Document [original]

Electron Paramagnetic Resonance of

Process-Induced Defects in Silicon

VOM FACHBEREICH PHYSIK DER UNIVERSITÄT PADERBORN

ZUR ERLANGUNG DES AKADEMISCHEN GRADES EINES

DOKTORS DER NATURWISSENSCHAFTEN

(DR. RER. NAT.)

GENEHMIGTE DISSERTATION

VON

BERTRAM LANGHANKI

1. GUTACHTER:P

ROF. DR. J.-M. SPAETH

2. GUTACHTER:P

ROF. DR. H. OVERHOF

TAG DER EINREICHUNG: 08.02.2001

TAG DER MÜNDLICHEN PRÜFUNG: 21.03.2001

Table of Contents

Introduction 1

1 Fundamentals of the measurement techniques 3

1.1 Theoretical fundamentals of EPR and ENDOR............................................ 3

1.1.1 The spin Hamiltonian ....................................................................... 4

1.1.2 Analysis of EPR spectra .................................................................... 6

1.1.3 Analysis of ENDOR spectra.............................................................. 7

1.2 Experimental measurement method and setup for EPR and ENDOR........... 7

1.3 Electrically Detected EPR .......................................................................... 11

1.3.1 On the mechanisms of EDEPR ....................................................... 11

1.3.2 Experimental setup for EDEPR ...................................................... 16

1.4 Fourier Transform Infrared Absorption ( FTIR ) ....................................... 17

2 Advances in EDEPR technology 21

2.1 EDEPR with microwave power modulation ............................................... 21

2.2 EDEPR with high microwave frequencies.................................................. 26

3 EDEPR investigation of implanted and heat-treated silicon 31

3.1 Motivation for Mo-implantation into silicon samples................................. 32

3.2 EPR of Mo-implanted and annealed FZ-silicon ......................................... 33

3.3 EDEPR of Mo- and Si-implanted and annealed FZ-silicon........................ 34

4 Oxygen related defects in silicon 47

4.1 Oxygen in silicon − an introduction ........................................................... 48

4.2 Thermal Double Donors.............................................................................. 49

4.3 Shallow Thermal Donors ........................................................................... 53

4.4 Radiation defects with participation of oxygen ......................................... 54

5 Magnetical and optical studies of shallow thermal donors in 57

hydrogenated Cz-Si crystals

5.1 Introduction................................................................................................. 58

5.2 Electronic properties of the shallow donors D1−D3................................... 60

5.3 EPR investigation of the shallow donors D1−D3....................................... 64

5.4 EDEPR investigation of the shallow donor D2 .......................................... 69

5.5 EPR investigation of shallow donor interaction with 29Si nuclei............... 71

5.6 ENDOR investigation of the shallow donors D1 and D2........................... 75

5.7 Discussion................................................................................................... 82

5.8 Conclusions................................................................................................. 91

6 On the mechanism of EDEPR 93

6.1 Investigation of Cz-silicon after heat-treatment at 470°C .......................... 93

6.1.1 Preparation and FTIR-characterisation of TDD.............................. 94

6.1.2 EDEPR of Cz-Si heat treated at 470°C........................................... 96

6.2 Presentation of further EDEPR experiments .............................................. 98

6.3 On the impact of electron-irradiation on the EDEPR signal...................... 100

6.4 On the mechanism responsible for the EDEPR detection of Pba and Pbb. 105

6.5 Peculiarities of EDEPR............................................................................. 107

6.6 Conclusions............................................................................................... 108

Summary 111

References 115

Introduction

In this work the class of Si/SiO2 interface defects is studied with the method of Electri-

cally Detected Electron-Paramagnetic Resonance ( EDEPR ). The interface defects,

called “dangling bond” defects or Pb-centres, are subject of considerable scientific as

well as technological interest. Their importance is easily explained regarding the inter-

face formation during oxidation processes and the improvement of metal-oxide semi-

conductor ( MOS ) devices. Since semiconductor devices are fabricated with Very

Large Scale Integration ( VLSI ), the impact of surface and interface defects on the de-

vice performance has increased significantly. The EDEPR investigation of (100)-

oriented Si/SiO2 interfaces reveals an unknown dangling bond centre at the interface

and yields the precise symmetry of a further Pb-centre below the interface.

In the realm of state-of-the art semiconductor device production, annealing procedures

have to be carried out especially after implantation of doping elements. Since oxygen is

the dominant contamination in silicon crystals grown by the Czochralski(Cz)-method,

which is used for the majority of semiconductor devices, the annealing procedures cause

the growth of oxygen precipitates. The defect centres are most efficiently created at

temperatures around (300−500)°C and are called Thermal Donors (TD) in general. Sev-

eral subsets of TDs with similar features are known, each subset consisting of certain

number of species which form subsequently upon annealing. The shallow donor char-

acter of the TDs is responsible for severe changes in the conductivity of the silicon

crystals, which explains the technological interest in the formation of these defects.

Apart from the economic aspect the scientific interest has remained high over the last

four decades due to the fact that in spite of intense investigations the detailed structure

of the TDs has persisted unclear.

A procedure to most efficiently create a subset of the TDs, the so-called Shallow Ther-

mal Donors (STD), had been developed recently. The method enables the selective

preparation of the first species of a family of STDs incorporating hydrogen (STD(H)).

Introduction

These are studied by means of Fourier Transform Infrared Absorption ( FTIR ), Elec-

tron-Paramagnetic Resonance ( EPR ) and Electron-Nuclear Double Resonance and

their formation next to the electronic and structural properties are analysed. A defect,

which is supposed to represent the very first species of the STD(H), is measured for the

first time. The results reveal the incorporation of one hydrogen atom and one silicon

atom in the defect core. Our experimental results support an atomic model for the

STD(H), which was previously calculated to be a shallow donor. According to this

model in addition to two interstitial oxygen atoms, the core structure of the STD(H) is

composed of a silicon atom and an interstitial carbon atom to which a hydrogen atom is

bonded also. The addition of the hydrogen atom renders the defect shallower according

to the theory. The atomic structure of further families of STDs is also discussed.

Furthermore the results from various experiments with EDEPR are summarised with the

intention to gain more knowledge about the applicability of the method. Although

EDEPR has been successfully applied to investigate various defects recently, an equal

number of attempts to detect EDEPR signals of other defects failed. Due to the fact that

the mechanism responsible for the detection of EDEPR has not been understood com-

pletely yet, the success of EDEPR experiments was not always predictable. The results

obtained in the final chapter support a donor-acceptor pair recombination mechanism

for EDEPR that was suggested earlier in this group. EDEPR spectra from samples

which had been irradiated with electrons were recorded with very high signal-to-noise

ratios. An “amplification” of signals occurring with weak intensities prior to irradiation

is observed and the mechanism of it is revealed.

When studying the dangling bond centres variations of the modulation technique for the

detection of the EDEPR signal have been introduced and the use of high microwave

frequencies up to 72GHz has been realised. The “active” measurement layer is limited

to only a few µm of depth from the sample surface for EDEPR in contrast to the whole

sample volume in conventional EPR. However, the limitation can be of significant ad-

vantage when surface or surface-near defects have to be studied. The greatest benefit of

EDEPR in comparison to EPR is the increased sensitivity regarding low defect concen-

trations in the samples.

Fundamentals of the measurement techniques

Chapter 1

Fundamentals of the measurement

techniques

Experimental methods used to analyse defects in semiconductors are manifold. When

being concerned with the atomic and geometrical nature of the defect in question, Elec-

tron Paramagnetic Resonance ( EPR ) and its extension Electron Nuclear Double Reso-

nance ( ENDOR ) are used. Both methods have been modified by the electrical detec-

tion of the magnetic resonance and have been called EDEPR and EDENDOR, respec-

tively. The advantage of electrical detection over the conventional method can be found

in a possible increased sensitivity regarding the defect concentration. In the following

only a brief description of the methods is given. For further details the reader is referred

to e.g. [Spaeth 1992][Stich 1995].

Next to the magnetic resonance techniques Fourier Transform Infrared Absorption

( FTIR ) was applied. This optical method was used to investigate the concentration and

energy levels of certain defects. The basics of the infrared absorption and the benefits of

the Fourier transformation method are explained briefly. The reader is referred to e.g.

[Kuzmany 1989] for a detailed description.

Fundamentals of the measurement techniques

1.1 Theoretical fundamentals of EPR and ENDOR

1.1.1 The spin Hamiltonian

When conventional EPR is applied to investigate a paramagnetic defect in a solid the

transition ∆ms= ± 1 of an unpaired electron in a static magnetic field 0

is directly de-

tected via the absorption of microwave power. The energy levels contributing to the

transition can be described by the spin Hamiltonian operator & . This operator contains

only energy terms that are related to the spin of electrons and nuclei involved in the

resonant process. For a given system with S = 1/2 and I ≥ 1 the spin Hamiltonian reads

as follows:

∑∑ ∑

⋅⋅+⋅−⋅⋅+⋅⋅=

ii i

iii0ini,nii0B IQIBI gSAIBgS 







&(1.1)

QNZHF/SHFEZ &&&&

with B

the Bohr magneton S

electron spin operator

gelectron g tensor 

B0magnetic field

nuclear spin operator of the nucleus i

Aihyperfine or superhyperfine structure tensor of the nucleus i

g,nuclear g factor of the nucleus i

nuclear magneton

Qiquadrupole tensor of the nucleus i .

