will be investigated using SPV.
5.1. Mixed lead halide perovskite: CH3NH3Pb(I1-XBrX)3
5.1.1. Equivalence between surface photovoltage (SPV) and photothermal deflection
spectroscopy (PDS) for CH3NH3PbBr3
Disorder in semiconductor leads to defect states below the band gap that participate in
the absorption process (optical) or charge separation (SPV). For example, disorder results in
a decrease of SPV signals towards lower photon energies [205]. For the optical absorption
process, the absorption coefficient can be expressed using the Urbach relation [63]:
𝛼𝛼 = 𝛼𝛼𝑜𝑜 𝑒𝑒𝑥𝑥𝑒𝑒ℎ𝑣𝑣−𝐸𝐸0
𝐸𝐸𝑢𝑢 5.1
where 𝐸𝐸0 = 2.3 eV for CH3NH3PbBr3, 𝛼𝛼𝑜𝑜= 2.9 × 104 cm-1 and 𝐸𝐸𝑢𝑢 is the Urbach
energy which is equal to the reverse of the absorption edge slope.
1
𝐸𝐸𝑢𝑢=(𝑙𝑙𝑙𝑙𝛼𝛼)
∆ℎ𝑣𝑣 5.2
75
In order to investigate defect states below the band gap by SPV, the amplitudes (R) of the
SPV signals were measured in the energy range between 2.0 to 2.5 eV, step width of 0.01 eV
with an average of 20 data points and then plotted on a logarithmic scale. The energy of the
exponential tail states (Et) measured by SPV was obtained by fitting the amplitude of the SPV
signals to the leading edge with an expression of the form:
𝑅𝑅Φ𝑝𝑝ℎ
= 𝐴𝐴 𝑒𝑒𝑥𝑥𝑒𝑒ℎ𝑣𝑣−𝐸𝐸𝑔𝑔
𝐸𝐸𝑡𝑡 5.3
where A is a proportionality constant and Eg is the approximate band gap. As a remark, a low
value of Et indicates a high level of electronic order in the perovskite absorber material with
low sub band gap states near the band edge.
Figure 5.1 shows the absorption spectrum of a CH3NH3PbBr3 layer measured by the
photothermal deflection spectroscopy (PDS) and the SPV spectrum of the same sample on a
logarithmic scale. The absorption coefficient (α) exhibited a sharp shoulder near the band gap
at about 2.3 eV. Below the shoulder i.e. between 2.2 to 2.3 eV, α follows an exponential
behavior. Eu amounted to 18 meV, which was consistent with the value of 18.9 meV, as
reported by Wenger et al. [206].
Figure 5.1: Absorption spectrum measured by PDS (red triangles) and spectrum of the PV amplitude
on a logarithmic scale (blue circles) for the same CH3NH3PbBr3 perovskite film. The solid lines are the
slope of the Urbach tails (Eu) (red line) and exponential tail energy (Et) (blue line). The dotted line
marks the slope of 18 meV. The black line represents the photon flux Фph.
Below photon energies of 2.2 eV, α was characterized by sub band gap absorption which
revealed the population of sub band gap states. The sub-band gap states may be due to a
contribution of the substrate which was limited by the defects present in the glass substrate
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[13]. Et was obtained to be 19 meV for CH3NH3PbBr3 perovskite films. The value of Et by SPV
was comparable with Eu with a slight deviation of about 1 meV. The discrepancy was brought
about by the difference in the sensitivity of each measurement method. As a remark, both
methods are sensitive to different regions of measurements. For instance, SPV is sensitive to
the measurement region where charge separation takes place whereas PDS probes the whole
region of the sample volume where absorption takes place. In addition, SPV is not a pure
optical method and detects separation of charge carriers excited from localized to delocalized
states. To characterize the material in more detail, the band gap in terms of Tauc gap was
determined using both PDS and SPV.
The Tauc model [178] was used to determine the band gap energy as shown in figure 5.2.
For PDS, the Tauc gap was obtained by plotting the squared product of the absorption
spectrum and photon energy i.e. (𝛼𝛼.ℎ𝑣𝑣)2against the photon energy (see figure 5.2 red
triangle and a line). The exponent 2 was used because CH3NH3PbBr3 has a direct band gap
[207] [208]. The band gap (Eg) of CH3NH3PbBr3 measured by PDS was about 2.295 eV. The
Tauc gap obtained was in excellent agreement with that reported in literature [207].
Figure 5.2: Tauc plots of the absorption spectrum measured by PDS (red triangles) and of the SPV
spectrum (amplitudes, blue circles) of the same CH3NH3PbBr3 sample. The red and blue lines mark
the linear fits to the band gaps.
For comparison with optical absorption from PDS, SPV was used to determine the band
gap in the spectral range near the direct band gap. The analysis of the Tauc plot of the
amplitude signal was done with the presumption that the amplitude signal was proportional to
the absorption coefficient, that the penetration depth was much shorter than the charge carrier
diffusion length and that the modulated SPV signals could be treated as small signals [209].
The Eg measured by SPV (figure 5.2 with blue circles and a line) was same as for PDS. The
77
band gap measured by SPV was found to be 2.308 eV which was in good agreement with
values obtained in literature [55, 18]. The Eg obtained by SPV and that obtained from PDS
differed by about 13 meV. The discrepancy is due to uncertainty in the analysis, i.e. it cannot
be completely assumed that the SPV signals are proportional to α, what is not surprising. As
a remark, modulated SPV signals are not necessarily directly proportional to the photon flux
as assumed for the small signal case, since the generation of SPV signals may involve many
processes taking part during charge separation. However, the signals are practically
proportional to the photon flux in the low signal regime when the dominant mechanism of
charge separation and relaxation do not change [205,175]. In addition, there is an interface of
perovskite with the liquid which might also influence the electronic states near the band gap.
5.1.2. Vegard’s law in CH3NH3Pb(I1-xBrx)3
Vegard’s law maintains at constant temperature a linear relationship between the crystal
lattice parameter (constant) and the composition of the constituent elements. Such a linear
relation exists in an ensemble of a random mixture of substitutional solid solutions. An accurate
knowledge of the dependence of the lattice parameter on the concentration of the constituent
elements allows for the determination of the composition of an alloy by simple measurement
of the lattice constant.
Figure 5.3 shows the GIXRD diffraction patterns for CH3NH3Pb(I1-XBrX)3 perovskite films
between 0 ≤ x ≤ 1 in the 2θ range of 13 15.5°.The CH3NH3PbI3 at x = 0 had a peak located
at 14.12° which corresponded to (110) planes for the tetragonal 14/mcm phase [12]. The
tetragonal phase of CH3NH3PbI3 was maintained until x = 0.13 and then changed to cubic
phase at about x = 0.2 [19]. A systematic shift in the GIXRD peak patterns towards higher 2θ
angles was observed with increasing bromide composition x. The systematic shift towards
higher 2θ angles was due to the gradual substitution of the larger iodine atoms with the smaller
bromine atoms which led to the decrease of the lattice spacing. For example, 2θ was equal to
14.12, 14.24, 14.32, 14.41, 14.46, 14.54, 14.65, 14.80 and 14.91° at x = 0, 0.13, 0.2, 0.29,
0.38, 0.47, 0.58, 0.84 and 1 respectively. Since the iodine atom is larger than the bromine
atom, the lattice undergoes contraction when I- anion was substituted for Br - anion. Therefore,
according to Bragg’s law nλ = 2dsinθ; a corresponding shift of diffraction peaks to higher 2θ
angles was observed with increasing x.
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Figure 5.3: GIXRD patterns of the CH3NH3Pb(I1-xBrx)3 films at x = 0, 0.13, 0.2, 0.29, 0.38, 0.47, 0.58,
0.84, and 1; magnified in the region of the tetragonal (110)T and cubic (100)C peaks for 2θ between
13.0 to 15.5.
Under slight rotation of the PbX6 octahedra along the (110) planes, while maintaining the
corner sharing structure, changed the tetragonal phase to the cubic phase in the ideal
CH3NH3PbX3 perovskite structure. This implied that the tetragonal phase could be described
by the pseudo-cubic lattice [19] as shown in figure 5.4. Figure 5.4 (a) shows the dependence
of the lattice parameter as a function of bromide composition x for the pseudo-cubic
CH3NH3Pb(I1-X BrX)3 films. The values of lattice constant correlated well with x, and showed a
linear relationship with x. The values were, 6.26, 6.245, 6.22, 6.195, 6.165, 6.137, 6.09, 6.04,
6.02, 5.99 and 5.94 at x = 0, 0.13, 0.2, 0.29, 0.38, 0.47, 0.58, 0.84 and 1 respectively. The
values compared well with the findings of Noh et al. [19].
According to Vegard’s law, the lattice parameter in the alloy varies linearly with
composition under constant temperature and negligible electronic effects. Therefore, the linear
variation indicated the formation of the cubic CH3NH3Pb(I1-X BrX)3 compound in the complete
range of 0 x 1 by a simple solution mixing process. In addition, the lattice constant
decreased with increasing x. This phenomenon occurred due to the substitution of the larger
iodine atom with smaller bromine atom that decreases the lattice spacing. For comparison, the
values of lattice constant from literature was shown [19]. The lack of significant deviations from
79
Vegard’s law indicates the absence of significant phase segregation in the CH3NH3Pb(I1-X BrX)3
films.
Figure 5.4: Dependence of the (a) lattice constant as a function of bromide composition x for samples
used in this work and for values in the literature after Noh et al. [19]; (b) band gap on the lattice
constant of pseudo-cubic CH3NH3Pb(I1-X BrX)3 perovskite films.
Figure 5.4(b) shows the band gap as a function of lattice parameter for the pseudo-cubic
CH3NH3Pb(I1-X BrX)3 perovskite films. Eg was 1.52, 1.56, 1.59, 1.62, 1.68, 1.72, 1.81, 1.89, 1.99,
2.14, & 2.3 for lattice parameter of 6.26, 6.245, 6.22, 6.195, 6.165, 6.137, 6.09, 6.04, 6.02,
5.99 and 5.94 respectively. As observed, Eg increased with decreasing lattice parameter
suggesting a lattice contraction due to increase in potential energy of the electrons in the
orbitals of an atom. As the lattice parameter decreases, the interatomic distance reduces as
well. This increases the binding force between valence electrons and the parent atom (i.e. the
valence electrons become more bound to the parent atom). This means that more energy is
required to make valence electrons move freely within the atom and become conduction
electrons. A direct outcome of the decreasing lattice parameter is the increase in the energy
gap.
5.1.3. Dependence of the band gap and of the exponential tail states on the
stoichiometry of CH3NH3Pb(I1-XBrX)3
For the approximate determination of the band gap, the so- called onset energy can be
used. The onset energy (Eon) allows for the linear approximation of the SPV signals through
the inflection point near the band gap to zero.
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Figure 5.5 shows the SPV spectra of the CH3NH3Pb(I1-X BrX)3 perovskite films with different
halide compositions. For all samples, the in-phase signals were negative while the signals
phase- shifted by 90° were positive. Negative values of in-phase signals implied that photo-
generated electrons were preferentially separated towards the external surface while holes
towards the bulk of the sample (i.e. like in a p-type semiconductor in depletion). The maximum
of the in-phase signal was -0.86, -0.82, and -0.55 mV for x = 0, 0.58 and 1, respectively. This
can imply, for example, that the band bending decreased with increasing bromide content. In
contrast, the phase-shifted by 90° signals were 0.2, 0.3, and 0.35 mV, for x = 1, 0.58 and 0
respectively. This points to an increase of the influence of slow relaxation processes with
increasing bromide content. Furthermore, in-phase and phase-shifted by 90° signals showed
opposite signs which implied one dominating mechanism of charge separation in which
electrons are preferentially separated towards the external surface. Mechanisms that lead to
charge carrier separation with opposite signs may be due to charge separation across space
charge regions and trapping of photo-induced charge carriers at interface states [28].
Figure 5.5: In-phase and phase-shifted by 90° SPV spectra (black and red circles, respectively) of
CH3NH3Pb(I1-X BrX)3 perovskite films for x = 1, 0.58 and 0 (a-c, respectively). The dashed lines mark
the approximations to the onset energies.
The onset energy (Eon) of CH3NH3Pb(I1-XBrX)3 perovskite films was tuned from 1.5 to 2.3
eV by varying different halide compositions. For pure CH3NH3PbI3 in which x = 0, (figure 5.5
81
a), the onset energy was approximately 1.5 eV. This was consistent with both experimental
and theoretical values reported in literature [28, 19] . When the bromide composition was
varied to 58% of the initial amount i.e. x = 0.58 (figure 5.5 b), the onset energy shifted to
approximately 1.92 eV. With pure bromide composition, i.e. CH3NH3PbBr3 with x = 1) (figure
5.5 c), the approximate onset energy shifted further to about 2.30 eV which was also in
agreement with reported values in the literature [210].
Figure 5.6: UV-Vis (a) absorption spectra on a linear scale, and (b) absorbance in logarithmic form
for CH3NH3Pb(I1-XBrX)3 films measured using an integrating sphere. For each spectrum in (b), the
slope of the Urbach tail is shown. The photographs show, CH3NH3Pb(I1-XBrX)3 films with different
concentrations of bromide ions (c).
To check the variation of the optical properties of the perovskite absorber layers, UV-vis
absorption spectra of CH3NH3Pb(I1-XBrX)3 films were measured in the compositional range
between 0 x 1 (see figure 5.6 (a)). The onset of the absorbance spectra was tuned from
an energy of 1.59 to 2.30 eV resulting in perovskite films of different colors. Figure 5.6 (a)
shows a systematic shift of the absorbance spectra towards shorter wavelength with increasing
bromide content i.e. the spectra blue shifted with increasing bromide content. The blue shift
may be attributed to different spin- orbit interactions between lead-iodide and lead-bromide
ions [19]. There was optical absorption for photon energies below the range influenced by the
Urbach tails. This absorption may be ascribed to absorption of the perovskite or by free carrier
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absorption in the ITO substrate. As a remark, the high background signals may also be
influenced by scattering at the rough surface of the perovskite films which was observed to be
higher for iodide rich perovskite films than for bromide rich films.
In order determine Urbach energy of CH3NH3Pb(I1-XBrX)3 films; the absorbance in
logarithmic form i.e. 𝑙𝑙𝑐𝑐𝑙𝑙2.303 𝐴𝐴
𝑑𝑑 were plotted against photon energy as shown in figure 5.6
(b). 𝐴𝐴 is the absorbance, and 𝑑𝑑 is the film thickness. The spectra continuously blue shifted
upon increasing x. All CH3NH3Pb(I1-XBrX)3 films in this family showed strong absorption onsets.
Moreover, all samples showed unusually sharp shoulder close to their corresponding onset
energies. Below the shoulder, logarithmic form of absorbance for CH3NH3Pb(I1-XBrX)3 films
exhibited purely exponential trend. The slope of the exponential part gives the Urbach energy
(Eu). Eu was obtained to be 28, 31, 48, 50, 50, 46, 35, 38, 38, 36 and 28 for x = 0, 0.06, 0.13,
0.20, 0.29, 0.38, 0.47, 0.58, 0.71, 0.84 and 1, respectively. The value of Eu was observed to
be lower for pure tri-iodide and tri-bromide perovskite but higher for mixed perovskite. This
observation was consistent with what was reported by Sadhanala et al. [211]. They observed
Eu of about 90 meV for CH3NH3Pb(I0.4Br0.6)3 films with significant population of sub band gap
states which was interpreted as the beginning of the formation of two species in perovskite
films. The relatively high value of Eu for CH3NH3Pb(I1-XBrX)3 films with 0 < x < 1, might be
attributed to the disordered lattice due to random distribution of iodide and bromide atoms in
the lattice sites [212]. It is also postulated that the introduction of bromide ions into the mixed
halide solution create more stress that induces more defect states hence the high disorder
observed in the material [213]. In addition, increased disorder in the mixed halide perovskite
tend to form localized states with a weak extended bonding. These localized states form sub-
band gap states in bromide and relaxation of charge carrier processes in the perovskite films
[214].
Figure 5.6 (c) shows the photographs of CH3NH3Pb(I1-XBrX)3 films between 0 x 1. By
varying the composition of bromide content in the CH3NH3Pb(I1-XBrX)3 films, the color was
tuned from dark for CH3NH3PbI3 at x = 0, red at x = 0.84 to yellow for CH3NH3PbBr3 at x = 1.
These arrays of colors may be desirable in the fabrication of colorful solar cells that can be
used in rooftops, windows and walls [19].
Figure 5.7 (a) shows the variation of Eg as a function of bromide composition (x) in
CH3NH3Pb(I1-X BrX)3 perovskite films measured using SPV and UV-Vis spectroscopy. For both
measurements, the values of Eg varied non-linearly with increasing Br composition x in the
alloy. The Eg was estimated from Tauc plots. The values of Eg reported from literature are
shown for comparison [19,33]. For example, the values of Eg obtained from SPV compared
well with the Eg measured by optical methods after Noh et al. at x = 0, 0.06, 0.29, 0.38, 0.47,
0.58, 0.71, 0.84 and 1. However, Eg measured by SPV seemed to be underestimated at x =
0.13 and 0.2 in relation to Eg deduced from UV-vis after Noh et al. [19] and Jacobsson et al.
83
[33]. The values of Eg measured by UV-Vis spectroscopy in this work were a little bit over-
estimated compared to the values obtained by Noh et al. but almost similar to the values
obtained by Jacobsson et al. The over and under-estimation of Eg in the two measurements
may be influenced by the formation of the perovskite and the interface with the substrate. In
addition, SPV measurements are only sensitive to the sample region where charge separation
takes place whereas UV-vis measurements probe the whole sample volume [215]. The non-
linear increase of Eg with increasing Br content as measured using SPV was described with a
quadratic equation 2.4 in chapter 2. List square fit of Eg reduced equation 2.4 into equation 5
.4 with a bowing parameter of 0.36 eV.
Eg = 1.5639 + 0.4 x + 0.36 x2 5.4
where x = 𝐵𝐵𝐵𝐵
𝐼𝐼+𝐵𝐵𝐵𝐵 5.5
The bowing parameter is a measure of the degree of non-linear behavior in the crystal
potential. The crystal potential in an alloy could be expressed as the sum of potential which
was constant throughout the crystal and that which fluctuated with distance due to statistical
variations of the alloy composition [216]. The bowing parameter of 0.36 eV in CH3NH3Pb(I1-X
BrX)3 perovskite films measured by SPV correlates well with the values of 0.33 and 0.29 eV
obtained by Noh et al. [19] and Jacobsson et al. [33], respectively.
To characterize the mixed perovskite further in more detail, SPV measurements were
performed on the samples to determine the electronic defect states close to the band edge of
CH3NH3Pb(I1-X BrX)3 absorber layers. The exponential tail states energy (Et or Eu) near the
band edge are a signature for disorder and may have a strong influence on electronic
properties of the material. For example, Et close to the band edge may contain information
about charge separation from defects states whereas Eu measure the disorder in the Urbach
tail.
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Figure 5.7: Dependence of the (a) band gap measured using SPV (red triangles), UV-Vis
spectroscopy (black diamonds) in comparison to values from the literature [19], [33] (blue circles and
olive stars, respectively) and (b) Et, Eu (open circles in run 1, red triangles with dotted line in run 2 and
black diamonds, respectively) on the stoichiometry of CH3NH3Pb(I1-XBrX)3 films. Run 1 were
measurements done previously in old glovebox whereas run 2 were measurements done in new hy-
sprint perovskite baseline glovebox.
Figure 5.7 (b) shows the dependence of exponential tail states Et and Eu on x. The values
of Et for CH3NH3Pb(I1-X BrX)3 films were determined for measurements done in run 2; which
was the glove box situated in new hy-sprint perovskite laboratory. The value of Et was constant
at 28 meV for x = 0 and 0.06 and thereafter increased to 30, 30.5, 31.5 and 31.8 meV for x =
0.13, 0.2, 0.29 and 0.38 respectively. Et dropped to 28 meV for x = 0.47 meV before increasing
strongly to 60 for x = 0.58. The values of Et remained constant at 28 meV for x = 0.71, 0.84
and 1 respectively. The relatively low Et in the films with higher iodide (i.e. x = 0, and 0.06)
content and high bromide content (x = 0.71, 0.84 & 1) could be correlated with low disorder in
those films. Similar trend was observed for Eu values of CH3NH3Pb(I1-X BrX)3 films. Eu of 28
meV was obtained at x = 0 and 0.06 and increased to 30, 38, and 40 meV for x = 0.13 0.2 and
0.29, respectively. Eu dropped slightly to 35 meV for x = 0.38 and 0.47. Eu again increased to
38 meV at x = 0.58 and thereafter remains constant at 36 meV for x = 0.71, 0.84 and 1.
The disorder is high in lower iodide content films and low in higher iodide content films on
both measurements. High disorder observed in CH3NH3Pb(I1-X BrX)3 films may be due to the
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introduction of bromide ion into the mixed halide solution which creates stress on its structure
that induced more defects in the material [213]. Sadhanala et al. [211] observed similar
behavior in which relatively large Urbach energy of about 90 and 60 meV was obtained for
films with 20 and 40% bromide content respectively. They also observed low Urbach energies
for pure tri-bromide films and perovskite films with 80 and 100% iodide content.
To demonstrate that the perovskite properties depend on the preparation conditions,
values of Et for perovskite prepared in the old glove box were also shown as run 1 in figure 5.7
(b). Et values ranged from 16 20 meV for CH3NH3PbI3, 35 45 meV for CH3NH3Pb(I1-X BrX)3
films at x = 0.58 and 16 22 meV for CH3NH3PbBr3 films. Lower values of Et were observed
in run 1 than in run 2. This means that the nature of the solvents present inside a glovebox
significantly affects the electronic properties of perovskite films. At a given x, scatter of Et, Eu
is possible, hence very sensitive to the preparation conditions. This implied that; Et, Eu can
strongly be increased at a certain value of x.
5.2. The role of storage and light soaking on the degradation of
CH3NH3PbBr3 coated with PMMA
Figure 5.8 shows the in-phase SPV spectra for ITO/ CH3NH3PbBr3/PMMA on day 1 and
after 30 days of storage in air under blue light soaking. A change of the sign in the value of in-
phase signal with blue light soaking on day 1 was observed. However, after 30 days of storage
in air, there was no change of sign. The change of the sign on day 1 under blue light soaking
might be attributed to photochemical reactions at the interface of CH3NH3PbBr3 with PMMA
given that not all solvents had completely evaporated from the film surface. After 30 days, no
change of the sign was observed because all solvents had completely evaporated from the
sample surface. At 0 h of light soaking, it was observed that the magnitude of the in-phase
signal on day 30 increased compared to that in day 1.
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Figure 5.8. In-phase SPV spectra for ITO/ CH3NH3PbBr3/PMMA on day 1 (a) and after 30 days of
storage in air (b) under blue light soaking for 0 hour (red closed circles), 1 hour (blue triangles) and 12
hours (olive stars).
The maximum of the in-phase signal increased from -0.33 mV on day 1 to -0.79 mV on
day 30. The increase in the signal intensity, might be due to passivating effect of PbBr2 which
cover the surface, thus preventing it from further degradation [217]. However, a pronounced
reduction of the maximum in-phase signal intensity from -0.79, -0.51 and -0.05 mV
corresponding to 0, 1 and 12 h of light soaking respectively was observed with light soaking
after 30 days. The observed effect showed a reversible behavior suggesting that CH3NH3PbBr3
had better stability compared to its counterpart CH3NH3PbI3 [218, 219]. There was also defect
generation with continued stay in air as indicated by the baseline which deviated from zero in
comparison to practically zero baseline below the band gap on day 1. The defect may be
induced by stress created by PMMA on CH3NH3PbBr3 layers when in contact with impurities
such as air, moisture and light. In addition, with continued storage in air, CH3NH3PbBr3 layers
degrade to PbBr2 and other constituent precursor elements. This results in the formation of an
interface region between CH3NH3PbBr3 and PbBr2 that introduces active defect states [220].
Figure 5.9 shows the exponential tail states (Et) as a function of illumination time in hours
for the CH3NH3PbBr3 film measured on the day 1, 7, and after 30 days of storage in air.
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Figure 5.9: Tail states (Et) as a function of illumination time in hours for CH3NH3PbBr3 film measured
on day 1 (black spheres with dashed line), 7 days (red circles with dashed line) and after 30 days
(olive stars with dashed line) of storage in air.
Et is a measure of the degree of disorder in CH3NH3PbBr3 perovskite films. Disorder in a
semiconductor results from defect states below or near the band gap that participates in charge
separation. Disorder leads to an exponential decrease in the SPV signals towards lower photon
energies [175]. Et showed similar trends for all days such that the value was low before light
soaking, increased after 1 h and thereafter decreases with prolonged light soaking for 12 h.
On day 1, Et was lower compared to other days and amounted to 20, 22, 20 and 19 meV
at 0, 1, 6 and 12 h of light soaking respectively. This was consistent with a practically constant
baseline as shown in figure 5.8. Et increased with storage time in air. For example, Et amounted
to 38, 40, 33.5 and 26 meV and 45, 65, 47 and 27 meV after 7 and 30 days respectively.
Interestingly, 1 h of light soaking showed the highest Et in all days whereas prolonged light
soaking (12 h), showed the lowest Et. The low value of Et after 12 h of blue light soaking may
be caused by activation of local ordering of trap states by the blue light. For comparison,
exponential tail states for the CH3NH3PbI3 coated with PMMA were of the order of 30 meV for
front illumination [209].
To characterize CH3NH3PbBr3 layers further, GIXRD was used in order to study the phase
composition of the films after storage in air for 30 days. Figure 5.10 shows the GIXRD phase
analysis for CH3NH3PbBr3/PMMA thin films on day 1 and after 30 days of storage in air. On
day 1, the GIXRD analysis revealed characteristic diffraction peaks of the cubic perovskite
phase with a preferential orientation at 14.98° corresponding to (100) plane of cubic perovskite
[198]. Other peaks appeared at 21.92°, 30.18°, 33.84°, 37.18°, 43.204° and 45.97°
corresponding to (110), (200), (210) (112) (220) and (300) planes, respectively of the
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crystalline cubic phase of perovskite [41]. However, after 30 days in air, some additional peaks
were observed at 26.06° and 35.28°. These peaks corresponded to the PbBr2 phase [221].
The peak intensity of the (100) at 14.98° decreased from 3576 to 2086 counts on day 1 and
30 respectively. Interestingly, there was an increase in the peak intensity for all the remaining
peaks, suggesting a change in preferential orientation of the peaks with longer storage in air.
Figure 5.10: GIXRD phase analysis for CH3NH3PbBr3/PMMA thin films on day 1 (red line) and after 30
days of storage in air (black line)
5.3. Influence of the substrate on the electronic properties of the
CH3NH3 PbI3 films
The substrate has a strong influence on the electronic properties of perovskite solar cells.
In this context, a substrate can be a bare substrate such as ITO or charge selective contacts
such as TiO2, PCBM, and SnO2 etc. For example, poor charge extraction properties of TiO2
were observed in TiO2-based perovskite devices with a high hysteresis. On the other hand,
SnO2 poses favorable band alignment with perovskite, has high electron mobility and can be
fabricated via low temperature processing [222].Besides, electron transporting fullerenes such
as PCBM have good charge extraction properties as well as passivate defects at the interface
with perovskite. PEDOT: PSS is an organic hole transporting material widely used in inverted
structure of solar cells. However, it has a latent problem such as: highly hygroscopic, very
acidic and has poor electron blocking properties. The acidic and hygroscopic nature of PEDOT:
PSS may cause degradation and hence reduce device stability [223]. Therefore, the
topography and chemical properties of the substrate can significantly influence perovskite
absorber layer grown on it. Furthermore, chemical properties and surface roughness of the
substrate may alter the interfacial energies that can have a strong impact on the nucleation of
the perovskite films [34].
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Figure 5.11 shows SPV overview spectra for CH3NH3PbI3 deposited on SnO2 and PEDOT:
PSS. For ITO/SnO2/CH3NH3PbI3, both in-phase and phase shifted by 90° signals were positive
indicating two mechanisms of charge separation in which photo-generated electrons were
separated towards SnO2 while holes towards the external surface.
Figure 5.11: SPV overview spectrum for CH3NH3PbI3 deposited on SnO2 (orange circles) and
PEDOT: PSS (olive stars)
For ITO/PEDOT: PSS/CH3NH3PbI3, both in-phase and phase shifted by 90° signals were
negative. This suggested that photo-generated electrons were separated towards the external
surface while holes towards PEDOT: PSS. CH3NH3PbI3 deposited in both the selective
contacts i.e. SnO2 and PEDOT: PSS, in-phase and phase shifted by 90° signals have the same
signs which implied two mechanisms of charge separation. Two mechanism of charge
separation occur when, for example, polarization of charge carriers significantly contributed to
the SPV signals. Polarization and photo-generated charge carriers possess opposite signs that
do not follow recombination of charge carriers when illumination was switched on and off [28].
Furthermore, for CH3NH3PbI3 deposited on SnO2, the in-phase signal was maximum at
about 0.824 mV whereas for CH3NH3PbI3 deposited PEDOT: PSS, the maximum was at -0.149
mV. Higher values of in-phase signals corresponded to faster transfer of photo-generated
electrons from CH3NH3PbI3 to SnO2 in comparison to hole transfer to PEDOT: PSS. Similarly,
the maximum value of phase shifted by 90°signal was 0.15 mV and -0.08 mV
ITO/PSnO2/CH3NH3PbI3 and ITO/ PEDOT: PSS /CH3NH3PbI3 respectively. This implied that
slow charge separation and relaxation was relatively faster for electrons separated towards
SnO2 than for holes towards PEDOT: PSS.