The electron Zeeman operator &EZ describes the magnetic interaction between the spin

 of an unpaired electron and the external magnetic field 

B0 whereas the correspond-

ing one of a nuclear spin i

 is given by the nuclear Zeeman operator &NZ . The interac-

tion between the electron spin S

 and the nuclear spin i

 of the central nucleus or a

neighbour nucleus is given by the hyperfine ( hf ) or superhyperfine ( shf ) term &HF/SHF.

The quadrupole term &Q contains the interaction between the nuclear quadrupole mo-

ment of a nucleus having I > 1/2 and the electric field gradient at its site.

Fundamentals of the measurement techniques

The hf or shf tensor A can be split into an isotropic part a and a traceless anisotropic

part B.

B1aA +⋅= . (1.2)

where 1 is the 3×3 unit matrix. Since the trace of the anisotropic hf or shf tensor is zero,

the tensor can be described in its principal axes system by two independent interaction

parameters

bzz

=(1.3)

and 2

byy

−

=xx

The scalar a, the so-called Fermi contact interaction constant, is proportional to the un-

paired spin density at the site of a nucleus in a one-particle approximation for the centre

wave function [Slichter 1989].

nnBe0

2)0(gga Ψ⋅=

µµµ

(1.4)

where

o is the permeability of a vacuum.

The matrix elements of the anisotropic part B are given by [Slichter 1989]

rd)r(

xx3

ggB 2

5ki

nnBe0













−= ∫

µµµ

(1.5)

The quadrupole tensor i

Q, which does not vanish for nuclei with spin 21>I, is de-

fined by

ik xx

)1I2(I2

∂∂

∂

⋅

−

=(1.6)

with eelementary charge,

Qquadrupole moment of a nucleus,

Velectric potential at the site of a nucleus.

The quadrupole tensor i

Q is also traceless and can be described analogously to the ani-

sotropic hf or shf tensor in its principal axes system by the two parameters

Fundamentals of the measurement techniques

qzz ′′

=(1.7)

and 2

qyy ′′′′ −

=xx

The z axis of the hf, shf or quadrupole tensor’s principal axes system is to be aligned

along the direction of the largest interaction by definition. Consequently, b and q yield

the axially symmetric parts of each tensor, whereas b′ and q′ describe the deviation

from axial symmetry.

The exact determination of the energy levels of a spin system requires a full diagonali-

sation of the appropriate spin Hamiltonian. For a rough estimation perturbation theory

of first or second order is often helpful, provided that one term of the Hamiltonian

dominates. For example if &EZ >> &SHF the interaction for a simple 21=

S system

with isotropic electronic and nuclear g-factors and one neighbour nucleus is given in

first order perturbation theory by

(

)

3/)1I(ImWBgmWmmBgmE 2

0nnISHFIS0BS +−+−+=

µµ

(1.8)

with )2cos(sinb)1cos3(baW 2'2

φϑϑ

+−+= (1.9)

and )'2cos('sin'q3)1'cos3(q3W 22

φϑϑ

+−= . (1.10)

and

′ are the angles between the z axis of the respective principal axes system and

the magnetic field vector,

and

′ the angles between the x axis and the projection of

the magnetic field vector into the xy plane of the respective principal axes system (see

e.g., [Spaeth 1992]).

1.1.2 Analysis of EPR spectra

EPR spectra are analysed by determining the energy differences between the levels

between which transitions obeying the selection rules 1û±=

m and 0û=

m occur.

For a 21=

S system equation (1.8) yields the energy positions of the allowed EPR

transitions according to first order perturbation theory.

SHFIBEPR WmBgh +=

µν

(1.11)

Fundamentals of the measurement techniques

In an EPR experiment the microwave frequency is fixed while the magnetic field is

swept. Thus equation (1.11) has to be solved for the corresponding resonant magnetic

fields. The interaction matrices can be obtained by rotating the magnetic field in two

perpendicular planes (or rotating the crystal relative to the fixed magnetic field). The

angular dependencies usually yield much more resonances than needed for the determi-

nation of the spin Hamiltonian parameters. Therefore, the interaction tensors are ad-

justed to the observed resonances in an iterative procedure where the deviation squares

of the measured and the calculated resonances are minimised.

1.1.3 Analysis of ENDOR spectra

ENDOR transitions obey the selection rules 0û=

m and 1û±=

m. According to

equation (1.8) first order theory yields

QQnnSHFSENDOR WmBgWmh +−=

µν

(1.12)

with

()

2mmm IIQ '

+= .

m and 'mI represent the nuclear spin states between which the ENDOR transition

occurs. Similar to the EPR analysis the corresponding interaction matrices are obtained

by recording ENDOR angular dependencies for a rotation of the magnetic field vector

in two perpendicular planes and fitting the interaction parameters to the experimental

data. According to their separation from the defect centre, neighbouring nuclei are clas-

sified in different shells. The symmetry of a shell is determined by symmetry elements

which transform the shell’s nuclei into each other. The origin of each symmetry opera-

tion is the point group symmetry of the defect. For example a centre of inversion is de-

termined by the Laue class of the centre (site). Each nucleus of a shell leads to a certain

number of ENDOR lines depending on the nuclear spin and electron spin and thus to

several ENDOR branches in the angular dependence [Spaeth 1992].

1.2 Experimental measurement method and setup for EPR

and ENDOR

In contrast to electrically detected EPR, the EPR transitions in conventional experi-

ments are detected via a microwave absorption. The nuclear magnetic resonance

Fundamentals of the measurement techniques

( NMR ) transitions are monitored via a change of the EPR effect. To observe this

ENDOR effect, the EPR transition has to be saturated partly by applying sufficiently

high microwave power. The rf-induced NMR transition leads to a partial desaturation of

the EPR, which is compensated by an increased microwave absorption (figure 1.1). The

latter is detected (see e.g., [Spaeth 1992]). In stationary ENDOR experiments [Sei-

del 1961] one can make use of a cross-relaxation probability 1

−

T, which allows the

stationary observation of the rf-induced desaturation of the EPR transition.

Figure 1.2 shows the schematic setup of a conventional X-band EPR-/ENDOR spec-

trometer, working as homodyne system in a reflex arrangement [Poole 1983]. A small

part of the 100 mW microwave power generated by a YIG-oscillator (1) is branched off

by a directional coupler (2) to a frequency counter. The main part is divided into the

main and the reference arm by a second directional coupler (2). A phase shifter (4) al-

lows to adjust the phase of microwave in the reference arm with respect to that of the

main branch. Afterwards a 90°-hybrid (7) divides the microwave into two branches

which are 90° phase-shifted against one another. Each branch is guided to the input of a

mixer. The microwave power of the main branch is adjustable by an attenuator (3). Via

a 3-gate-circulator (5) the microwave gets into a waveguide which ends in a TE011 mi-

crowave resonator (17). The coupling is done by a small hole at one side of the resona-

tor. An adjustable antenna in front of the hole allows to adapt the wave resistance of the

Figure 1.1 Schematic diagram explaining the EPR and ENDOR effect of a simple

system having S=1 2 and 21=

The relative occupation of levels 1-4

is marked by their lengths considering a non-saturated EPR transition (fig-

ure 1.1a) and the stationary occupation for saturated EPR and NMR tran-

sitions, including possible relaxation mechanisms (figure 1.1b).

Fundamentals of the measurement techniques

resonator to that of the waveguide. In case of ideal adjustment no microwave power is

reflected by the cavity. An absorbing medium in the resonator causes an unbalanced

condition of the microwave bridge. The signal reflected in this case reaches a micro-

wave amplifier (6) via the 3-gate-circulator, is amplified and guided via a power di-

vider, both outputs having the same phase, into the respective second input of the two

mixers. Each mixer multiplies the input signals. The output voltage Uout of the two mix-

ers is [e.g. Spaeth 1992]

cos

MWout ⋅⋅= aPU , (1.13)

where PMW is the microwave power reflected by the resonator, a is a device specific

constant and

the phase difference between both input signals. In case of identical

phases equation (1.13) yields a positive dc voltage, whereas in case of

= 90° the dc

voltage part equals zero. Using the phase shifter (4) the relative phase is adjusted in a

way that the input signals of the mixer on the right have identical phases at the reso-

nance frequency of the microwave cavity. An incomplete coupling into the resonator

leads to a dc voltage at the mixers output, which is used to adjust the coupling plate

accordingly (not depicted in figure 1.2). This automatic control loop makes a steady

coupling possible, even though e.g. a temperature drift changes the position of the cou-

pling plate or the resonance frequency of the cavity.

The automatic frequency control (AFC) is done by the mixer on the left. If the fre-

quency of the YIG-oscillator (1) deviates from the resonance frequency of the cavity,

the signal reflected by the resonator is phase-shifted with respect to the reference

branch. This leads to a dc voltage at the output of the left mixer (9), which is used for

the adjustment of the YIG-oscillator frequency.

The resonance absorption of the paramagnetic sample causes the balanced microwave

bridge to deviate from the balance. The reflected microwave power changes and leads to

a change in the dc voltage (eqn. (1.13)) at the output of the mixer on the right. This

voltage is the final signal (10). To improve the sensitivity the lock-in technique with

modulation of the magnetic field is used.