Figure 5.12 shows a strong influence of the substrate on the band gap and disorder in the
material for CH3NH3PbI3 deposited on SnO2 and PEDOT: PSS. The dependence of Et on light
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soaking time under nitrogen atmosphere for CH3NH3PbI3 deposited on SnO2 and PEDOT: PSS
is shown in figure 5.12 (a). For the case of SnO2 / CH3NH3PbI3, Et decreased with light soaking
time and amounted to 30, 24, 21, 19, and 17 meV at 10, 20, 40, 60 and 120 min, respectively.
On the other hand, for PEDOT: PSS/ CH3NH3PbI3, Et increased with light soaking time and
amounted to 30, 31, 32, 35, 36 at 10, 20, 40, 60, and 120 min, respectively. The high value of
Et for CH3NH3PbI3 deposited on PEDOT: PSS, may be attributed to acidic, hygroscopic and
photo-oxidation nature of PEDOT: PSS [223] which increases the disorder and therefore the
amount of defects in the material in comparison to CH3NH3PbI3 deposited on SnO2.
Figure 5.12: Dependence of light soaking on (a) Et and (b) Eg measured for SnO2 (red circles) and
PEDOT: PSS (blue triangles).
The dependence of Eg on the light soaking time is also shown in figure 5.12 (b) for
CH3NH3PbI3 deposited on SnO2 and PEDOT: PSS respectively. Eg was practically constant at
1.575 eV for light soaking up to 120 min for SnO2 / CH3NH3PbI3, but decreased slightly to 1.57
and 1.56 eV at 180 and 720 min, respectively. The almost constant Eg, show that SnO2/
CH3NH3PbI3 interface have well aligned energy levels, suggesting exceptionally better charge
selectivity, low trap density, low degree of charge accumulation and low recombination rate
and hence low exponential tail energy [164, 163]. However, there was gradual decrease of the
band gap with longer light soaking time (i.e. at 180 and 720 min), an indication of defect
generation due to degradation induced by illumination. On the other hand, Eg for PEDOT: PSS/
CH3NH3PbI3, decreased with light soaking time and amounted to 1.563, 1.562, 1.55, 1.54 eV
at 10, 20, 40, 60 min, respectively, of light soaking and increased slightly to 1.553 eV after 120
min of light soaking time. The reduced Eg may be due to some disorder at the interface between
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CH3NH3PbI3 and PEDOT: PSS. Furthermore, a high density of defect states present in
PEDOT: PSS/ CH3NH3PbI3 may be responsible for the reduced band gap. The acidic and
hygroscopic nature of PEDOT: PSS creates stress at the interface with perovskite leading to
the formation of defects.
To characterize CH3NH3PbI3 absorber layers in more detail, SPV measurements were
extended to study absorber properties with different electron transporting materials (ETMs)
interfaces. The strong influence of the substrate and light soaking on the band gap, the
exponential tail states and deep defect states of CH3NH3PbI3 layers were demonstrated for
TiO2 and SnO2 substrates by spectral dependent modulated SPV. Figure 5.13 shows layers of
CH3NH3PbI3 absorber layers deposited onto TiO2 and SnO2 substrates and investigated by
spectral dependent modulated SPV. The influence of light soaking with blue light was studied
at the TiO2/CH3NH3PbI3 and SnO2/CH3NH3PbI3 systems.
Figure 5.13 (a) shows the overview spectra for the TiO2/CH3NH3PbI3 interface.10 min after
preparation, the in-phase signals were positive in the whole range of photon energies. On the
other hand, the phase shifted by 90° were negative between 1.55 to 1.89 eV, changed the sign
to positive up to photon energy of 3.1 eV and thereafter remained at 0 mV above 3.1 eV. After
blue light soaking for 18 h, the in-phase signals changed the sign from positive to negative
(see arrow A in figure 5.13 (a)), whereas the phase shifted by 90° signals increased in
magnitude (i.e. an increase in slow response as indicated by the arrow B in figure 5.13 (a)).
The change of the sign after 18 h of blue light soaking may be attributed to the interaction of
light with TiO2 which induced oxygen vacancies [224]. Such oxygen vacancies lead to
accumulation of excess negative charge at the perovskite surface which results in a change of
the sign. Furthermore, an increase in the slow response after 18 h of blue light soaking may
be correlated to the presence of an amorphous region between the TiO2 and CH3NH3PbI3
interface which leads to slow charge separation and transport [225].
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Figure 5.13: Spectral dependent modulated SPV for TiO2/CH3NH3PbI3 and SnO2/CH3NH3PbI3
systems. Figures (a) and (b) represent overview SPV spectra measured 10 min after preparation
(black diamonds) and after 18 h of blue light soaking (blue triangles). The dependence of the PV
amplitude divided by the photon flux as a function of photon energy for (c) TiO2/CH3NH3PbI3 and (d)
SnO2/CH3NH3PbI3.
For SnO2/CH3NH3PbI3 (see figure 5.13 (b)), 10 min after preparation, the in-phase signals
were positive indicating that the photo-induced electrons were preferentially separated towards
the SnO2 substrate whereas holes were separated towards the surface of perovskite. The
phase shifted by 90° signals were slightly negative between 1.56 and 1.7 eV and thereafter
change the sign to a positive value above 1.7 eV. After 18 h of light soaking, the magnitude of
in-phase signals increased from 0.29 to 0.54 mV at a photon energy of 1.7 eV. In contrast,
phase shifted by 90° signals changed the sign with the value increased from 0.02 mV at energy
of 1.85 eV to -0.60 mV at 1.7 eV. As a remark, opposite signs of in-phase and phase shifted
by 90° signals indicated one mechanism of charge separation, relaxation and transport [28].
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For TiO2/CH3NH3PbI3, the band gap (Eg) reduced after light soaking with blue light from
1.60 to 1.58 eV. The tail states, i.e. the disorder, remained unchanged (i.e. Et = 30 meV)
whereas the SPV signals related to deep defects increased after light soaking (see figure 5.13
c). Figure 5.13 (d) shows CH3NH3PbI3 deposited on SnO2 substrate. The band gap Eg,
remained constant at 1.60 eV. The value of Et decreased from 30 to 21 meV after light soaking,
i.e. the degree of disorder decreased. After light soaking with blue light, the SPV signals related
to fundamental absorption strongly increased whereas the deep defects related signals
remained constant.
The influence of the substrate on the microscopic structure of CH3NH3PbI3 layers is shown
in the figure 5.14. The SEM micrograph of CH3NH3PbI3 perovskite active layers on TiO2
showed a pronounced difference in the grain size which was of the order of 140 nm in
comparison to that on SnO2.
Figure 5.14: Cross-section and top view micrographs of CH3NH3PbI3 perovskite layers deposited on
(a) TiO2 and (b) SnO2 substrates. The upper parts in both figures represent the cross-section images
whereas the lower part gives the top view images.
The thickness of CH3NH3PbI3 deposited on Ti02 (see figure 5.14 (a)) was about 300 nm
with TiO2 itself having a thickness of about 15-30 nm. Since the average grain size of about
140 nm was much smaller than the thickness of perovskite layer, it indicated that the number
of grain boundaries were significantly high. An increased number of grain boundaries is not
desirable for photovoltaic devices because of increased recombination rate of charge carriers
during transport.
For the case of CH3NH3PbI3 deposited on SnO2 (see figure 5.14 b), the thickness of the
perovskite layer was about 400 nm with an average grain size of about 230 nm. The grain
sizes were much larger compared to CH3NH3PbI3 films deposited on TiO2 substrate. This
suggested that most of the grains were extended from the SnO2 substrate to the perovskite
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surface with the vanishing of grain boundaries that were parallel to the substrate, allowing for
secondary grain growth that increased the size of the grains [16].
To further investigate the electronic properties, modulated SPV was extended to
determine the energy of the exponential tail states at the interface of CH3NH3PbI3 with different
electron transport layers (ETLs). The ETLs used at the interface with CH3NH3PbI3 were TiO2,
SnO2, ICMA, C60, PCBM, and SnO2-PCBM and TiO2-PCBM.
Figure 5.15 shows the overview SPV spectra of CH3NH3PbI3 deposited on SnO2-PCBM,
TiO2-PCBM & TiO2.For the as-prepared SnO2-PCBM, TiO2-PCBM, and TiO2; the in-phase
signals were positive, reached a maximum height at 5.13, 5.10 and 4.11 mV (see figures 5.15
(a-c), respectively). On the other hand, the phase-shifted by 90° signals were negative with a
maximum photovoltage values of -0.69, -1.31 and -1.00 mV (a-c respectively).
Figure 5.15: Examples for the overview SPV spectra of modulated in-phase (blue lines) and
phase shifted by 90° (red lines) SPV spectra for as prepared SnO2-PCBM (a), TiO2-PCBM (b), TiO2 (c)
and TiO2 after 1 h in air (d).
After the initial measurement, TiO2 was placed in air for 1 h and additional measurement
were performed. Interestingly, there was a change of the sign for both in-phase and phase
shifted by 90° signals (figure 5.15 d). The in-phase signal changed the sign to negative while
phase shifted by 90° signals became positive. The change of the sign was probably caused
by polarization at the interface between TiO2 and perovskite. The accumulation of electrons at
TiO2/CH3NH3PbI3 interface creates charging and discharging effects which lead to polarization
and is speculated to initiate degradation and hence the reason for the change of the sign of
SPV signals. It can also be due to charge accumulation at TiO2/CH3NH3PbI3 interface which
lead to slow charge extraction hence a change of the sign. In general, all samples showed a
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dominant SPV onset at about 1.50 eV which was the band gap of CH3NH3PbI3 as reported in
the literature [24].
Figure 5.16 (a) shows spectra of the SPV amplitude on a logarithmic scale. The value of
Et for the double layer of ITO/SnO2-PCBM/CH3NH3PbI3 amounted to 18 meV. For comparison,
Et for single layer of ITO/SnO2 or PCBM/CH3NH3PbI3 has also been shown to be 23 meV. The
values of Et were comparable for CH3NH3PbI3 deposited on single layer as well as on double
layers. To further characterize the electronic properties, the so called Tauc plot which
corresponds to the squared ratio of the product of the SPV amplitude and photon energy to
the photon flux (see figure 5.16 (b). Eg was 1.58 eV which was comparable for both single as
well as double layers of CH3NH3PbI3 on SnO2-PCBM.
Figure 5.16: Spectra of the PV amplitude for ITO/SnO2-PCBM/CH3NH3PbI3 and
ITO/SnO2/CH3NH3PbI3 (red and blue spheres, respectively) (a) and Tauc plot of ITO/SnO2-
PCBM/CH3NH3PbI3 (b). The photon flux is shown for comparison (dark cyan line in (a)). The solid lines
represent the fits for determining the corresponding Et (a) and Eg (b).
Similarly, figure 5.17(a) shows the exponential tail slope parameter Et measured for
several batches of CH3NH3PbI3 layers on glass/ITO/ETL substrates by SPV measurements.
CH3NH3PbI3 layers deposited on TiO2, a scatter in the value of Et was observed and ranged
between 27 to 58 meV. The high value of Et observed was proposed to be due to the presence
of a thin amorphous layer at the interface of CH3NH3PbI3/TiO2 as reported in the literature for
evaporated perovskite samples [225]. Et ranged between 20 and 30 meV for CH3NH3PbI3
deposited on SnO2, whereas for ICMA, Et amounted to 26, 38 and 18 meV for batch 1, 2 and
3, respectively. Low scatter was observed for CH3NH3PbI3 deposited on C60, PCBM, SnO2-
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PCBM and TiO2-PCBM and amounted to 26, 22 and 20 meV; 24, 23, 19 meV; 23, 24 and 18
meV; 21, 24 and 23 meV in that order respectively. The value of Et was comparable for
fullerenes and double layers with some scatter for CH3NH3PbI3 deposited on SnO2, with
pronounced scatter on TiO2. CH3NH3PbI3 coated on TiO2, showed higher values of exponential
tail states energy Et with an average value of 40 meV and a lower value of 27 meV.
The relatively large value of Et for CH3NH3PbI3 deposited on TiO2 may be correlated to the
significant density of shallow traps in the TiO2 which allows excitation of charge carriers from
the valence band of perovskite into defect states at the interface with TiO2. Another reason for
high Et for CH3NH3PbI3 deposited on TiO2 might be due to the presence of a thin amorphous
layer within CH3NH3PbI3 film on the surface of TiO2 as reported in the literature for evaporated
perovskite samples [225]. Moreover, there were several grain boundaries for CH3NH3PbI3
deposited on TiO2 (see SEM micrographs in figure 5.14).The grain boundaries acted as
recombination centers which cause high Et.
Figure 5.17: The Exponential tail states (Et) (a) and the so called Tauc gap (Eg) obtained
from SPV measurements of CH3NH3PbI3 absorber layers grown on different ETL coated substrates.
Figure 5.17 (b) shows the Tauc gap (Eg) measured for several batches of CH3NH3PbI3
layers deposited on glass/ITO/ETL substrates. Eg was assumed to be equivalent to the
absorption processes in the optical measurements. Eg ranged from 1.56 to 1.58 eV for all
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CH3NH3PbI3 layers on every ETLs with ICMA, SnO2 and TiO2 showing slightly larger spread in
comparison to other ETLs. The largest spread in Eg was observed in TiO2 which may probably
be due to the defect states near the interface which retarded charge transfer. The chemical
potential at the TiO2/CH3NH3PbI3 interface may result in radical reactions which create
instabilities at the interface. CH3NH3PbI3 deposited on double layers of TiO2-PCBM and SnO2-
PCBM showed a constant band gap of 1.58 eV. The constant band gap of the CH3NH3PbI3 on
double layers ETLs was deduced to be due to better charge transport and extraction properties
of the bilayers. This observation could also be correlated to a smaller spread in the value of
exponential tail states Et. Generally, Eg is almost similar in all ETLs which was supported by
the similar morphology across all ETLs as seen from scanning electron microscopy (SEM) (see
figure 4.5 in methods section). This further promotes the assumption of a minor influence of
the underlying substrate on the perovskite absorber grown on top of ETLs.
5.4. Effects of light soaking on the transport length of CH3NH3PbI3
Figure 5.18 (a) shows Goodman [32] plots for TiO2/ CH3NH3PbI3 layers at SPV signals of
0.55, 0.75, 0.85, 0.95 and 1.05 mV under 20 min of blue light soaking. The corresponding
diffusion length was extrapolated at negative intercepts of absorption length and amounted to
820 nm. For comparison, the diffusion length of c-Si of about 0.13 mm was obtained in figure
5.18 (b).
Figure 5.18 (c) correlates the values of the transport length of photo-induced charge
carriers with values of SPV signals for CH3NH3PbI3 layers and crystalline silicon wafers (c-Si).
A certain scatter in the values of L for CH3NH3PbI3 layers was observed in comparison to that
of c-Si. The accuracy in determining L in CH3NH3PbI3 layers is lower as compared to
corresponding measurement of L in c-Si. This is because of the rough nature of CH3NH3PbI3
layers as well as availability of very few data points of absorption coefficients from the literature
[102].
Figure 5.18. Goodman plot of (a) TiO2/CH3NH3PbI3 under blue light soaking for 20 minutes and
crystalline silicon (c-Si) (b) measured at different constant SPV signal. The diffusion length photo-
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generated charge carriers as a function of constant SPV signals obtained for CH3NH3PbI3 layers (red)
and c-Si (blue) (c).
For better understanding of the effect of light soaking on transport length, the sample was
illuminated with blue light at different light soaking times from 0 min to 48 h (figure 5.19). The
scatter in the value of the transport length with SPV was analyzed for the as-prepared sample,
20 min and 30 min of light soaking (figure 5.19 a-c). The scatter could be induced by the
variation in the quasi Fermi levels over the absorber thickness and in-homogeneity of
perovskite film. Dittrich et al. also observed a scatter in the value of transport length for both
CH3NH3PbI3 films and powders [102]. The scatter in the value of L, may also be attributed to
the trapping of charge carriers at the TiO2/CH3NH3PbI3 interface which may influence transport
hence limiting the diffusion length as well as the drift length.
Figure 5.19. Dependencies of transport length of TiO2/ CH3NH3PbI3 as a function of different constant
SPV signals for light soaking times at 0 min (a), 20 min (b), 30 min (c), 1 h –green star (d), 12 h- black
symbols (d) , 24 h (e) and 48 h (f).
1 h of light soaking showed very low scatter (figure 5.19 d), while for 12 h, there was a
dependence of the transport length L on the SPV signals (figure 5.19 d-violet symbols). This
was a clear indication of the splitting of quasi Fermi level across the absorber layer. In general,
there was a decrease in transport length within 12 h of light soaking time. The transport length
decreased from 860, 820, 780 and 750 nm for as-prepared, 20 min, 30 min and 1h of light
soaking, respectively. The decrease in the value of transport length might be due to light
induced degradation which arises due to trap states and charging- discharging effect at TiO2/
CH3NH3PbI3 interface.
For prolonged light soaking i.e. 24 h and 48 h (figure 5.19 e and f), the diffusion length
increased. The increase in the value of diffusion length with prolonged light soaking time was
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probably analyzed by the change of the nature of trap states implying that less charge carriers
were trapped leading to increase in transport length. Another possible explanation for a larger
diffusion length under prolonged light soaking may be due to compensation of traps and
defects states. There is a generation of defect states which neutralize the trap states leading
to an increase of the diffusion length. Previous findings by electron beam induced current
(EBIC), concluded that increased diffusion length due to illumination depended on the photo-
generation of charge carriers [226].
In-homogeneities in the perovskite films led to the scatter of the diffusion length over a
large range. For this reason, the mean transport length was taken as a representative value
for the overall ability of charge carriers to diffuse in the material. The mean diffusion length
was plotted as a function of illumination time (see figure 5.20).
Figure 5.20: Mean transport length L of TiO2/ CH3NH3PbI3 as a function of illumination time.
A decrease in the mean L within 12 h of illumination time was observed. This decrease
was probably caused by trap states and charging-discharging effects between TiO2 and
CH3NH3PbI3. With longer light soaking time, L increased. The increase in L might be due to
changing nature of the traps due to generation of compensating defects which neutralize the
trap states. In addition, a strong variation of L with SPV signal indicated the in-homogeneous
nature of the film which could lead to changes of the quasi Fermi levels over the whole range
of film thickness.
A simplified model was designed to explain the behavior of the transport length with light
soaking time. Figure 5.21 (a) presents an idealized band diagram in which an absorber material
(perovskite) was sand-witched between hole transporting material (HTM) and the electron
transporting material (ETM). In this model, photo-generated electrons are attracted towards
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ETM while holes towards HTM. In such a case, the transport length L corresponds to the
absorber layer thickness as illustrated in figure 5.21 (a). The scenario above is an ideal case
which rarely occurs. In reality, disorder exists in materials and hinder transport of charge
carriers.
Figure 5.21: Ideal band diagram with absorber material (perovskite) sand-witched between hole
transporting material (HTM) and electron transporting material (ETM) (a). Band diagram with traps
near TiO2 (b) and band diagram showing grain boundaries (GB) in perovskite (c).
Figure 5.21 (b) shows a band diagram in which traps appear between TiO2 and
CH3NH3PbI3 or within the absorber material itself. In this study, there was no HTM and ETM
was TiO2.This means that photo-generated electrons will be attracted toward TiO2 while holes
towards the perovskite surface. This will create upward band bending at the TiO2/ CH3NH3PbI3
interface. Some photo-excited electrons become trapped at the TiO2/ CH3NH3PbI3 interface
and others within the perovskite itself. These trap states will create defects that lead to charge
carrier recombination hence the reduction in transport length. It was also speculated that the
charging and discharging effect at the TiO2/ CH3NH3PbI3 interface may also lead to a reduction
in the value of the transport length of CH3NH3PbI3 layers. Prolonged light soaking may change
the nature of trap states which can lead to the reduction of the defect density leading to
increase in the transport length.
Grain bounderies contain large density of charge traps which act as recombination
centres.In larger grains, photogenerated electrons travel freely without encountering grain
bounderies hence reducing charge loss by recombination. On the other hand,smaller grain
size reduce light harvesing efficiency due to recombination at grain bounderies leading to
shorter diffusion length [171] as demonstrated in the figure 5.21 (c). As a remark, diffusion
length can be long or short depending on the nature of grain sizes and grain bounderies.
101
5.5. Summary
Material properties of CH3NH3Pb (I, Br)3 films that relate to degradation, stoichiometry,
band gap (Eg), exponential tail states (Et) or Urbach energy (Eu) and diffusion length (L) were
investigated. For CH3NH3PbBr3 perovskite films, Et of 19 meV and Eu of 18 meV were obtained
by SPV and PDS, respectively. The value of Et obtained by SPV was comparable with Eu with
a slight deviation of about 1 meV. The discrepancy was because both methods are sensitive
to different regions of measurements. For instance, SPV is sensitive to the measurement
region where charge separation takes place whereas PDS probes the whole region of the
sample volume where absorption takes place.
Vegard’s law was used to obtain the composition of CH3NH3Pb(I1-X BrX)3 films. The lattice
constant decreased linearly with increasing CH3NH3Pb(I1-X)BrX)3 composition. Similarly, Eg
decreased with increasing lattice parameter suggesting a lattice contraction due to an increase
in the potential energy of the electrons in the orbitals of an atom. The variations of Eg and Et
with the stoichiometry of the CH3NH3Pb(I1-XBrX)3 perovskite films were investigated by
modulated SPV and UV-Vis spectroscopies. Eg of CH3NH3Pb(I1-XBrX)3 films was tuned from
1.56 eV to 2.30 eV by varying the bromide composition in CH3NH3Pb(I1-XBrX)3 films. Eg blue
shifted with increasing content of bromide and a bowing parameter of 0.36 eV was obtained.
The blue shift was attributed to different spin- orbit interactions between lead-iodide and lead-
bromide ions.
The values of Eu and Et were observed to be lower for tri-iodide (CH3NH3PbI3) and tri-
bromide (CH3NH3PbBr3) perovskites but higher for mixed perovskites. Higher disorder
observed in CH3NH3Pb(I1-X BrX)3 films may be due to the introduction of bromide ion into the
mixed halide solution which creates stress on its structure that induced more defects in the
material [213].
Light soaking studies under blue illumination on SnO2/ CH3NH3PbI3 and PEDOT: PSS
/CH3NH3PbI3 showed that there was a strong influence of the substrate on the band gap and
disorder. On PEDOT: PSS, the disorder increased with increasing blue light soaking time in
N2, in contrast to SnO2 substrates showing a constant band gap and decreasing disorder. The
influence of blue light soaking was also investigated for CH3NH3PbBr3 coated with and without
PMMA. It was observed that there was a strong influence of light soaking on the direction of
modulated charge separation since a change of sign occurred for CH3NH3PbBr3 coated with
PMMA.
The values of Eg and Et depended sensitively on the kind of interface as shown by
modulated SPV spectroscopy. CH3NH3PbI3 deposited on double layers of TiO2-PCBM and
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SnO2-PCBM showed a constant band gap of 1.58 eV and low scatter in the value of Et. This
was attributed to the modification of theTiO2 or SnO2/CH3NH3PbI3 interfaces by the PCBM
which allowed for efficient charge separation and transfer. In contrast, CH3NH3PbI3 deposited
on TiO2 showed relatively large values of Et which was correlated to the significant density of
shallow traps in the TiO2 that allowed for the excitation of charge carriers from the valence
band of perovskite into defect states at the interface with TiO2.
The diffusion or transport length (L) was measured for CH3NH3PbI3 layers by the method
after Goodman [32]. L was studied as a function of degradation under light soaking. A decrease
of L with increasing time of light soaking was observed. The decrease was attributed to light-
induced degradation which arises due to trap states and charging- discharging effect at the
TiO2/ CH3NH3PbI3 interface. After 12 h of light soaking, L depended on the value of the
modulated SPV signal, i.e. on the generation rate. The strong variation of L with modulated
SPV signals was an indication of defects and/or inhomogeneity of the films which led to
changes in the quasi Fermi levels over the whole range of film thickness.
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CHAPTER 6
Temperature dependent, modulated surface photovoltage
measurements on stabilized CH3NH3PbI3 layers
The band gap and its dependence on temperature belong to the most important properties of
a semiconductor material. Under operating conditions, the temperature of a solar cell can vary
over a relatively wide range up to about 70°C. Temperature fluctuations affect the efficiency of
perovskite based solar cells. The precise knowledge of the temperature dependence of the
band gap for methyl ammonium lead iodide and related perovskites is essential for deeper
understanding of the temperature dependence of solar cells and origins behind. Results of the
temperature dependence of the band gap of CH3NH3PbI3 perovskite layers measured by
modulated SPV are presented in this chapter. Some of the results were published in [209].Bare
CH3NH3PbI3 is not stable in vacuum, which is required for measurements in a cryostat. For this
reason, a protective PMMA layer was developed and tested for CH3NH3PbI3, whereas the
phase composition and electronic properties were characterized by GIXRD and modulated
spectral-dependent SPV, respectively. The temperature dependence of SPV spectra was
analyzed. The band gap and the energy parameter of the exponential tails of CH3NH3PbI3
increased with increasing temperature. The results show that thermal expansion is the
predominant contribution to the temperature dependence of the band gap of CH3NH3PbI3 and
that the dynamic disorder is limited by phonons.
6.1. Stabilization of CH3NH3PbI3 with PMMA for temperature-dependent
measurements
6.1.1. Criteria for PMMA as a protective layer
Hybrid organic-inorganic lead halide perovskites are known to be unstable in air [227],
under moisture [13], heat [161,228], vacuum [229] and under illumination [155]. In order to
enhance the stability in air, a protection polymer such as poly (methyl methacrylate) (PMMA)
has been applied [192,230]. PMMA is a transparent polymer which can be dissolved in
numerous organic solvents, for example, butyl acetate (BA) or toluene. These solvents are so-
called anti-solvents for CH3NH3PbI3 films, i.e. CH3NH3PbI3 cannot be dissolved in these
solvents. Furthermore, PMMA is an amorphous insulator and it can be assumed that PMMA
does not (chemically) interact with the perovskite due to its inertness. These properties make
PMMA a suitable material as a protective layer on the surface of CH3NH3PbI3 perovskite films.
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In order to use PMMA as a protective layer for temperature-dependent SPV measurements,
different parameters were tested in order to test its influence on CH3NH3PbI3 films.
First of all, a protective layer should act as a diffusion barrier for CH3NH3PbI3, i.e. in-
diffusion and out-diffusion of molecules shall be avoided (figure 6.1 (a)). For bare CH3NH3PbI3
samples in air, there is in-diffusion of water and oxygen into the perovskite and out-diffusion of
methylamine, hydroiodic acid and other components evolving during decomposition. For
temperature-dependent measurements, a stable perovskite sample over a wide temperature
range is needed at least for the time of measurements. A diffusion barrier at the surface of
CH3NH3PbI3 causes an increase of the concentration of reaction products at the interface with
PMMA and reduces therefore drastically the decomposition rate of CH3NH3PbI3 in the bulk or
near surface region.
Figure 6.1: PMMA as a protective layer of CH3NH3PbI3 for preventing in-diffusion and out-diffusion of
molecules in different ambient (a), test samples for the influence of PMMA on degradation of
CH3NH3PbI3 (b).
The role of the PMMA for stabilization of CH3NH3PbI3 was tested by comparing bare
CH3NH3PbI3 layers with CH3NH3PbI3 layers treated in the solvent (BA) and CH3NH3PbI3 layers
with different thicknesses of the PMMA layer ( see figure 6.1 (b)). The thickness of the PMMA
layer can strongly influence the in- and out-diffusion of molecules since, if the polymer is too
thin, molecules can penetrate through pores and, if the polymer is too thick, stress can lead to
the formation of cracks during the evaporation of the solvent. In order to find out the optimum
thickness of PMMA, the concentration of PMMA in BA was varied by dissolving 20, 40, 60, 80
and 100 mg in 1 ml of BA and the solutions were spin coated onto CH3NH3PbI3 under identical
conditions. The in- and out-diffusion of molecules was indirectly tested by investigating the
degradation in air.
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6.1.2. Influence of PMMA on the exponential tails in CH3NH3PbI3 layers
Figure 6.2 shows the in-phase (x-signal) and phase shifted by 90°(y-signal) SPV spectra
for the as-deposited sample without PMMA coating (a) and of samples (b) coated with PMMA
before annealing (c), annealed but without PMMA coating and (d) coated with PMMA after
annealing. As a remark, in-phase and phase shifted by 90° signals corresponded to fast and
slow responses, respectively, in relation to periodic modulation of SPV signals.
Figure 6.2: An overview spectrum of in-phase (black line) and phase shifted by 90° (red line) for
CH3NH3PbI3 films (a) as-deposited without PMMA (b) with PMMA before annealing (c) annealed
without PMMA and (d) with PMMA after annealing. The concentration of PMMA in BA was 40 mg/ml.
All samples showed a dominant onset of the SPV signals at around 1.55 eV which is close
to the band gap of CH3NH3PbI3 [24]. For the as-deposited sample with no PMMA coating
(figure 6.2. (a)), the in-phase signals were positive around the onset energy, reached a
maximum of about 0.05 mV at the photon energy of 1.66 eV and decreased to zero at about
2.5 eV. The positive value of in-phase signals shows that photo-generated electrons were
preferentially separated towards the internal interface while holes towards the surface. A
second onset at the energy of about 3.1 eV, which is close to the band gap of CH3NH3PbCl3,
was observed for the phase shifted by 90° signal. The absence of the onset at 3.1 eV in the
in-phase signals shows that the modulated separation of charge carriers photo-generated in
CH3NH3PbCl3 was very slow.