Fundamentals of the measurement techniques

The resonator (17), into which the sample is placed, is part of a helium flux cryostat

(16) such that temperatures down to 4.2K can be achieved. The temperature is stabilised

by a resistor heater at the helium vaporiser and by a helium flux control. The microwave

resonator (17) is situated in the homogeneous field region of a conventional electro-

magnet (15). The magnetic field modulation required for the lock-in detection of EPR

measurements is generated by “EPR rods” (19), the radio frequency additionally re-

quired for ENDOR measurements by ENDOR rods (18). Both, EPR and ENDOR rods

are placed in Helmholtz arrangement.

Fig. 1.2 Schematic diagram of an EPR / ENDOR spectrometer: (1) YIG-oscillator,

(2) directional coupler, (3) attenuator, (4) phase shifter, (5) 3-gate-circulator,

(6) microwave amplifier, (7) 90°-hybrid, (8) power divider, (9) dispersion

signal, (10) absorption signal, (11) reference signal, (12) HF-switch,

(13) HF-amplifier, (14) NF-amplifier, (15) magnet, (16) cryostat,

(17) resonator, (18) ENDOR rods, (19) EPR rods, and (20) sample.

Fundamentals of the measurement techniques

1.3 Electrically Detected EPR

The method of Electrically Detected EPR ( EDEPR ) was established in the group of

Prof. Dr. J.-M. Spaeth only a few years ago and will explained in a more detailed fash-

ion therefore. When performing EPR measurements a conductivity change of the sam-

ple can be monitored using electrical contacts on the sample surface. At first the method

was called Spin-Dependent Recombination ( SDR ) or Spin-Dependent Photoconduc-

tivity ( SDPC ) (when used with excitation light ), but rarely used to identify defects in

semiconductors until the beginning of the 1990’s. The method gained attraction after

several publications by Stich et al. and the name Electrically Detected EPR ( EDEPR )

was established by these [Stich 1993]. Mainly two reasons can explain the previous

neglect of this sensitive method. First, the majority of experiments using EDEPR were

performed at room temperature, yielding only broadened and isotropic resonance lines

at g ≈ 2, e.g. [Solomon 1976]. No structural information could be derived from this

spectra. Secondly, no suitable model explaining the phenomenon of EDEPR was pre-

sented, that could have given useful information under which conditions this method

would work best. With each new defect to investigate the experimentalist had to test

whether EDEPR would work or not.

In recent years an increased number of publications dealing with EDEPR can be found,

e.g. [Bayerl 1998, Carlos 1997, Maier 1996]. The sensitivity gain regarding the defect

concentration and the lower costs of EDEPR, both compared to conventional EPR, and

the frequency independence of the EDEPR effect can be seen as one reason. Even

stronger though the possibility to investigate small and integrated semiconductor de-

vices and epitaxial layers has promoted the application of this method.

1.3.1 On the mechanisms of EDEPR

Several models explaining the EDEPR effect have been suggested in the past, yet no

final theory could be presented until now. However, there is strong evidence that a spin-

dependent recombination takes place between weakly exchange coupled donors and

acceptors [Greulich-Weber 1995]. With the EDEPR models presented by Lépine and

Kaplan two of the recent theories are presented in the following. For a further discus-

sion of the models the reader is referred to the original literature or to [Stich 1997].

Fundamentals of the measurement techniques

After measurements of the recombination at surface defects on crystalline silicon Lé-

pine et al. proposed a model explaining the spin dependent conductivity [Lépine 1970,

Lépine 1972]. It is based on the Schockley/Read/Hall-model ( SRH ), describing the

capture and recombination of an electron and a hole at one defect [Schockley 1952, Hall

1952]. According to Lépine the recombination centre may be considered to have an un-

paired electron spin, thus being paramagnetic prior to the capture of an electron. The

Pauli principle only allows the occupation of one state by two electrons when having

different spin orientations. Thus, the recombination is spin dependent, as the values for

the capture cross section for the recombination centre are different for parallel and anti-

parallel orientation of the conduction electron spin. Consequently, the recombination

rate is strongly dependent on the spin orientation of the charge carriers and the recom-

bination centres.

In an external magnetic field the spins align parallel to the magnetic field, a reduction of

the recombination rate is the consequence. An increase of the recombination rate can be

achieved if the degree of spin polarisation is lowered by a saturation of EPR transitions

at the paramagnetic recombination centres. As a consequence, the EPR transitions lead

to a decrease of the conductivity of the crystal.

Characteristic for the Lépine model is the dependence on the polarisation of the recom-

bination centres and the conduction electrons. The value ∆σ, representing the conduc-

tivity change of the crystal upon total saturation of the EPR transitions, is given as fol-

lows:

re Pp ⋅∝∆

(1.14)

with

pe : polarisation of the conduction electrons

Pr : polarisation of the unpaired hole at the recombination centre.

Several studies proved the proposed dependence of the conductivity from the polarisa-

tion of the recombination centres to be wrong [Kaplan 1978, Mima 1980,

Vlasenko 1986, Barklie 1994]. A major deficiency of the Lépine model is the predicted

low EDEPR conductivity change of only ∆σ/σ =10−6 [Lépine 1972] whereas one of

∆σ/σ =10−3 is observed in many experiments [Stich 1997]. Several variations to the

model of Lépine have been presented [Woisinski 1977, White 1977]. Nevertheless, it

Fundamentals of the measurement techniques

has to be noticed that all models based on the spin-polarisation caused by an external

magnetic field can not explain the magnitude of the detected spin-dependent effect. The

first model to explain the process sufficiently was presented by Kaplan, Solomon and

Mott and is called the KSM model [Kaplan 1978].

In contrast to the model presented by Lépine the KSM model is based on the assump-

tion that electrons and holes are captured spin-independently, forming electron-hole-

pairs subsequently. Two possibilities for this process were suggested. First, the electron-

hole-pairs could be created at one defect, leading to an exciton-like recombination. Sec-

ondly, the pairs of electrons and holes could be trapped by donors and acceptors, re-

spectively, preceding a donor-acceptor-recombination.

Following the KSM model the spin-dependence of the recombination can be explained

by the fact, that with the recombination of the electron-hole-pairs a compensation of

both spin and charge takes place, leading to a diamagnetic ground-state. Therefore the

recombination of electron-hole-pairs is allowed for anti-parallel spins but forbidden for

parallel spin conditions. In the case of an applied magnetic field the spins will turn into

parallel orientation, making the recombination of electrons and holes impossible. When

EPR transitions of the electrons and holes are induced, electron-hole-pairs will be

shifted from parallel to anti-parallel spin orientation, thus leading to an increased re-

combination rate. It has to be noticed that in this model only the spin-correlation-effect

of the electrons and holes within the electron-hole-pairs has an influence on the recom-

bination rate. The latter is not dependent on the magnitude of an external magnetic field

and hence the polarisation of electrons and holes.

Characteristic for EDEPR explained by the donor-acceptor-recombination mechanism is

the microwave power dependence of the recorded signal. In contrast to EPR a different

saturation of the signal is observed. For small microwave power the signal increases

proportional with increasing power until it converges asymptotically a maximal signal.

According to Stich the power dependence of the EDEPR signal of the spin-dependent

recombination of donor-acceptor-pairs can be written as follows:

REPR

EDEPR TW1

CS +

=(1.15)

with

)PW(yprobabilittransitionEPR:W MWEPREPR ∝

Fundamentals of the measurement techniques

The amplitude- ( C ) and “curve”-parameters ( TR ) are given by

a/cC =(1.16)

a/bTR=. (1.17)

The parameters a, b and c are composed of terms describing the generation and disso-

ciation rates and the recombination probability of the donor-acceptor-pairs. Since the

rates and the probability are positive, both parameters C and TR are positive as well. It

is implicit that for high microwave power the term ( WEPR·TR>>1 ) determines the

maximum EDEPR signal. For a detailed explanation of the formula the reader is re-

ferred to [Stich 1997].

The power dependence of an EPR signal can be calculated as follows:

MW2

1EPR P)

PC1

(CS +

=(1.18)

with

C1: proportional constant

C2: “curve”-parameter of the conventional EPR

PMW : microwave power.

The EPR signal grows proportionally to the microwave power at first. Yet, for relative

low PMW the signal reaches it maximum and decreases hyperbolically proportional to

1/PMW with further increasing microwave power. Compared to the EDEPR signal a

totally different microwave power dependence is detected for the EPR signal. The

power dependence of an EPR and an EDEPR signal is illustrated in figure 1.3.

An further, important difference between EPR and EDEPR is the “active” measurement

volume of the sample. For EPR defects in the whole ( “bulk” ) sample contributes to the

recorded signal. According to investigations by Stich only a layer with a depth of ap-

prox. 5µm from the surface is measured [Stich 1997]. The measurement layer thickness

is limited by the penetration depth of the above-band-gap light needed for the creation

of excess charge carriers in the sample at low temperatures.

To determine the lowest number of spins detectable with EDEPR Stich performed

measurements of phosphorous donors in a Cz-Si sample [Stich 1997]. The results

Fundamentals of the measurement techniques

yielded an absolute number of N = 4·107 spins. A comparison with the theoretical lower

limit of spins detectable in EPR of N = 1011 spins ( assuming 1cm3 sample vol-

ume )[Spaeth 1992] reveals the significantly higher sensitivity with respect to the defect

concentration of EDEPR over EPR.

Several different defect systems have been studied with EDEPR in the group of Prof.

Dr. J.-M. Spaeth and the mechanism of the method has been investigated as well. For

example it was found that the donor-acceptor recombination rate R0 is correlated with

the EPR transition probability WEPR according to EPR0WR ∝[Stich 1997]. Further, the

EDEPR signal intensity is dependent on the recombination rate R0. This donor-

acceptor-recombination model established by Stich was developed for middle to low

defect concentrations ( 1016−1013 )cm−3. For samples with high defect concentrations

( >1018 )cm−3 a high vicinity between the defect centres ( donors and/or acceptors ) ap-

pears. A different conduction mechanism is found which is described as hopping con-

ductivity. The mechanism responsible for the spin dependent charge transport at high

defect concentrations was studied by Grasa-Molina [Grasa-Molina 2000]. As an impor-

tant result an increase of the conductivity, ∆σ/σ>0, was observed for EDEPR in the

range of hopping conductivity.

Fig. 1.3 Schematic illustration of the EPR and EDEPR signal dependence on the

microwave power. For the EDEPR signal a donor-acceptor-pair recombina-

tion according to Stich is assumed [Stich 1997]. The max. microwave power

is PMWmax = 400mW.

Fundamentals of the measurement techniques

As an important result of the studies it is noted that no quantitative analysis of defect

concentrations can be performed on the basis of EDEPR measurements, even though a

few publications have stated otherwise. In the final chapter of this work results of

EDEPR measurements of several samples containing relative low defect concentrations

( 1011−1015 )cm−3 are presented. The results are discussed in order to reveal the mecha-

nism of the spin-dependent process. The findings indicate that a donor-acceptor-pair

recombination as proposed by Stich gives rise to the recorded magnetic resonances

[Stich 1997].

1.3.2 Experimental setup for EDEPR

In contrast to the setup for conventional EPR no sensitive devices for the detection of

the absorbed microwave quanta is needed. Instead, the EPR effect is detected via the

change of conductivity of the sample. Therefore a voltage is applied across the sample

in a manner, that the resulting current through the sample is constant. The sample volt-

age is amplified and analysed using a lock-in amplifier combined with modulation of

either magnetic field, microwave power amplitude or microwave frequency. Thus, the

conductivity change can be detected easily. Except for samples with a very high con-

centration of defects an illumination of the specimen is necessary in order to create ex-

cess charge carriers. This is usually done with above-band-gap light by using a halogen

or Hg-high-pressure lamp.

Fig. 1.4 Schematic diagram of the setup for detection of a conductivity change via

current-voltage measurement. Above-band-gap light is needed at low tem-

perature to create excess charge carriers.

Fundamentals of the measurement techniques

A simple setup for this purpose is outlined in figure 1.4. In the case of a sample con-

sisting of a p/n junction the conductivity change can also be detected by measuring the

voltage across a resistor being attached to the sample contacts. For the latter method

above-band-gap excitation light is needed to generate the photo-voltage.

Electrical contacts on the sample surface are needed. These should show an Ohmic I/U

characteristic and a low contact resistance even at low temperatures. The preparation of

the contacts can be carried out either by evaporation of a suitable metal ( Al, Pb or Ti

for n-type-silicon and Pt for p-type silicon ) onto the cleaned surface or by applying

aluminium to the sample mechanically [Langhanki 1996].

1.4 Fourier Transform Infrared Spectroscopy ( FTIR )

To determine the concentration of defects in solids the method of infrared absorption

spectroscopy is used often. Several disadvantages of the conventional, dispersive

method in the infrared spectral range have led to the development of the Fourier Trans-

form Infrared Spectroscopy ( FTIR ). The basis of this method and its setup are de-

scribed briefly below.

When performing infrared absorption measurements to characterise defects in semicon-

ductors two absorption processes have to be distinguished: whether they are caused by

phonons or electrons. The phonon absorption ( vibration of atoms or molecules ) was

used to determine the concentration of interstitial oxygen and substitutional carbon in

silicon in this work. The electronic absorption lines arising from the transition of an

electron from ground to an excited state, for example, give information about the con-

centration of certain defects investigated in this work ( Thermal Donors, TD and Shal-

low Thermal donors, STD ).

In the case of light being transmitted through a material with the thickness dx its inten-

sity I is reduced by

dI = −

dx I. (1.19)

The absorption coefficient

is depending on the material and is of the dimension of

m−1. Upon integration the intensity decrease by a thickness of the material of x results in

I(x) = I(0)·exp(−

x). (1.20)

Fundamentals of the measurement techniques

The transmission T is given by the fraction of the transmitted light as follows

)0(

)(

T=. (1.21)

Consequently, prior to recording the IR spectrum of the sample a background spectrum

with an empty sample holder has to be recorded.

The value of the noise level appearing between the absorption lines in the spectrum is

usually lower than a value Tmax given for a certain material. Therefore a constant value

for the background absorption

) has to be subtracted from the measured spectrum

in order to gain the absorption

) caused by the defects.

) =

(

) -

) (1.22)

In the case of a known capture cross section

opt for the absorption process the concen-

tration NT of the defect can be derived as follows:

K)(

)(

opt

T⋅==

να

νσ

να

. (1.23)

In literature, the calibration factor K is often given instead of the optical capture cross

section, being the inverse of the latter.

The method of Fourier Transform IR measurement makes use of the interference of two

light beams in an interferometer. The light from a special broad band IR source is re-

flected and transmitted with 50% each at a beamsplitter. After reflection of the beam at

mirror M1 ( fixed ) and mirror M2 ( movable ) an interference pattern occurs at the IR

detector. The intensity I(x) of the interference pattern depends on the position of the

mirror M2. A schematic setup for FTIR is given in figure 1.5. With the help of Fourier

transform, the desired spectrum S(

) can be derived from the interference function I(x).

As the whole spectral range is recorded in the measurement process simultaneously, the

total measurement time is reduced greatly ( “multiplex-advantage” ).

To investigate the above mentioned defects the existing Bruker IFS28 FTIR spec-

trometer had to be modified to enable measurements at low temperatures. A Leybold

cryostat for continuous helium flow was used, allowing temperatures down to T=6K.

Special care had to be taken selecting the cryostat windows as these have to transmit in

the infrared spectral region, thus ZnS material was chosen.

Fundamentals of the measurement techniques

The spectral range of the instrument is limited to ( 7500–500 )cm−1, due to the window

material ( ZnS ) of the implemented cryostat, with a spectral resolution of 1cm−1. KBr

with a multilayer coating is used as the beamsplitter. The temperature available is be-

tween 6K and 400K and controlled by an Oxford DTC2. For measurements in which the

absorption lines of water vapour in the air could superimpose the desired signals the

whole measurement chamber and light path can be evacuated. A special feature of the

used FTIR spectrometer can be found in a second interferometer implemented in the

apparatus, used to determine the position of the moveable mirror M2 precisely

( ∆x ≈ 5nm ) and reproducibly. This feature is called “Connes-advantage”.

Fig. 1.5 Simplified block diagram of the setup for a Fourier Transform Infrared Ab-

sorption spectrometer FTIR.

Fundamentals of the measurement techniques

Advances in EDEPR technology

Chapter 2

Advances in EDEPR technology

The electrical detection of EPR has been discovered over three decades ago as outlined

in chapter 1.3. Nevertheless, little attention has been paid to this method for a long time

and consequently the development of special features in this context, making use of the

advantages of the electrical detection, has been neglected. Only few studies have been

published dealing with different approaches to EDEPR [Woisinski 1976,

Szkielko 1978]. In this work the attempt has been made to combine recent develop-

ments in EPR, like the application of high microwave frequencies, with EDEPR. It will

be shown that apart from these adaptations further extensions have been developed

leading to new set-ups for the electrical detection of EPR.

2.1 EDEPR with microwave power modulation

In the majority of studies with conventional EPR or EDEPR the static magnetic field B



is modulated in order to allow the use of a lock-in amplifier. Typical modulation fre-

quencies are 100kHz for EPR and 5kHz for EDEPR, respectively. The use of magnetic

field modulation requires either metallic rods inside the microwave cavity or solenoids

outside the cavity walls. In the first case the quality factor Q is lowered. In the case of

solenoids, more space is needed inside the cryostat, that has to be placed in the limited

gap between the coils of the electro-magnet. In any case heat is transferred to the reso-

nator from outside by the electrical connections.

Using microwave amplitude modulation these problems can be avoided as neither the

rods nor the solenoids for modulation are needed. Further, when spectra consisting of

Advances in EDEPR technology

several overlapping EPR lines have to be examined, the determination of the individual

line positions can be simplified.

It is noted that all spectra presented in this chapter have been measured using white light

illumination of the sample by a halogen lamp in order to generate excess charge carriers

for the spin dependent recombination process. Further, all spectra have been recorded at

10K. The spectra are shown as examples in order to illustrate the developed EDEPR

features. A detailed study of the samples presented in figures 2.(1−3) and 2.(4−6) is

given in chapter 3 and chapter 6, respectively.

In figure 2.1 two EDEPR spectra of a silicon sample with surface defects due to the

implantation of Si- and Mo-atoms are shown. For spectrum (a) conventional sinusoidal

magnetic field modulation is used. The number of derivative lines overlapping in the

centre of the spectrum can hardly be estimated, let alone the position of the zero line

Fig. 2.1 X-band EDEPR spectra of a silicon sample with surface defects due to im-

plantation of Si- and Mo-atoms using (a) sinusoidal modulation of the mag-

netic field with 5kHz/0.1mT and (b) square-wave microwave amplitude

modulation with 0.7kHz/30dB.