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For the sample coated with PMMA before annealing (figure 6.2 (b)), the in-phase signals
were positive between energies of 1.51 to 2.3 eV and then became negative at energies above
2.3 eV. The change of sign at about 2.3 eV may be related to polarization of charge carriers at
interface with PMMA which creates charging and discharging effects at the interface. An
additional onset was observed in the in-phase signal at about 3.1 eV corresponding to the
appearance of CH3NH3PbCl3. Therefore, the modulated charge separation caused by photo-
generation in CH3NH3PbCl3 was much faster for the sample coated with PMMA before
annealing.
For the annealed sample without the PMMA coating (figure 6.2 (c)), the in-phase and
phase shifted by 90° signals showed an onset at about 1.58 eV, which was very similar to the
onset of the as-deposited sample. An additional signature at about 2.3 eV, which is close to
the band gap of PbI2, was also observed in the spectrum of the in-phase signals. Therefore,
annealing of the un-protected CH3NH3PbI3 caused some degradation to PbI2. No signature
was observed for the CH3NH3PbCl3 phase after annealing of the un-protected sample, i.e.
chlorine species evaporated during the annealing [27]. The in-phase signals were positive and
reached a maximum of 0.14 mV at 1.7 eV. The phase shifted by 90° signal were positive and
rather low at about 1.5 eV and thereafter became negative at photon energies above 1.8 eV.
The appearance of PbI2 at the CH3NH3Pbl3 surface is a clear indication for the deficiency of
methyl ammonium cation and iodide anion in the interface region which causes n-type doping
of CH3NH3PbI3 as demonstrated by positive in-phase signal [27] .
The SPV spectra of the sample onto which PMMA was deposited after annealing (figure
6.2 (d)), showed the largest signals related to charge separation in CH3NH3PbI3 without any
signatures for additional phases. Both in-phase and phase shifted by 90° were negative
suggesting a change in the direction of charge separation in comparison to the other samples.
Negative values of in-phase signals indicated the formation of a surface space charge region
of a p-type doped semiconductor with a slight excess of methyl ammonium and iodide ions.
Furthermore, the same sign of the in-phase and phase shifted by 90° were attributed to two
mechanisms of charge separation with opposite directions in which trapping and de-trapping
of charge carriers lead to slow modulation period [28].
Figure 6.3 (a) shows the PV amplitudes and photon flux on a logarithmic scale as a
function of photon energy of the same samples shown in figure 6.2. Incidentally the amplitudes
were dominated by the in-phase signals. The spectra were analyzed according to Chapter 3.
The values of the band gap were about 1.58 eV and 1.57 eV for CH3NH3PbI3 without and with
PMMA respectively. PMMA coated on the CH3NH3PbI3 reduced the band gap slightly, implying
that the band gap of CH3NH3PbI3 depends on the preparation condition. This is important for
the analysis of SPV spectra at different temperatures. The exponential tails (Et parameter)
depended on the preparation conditions and PMMA coating. The values of Et were 13, 15, 22
107
and 29 meV for as-deposited CH3NH3PbI3 without annealing, annealed CH3NH3PbI3, without
PMMA, CH3NH3PbI3 with PMMA before annealing and CH3NH3PbI3 with PMMA after
annealing, respectively. Therefore, the lowest degree of disorder was obtained for the as-
deposited sample which was not annealed without PMMA coating. Furthermore, deposition of
PMMA caused a strong increase of disorder in CH3NH3PbI3 due to stress induced by the
formation of the CH3NH3PbI3/PMMA interface, and this stress has more influence on the
disorder in the annealed CH3NH3PbI3 layer.
The high disorder observed in samples coated with PMMA may be attributed to the
interaction between PMMA and perovskite layers which increases the stress in CH3NH3PbI3
films. It is speculated that, the formation of PMMA induces stress underneath which creates
defects that lead to partial relaxation by introducing some disorder that increased the
fluctuations among the PbI6 octahedra. This implied that the rotation of PbI6 octahedra depends
on local stress induced by PMMA on CH3NH3PbI3 layers. Furthermore, PMMA changed the
nature of chemical bonds at and near the surface of CH3NH3PbI3, which can also cause an
increase of disorder and of surface defect states.
Figure 6.3: Spectra of the photovoltage amplitude near the band edge of CH3NH3PbI3 and
corresponding photon flux (a) and a plot of the maximum photovoltage amplitude as a function of the
energy characterizing the exponential tails (Et) (b)
The maximum photovoltage amplitude (Rmax) tended to increase with the parameter
describing the exponential tails (Et). The corresponding values of Rmax and Et are correlated in
figure 6.3 (b). Rmax increased with increasing Et (between 15 and 29 meV). CH3NH3PbI3 without
PMMA coating exhibited a low Et, whereas CH3NH3PbI3 coated with PMMA showed more
defect states as demonstrated by the high value of Rmax. The highest Rmax was obtained for the
highest Et. For the as-deposited sample without PMMA coating, the value of Rmax was 0.05 mV
corresponding to Et of 15 meV. For the annealed CH3NH3PbI3 sample without PMMA coating,
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Rmax increased to 0.07 mV, whereas Et increased from 13 to 15 meV. This implies that for bare
CH3NH3PbI3 samples, annealing lead to an increase of stress in the layers. Rmax increased
strongly by more than three times in comparison to CH3NH3PbI3 coated with PMMA after
annealing. This means that PMMA created more stress on the perovskite layer, hence more
defects resulting into higher Et of 29 meV.
During modulated SPV, separation of photo-generated electrons and holes takes place
under illumination and recombination occurs in the dark. Recombination of charges separated
in space is limited by transport in CH3NH3PbI3, whereas the charge carriers have to overcome
some barrier(s). As a result, some permanent charging occurs and only a certain part of photo-
generated charge carriers contributes to the SPV signal. With an increasing density of defects
states in the region of barrier(s), the probability for hopping increases so that recombination
will become faster. As a result, the modulated photovoltage amplitude can increase with the
density of defect states. For comparison, the effective densities of states are rather high at the
conduction and valence band edges of c-Si (1–3 x 1019 cm-3) [231] or a-Si:H (10201021 cm-3
[232], Et about 5060 meV). Incidentally, the SPV signals decrease with increasing density of
defect states if the recombination is not limited by transport. Furthermore, one has to keep in
mind that an increase of Et can distort the onset energy [27] and hence lower the band gap.
This can explain the slightly reduced band gap for CH3NH3PbI3 coated with PMMA in
comparison to the uncoated sample.
6.1.3. Dependence of the phase composition of CH3NH3PbI3 on PMMA coating and
storage time in air
Figure 6.4 represents the GIXRD patterns of CH3NH3PbI3 layers coated with PMMA
deposited from solutions with the concentration of 0, 20, 40 60, 80 and 100 mg/ml for as-
deposited samples. All samples exhibit similar perovskite peak except for CH3NH3PbI3 coated
with PMMA at a concentration of 80 and 100 mg/ml which showed additional peaks
(represented by black arrows in figure 6.4). The GIXRD diffraction patterns were observed at
about 14.2°, 20.01°, 23.5°, 28.5°, 31.9°, 35.07°, 37.27°, 40.5° and 43.5° which are the
characteristics peaks of the tetragonal CH3NH3PbI3 structure (COD 7218931). These diffraction
peaks corresponded to (110), (112), (211), (202), (220), (310), (312),(321) (224) and (314)
tetragonal planes of crystalline CH3NH3PbI3, respectively [27, 12]. Two dominant peaks at
14.2° and 28.5° for the (110) and (220) planes respectively were observed in all the samples,
indicating the formation of the crystalline perovskite in the tetragonal phase. Moreover, the
samples had different diffraction intensities suggesting some differences in the preferential
orientation of crystals in the CH3NH3PbI3 layers. The peak intensity was relatively high for
109
CH3NH3PbI3 coated with PMMA at a concentration of 40 mg/ml compared to other samples.
This implied that 40 mg/ml seems to be an optimum concentration of PMMA.
The diffraction peaks at about 15.7° and 31.8° were also observed for all samples. These
peaks could be correlated to the (100) and (200) diffraction peaks of CH3NH3PbCl3 [192]. The
peak intensity at 15.7° was relatively high for CH3NH3PbI3 un-coated with PMMA at a
concentration of 0 mg/ml and the intensity reduced with higher concentration of PMMA. On the
other hand, the peak intensity for the (200) peak at 31.8° was relatively high for CH3NH3PbI3
coated with 100 mg/ml of PMMA compared to other samples. Coating PMMA on top of
CH3NH3PbI3 layer could significantly increase the amount of CH3NH3PbCl3 in the final
perovskite films. This means that coating PMMA on the surface of CH3NH3PbI3 prevented the
evaporation of CH3NH3PbCl3. Some weak extra peaks were also observed for CH3NH3PbI3
coated with 100 mg/ml at 12.67° and 37.25° and these were ascribed to the (001) and (003)
peak of PbI2 [197, 233]. The additional peaks (shown by black arrows in figure 6.4) were
observed for CH3NH3PbI3 coated with 80 and 100 mg/ml of PMMA. For 80 mg/ml of PMMA,
additional peaks appeared at 21.5°, 23.09°, 36.11°, 47.70° and 48.8°. Similarly, the non-
identified peaks at 42.5°, 45.7°, and 47.5° were also observed for CH3NH3PbI3 coated with
PMMA at a concentration of 100 mg/ml. These peaks were not identified and can be related
to intermediate phases that coexist with tetragonal perovskite phase [27].
Figure 6.4: GIXRD of Mo/CH3NH3PbI3 coated with PMMA at concentration varied from 0 to 100 mg/ml
for as-deposited sample. The olive stars indicate PbI2 peaks whereas black arrows indicate non
identified peaks.
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Figure 6.5 shows the GIXRD of CH3NH3PbI3 coated with PMMA of at a concentration of
0, 20, 40, 60, 80 and 100 mg/ml after storage in air for 43 days. All samples showed
CH3NH3PbI3 peaks at 14.2°, 20.01°, 23.5°, 28.5°, 31.9°, 35.07°, 37.27° and 40.5°
corresponding to (110), (112), (211), (202), (220), (310), (312), (321) and (224) respectively to
tetragonal planes of crystalline CH3NH3PbI3 [234, 12]. In addition, the intensity of the tetragonal
CH3NH3PbI3 peaks decreased for all samples with strongest reduction observed for
CH3NH3PbI3 coated with 0 and 60 mg/ml of PMMA. The decrease in the intensity of
CH3NH3PbI3 peaks in the tetragonal phase may be attributed to degradation of perovskite to
constituent elements.
Figure 6.5: GIXRD of CH3NH3PbI3 coated with PMMA at concentration varied from 0 to100 mg/ml
after 43 days of storage in air. The olive stars indicate PbI2 peaks, black arrows indicate non-identified
peaks whereas blue arrow indicate the formation of (200) cubic peak of perovskite.
Some diffraction peaks at 12.67°, 25.5°, 38.77° and 39.5° corresponding to (001),(101),
(003) and (110) planes of PbI2 [235] were observed for CH3NH3PbI3 coated with 0 and 60
mg/ml of PMMA. The (001) diffraction peak at 12.67° was observed for all samples except for
CH3NH3PbI3 coated with 40 mg/ml of PMMA. The intensity of the PbI2 peak was higher for the
samples with 0 and 60 mg/ml of PMMA. For the sample with 0 mg/ml of PMMA, it was
speculated that the butyl acetate solvent chemically reacted with CH3NH3PbI3 accelerating
faster degradation into PbI2 whereas CH3NH3PbI3 coated with 60 mg/ml could have favored
the growth of (001) peak of PbI2. Some extra peaks at 29.42°and 37.45° corresponding to
111
(200) and (112) cubic phase of perovskite structure [12] were detected. For CH3NH3PbI3
coated with 80 mg/ml of PMMA, this indicated that CH3NH3PbI3 existed in two phases with
continued storage in air, i.e. tetragonal and cubic perovskite phases. In addition, a non-
identified (NI) peak at 36.03° was also observed CH3NH3PbI3 coated with 80 mg/ml and absent
in all samples. CH3NH3PbI3 coated with 40 mg/ml of PMMA did not show any impurity phase
even after storage in air for 43 days. This finding suggests that the optimum concentration of
PMMA is 40 mg/ml for forming a protection layer on CH3NH3PbI3.
Figure 6.6: Dependence of the (110) CH3NH3PbI3 (a) and (001) PbI2 (b) peaks on the
concentration of PMMA for as prepared (olive-orange bars) samples and for samples stored in air for
43 days (cyan-violet bars).
As a summary of the XRD measurements, figure 6.6 (a) shows the bar chart of the intensity
of the (110) CH3NH3PbI3 peak for as-prepared samples and for samples stored in air for 43
days. Incidentally, the GIXRD measurements were performed under identical conditions. The
intensity of the (110) peak for the as-prepared samples were about 3721, 1429, 1989, 8218,
6218 and 1001 counts respectively. These quite large variations of the peaks were probably
caused by fluctuations of the roughness (The dependence of the GIXRD signals on the
preparation conditions was not investigated). After the samples have been stored in air for 43
days, the intensity of CH3NH3PbI3 coated with PMMA reduced dramatically for some samples
showing strong reduction in the magnitude of the (110) peak of CH3NH3PbI3. CH3NH3PbI3
coated with PMMA with 60 mg/ml showed the strongest drop of the peak intensity from 8218
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counts (as-prepared) to 166 counts (after storage in air for 43 days). Un-coated perovskite (0
mg/ml of PMMA) also showed a stronger drop of CH3NH3PbI3 peak intensity from about 3721
counts (as-prepared) to 263 counts (after storage in air for 43 days). The strong reduction in
the intensity of the peak is mainly related to the ongoing decomposition of CH3NH3PbI3 phase
to other phases such as the formation of PbI2 phase and in the presence of oxygen and light,
the deprotonation of CH3NH3+ to CH3NH2 and molecular hydrogen [155]. 40 mg/ml did not show
any PbI2 peak even after 43 days of storage in air hence the conclusion that 40 mg/ml was the
optimum concentration of PMMA to be coated on the surface of CH3NH3PbI3 layers.
Figure 6.6 (b) shows the bar chart for the (001) peak of the PbI2. As can be seen, no PbI2
peak was observed for the as-prepared samples. However, after storage of the samples in air
for 43 days, the signature related to the (001) PbI2 peak was observed for some samples. The
highest intensities of the PbI2 peak were observed for the un-coated CH3NH3PbI3 (2139 counts)
and for the CH3NH3PbI3 coated with PMMA with 60 mg/ml (1169 counts). The intensities of the
(001) PbI2 peak were low for the CH3NH3PbI3 samples coated with PMMA with 20, 80 and 100
mg/ml (12, 13 and 19 counts, respectively). The un-coated sample (0 mg/ml of PMMA) was
equivalent to coating the solvent of butyl acetate on the surface of CH3NH3PbI3 layer.
Therefore, as the solvent evaporates, the reduction of the volume created stress in the layer
and on the surface region of the CH3NH3PbI3 layer. As a result, pores and cracks are developed
in the CH3NH3PbI3 layers, which enable penetration and diffusion of moisture and oxygen into
the perovskite sample. CH3NH3PbI3 in the presence of moisture decomposed to CH3NH3I and
PbI2 which further decompose to methylamine (CH3NH2) and hydroiodic acid (HI) [236].