Advances in EDEPR technology

crossing of the individual lines. The spectrum in part (b) is recorded applying micro-

wave amplitude modulation with an maximal attenuation of 30dB. The amplitude was

square wave ( “on−off” ) modulated and therefore an integrated EDEPR signal is ob-

tained. At least four lines can be separated and their peak position determined precisely.

In general the method of effect modulation ( for example magnetic field modulation )

resulting in a differential signal is supposed to be superior for spectral resolution to one

yielding an integrative signal [e.g. Poole 1983]. However, the present case reveals an

exception from this rule.

For spectra with several resonance lines the question occurs whether the individual lines

belong to one or several defects. In a first attempt this question can be answered by

analysing the microwave power dependence of the individual lines. If the lines behave

in a similar manner it can be assumed that their origin is the same. When regarding the

spectrum in figure 2.1(a) the investigation of the power dependence will not give any

answers about the individual signal behaviour as the lines can not be separated. Again

Fig. 2.2 Power dependent X-band EDEPR spectra of the sample presented in figure

2.1. The microwave power was reduced from 400mW to 40mW and square-

wave modulated with 0.7kHz/30dB attenuation.

Advances in EDEPR technology

the amplitude modulation is superior as the development of each signal can be traced.

An example for a power dependence taken with source amplitude modulation is given

in figure 2.2. The evaluation of the line intensities of the resolved resonances shows that

all four appear with the same microwave power dependence.

To gain structural information about a defect angular dependent magnetic resonance

measurements are performed. An angular dependence starting with the spectrum pre-

sented in figure 2.1(a) could only be interpreted using a simulation program with vari-

ous assumptions, giving rise to a high degree of uncertainty of the results. In figure 2.3

an angular dependence is shown making use of the source amplitude modulation tech-

nique. Again, certainty about the position of the individual resonance lines is achieved,

resulting in a clear pattern of the symmetry of the defect. In this case two defects with a

trigonal symmetry each can be detected.

For a further example of the benefits of EDEPR with source amplitude modulation a

silicon sample irradiated with fast electrons was examined. The spectra recorded with

Fig. 2.3 Angular dependent X-band EDEPR spectra of the sample introduced in fig-

ure 2.1. Square-wave source amplitude modulation with 0.7kHz/30dB is

used. The angles given represent the orientation of the sample surface rela-

tive to the static magnetic field.

Advances in EDEPR technology

both the conventional and the source modulation technique are given in figure 2.4. The

two dominant lines in figure 2.4(a) arise from the hyperfine splitting of 31P with an

electron-spin S = 1/2 and spin I = 1/2 of the central nucleus. Phosphorous is the shallow

dopant of this n-type silicon sample.

Next to this doublet six lines can be seen that are due the excited neutral triplet-state of

the vacancy-oxygen pair (V−O)0* , labelled SL1 in literature. [Brower 1971] The SL1

( S = 1/2 ) signal arises only after illumination of the sample giving raise to a recombi-

Fig. 2.4 X-band EDEPR spectra of a silicon sample after irradiation with fast elec-

trons using modulation of (a) magnetic field with 5kHz/0.1mT and (b) mi-

crowave amplitude with 0.7kHz/30dB ( square-wave ). The integration time

for (b) was only 30% of that needed for spectrum 2.4(a).

Advances in EDEPR technology

nation of free charge carriers at the vacancy-oxygen centre (V−O). The vacancies itself

are introduced into the crystal by irradiation with fast electrons. Further lines appearing

shall not be of interest here and are explained in detail in [Stich 1997]

Remarkable for the spectrum 2.4(b) is the short integration time ( one third ) compared

to the one needed to record the spectrum in 2.4(a). In spite of the shorter measurement

time more details are resolved such as the SL1-hyperfine satellite lines. They are caused

by the hyperfine interaction of the SL1 electron spin S = 1 with the nuclear spin I = 1/2

of the 29Si atoms which are present in the crystal with a natural abundance of 4.7%.

It is not directly apparent why the method of source amplitude modulation is more ef-

fective than the sinusoidal magnetic field modulation ( effect modulation ). From

ENDOR measurements it is known that a square-wave modulation of the radio-

frequency is superior to a modulation with a sine function [Spaeth 1992]. The advantage

arises from the fact that the square-wave’s fundamental Fourier component, as detected

by a lock-in amplifier, is higher by about 30% than its amplitude. This results in a 30%

signal improvement, a value in good agreement with the one obtained in this work for

EDEPR.

For magnetic field modulation it is known that with the use of modulation amplitudes

higher than the line-width a broadening of the respective line will occur [Poole 1983].

However, this is not the case for source amplitude modulation. Hence, the modulation

amplitude can be increased significantly to improve the signal-to-noise ratio.

2.2 EDEPR with high microwave frequencies

In recent years great efforts have been undertaken to increase the microwave frequen-

cies used to measure EPR. In spite of the difficulties in the technique of the microwave

generation, guidance and control and the dimensions of the utilised microwave cavity

decreasing proportionally to the increasing frequency, the benefits are on hand. With

respect to equation 1.11 the use of high frequencies enables the separation of resonance

lines being only distinguishable by small differences of their g-value. Many spectra

known for their overlapping EPR lines when measured in the most commonly used X-

band ( 8-12 )GHz frequency region were resolved clearly after investigation with high

frequencies and corresponding high magnetic fields.

So far EDEPR measurements were exclusively performed with X-band microwave

sources except for tests with low frequency / low field EDEPR. The latter clearly

Advances in EDEPR technology

showed the frequency independence of the EDEPR effect but could not, of course, im-

prove the resolution of details.

For this work the setup needed for EDEPR was transferred to a K-band ( 25GHz )

spectrometer, providing an advantage in spectral resolution by a factor of 2.5. A spec-

trum of a Cz-Si sample after electron irradiation and heat treatment ( 30min / 450°C )

measured at 25GHz is presented in figure 2.5.

The dimensions of a microwave cavity used for K-band frequencies are 15mm diameter

and a length of 13 mm, generally spoken. Mounting the rods for magnetic field modu-

lation and even more to insert a sample with dimensions of several millimetres into such

a small cavity decreases often the quality factor Q of the cavity. In the case of EDEPR

where thin wires are needed to electrically connect the sample contacts even more mate-

Fig. 2.5 K-band ( 25GHz ) EDEPR spectra of a silicon sample after electron irradia-

tion and heat treatment ( → shallow thermal donor, STD ). Sinusoidal

modulation of the microwave frequency was used in an experimental set-up

without a microwave resonator. The resonances appearing between

( 874−882 )mT are depicted in more detail in figure 2.6.

Advances in EDEPR technology

rial with high conductivity is inserted into the resonator, which can lead to a complete

loss of its resonant characteristics. The only way to proceed was to get rid of the cavity

together with the adjacent modulation rods and to place the end of the microwave

waveguide directly in front of the sample. For the spectrum in figure 2.5 a modulation

of the microwave frequency was applied, making use of a sinusoidal variation of the

reflector voltage of the employed Varian microwave clystron.

A further idea of these experiences was to transfer the EDEPR equipment to a V-band

( 72GHz ) spectrometer, especially, as EDEPR measurements at frequencies as high as

72GHz have not been reported so far. The result of the implementation of this idea is

Fig. 2.6 V-band ( 72GHz ) EDEPR spectrum of a silicon sample after electron irra-

diation and heat treatment. The dominating two lines are arise from 31P. The

high field 31P-line superimposes one of the four lines of an anisotropic oxy-

gen precipitation centre. The latter could not be resolved with K-band fre-

quency ( 25GHz ) and the selected resonance lines are identical to those ap-

pearing in figure 2.5 in the range of ( 874−882 )mT. The orientation of the

sample is B



|[011]+20°. The spectrum was recorded using a modified high-

field ODMR set-up without microwave resonator and with illumination of

the sample. The microwave power was square-wave modulated with 30dB

attenuation and a frequency of 500Hz.

Advances in EDEPR technology

displayed in figure 2.6. The sample already investigated in K-band ( figure 2.5 ) was

used to show the resolution enhancement by the application of high microwave fre-

quency. The two lines dominating the spectrum are due to the hyperfine splitting of the

shallow dopant 31P ( I = 1/2 ). As the hyperfine splitting does not change with the mi-

crowave frequency the 31P lines are ideal calibration peaks as their g-factor

( g=1.99850 ) is known precisely as well [Feher 1959]. With the help of the 31P lines

and the obtained spectral resolution the principal values of the g-tensor of the defect can

be determined with high precision.

In summary it has been shown that the electrical detection of EPR can be applied in a

versatile manner, making use of various modulation techniques and microwave fre-

quencies.

Advances in EDEPR technology

EDEPR-investigations of implanted and heat-treated FZ-silicon

Chapter 3

EDEPR investigation of implanted

and heat-treated FZ-silicon

In the following chapter the results of magnetic resonance studies of silicon samples

after implantation of molybdenum (Mo) and silicon (Si) atoms are presented. The strong

resonances detected with EDEPR at low temperatures were attributed to Mo-atoms at

first sight. After detailed consideration of both the determined g-factors and the forma-

tion kinetics of the resonance lines this explanation had to be revised. The obtained

spectra can be explained by Si/SiO2 interface defects and dangling bond centres within

the silicon bulk material.

The well known resonance lines of interface defects obtained by room temperature EPR

measurements, called Pb-centres in the literature, are generally attributed to one defect

centre. However, investigations by Stathis et al. already indicated that two independent

defect centres, called Pb0 and Pb1, should be the origin of the signals occurring on (100)

oriented Si/SiO2 interfaces [Stathis 1994].