6.1.4. Modulated SPV measurements of CH3NH3PbI3 layers coated with PMMA
Figure 6.7 shows overview spectra of the modulated in-phase signals for CH3NH3PbI3 thin
films coated with PMMA deposited for different concentrations (0, 20, 40, 60, 80 and 100 mg/ml
in butyl acetate). All samples showed the same onset energies of the SPV signals at about 1.5
eV, i.e. near the band gap of CH3NH3PbI3 [24]. The existence of the CH3NH3PbI3 phase is in
agreement with the grazing incidence X-ray diffraction measurement (see figure 6.4). The
concentration of the PMMA had no influence on the measured onset energy.
For CH3NH3PbI3 coated with 0 mg/ml of PMMA, the in-phase signal was negative at
photon energies below 1.5 eV, became positive at photon energy of about 1.5 eV, reached a
maximum at 1.7 eV and again became negative at photon energies above 2 eV. The change
of sign may be related to impurity phases. The sign of the in-phase-signals was positive over
the whole spectrum for the other samples. A positive sign of the in-phase signal means that
photo-generated electrons are preferentially separated towards the bulk while holes move
113
towards the surface. A precise analysis of the band gap and of the exponential tails is not
possible if the sign of the SPV signal changes near the band gap.
For CH3NH3PbI3 coated with 20 mg/ml of PMMA, the positive value of the in-phase signal
reached maximum height at 0.5 mV corresponding to photon energy of 1.7 eV. Similarly,
CH3NH3PbI3 coated with 40 mg/ml of PMMA, the in-phase signal increased to the maximum
height at 0.55 mV at photon energy of 1.7 eV. The magnitude of in-phase increased further for
60 mg/ml of PMMA with a maximum in-phase signal at 0.76 mV at photon energy of 1.7 eV.
However, the magnitude of in-phase signal decreased to 0.41 mV at 1.7 eV for 80 mg/ml of
PMMA. The value of in-phase signal decreased from 0.76 mV for 60 mg/ml of PMMA to 0.41
mV for 80 mg/ml of PMMA and continued to decrease further to 0.2 mV for 100 mg/ml of
PMMA. In general, maximum value of in-phase signal was realized for CH3NH3PbI3 coated
with 60 mg/ml of PMMA, followed by 40 mg/ml of PMMA. However, as the concentration was
increased i.e. for 80 and 100 mg/ml, the coating sample became thick and increasingly
obscured the signal causing observed amplitude decrease.
Figure 6.7: Modulated in-phase SPV signals for CH3NH3PbI3 coated with PMMA at a concentration of
0, 20, 40, 60, 80 and 100 mg/ml of butyl acetate, (a) (f) respectively.
Figure 6.8 shows the maximum in-phase SPV signals (Xmax) plotted on a logarithmic scale
versus storage time in air for 43 days. For CH3NH3PbI3 coated with 0 mg/ml of PMMA, a change
of sign occurred for as-prepared sample as well with continued storage in air. A kink was
observed at about 2.3 eV corresponding to an impurity phase of PbI2 [237]. The impurity phase
of PbI2 at about 2.3 eV was observed for all days which is consistent with the appearance of
PbI2 peak at 12.67 ° [238] as confirmed by the GIXRD spectrum (see figure 6.5). On the other
hand, CH3NH3PbI3 coated with 20 mg/ml of PMMA, showed no change of sign, but the sample
exhibited a lot of variability in the value of maximum in-phase signal suggesting that the sample
was not stable, hence not suitable for stability study.
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Interestingly, the CH3NH3PbI3 sample coated with 40 mg/ml of PMMA displayed no
change of sign nor in the value of in-phase signal, however, there was a drop in the value of
in-phase signal on the second day of measurement by more than one order of magnitude.
Thereafter, Xmax increased to 0.08 mV on the fifth day, 0.15 mV on the 9th day and 0.38 mV on
the 19th day. After 19th day of storage in air, the value of Xmax dropped slightly to 0.28 mV on
the 32nd day of storage in air. The initial drop in the value of Xmax could be postulated to be due
to degradation when the sample was exposed to air initially. With continued exposure to air for
several days, there was passivation of surface defects hence the increase in value of Xmax.
CH3NH3PbI3 coated with 60 mg/ml of PMMA had the highest value of Xmax at the beginning of
about 0.75 mV. A sharp drop from 0.75 mV on the first day to 0.27 mV on the second day was
observed and a further sharp drop to 0.12 mV on the 5th day. A change of sign occurred on the
9th day from positive to negative Xmax. After 19th day, Xmax changed sign to positive value at
0.016 mV and increased further to 0.028 mV on the 32nd day. The drop in the value of Xmax
together with the change of sign was attributed to the degradation of CH3NH3PbI3 to its
constituent precursor’s salts. The increase in the value of Xmax after 19th day was postulated to
be as a result of charge separation of accumulated charges that pile up to cause a larger
signal. A similar trend was observed also for CH3NH3PbI3 coated with 80 and 100 mg/ml of
PMMA, whereby there was a drop in the value of Xmax, changed sign to negative on the 9th day
of storage in air and thereafter changed sign again to positive on the 19th day.
Figure 6.8: Evolution of the maximum in-phase SPV spectra with time for the perovskite
coated with PMMA at a concentration of 0, 20, 40, 60, 80 and 100 mg/ml during storage in air for 43
days.
Figure 6.9 shows exponential tail states Et as a function of PMMA concentration coated
on CH3NH3PbI3 films for as-prepared samples and for the samples stored in air for 43 days.
115
For as-prepared samples, the 0 mg/ml changed sign, hence precise analysis of Et was not
possible. The value of Et increased from 18 to 25 meV as the concentration of PMMA
increased from 20 to 100 mg/ml, respectively initially. After over 43 days of storage in air, Et
slightly increased to 22 and 20 meV for 20 and 40 mg/ml of PMMA respectively. On the other
hand, CH3NH3PbI3 films coated with PMMA at a concentration of 60, 80, and 100 showed slight
decrease in Et compared to as-prepared samples. In general, 40 mg/ml of PMMA had the
lowest Et in all the cases. The low value may be responsible for surface defect passivation
which hinders degradation of the perovskite films to PbI2. Therefore 40 mg/ml sample showed
the least amount of tail states of about 18 meV which was relatively higher compared to the
Urbach tail energy of about 15 meV, measured by De Wolf et al. [13]. The high value of Et may
be due to preparation conditions and the presence of the coating layer of PMMA which induced
stress on CH3NH3PbI3 layers creating defects. Since the criteria is to have a stable sample
with no change of phase and low disorder, CH3NH3PbI3 coated with 40 mg/ml of PMMA was
chosen for the experiment and used to study temperature dependent measurement in the
subsequent sections.
Figure 6.9: Exponential tail states Et as a function of PMMA concentration coated on CH3NH3PbI3
sample for as-prepared (red diamond) and after 43 days of storage in air (blue spheres).
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6.2. Temperature dependent measurements of the modulated surface
photovoltage for the band gap of CH3NH3PbI3 stabilized with PMMA
6.2.1. Stability of CH3NH3PbI3 over wide temperature range
For temperature dependent measurement by SPV, the sample to be investigated (i.e.
CH3NH3PbI3 coated with 40 mg/ml of PMMA) was connected to a temperature controller for
the variation of temperature. A liquid nitrogen cryostat was used to vary the temperature
between -182° C to 80°C. The SPV measurements at different temperature range were then
undertaken.
Figure 6.10 shows the overview spectra of the in-phase and phase-shifted by 90° SPV
signals measured at 32°C before starting and after finishing the temperature dependent
measurements. All spectra showed a dominant SPV onset at photon energies between 1.5
and 1.6 eV with no impurity phase of PbI2 observed.
Figure 6.10: SPV overview spectra of the in-phase (filled symbols) and phase-shifted by 90° (open
symbols) SPV signals measured at 32°C after stabilization (circles), and after cooling and heating
cycles with a maximum temperature of 80°C (triangles).
Near the band gap Eg, the signs of the in-phase and phase-shifted by 90° signals were
positive indicating two mechanism of charge separation in which photo-generated electrons
were preferentially separated towards the substrate and holes to the sample surface [28].
Immediately after stabilization, in-phase signal was 0.41 mV, but after heating and cooling to
80°C, the value reduced to 0.1 mV. This implied that after complete temperature dependent
measurements, the in-phase signals reduced by about four times their initial value. On the
contrary, the signal of the phase shifted by 90° was 0.04 mV and 0.1 mV at the start and end
117
of temperature dependent measurement, respectively. Suggesting that phase shifted by 90°
signals increased by more than two times its initial value. Charge separation under two
mechanism may be caused by many processes including partial trapping and de-trapping of
charge carriers at the interface of PMMA with CH3NH3PbI3 [28]. This behaviour can be
interpreted as a reduction of the diffusion length of photo-generated charge carriers due to
degradation and defect generation.
The SPV phase angle gives information about the direction of charge separation in relation
periodic modulation. For instance, a phase angle of 0° or 180° means a fast response relative
to the periodic modulation of incident light. Whereas, a phase angle of 90° or -90° (270°) means
a slow response with respect to the modulation period [205]. Figure 6.11 shows the phase
angle measured at 32° C before starting temperature dependent measurement (violet star)
and after cooling and heating cycles (red spheres). After stabilization, near the band gap at
about 1.5 eV, the phase angle increased towards 0° and remains nearly constant from 1.6 eV
to about 2.5 eV. Similar behaviour was demonstrated after cooling and heating cycles in which
the phase angle increased towards 90° and remains constant at about 45° in the energy range
between 1.6 and 2.5 eV. A shift in phase angle from 0° during stabilisation to 45° after cooling
and heating cycles implied that there exist many mechanism of charge separation and
relaxation in which photo-generated electrons are separated towards the bulk (internal)
whereas photo-generated holes are preferentially separated towards the external surface.
Figure 6.11: SPV phase angle measured at 32°C after stabilization (violet stars), and after cooling
and heating cycles with a maximum temperature of 80°C (red spheres).
6.2.2. Temperature dependencies of the in-phase and phase shifted by 90° signals
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Figure 6.12 (a) shows in-phase and the 90° phase shifted SPV signals measured at 32°C
(room temperature) immediately after stabilization (blue circles),after cooling (red triangles)
and after heating (black stars) as a function of photon energy. After stabilization, the in-phase
signal was positive for all energies above 1.49 eV and peaked at 0.35 mV corresponding to an
energy of 1.63 eV. The 90° phase shifted signal was negative for all energies below 1.56 eV
and thereafter became positive. After cooling to room temperature (red triangles), in-phase
signal remained positive, with the signal height increasing from 0.35 mV to 0.42 mV. Cooling
enhances transport and separation of photo-generated charge carriers. The 90° phase shifted
signal increased slightly after cooling and became positive for all values above 1.56 eV. After
heating and cooling the sample to room temperature (black stars), the in-phase signal
decreased by about 4 times the initial value whereas the phase shifted one increased by more
than two times. This behaviour was interpreted to be due to degradation of the sample after
exposure to high temperature measurements. The band gap remained constant at 1.51 eV for
the stabilization, heating and cooling.
Figure 6.12: SPV spectrum of CH3NH3PbI3 layers measured at 32°C (a), after cooling at -
20°C,-100°C & -182° C (b), heating at 60°C (c) and at 80°C (d) measured in the energy range near the
band gap between 1.42 to 1.67 eV
119
Figure 6.12 (b) shows the in-phase and the 90° phase shifted signals in the cooling regime.
At -20°C, the in-phase signal was positive while the 90° phase shifted signal was negative.
Opposite signs in the value of in-phase and phase shifted by 90° signals revealed a one
mechanism of charge separation in which photo-generated electrons are preferentially
separated towards the internal interface whereas holes towards external surface. The value of
the in-phase and the 90° phase shifted signals had a maximum height of 0.64 corresponding
to energy of 1.63 eV and -0.19 mV at photon energy of 1.62 eV, respectively. In-phase and the
90° phase shifted signals decreased further to 0.29 mV and -0.12 mV, respectively as the
cooling continues to -100°C. On cooling further to -182°C,the in-phase and phase shifted by
90° decreased further to 0.17 mV and -0.07 mV respectively.
When the sample was heated to 60°C (figure 6.12 (c)), the in-phase signal decreased by
3 orders of magnitude i.e. from 0.36 mV (at 32° C) to 0.14 mV (at 60° C). Both the in-phase
and the 90°phase shifted signals were positive at energies above 1.52 eV, with the onset
energy at 1.52 and 1.54 eV, respectively. The positive value of the in-phase and the 90°
phase shifted signals implied that there are two mechanism of charge separation with
electrons preferentially separated towards the interface and holes to the surface and that
trapping of charge carriers lead to charge separation with opposite directions [28].
For the sample heated to 80°C (figure 6.12 d), in-phase signal changed sign from positive
to negative while the 90° phase shifted signal remained positive. The change of sign of the in-
phase signal give evidence for the onset of degradation of CH3NH3PbI3 at the interface with
PMMA. This is because at about 80°C, recombination of charge carriers increases due to
thermal activation and the cycle is non reversible. The degradation at this temperature has
also been observed for PMMA based hole transporting materials that approach the glass
transition temperature of the polymer [160].
Figure 6.13 illustrates the measurement regime showing the temperature dependencies
of the maxima of the in-phase (Xmax) and the 90° phase shifted (Ymax) signals. The temperature
dependencies of Xmax and Ymax follow similar trends independent of whether the signals were
obtained in the low or high temperature cycles. For low temperature measurements (figure
6.13 (a)), the values of Xmax reached a maximum at about 0°C and a minimum at about -160°
C. Similarly Ymax reached a maximum at -60° C and changed sign between 20 and 32°C.
During a cycle of low temperature measurements , the values of Xmax and Ymax at 32°C
increased by about 20%, with no change of sign of the Xmax suggesting that there was no
degradation at low temperatures.
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Figure 6.13: Temperature dependencies of the maxima of the in-phase (filled triangles, Xmax) and the
90°phase shifted (open triangles, Ymax) SPV signals at low temperature (a) and high temperature (b)
measurements, respectively. The arrows mark the regime of cooling or heating. The dashed arrows
mark the relaxation overnight of Xmax to the initial temperatures after the measurements at low (red
symbols) or high (olive symbols) temperatures (to points (9) or (18), respectively).
However, for high temperature measurements (figure 6.13 (b)), Xmax reaches a maximum
at -20°C before its value starts to reduce during continued measurements up to 70°C and
changes to negative at 80°C giving evidence of ongoing degradation at the PMMA /
CH3NH3PbI3 interface. Therefore a reliable analysis of the in-phase signals was only possible
between -182 and 60°C. The value of Ymax increased linearly from -40° C to 20° C, changed
the sign to positive value at about 30°C and thereafter remained constant with increasing
temperature. The change of sign in both the value of in-phase and phase shifted by 90° signals
may be related to the degradation at the interface between CH3NH3PbI3 and PMMA.