Two separate defect centres can clearly be distinguished by EDEPR at low temperatures

in this study. One of them is very similar to the Pb0-centre reported in the literature and

an identification is tempting, whereas the other centre is detected for the first time. An

explanation of the resonances due to two dangling bond centres at and below the tech-

nologically important (100) Si/SiO2 surface is given and the results are critically com-

pared with those reported in the literature.

In this chapter no detailed discussion of the EDEPR mechanism responsible for the de-

tection of the dangling bond resonances is presented since in a later chapter the EDEPR

mechanism will subject of the investigations.

EDEPR-investigations of implanted and heat-treated FZ-silicon

3.1

Motivation for Mo-implantation into silicon samples

In order to dope FZ-silicon with the intention to generate shallow acceptors ( p-type

silicon ) boron is generally added to the melt during the silicon crystal growth process.

For acceptor-doping during device fabrication boron is implanted into the device. Since

boron is a rather small atom the penetration depths are large. This rules out the method

for multiply stacked, state-of-the-art thin layers, where separate layers have to be doped

individually. A procedure to avoid the penetration of boron through several layers was

found by complexing it with fluorine (F) to BF2 prior to implantation. Both the size and

the weight of the BF2 greatly reduce the implantation penetration depth to a few hun-

dred Å. Annealing procedures after implantation are used to dissociate the molecule and

to out-diffuse the fluorine, resulting in a boron doping of the specific layer.

Unfortunately, high molybdenum concentrations up to 1018cm−3 were found by secon-

dary ion mass spectroscopy ( SIMS ) in devices prepared this way. Molybdenum is a

strong minority lifetime killer in silicon, forming an electrically active deep level at

EV+0.31eV and thus acting as a powerful recombination centre [Rohatgi 1980][Ghandhi

1983]. Moreover, molybdenum has been characterised as a fast diffuser, with a diffu-

sivity in the range of 10−8cm2/s at elevated temperatures [Tobin 1985]. This makes it a

dangerous contaminant, particularly in devices requiring long minority carrier lifetimes

such as bipolar transistors and solar cells. The explanation for the Mo-contamination

can be found in the coincidence of the charge-to-mass ratio for doubly ionised 98Mo2+

and the 11B19F2+ molecular ion. Thus, the molybdenum ion is not filtered out by the

mass analyser magnet of the implantation set-up and the element is co-implanted.

With the intention to study the effect of molybdenum in silicon, p-type FZ-silicon sam-

ples ( boron-doped, n(B)=2·1015cm−3 ) were implanted with molybdenum at 50keV and

a density of 1.3·1011cm−2. The projected penetration depth for the Mo-atoms is 350Å

[Michel 2000] according to calculations with a program called “TRansport of Ions in

Matter”, TRIM. In the TRIM program the energy dependence of stopping powers for

each element is given as a data base, and the main fitting parameter is the density of

silicon. Selected samples were implanted with Si-atoms with various energies addition-

ally and others were annealed after the implantation. The samples were provided by Dr.

J. Michel from the MIT, Cambridge, MA, USA.

EDEPR-investigations of implanted and heat-treated FZ-silicon

3.2

EPR of Mo- and Si-implanted and annealed FZ-silicon

In figure 3.1 EPR spectra of a silicon sample implanted with molybdenum and annealed

at 838°C for 10h are shown. The spectra were recorded using two microwave frequen-

cies of 9.8GHz and 25.0GHz, respectively. In each spectrum a single, weak resonance

line is detected. Angular dependent measurements revealed an isotropic behaviour of

the line with a g-factor of 1.9984±0.0004. The angular dependence showed particulari-

ties regarding the line-shape which have been called “breathing behaviour” in the lit-

erature, being a cyclical broadening of the linewidth upon rotation of the sample

[Wörner 1985]. Both, the change of the line-shape and the isotropic g-factor indicate an

identification of the observed resonance with the so-called New Donors ( g=1.9984 ),

arising after heat treatment at high temperatures ( 550−800 )°C [Suezawa 1983]. In the

literature the resonance has been associated with a superposition of several resonances

Fig. 3.1 EPR spectra of a FZ-silicon sample after molybdenum-implantation and

annealing at 837°C for 10h. The spectra were recorded at 10K with X-band-

( upper curve ) and K-band-frequency ( lower curve ). Illumination of the

sample showed no change of the spectrum in both cases.

EDEPR-investigations of implanted and heat-treated FZ-silicon

after annealing being due to interface traps at Si/SiOx interfaces as they occur in amor-

phous environment [Hölzlein 1984]. In the present case such interfaces and amorphous

regions in the silicon crystal are most likely to appear after the implantation of molyb-

denum or silicon atoms.

It is noted that the resonances presented in figure 3.1 are directly related to the anneal-

ing process and did not occur without it. However, they appeared with increased signal

intensity for samples which had been implanted with Si or Mo prior to annealing.

3.3 EDEPR of Mo- and Si-implanted and annealed FZ-silicon

As no further information about molybdenum in silicon could be gained by EPR meas-

urements EDEPR was applied to investigate the samples. Ohmic contacts were fabri-

cated on the implanted side of the specimen and illumination with white light from a

halogen lamp was used on this sample side to create excess charge carriers at low tem-

peratures. In figure 3.2 four EDEPR spectra recorded with identical integration times

for the entire spectrum are shown.

Spectrum 3.2.a is obtained from a non-implanted FZ-silicon sample which has been

annealed at 838°C for 30min. It has been magnified by a factor of 10. The samples for

spectra 3.2.b ( magnified by a factor of 5 ) and 3.2.c were implanted with silicon atoms

( 22keV, 1.3·1013cm−2 ) and molybdenum atoms ( 50keV, 1.3·1011cm−2), respectively,

and subsequently annealed at 838°C for 30min and 10h, respectively. The spectra 3.2.a–

c show a striking similarity of both the line shapes and positions of the resonances.

Only the spectrum in 3.2.d, obtained from a sample after Mo- ( 50keV, 1.3·1011cm−2 )

and Si-implantation ( 7MeV, 4·1014cm−2 ), and annealing at 838°C for 5h after each

implantation step, shows differences. The spectrum reveals clear changes in line shape

after the implantation of high-energy Si-atoms by new resonances superimposing the

precedent group of resonance lines. The change in line-shape is most probably due to an

increased damage after the implantation of the Si-atoms and will be discussed later.

In the spectra of Mo-implanted samples resonances lines of Mo should appear corre-

sponding to the natural abundance of approximately 25.5%, taking into account the

isotopes 95Mo( 15.9% ) and 97Mo( 9.6% ). Though both isotopes show a nuclear spin of

I=5/2 no hf structure could be detected. As can be seen clearly in figure 3.2.b the same

group of superimposed resonance lines found in the Mo-implanted sample appears in

the spectrum of a Si-implanted one as well. Especially remarkable is the appearance of

EDEPR-investigations of implanted and heat-treated FZ-silicon

this group of lines in the specimen exclusively annealed. Therefore, an identification of

these lines with resonances due to Mo-atoms must be ruled out.

Taking into account the g-factors and the presence of the detected resonance lines even

in nominally non-implanted samples leads to the family of intensively studied and yet

controversially discussed surface defects, also known as “dangling bonds”, dislocation

Fig. 3.2 EDEPR spectra of FZ-silicon samples after

a) annealing at 838°C for 30min,

b) implantation of Si-atoms ( 22keV) and annealing at 838°C for 30min,

c) implantation of Mo-atoms ( 50keV) and annealing at 838°C for 10h,

d) impl. of Mo- and Si-atoms ( 50keV / 7MeV ) and ann. at 838°C for 10h.

The samples were illuminated with white light and a sample current of 5µA

was applied. The spectra were recorded in X-band at T=10K using magnetic

field modulation ( 5kHz ) for an sample orientation of B

||011].

EDEPR-investigations of implanted and heat-treated FZ-silicon

or interface centres. The commonly used abbreviation for these defects is “Pb-centres”.

It has been established that they appear at Si/SiO2 interfaces which not necessarily have

to be located within the volume of a specimen but can also can be found at the surface

of the specimen. The “omnipresence” of the Si/SiO2 interface defects can be explained

by the fast oxidation of a pure silicon surface to SiO2 with a thickness of SiO2 of 24Å in

24h after exposition to air even at room temperature [Archer 1957].

The dangling bonds at the (111)-oriented Si/SiO2 interface were detected first and are

labelled Pb-centres. Room temperature EPR and photo-conductive resonance ( PCR )

have been widely used to investigate the structure of the Pb-centres [Poindexter 1978]

[Brower 1986] [Cantin 1995]. The paramagnetic centre giving rise to the Pb resonances

is shown in figure 3.3. It is apparent that it shows axial symmetry along a [111] direc-

tion. The paramagnetism is supposed to arise from an unpaired electron localised in a

dangling bond silicon hybrid orbital of a Si-atom being bonded covalently to the three

lower Si-atoms. These dangling bonds are also made responsible for charge trapping at

the interface [Lenahan 1982].

At (111) Si/SiO2 only the single variety Pb-centre of a dangling bond defect arises. Be-

cause of it’s relative simplicity, the majority of fundamental research about defects at

the Si/SiO2 interface has been carried out at the (111) surface. Therefore, the knowledge

about this Pb centre is quite detailed.

However, for semiconductor integrated circuits the (100) surface is the preferred one.

As the dangling bond defect structure appears to be more complicated for the (100)

Si/SiO2 interface the experimental results have been discussed controversially and the

understanding is incomplete. Two resonances have been presented forming at this inter-

face, called Pb0 and Pb1. They appear with g-values of g=2.0060 and g=2.0032, respec-

Fig. 3.3 Model of the Pb-defect occurring at (111) Si/SiO2 interfaces after Poindexter

et al. [Poindexter 1981].

EDEPR-investigations of implanted and heat-treated FZ-silicon

tively, for a sample orientation of B

||[110] [Poindexter 1981][Stathis 1991]. The pre-

cise structure of the responsible defects and the relation to the Pb centre at the (111)

surface has not yet been clarified.

In search of the origin of the Pb0 resonance Stathis and Dori proposed either a defect

being fundamentally different from a dangling bond, or a dangling bond lying deeper

inside the bulk silicon material away from the interface [Stathis 1991]. An atomic

model of the proposed structure of Pb0 and Pb1 at the (100) Si/SiO2 interface is dis-

played in figure 3.4. It is recalled that at the (111) interface only one type of dangling

bond arises with an axial symmetry. For samples oriented with a (100) plane at least

two different dangling bond structures have been proposed. Both show axial symmetry

about the (111) direction. The Pb1 centre is supposed to arise directly at the Si/SiO2 in-

terface whereas the Pb0 is located below the interface. By the observation of different

reactions on treatment with atomic hydrogen on the Pb0 and Pb1 at the (100) Si/SiO2

interface strong indications were presented arguing against a single origin for both cen-

tres [Stathis 1994]. So far, the (100) interface had been studied with EPR with magnetic

field modulation. The resulting resonances with differential line-shapes are strongly

overlapping, inhibiting a detailed investigation of the individual resonances.

It is noted that no EDEPR resonances of these Pb-defects could be measured at room

temperature in this study. Experiments were carried out with modulation frequencies up

to 100kHz with and without above-band-gap illumination. It seems that the EDEPR

effect is not observable at room temperature because of spin dependent recombination

times being too fast to be influenced by the available microwave power, i.e. spin flip

Fig. 3.4 Model of the Pb0 and Pb1 defects occurring at (100) Si/SiO2 interfaces after

Poindexter et al. [Poindexter 1981].

EDEPR-investigations of implanted and heat-treated FZ-silicon

rates. Experiments using conventional X-and K-band EPR were not successful with

respect to the dangling bond resonances since the total number of these paramagnetic

centers was not high enough in the available samples. It is recalled that the minimum

absolute number of paramagnetic centres needed for the detection of EPR is N = 1011

[Spaeth 1992]. As a consequence, the number of present Pb-centres is estimated to be

lower than this value. The detection of the Pb-centres with EDEPR at low temperatures

underlines the higher sensitivity regarding the defect concentration of this method.

The findings are supported by taking into account the generally excepted value of a Pb-

centre density of 1012cm−2 for samples annealed in oxygen atmosphere [Caplan 1979].

The samples investigated in this work have been annealed in an inert atmosphere ( Ar )

and their surface area is approx. 0.1cm2 only. Consequently, the total number of inter-

face defects is smaller than N = 1011. The value is too low for EPR but sufficient for

EDEPR as confirmed by the experimental results.

Fig. 3.5 EDEPR spectra of a FZ-silicon sample after implantation of Mo- and Si-

atoms ( 50keV / 7MeV ) and annealing at 838°C for 10h. The sample was

illuminated with white light and a sample current of 5µA was applied. The

spectra were recorded in X-band at T=10K using a) square wave microwave

amplitude modulation with 700Hz/30dB attenuation and b) magnetic field

modulation ( 5kHz ). A further set of spectra is shown in figure 2.1.

EDEPR-investigations of implanted and heat-treated FZ-silicon

Various procedures were used to increase the absolute number of Pb-centres to enable

their detection with EPR. Some authors prepared porous silicon layers with a thickness

up to 120µm, hence containing a large number the interface defects [e.g. Mao 1993].

Others stacked together up to 35 samples to increase the investigated Si/SiO2 interface

area up to 30cm2. The defects at the interface were prepared by long-term annealing in

O2 atmosphere at 900°C [e.g. Brower 1983].

In the present case the samples with Mo-implantation had been oriented with a (100)

surface. Thus, they are candidates for the investigation of the Pb0 and Pb1 centres at the

(100) Si/SiO2 interface. In figure 3.5 two spectra from a sample after Mo- and Si-

Fig. 3.6 EDEPR spectra of a FZ-silicon sample after Mo- and Si-implantation with

50keV and 7MeV, respectively. Annealing steps were carried out at 838°C

for 5h after each implantation. Microwave power modulation ( 700Hz ) was

used in X-band at 10K. The sample was rotated in a )110( –plane, the rota-

tion angle being limited to 65° by the necessity of sufficient illumination of

the sample surface with white light.

EDEPR-investigations of implanted and heat-treated FZ-silicon

implantation and annealing are shown. Spectrum 3.5 (b) is recorded using conventional

magnetic field modulation ( 5kHz ) whereas for spectrum 3.5 (a) a square-wave modu-

lation ( 700Hz/30db ) of the microwave power amplitude as described in chapter 2 was

applied. The spectrum 3.5 (a) shows the high signal-to-noise ratio and an increased

spectral resolution of this EDEPR technique.

In figure 3.7 angular dependent EDEPR spectra of the sample presented in figure 3.5.a

are given. The pattern was obtained by rotation of the sample in a )110( -plane from

||[011] towards B

||[100]. Next to the three dominant resonance lines placed centrally

in the spectra a further group of resonances can be detected. The latter appears with re-

duced intensity and a larger anisotropy. It lies centrally below the dominant lines. In

comparison with the spectra published so far the obtained resolution is significantly

higher and this second group of lines is detected for the first time. For clarification rea-

sons the dominant group of lines will be labelled Pba whereas the underlying one will be

referred to as Pbb in the following. The angular dependence of the detected resonances

can be simulated assuming a [111] threefold axially symmetric g-tensor. The resulting

g-factors are given in table 3.1. The intensity ratio between the two defects was esti-

mated to 3:1 from the EDEPR lines. In figure 3.7 both the experimental data points ob-

tained from the angular dependent EDEPR spectra ( figure 3.6 ) and the results of cal-

culations using trigonal symmetry ( solid lines ) are given.

Centre g|| g⊥Refs.

Pba on (100) 2.0008 2.0098 this work

Pbb on (100) 1.9974 2.0160 this work

Pb at Si/SiO22.0012 2.0081 Caplan 1979

Pb at Si/SiO22.0013 2.0090 Stesmans1986

Porous Si 2.0023 2.0090 Mao 1993

Table 3.1 Values of the g-factors of dangling-bond-related paramagnetic defects

(S=1/2) investigated in this work (∆g ||/⊥= ±0.0004) and compared to those

of several related centres published previously.

EDEPR-investigations of implanted and heat-treated FZ-silicon

From the rotation pattern it can be derived that the axial directions of the dangling

bonds are distributed in all the four [111] crystal axes of the original silicon lattice. Re-

suming the results so far, both centres, Pba and Pbb, can be attributed to dangling bonds

located in silicon or at the (100) Si/SiO2 interface. The difference in origin of the two

centres is not apparent, yet.

The intensity of the dominant group of resonance lines, Pba, is significantly enhanced

after the implantation of fast Si-atoms only. The implantation of low-energy Mo-atoms

increased the broader Pbb signal already being present after annealing of the sample. All

Fig. 3.7 Experimental ( open squares and circles ) and theoretical ( solid lines ) rota-

tion patterns of the EDEPR angular dependent spectra presented in figure

3.6 ( microwave amplitude modulation ). The rotation takes place in a

)110(

plane. The spin Hamilton-parameters used for the calculation of the

solid lines are given in table 3.1.

EDEPR-investigations of implanted and heat-treated FZ-silicon

samples have been chemically polished with acids containing HF. This procedure is

known to give rise to dangling bond related resonances, which can be intensified by

subsequent annealing [Mendz 1980]. Further, the projected range of 50keV Mo-

implantation was estimated to be 340Å by TRIM calculations, whereas the correspond-

ing value for 7MeV Si-implantation is calculated to 3.5µm.

Since the depth of the “active” measurement layer in the case of EDEPR is approxi-

mately 5µm ( the penetration depth of the above band gap light ), the implantation with

an impact reaching further below the surface will increase the EDEPR signal. This sup-

ports the assumption of the Pba center being caused by the implantation of the high en-

a) b)

Fig. 3.8 Suggested models for the dangling bond defects detected in this work at and

below a (100)Si/SiO2 interface. Two of the four possible sites of the Pba–

centre in the bulk material are depicted in a). In b) one of the four possible

sites of the Pbb-centre at the Si/SiO2 interface is shown. To simplify the

understanding only two additional oxygen atoms, indicating the SiO2 part of

the crystal, are inserted in b). The arrows pointing along [111] direction

indicate the dangling bonds due to Si-vacancies. It is noted that the Si-lattice

is rotated by 90° about the [100] axis for b) respective to a).

EDEPR-investigations of implanted and heat-treated FZ-silicon

ergy Si-atoms. It also explains the weakness of the EDEPR signal detected after an-

nealing only or low energy implantation. In figure 3.8 selected sites are shown of the

suggested structures of Pba- and Pbb-centres in a silicon crystal oriented along [100].