Figure 6.14 (a) presents the SPV spectra of the in-phase and the 90° phase shifted SPV
signals measured at 32° C after cooling. The onset energies of the in-phase and the 90° phase
shifted signals (Eon-X and Eon-Y, respectively) were obtained from the intersection points of the
corresponding baselines and of the tangents in the inflection points of the spectra. For the
given spectra, the values of Eon-X and Eon-Y were 1.518 and 1.539 eV, respectively.
121
Figure 6.14: Spectra of the in-phase (filled circles) and phase-shifted by 90° (open circles) SPV
signals measured around the band gap of CH3NH3PbI3 at 32°C after cooling (a), of the in-phase SPV
signals on a logarithmic scale (b). The solid lines in (a) describe the definitions of the onset energies
(Eon-X and Eon-Y). The black and blue solid lines in (b) describe the slope of the exponential tails (Et)
and the photon flux, respectively.
Figure 6.14 (b) shows the in-phase SPV signals on a logarithmic scale. The exponential
increase of the signal can be described by the energy of the band tails (Et). The value of Et
amounted to 30 meV for the given spectrum which was significantly larger than for uncoated
layers of CH3NH3PbI3 (Et can be as low as 15 meV, see, for example [13]). Therefore, the
interaction between the PMMA and the CH3NH3PbI3 layers resulted into an increase in the
amount of disorder in the film. As remark, consideration of the spectrum of the photon flux
would lead to a slight decrease of Et due to the fact that different processes, some with even
opposite signs of charge separation may contribute to SPV signals causing non-linear
behaviour.
Figure 6.15 shows the temperature dependencies of the onset energies of the in-phase
(Eon-X) and the 90° phase shifted (Eon-Y) signals between -182°C and 60°C. At temperatures
between -182°C to -20°C, Eon-X and Eon-Y have similar dependencies even though the values of
Eon-X were larger than the values of Eon-Y by about 0.01 eV. The values of Eon-X increased from
1.52 eV at -20° C to 1.522 eV at -60° C and thereafter decreased to 1.513 eV at -182° C. At
20° C, the value of Eon-X was 1.516 eV, increased to 1.518 eV at 32° C and became saturated
for higher temperatures at 1.524 eV. On the contrary, the value of Eon-Y changed dramatically
from 1.501 eV at 0°C to 1.548 eV at 40°C. Note that the reason for this strong change may be
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due to variation in the dominating mechanisms of modulated trapping and de-trapping
processes leading to a change of sign of the phase shifted by 90° signal as shown in figure
6.13. Moreover, above 40°C, the value of Eon-Y decreased towards Eon-X with the increase in
temperature.
Figure 6.15: Temperature dependencies of Eon-X, and Eon-Y, (filled diamonds, and filled stars,
respectively).The arrows describe the temperature dependencies from low to high temperatures.
6.2.3. Temperature dependence of the exponential tail states of CH3NH3PbI3 stabilized
with PMMA
The temperature dependence of the steepness parameter is used to deduce the physical
origin of the exponential tail states during the charge separation process. Under this approach
it is assumed that the dominant cause of exponential tail states is due to electron-phonon
interaction as well as the contributions from charged defects [239].
Figure 6.16 (a) shows the temperature dependence of the exponential tail states Et for
CH3NH3PbI3/PMMA. The value of Et decreased monotonously with decreasing temperature
from 24 meV at 0°C to 13 meV at -160 °C but scattered between 25 and 30 meV in the
temperature range between 20 and 60 °C which can be correlated to an additional indication
for the change of stress at the PMMA/ CH3NH3PbI3 interface. Furthermore, disorder can
increase in the tetragonal phase of CH3NH3PbI3 with increasing temperature due to increased
thermal vibration of CH3NH3+ cations as well as continuous tilting of the average Pb-I-Pb bond
angle towards 180° [47]. In addition, an increase in the disorder can be as a result of the re-
organisation of photoferroic domains [236]. Further, the increase of Et from 13 meV at −160°C
to 18 meV at −182 °C gives evidence for an increase of disorder in CH3NH3PbI3 with
123
decreasing temperature in this range and might be an indication for a starting phase transition
to orthorhombic phase. The absence of a signature of the orthorhombic phase would not be
surprising if taking into account that the orthorhombic phase of CH3NH3PbI3 does not exist at
pressures above 100 MPa [240] and that the reduced temperature of the phase transition from
the tetragonal to the cubic phases of CH3NH3PbI3 may be related to a pressure between 200
and 300 MPa.
Figure 6.16: Dependence of Et as a function of temperature. Solid line (red) is a fit whose value is
given by equation 5.1.(a) and steepness parameter as a function of temperature at phonon energies
of 150´meV (blue line), 100 meV (orange line) and 50 meV (olive line)(b) for CH3NH3PbI3/PMMA.
An analysis of the temperature dependence of the slope, i.e. the steepness parameter of
Et was obtained (see the red line in figure 6.16 (a)). The variation of the steepness parameter
was fitted with an empirical relation given by [96,241,242]:
𝜎𝜎=𝜎𝜎02𝑘𝑘𝐵𝐵𝑇𝑇
𝐸𝐸𝑝𝑝ℎ 𝑡𝑡𝑡𝑡𝑡𝑡𝐸𝐸𝑝𝑝ℎ
2𝑘𝑘𝐵𝐵𝑇𝑇+𝐸𝐸𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑒𝑒𝑙𝑙 6.1
where 𝜎𝜎0 is a material dependent parameter which describes the excitation energy of
CH3NH3PbI3 layers, 𝐸𝐸ph is the phonon energy associated with Et, kB is the Boltzmann constant
which is approximately 26 mV at 300 K while T is the absolute temperature. Eoffset = 5 meV is
an offset energy which arises due to coating PMMA on CH3NH3PbI3 layers. The steepness
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parameter increased with increasing temperature in the range of -160 to 80 °C. It reflects the
thermal occupancy of phonon modes in the crystal and attributes Et to electron phonon
interaction as well as charged defects. The fittings yielded σo = 0.2475 and Eph = 150 ± 40
meV. The value of Eph was in agreement with the one obtained by Ledinski et al. [243] using
Fourier transform photoelectron spectroscopy. The large value of phonon energy of about 150
meV may be attributed to longitudinal optical phonons which causes increased localization due
to the tilting of the inorganic PbI6 octahedral. Moreover disorder leads to the deformation of the
energy bands forming exponential tail states Et which influence the charge separation process
at the band edge. Figure 6.16 (b) shows the dependence of steepness parameter (𝜎𝜎) on
temperature. As phonon energy (Eph) is decreased from 150 to 50 meV, the steepness
parameter increased. It is evident that a decrease in phonon energy causes an increase in 𝜎𝜎
and hence an increase in Et.
The band gap Eg was determined by analysing the intersection point in the Tauc plot [178]
(i.e. the Eg-Tauc in figure 6.17 (a)) and the inflexion point of the in-phase signals (Eg-ip, figure
6.17(b)). A linear dependence of the in-phase signal on the photon flux has been assumed for
the Tauc plot. This reasonable assumption means that the limiting factors did not change within
the analysed part of a given spectrum and that the SPV signals could be treated as small
signals.
Figure 6.17: The so called Tauc plot from SPV measurements corresponding to the second power of
the product of the in-phase (X) signal and photon energy divided by the photon flux (Φph) plotted
against incident photon energy (a); the first derivative of the in-phase SPV signals (b). The solid lines
in (a) and (b) describe the determination of the Eg-Tauc, and the fit of the peak with a Gaussian function
giving the value of Eg-ip at the peak position respectively.
125
The Tauc gap was obtained by extrapolating the linear fit at photon energies above the
exponential range to the photon energy axis. The inflexion point was obtained by fitting the first
derivative with the Gaussian function. The values of Eg-Tauc and Eg-ip were 1.546 and 1.56 eV,
respectively, for the given spectrum. The small deviations in the band gap can be attributed to
different analysis methods employed in the determination of the band gap energy.
The temperature dependencies of Eg-ip and Eg-Tauc were given in figure 6.18. Eg-ip and Eg-
Tauc decreased monotonously with decreasing temperature at temperatures below or equal to
32°C. This anomalous behaviour in which band gap increases with increase in temperature
between -182° to 32°C may probably be due to lattice dilation which arises due to thermal
expansion [31, 64] and consequently changes the energy band gap. Eg-ip and Eg-Tauc increased
steeply by 0.01 eV between 32°C and 40°C and decreased to 1.569 at 50°C and 1.567 at
60°C.
Figure 6.18. Temperature dependent of Eg-ip and Eg-Tauc (filled diamond and spheres, respectively).
The solid lines describe the temperature dependencies of Eg-ip and Eg-Tauc below 30-40°C by the
empirical function (equation (5.2)).
The steep increase of Eg between 32°C and 40°C is probably related to the phase
transition from the tetragonal to the cubic phases if taking into account that the interaction
between PMMA and CH3NH3PbI3 could reduce the transition temperature. The decrease of Eg-
ip and Eg-Tauc between 32 and 40 °C can be related to phase transition from tetragonal to cubic
phases at 54°C [41].It is known from literature that the transition temperature of CH3NH3PbI3
from tetragonal to cubic phases decreases with increasing pressure [240]. Therefore, the
discrepancy between the transition temperatures measured for CH3NH3PbI3 at normal
pressure [44] and measured for CH3NH3PbI3 coated with PMMA can be caused by an
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interaction between PMMA and CH3NH3PbI3 layers leading to an increase in stress in
CH3NH3PbI3. With respect to the phase diagram of CH3NH3PbI3, the stress between
CH3NH3PbI3 and PMMA layers would be equivalent to a pressure between 200 and 300 Mpa
in the CH3NH3PbI3 layers.
The values of Eg above 32−40 °C can be related to the temperature dependence of Eg of
the cubic phase of CH3NH3PbI3. The decrease of Eg with increasing temperature by (1−2) ×
103 eV/K between 40 and 60°C seems reasonable for the cubic phase of CH3NH3PbI3 in
comparison to conventional semiconductors [30].The decrease of Eg of the tetragonal phase
of CH3NH3PbI3 with decreasing temperatures can be empirically described by a quadratic
dependency:
𝐸𝐸𝑔𝑔(𝑇𝑇)=𝐸𝐸𝑔𝑔(𝑇𝑇0)𝑏𝑏𝑘𝑘𝐵𝐵(𝑇𝑇0𝑇𝑇)2 6.2
where T0 is the temperature of the phase transition from the cubic to tetragonal phase (310 K
has been chosen). The band and gap Eg can be Eg-ip and Eg-Tauc in which Eg-ip(T0) and Eg-Tauc(T0)
are equal to 1.560 and 1.546 eV, respectively. 𝑘𝑘𝐵𝐵 is the Boltzmann constant (8.62×10-5 eV/K)
and b is a free parameter (about 0.0055 and 0.0048 for Eg-ip(T) and Eg-Tauc(T) respectively). No
specific signature of Eg has been observed for the transition from the tetragonal to the
orthorhombic phases at around −111 °C [240].
The shift of Eg is caused by the dilation of the crystal lattice due to thermal vibrations. This
results in a lattice deformation potential [244] with respect to the volume of the unit cell. The
lattice deformation potential is just the slope of Eg relative to the change in the volume of the
unit cell. Given that, Eg of CH3NH3PbI3 layers increases with increase in temperature, lattice
dilation was the dominant parameter which contributed to positive temperature coefficient as
well as positive band gap deformation potential of the system with respect to volume [236]. In
the tetragonal phase of CH3NH3PbI3 layers, the PbI6 octahedron was tilted in the ab-plane
resulting in the doubling of the volume of the unit cell [245]. A similar behavior was also
observed in orthorhombic phase in which unit cell volume increases two times further along
the c-axis. For the given temperature range, the change of Eg for the PMMA/CH3NH3PbI3
system investigated by the surface/interface sensitive SPV was less by about 3 times in
comparison to small (uncoated) single crystals of CH3NH3PbI3 investigated by PL [246]. The
lattice parameters perpendicular or along to the c-axis of the tetragonal phase of in
CH3NH3PbI3 decrease or increase, respectively, and the rotation angle of the PbI6 octahedron
increases monotonically with a decrease in temperature [247]. The corresponding increase of
the Pb−I−Pb bond length along the c-axis with decreasing temperature and local variations in
the rotation angle of the PbI6 octahedron depended on the behavior of the CH3NH3+ cation and
of local stress. It can be supposed that the increase of the lattice constant along the c-axis with
decreasing temperature was the reason for the unusual behavior of the temperature
127
dependence of Eg of the tetragonal phase of CH3NH3PbI3 and that a reduced degree of
freedom for local rotation of the PbI6 octahedron may be the origin for changes in phase
transitions toward the cubic phase at higher temperatures and toward the orthorhombic phase
at lower temperatures.
6.3. Summary
Modulated SPV spectroscopy was used to investigate the temperature dependence of Eg
and Et for CH3NH3PbI3 layers. To avoid the degradation of CH3NH3PbI3 in vacuum during
temperature dependent SPV measurements, a poly (methyl methacrylate) (PMMA) layer was
deposited on CH3NH3PbI3 films and optimized in order to stabilize the CH3NH3PbI3 films. The
stabilization of CH3NH3PbI3 films with PMMA was necessary since a stable perovskite sample
was required for temperature-dependent measurements over a wide temperature range.
Before the temperature dependent measurements were performed, the influence of
PMMA on exponential tails (Et parameter) of CH3NH3PbI3 layers was studied using modulated
SPV. Et depended on the preparation conditions and PMMA coating. Low values of Et of about
13 meV was obtained for the CH3NH3PbI3 layers without PMMA coating whereas high values
of Et of about 28 meV was obtained for CH3NH3PbI3 layers coated with PMMA. This means
that the deposition of PMMA caused a strong increase of disorder in CH3NH3PbI3 due to stress
induced by the formation of the CH3NH3PbI3/PMMA interface. The high disorder observed in
samples coated with PMMA may be attributed to the interaction between PMMA and perovskite
layers which increases the stress in CH3NH3PbI3 films. It was speculated that the formation of
PMMA induces stress underneath which defects are created that lead to partial relaxation by
introducing some disorder that increased the fluctuations among the PbI6 octahedra.
The temperature dependencies of Eg and Et were investigated using modulated SPV
spectroscopy. Eg and Et of CH3NH3PbI3 increased with increasing temperature. The results
showed that thermal expansion gives the predominant contribution to the temperature
dependence of the band gap of CH3NH3PbI3. A jump in the value of Eg near the region of phase
transition was observed and was related to the phase transition from the tetragonal to the cubic
phases.The value of Et increased monotonously with increasing temperature from 13 meV at
-160 °C to 24 meV at 0°C but scattered between 25 and 30 meV in the temperature range
between 20 and 60 °C. The scatter was related to stress at the PMMA / CH3NH3PbI3 interface.
Furthermore, with increasing temperature, disorder can increase in the tetragonal phase of
CH3NH3PbI3 due to increased thermal vibrations of CH3NH3+ cations as well as continuous
tilting of the average lead-iodine-lead bond angle towards 180° [47]. The temperature
dependence of Et was fitted with a model which takes into account phonon-induced disorder
and a phonon energy Eph of 150 ± 40 was obtained.
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CHAPTER 7
Summary and Outlook
In this thesis, selected electronic, structural and optical properties of hybrid organic-
inorganic lead halide perovskite (CH3NH3Pb(I1-XBrX)3) were studied as functions of preparation
conditions, interfaces and degradation. The band gap, the characteristic energy of the
exponential tails and the diffusion length changed depending on time of storage in different
ambient and light soaking, on substrates and coatings and on temperature treatments, which
are important factors for the stability of perovskite solar cells. Modulated surface photovoltage
(SPV) spectroscopy was used as the main method to characterize the electronic properties
related to Eg, Et and L. The SPV measurements were performed in nitrogen atmosphere in a
home-made chamber. SPV analysis does not require a preparation of contacts and can be
performed ex-situ after different stages of layer preparation and/or treatments or in-situ, for
example, during light soaking.
Thin layers of CH3NH3Pb(I,Br)3 films were fabricated by spin coating of a solution onto
various substrates at room temperature in a glove box. The formation of the CH3NH3Pb(I,Br)3
films depended on solvents, additives, temperature and substrates. The samples were in air
for 1 2 min during the transfer from the glove box into the measurement chamber. In some
experiments, Eg and Et determined by SPV were correlated with Eg and the Urbach tails (Eu),
which were obtained from UV-Vis spectroscopy and PDS measurements. GIXRD was used
for the determination of the phase composition and of the stoichiometry of CH3NH3Pb(I1-xBrx)3
films. Vegard’s law was used to obtain the composition of CH3NH3Pb(I1-XBrX)3 films since the
lattice constant decreases linearly with increasing x in CH3NH3Pb(I1-X)BrX)3 composition.
The variation of Eg with the composition of bromide (x) in CH3NH3Pb(I1-XBrX)3 perovskite
films was investigated by modulated SPV and UV-Vis spectroscopies. Eg of CH3NH3Pb(I1-
XBrX)3 films was tuned from (1.56) 1.59 eV to 2.30 eV by varying the stoichiometry of the
perovskite. Eg of CH3NH3Pb(I1-XBrX)3 films blue shifted with increasing content of bromide
whereas the bowing parameter was 0.36 eV. The blue shift can be attributed to different spin-
orbit interactions between lead-iodide and lead-bromide ions. The lowest values of Et of up to
about 15 meV were obtained for the pure CH3NH3PbI3 and CH3NH3PbBr3 films.
The values of Eg and Et depended sensitively on the kind of interface as shown by
modulated SPV spectroscopy. CH3NH3PbI3 deposited on double layers of TiO2-PCBM and
SnO2-PCBM showed a constant band gap of 1.58 eV and low scatter in the value of Et. This
was attributed to the modification of the TiO2 or SnO2/CH3NH3PbI3 interfaces by the PCBM
129
which allowed for efficient charge separation and transfer. In contrast, CH3NH3PbI3 deposited
on TiO2 showed relatively large values of Et which was correlated to the significant density of
shallow traps in the TiO2 that allowed for the excitation of charge carriers from the valence
band of perovskite into defect states at the interface with TiO2.
The diffusion or transport length was measured for CH3NH3PbI3 layers by the method after
Goodman. L was studied as a function of degradation under light soaking. For the investigation
of L, the modulated SPV signals were kept constant by varying the light intensity and the light
intensity was plotted as a function of the absorption length. A decrease of L with increasing
time of light soaking was observed. The decrease was attributed to light-induced degradation
which arises due to trap states and charging- discharging effect at the TiO2/ CH3NH3PbI3
interface. After 12 h of light soaking, L depended on the value of the modulated SPV signal,
i.e. on the generation rate. The strong variation of L with modulated SPV signals was an
indication of defects and/or inhomogeneity of the films which led to changes in the quasi Fermi
levels over the whole range of film thickness. As remark, the analysis of L after Goodman was
not for all samples straight forward, i.e. the development of a model including inhomogeneity
due to combined diffusion and drift, variation of built-in electric fields and changes in the
composition would be useful in the future.
The temperature dependence of Eg and Et was investigated for CH3NH3PbI3 layers by
modulated SPV spectroscopy. In order to avoid degradation of CH3NH3PbI3 in vacuum during
temperature dependent SPV measurements, a poly (methyl methacrylate) (PMMA) layer was
deposited on CH3NH3PbI3 films and optimized for stabilization of CH3NH3PbI3 films. The
stabilization of CH3NH3PbI3 with PMMA was necessary since a stable perovskite sample was
required for temperature-dependent measurements over a wide temperature range. Eg and Et
of CH3NH3PbI3 increased with increasing temperature. The value of Et increased
monotonously with increasing temperature from 13 meV at -160 °C to 24 meV at 0°C but
scattered between 25 and 30 meV in the temperature range between 20 and 60 °C. The scatter
can be related to stress at the PMMA / CH3NH3PbI3 interface. Furthermore, with increasing
temperature, disorder can increase in the tetragonal phase of CH3NH3PbI3 due to increased
thermal vibrations of CH3NH3+ cations as well as continuous tilting of the average Pb-I-Pb bond
angle towards 180° [47]. In addition, the temperature dependence of Et was fitted with a model
taking into account phonon-induced disorder and a phonon energy Eph of 150 ± 40 was
obtained.
In comparison to covalent semiconductors, unusual behavior of the increase in Eg of the
tetragonal phase of CH3NH3PbI3 layers with increasing temperature is attributed to lattice
dilation which occurred due to thermal expansion. The lattice dilation is produced by thermal
vibrations of the ions around their mean position which increases due to increased thermal
energy. The effect can be quantified by the positive temperature coefficient of the energy band
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gap [64]. In contrast, in covalent semiconductors such as silicon and gallium arsenide, the
electron-phonon interaction is the dominant factor which leads to a decrease of Eg with
increasing temperature [79, 60]. A jump in the value of Eg near the region of phase transition
has been observed and was related to the phase transition from the tetragonal to the cubic
phases.
It has been shown that modulated SPV spectroscopy is a well suitable method for very
efficient, sensitive and reliable characterization of hybrid organic-inorganic metal halide
perovskites. In this context, modulated SPV spectroscopy can be well applied for the
characterization of perovskites with respect to preparation technologies and treatments, for the
monitoring and analysis of degradation processes and for the investigation of fundamental
dependencies of parameters.
The reproducibility of CH3NH3PbI3 and other perovskite layers is rather challenging in
relation to the preparation conditions and stability of solar cells based on related absorbers.
For example, the continued evaporation of CH3NH3, HI and degradation to PbI2 makes the
reproducibility of CH3NH3PbI3 layers a challenge. One way to get higher stability is to form a
dense interface between the CH3NH3PbI3 absorber layer and charge selective contacts. This
implies the preparation of interfacial materials which can enhance the growth of perovskite,
passivate defects and offer protective barriers for CH3NH3PbI3 perovskites. Another way to
stabilize perovskites is to use perovskites with mixed cations and halides (i.e. the so- called
triple cations which contains Cs+, MA+ and FA+). Solar cells based on mixed cations and
halides are much better reproducible and thermally and structurally stable at higher efficiencies
in comparison to bare CH3NH3PbI3. The further improvement of the materials and
combinations of materials with perovskites requires a further optimization of the compositional
design of the perovskite. This is beneficial for tandem solar cell applications. Furthermore, it
would be interesting to determine L after Goodman [32] using SPV spectroscopy for mixed
perovskites based on cations and halides. For this purpose, however, the layer shall be
homogeneous in the composition and the absorption spectra shall be measured with high
precision.
131
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Publications
Journal articles
Thomas Dittrich, Celline Awino, Pongthep Prajongtat, Bernd Rech, and Martha Ch. Lux-
Steiner, Temperature dependence of the band gap of CH3NH3PbI3 stabilized with PMMA: A
modulated surface photovoltage study. J. Phys. Chem. C, 2015, 119, 23968−23972.
Lukas Kegelmann, Christian M. Wolff, Celline Awino Omondi, Felix Lang, Eva Lisa Unger, Lars
Korte, Thomas Dittrich, Dieter Neher, Bernd Rech, and Steve Albrech. It takes two to tango
double-layer selective contacts in perovskite solar cells for improved device performance and
reduced hysteresis. ACS Appl. Mater. Interfaces, 2017, 9 (20), pp 1724517255.
Celline Awino, Thomas Dittrich, Lukas Kegelmann, Steve Albrecht. Effects of light soaking on
the transport length of CH3NH3PbI3, 2018, to be submitted.
Conference presentations
Celline Awino, Thomas Dittrich, Eva Unger, Lukas Kegelmann, Steve Albrecht, Bernd Rech.
Modulated surface photovoltage spectroscopy of CH3NH3Pb(I,Br)3 thin films. DPG Spring
meeting, 19-24 March 2017 Dresden Germany.
Celline Awino,Thomas Dittrich, Eva Unger, Lukas Kegelmann, Steve Albrecht, Bernd Rech.
Characterization of lead halide perovskites. European material research society (EMRS 2017
spring meeting), Strasbourg France May 2017
153
List of abbreviations and symbols
Abbreviation description
AE activation energy
Ag silver
A.M 1.5 G air mass of 1.5 global
a-Si-H hydrogenated amorphous silicon
ASTM American society for testing of materials
Au gold
c-Si crystalline silicon
BA butyl acetate
°C Degrees centigrade
CB conduction band
CdSe cadmium selenide
CdTe cadmium tellurium
CH3NH3PbI3 methyl ammonium lead iodide
CH3NH3PbBr3 methyl ammonium lead bromide
CsSnI3 cesium tin iodide
Cm2 squared centimeter
D charge carrier diffusion coefficient
dEg/dT temperature coefficient
DFT density functional theory
Ec conduction band minimum
EF Fermi energy
Eg energy band gap
Eg-ip energy band gap due to inflexion point
Eg-Tauc Tauc gap energy
Eoffset offset energy
Eon-X onset energy of the x- or in-phase signal
Eon-Y onset energy of the y- or phase shifted by 90° signal
Eph electron phonon energy
Et exponential tail states
Ev maximum of valence band
eV electron volt
eV/K electron volt per kelvin
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Evac vacuum level
fmod modulated frequency
FTPS Fourier transform photoelectron spectroscopy
FTO fluorine doped tin oxide
GaAs gallium Arsenide
Ge germanium
GIXRD grazing incidence x-ray diffraction
EA electron affinity
h hour
HOMO highest occupied molecular orbital
I iodine
InP indium phosphide
IE ionization energy
Isc short circuit current
J joules
KB Boltzmann constant (~ 26 meV) or 8.62 ×10−5 eV/K
KWh killo-watt hour
L diffusion length
LUMO lowest unoccupied molecular orbital
meV milli-electron volt
mg milli-gram
min minute
ml milli-litre
mg/ml milli-gram per milli-litre
Mo molybdenum
Mo effective mass
MPa mega-pascal
mV milli-volt
Pb lead
PCE power conversion efficiency
PEDOT: PSS poly (3, 4-ethylenedioxythiophene)polystyrene sulfonate
PL photoluminescence
PDS photo-thermal deflection spectroscopy
Pb-I-Pb lead-iodine-lead
PMMA poly (methyl methacrylate)
PTAA poly (triaryl amine)
SCs solar cells
155
SEM scanning electron microscopy
SPV Surface photovoltage
VB valence band
Voc open circuit voltage
VS volt-second
rad radians
Rmax maximum amplitude
RT reflection and transmission
t time
T absolute temperature
To phase transition temperature
tan h hyperbolic tangent function
TCO transparent conducting oxide
Tmax maximum temperature
TW tella Watt
TWh tella Watt hour
Xmax maximum in-phase signal
Ymax maximum phase shifted by 90° signal
Wm-2eV-1 Watts per squared meter per electron volt
% percent
σ steepness parameter in relation to absorption
σo material dependent steepness parameter
μ charge carrier mobility
τ charge carrier lifetime
q electronic charge (1.6 × 10−19) J
Φ work-function
Φ Angle of rotation of the position detector in relation to PDS
Фph photon flux
hν photon energy
h+ hole
e- electron
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157
Acknowledgements
I am very grateful to Prof. Dr. Bernd Rech for giving me the opportunity to perform my PhD
studies and research at the Institut für Silizium-photovoltaik at the Helmholtz-Zentrum Berlin
für Materialien und Energie GmbH and for taking the responsibility as the first reviewer of my
thesis. I am also grateful to Prof. Dr. Roland Scheer, the external reviewer of my thesis, from
the Martin Luther Universität, Halle. Special thanks goes to my supervisor and mentor PD Dr.
Thomas Dittrich for accepting me as his student and for his tireless, professional guidance and
training during my entire studies. I am also grateful to Prof. Dr. Martha Lux-Steiner for giving
me the opportunity to perform experiments at her former Institut für Heterogene Materialien
and for the exciting and interesting experience at the ISU energy 2015 (International Summer
University of renewable energy, Falera).
I am grateful to Prof. Dr. Nobert Nickel and Dr. Jörg Rappich for support of my research
at the Institut für Silizium-photovoltaik; Dr. Eva Unger and Steve Albrecht for their open minded
support within the young investigator groups. I am also grateful to Lukas Kegelmann and Katrin
Hirselandt for fruitful collaboration and for some technical support. I am also very grateful to
PD Dr. Thomas Dittrich, Prof. Dr. Pongthep Prajongtat and Dr. Attitaya Naikeaw for introducing
me to the world of perovskites and surface photovoltage at the former Institut für Heterogene
Materialien.
Thanks to Dr. Steffen Fengler and Santiago Pineda Solano for enlightening discussions
about SPV. Many thanks goes to Dr. Karolina Mack of the Kompetenz-zentrum Dünnschicht-
und Nanotechnologie für Photovoltaik Berlin (PVcomB) for the introduction into UV-vis
spectroscopy and the assistance in interpretation. Thanks to Dr. Eva Unger for some PDS
measurements and for discussions. I thank Dr. Michael Tovar for introduction to XRD
measurements at the Abteilung Struktur und Dynamik von Energiematerialien of the HZB and
Carola Klimm for sample characterization by SEM. Special thanks also goes to Dr. Ruslan
Muydinov of Technologie für Dünnschicht-Bauelemente (TU Berlin - Fakultät IV) and
Kompetenz-zentrum Dünnschicht-und Nanotechnologie für Photovoltaik Berlin (PVcomB) for
collaboration and support.
I also thank Marion Krusche for assistance and patience with administrative work. Thanks
also to Dr. Sonya Calnan, Dr. Albert Juma and Lydia Radoli for corrections and feedback.
My PhD studies would not be possible without the financial support from the Catholic
academic exchange service (KAAD) and the Helmholtz Zentrum Berlin. I am grateful for the
scholarships.
Last but not least, special thanks goes to my husband Charles Ogoma and children; Noela
Atieno, Marvin Ochieng, Wilson Maguma and Jeremy Monyi for their patience, motivation and
understanding over the whole period of my PhD studies.
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