The presence of dangling bonds implies the presence of vacancies ( VSi ) in the lattice

which are created by the implantation. It is known for n-type silicon samples that the

VSi heal out even at room temperature. Thus it is to question why dangling bonds are

observable after long term annealings at high temperatures as found in this study. It is

noted that the sample used in this investigation was boron-doped with a concentration of

n(B)=2·1015cm−3. For similar samples Awadelkarim et al. observed a high thermal sta-

bility of radiation defects ( dangling bond type ) even for long term annealings at 400°C

[Awadelkarim 1989]. Their results indicated that the defects are trapped by boron which

a) b)

Fig. 3.9 Room temperature X-band EPR spectra of Pb-centres at the (100) Si/SiO2

interface. In a) spectra of the Pb-centres after various preparation steps pub-

lished by Stathis et al. are shown [Stathis 1991]. In b) three spectra of the

Pb-centre studied by Mao et al. are given depicting the main crystallographic

orientations [Mao 1993].

EDEPR-investigations of implanted and heat-treated FZ-silicon

can explain the observation of the Pba and Pbb centres in this study.

When comparing the two atomic models of the Pba and Pbb centres presented in figure

3.8 their similarity in structure is obvious. Both are of tetrahedral form and consist of

four silicon atoms on their regular lattice sites. However, a significant difference in ani-

sotropy is found for Pbb and Pba. The increased anisotropy for Pbb can be explained by

the strongly distorted crystal field in the Si/SiO2 interface. For examples reconstructions

of the silicon crystal occur at this interface which can show a strong mismatch of the

lattice parameters. Since the g-value is strongly influenced by the crystal field, the per-

turbed surrounding of the Pbb, compared to the idealised perfect cubic one of the Pba, is

responsible for the increased g-factor anisotropy.

There is only a very limited number of publications with values for g-factor anisotropy

of the dangling bonds centres. The reason is probably the poor signal-to-noise ratio of

the spectra recorded at Si/SiO2 interfaces. Nevertheless, the values available are in the

range of g⊥= (2.0012−2.0023) and g||= (2.0081–2.0090) [Caplan 1979][Stesmans

1986][Mao 1993], thus the data obtained for Pba in this work are in good agreement

with those published so far.

In the work of Mao et al. crystalline silicon was heavily anodised in strong HF solu-

tions in order to create porous silicon layers of a thickness up to 120µm. Their room

temperature EPR measurements revealed a weak dangling bond signal, which was at-

tributed to a trigonally symmetric angular pattern after decomposition and computer

simulation. The resonances were supposed to arise from crystalline phase particles

within the porous layer. The Si-surface/interface structure prepared by Mao et al. is

probably comparable to the one created by high-dose high-energy implantation. There-

fore, because of the good agreement between the g-values presented by Mao et al. and

this work ( see Tab. 3.1 ) an identification of both centres with Pb0 is tempting.

Spectra of Pb-centres obtained in this work with those presented in literature shall be

compared, selecting the works of Stathis and Dori and Mao et al. Both groups have car-

ried out room temperature EPR measurements and find dangling bond related signals. In

figure 3.9.a EPR spectra of the two centres Pb0 and Pb1 detected by Stathis and Dori are

shown for an orientation of B

||[100]. No details about an angular dependence of the

resonances are given by the authors. The g-factor of 2.0060 determined by Stathis et el.

for B

||[100] is very close to the one presented in this work for the Pba centre, g=20062.

From the EPR spectra presented in figure 3.9.b by Mao et al. determined a trigonal

symmetry of the g-tensor. The signal-to noise ratio and the spectral resolution are poor

EDEPR-investigations of implanted and heat-treated FZ-silicon

in both publications, but the spectral range of the group of resonances in both publica-

tions is comparable with the one of the Pba centre of this work.

In summary the simultaneous detection of two trigonal dangling bond centres at and

below a (100) Si/SiO2 interface is reported for the first time. It is noted that the detected

dangling bond centre Pba is very similar to the Pb0 defect reported in the literature

[Caplan 1979][Stesmans 1986][Mao 1993]. The Pb0 centre is related to implantation

damage below the Si/SiO2 interface, leading to dangling bonds within the bulk material.

When assuming a positive identification of Pba with Pb0 the result underlines the obser-

vation that the Pb0 centre is generated by particle radiation [Vranch 1988]. However, the

identification of the Pba centre found here with the known Pb0 center must remain

somewhat speculative.

The more anisotropic Pbb centre can be attributed to dangling bonds at the (100) Si/SiO2

interface, occurring after annealing or low energy particle implantation. The EDEPR

signal of the Pbb centre can be increased by annealing in an oxygen containing atmos-

phere. The Pbb centre has been detected for the first time due to the increased sensitivity

and low noise figure of low temperature EDEPR measurements.

EDEPR-investigations of implanted and heat-treated FZ-silicon

Oxygen related defects in silicon

Chapter 4

Oxygen related defects in silicon

The need to understand the behaviour of oxygen impurities in silicon is caused by the

requirements of device fabrication. Infrared absorption measurements have shown that

isolated oxygen atoms occupy interstitial sites in the lattice. Their absorption lines en-

able the estimation of the oxygen concentration in the specimen. After heat treatment

cycles oxygen precipitation has been observed by several methods ( EPR, ENDOR,

DLTS, FTIR, PTIS ). The defects created as a consequence of heat-treatment are called

thermal donors in general. According to the temperature and duration of the annealing

different families of thermal donors can be distinguished. Annealing at high tempera-

tures ( T ≥ 600°C ) gives rise to the so called “New Donors” ( ND ). At intermediate

temperatures ( 450°C ≤ T ≤ 550°C ) the most prominent oxygen clusters develop which

appear with a double donor characteristic and are called “Thermal Double Donors”

( TDD ). After long term annealing at these intermediate temperatures, oxygen clusters

labelled “Shallow Thermal Donors” ( STD ), which can be singly ionised, develop ad-

ditionally.

Several elements which can be present in or added to the crystal have been investigated

regarding their interaction with oxygen. Some of these elements enhance the formation

of oxygen precipitates, such as hydrogen (H) whereas the formation of TDD is sup-

pressed by high concentrations of carbon (C), for example.

This chapter is presented to provide a general survey of the oxygen-related defects in

silicon. The STDs are studied in detail in chapter 5 whereas the results of EDEPR

measurements of TDDs are discussed in chapter 6.

The radiation-induced A-centre, introduced in this chapter as well, plays an important

role not only for the STDs and TDDs but for the mechanism of EDEPR as well.

Oxygen related defects in silicon

4.1 Oxygen in silicon – an introduction

For the fabrication of silicon single crystals two different processes can be applied. One

of them makes use of a polycrystalline silicon rod which is pulled through a high fre-

quency ( HF ) coil. With sufficient HF power the silicon heats up to 1420°C and is

transferred into a single crystal in a “float zone” manner, the process giving the name

for this material ( FZ-silicon ). The single crystals gained by this method excel them-

selves as highly pure with contamination of less than 0.5ppb.

Silicon crystals used for the fabrication of 90% of the integrated circuits are grown by

the much less expensive Czochralski ( Cz ) technique. Ultra pure polycrystalline silicon

is melted in a silica crucible at a temperature above 1400°C, a rotating seed crystal is

dipped into the melt and then slowly withdrawn while the crucible is rotated in the op-

posite sense. Oxygen from the crucible enters the melt and oxygen is subsequently in-

corporated into the growing crystal at a concentration close to 1018cm−3 ( ~10ppm ).

Oxygen in silicon is electrically neutral and occupies bond-centered interstitial sites, see

figure 4.1 [Kaiser 1957]. Kaiser et al. found an infrared absorption band ( 9µm ) corre-

lated to the isolated Oi which is commonly used to determine its concentration in silicon

crystals. Next to the 16O band absorption lines corresponding to the isotopes 17O and

18O ( natural abundance 0.04% and 0.2%, respectively ) can be found with infrared

spectroscopy. An example for a low temperature ( 7K ) FTIR measurement of an 17O

enriched sample is given in figure 4.2.

Fig. 4.1 Interstitial site of oxygen in the silicon lattice. The arrow indicates the di-

rection of the localised vibrational mode ( LVM ) of the oxygen atom.

Oxygen related defects in silicon

The FTIR spectrum shows three significant peaks which are due to the three isotopes of

oxygen. Each IR line has two satellites on its low energy side with separations of

1.9cm−1 and 3.8cm−1, respectively, due to Oi atoms with various combinations of

neighbouring 28Si ( 92.3% ), 29Si ( 4.7% ) and 30Si ( 3% ) isotopes [Pajot 1967]. Each of

the dominant lines is also accompanied by a line of lower energy, called “hot band”

( hb ). These hot lines were attributed to transitions from thermalised levels close to the

ground state which are due to the splitting of the vibrational levels. The splitting is ex-

plained by the orientational degeneracy of the O atom between equivalent sites in the

crystal [Hrostowski 1960].

4.2 Thermal Double Donors

In 1955 Fuller et al. observed an increase of the donor concentration in silicon after heat

treatment cycles in the temperature region of 450°C [Fuller 1955]. The incorporation of

oxygen in this defect was examined by Kaiser et al. later [Kaiser 1957]. The formation

of these defects is attributed to the sequential clustering of oxygen atoms and at least 16

Fig. 4.2 FTIR spectrum of Cz-silicon enriched with 17O. Inserted in the range of the

dominant 16O absorption are computer simulations of lines are that are due

to the interaction of the interstitial O with the three silicon isotopes. The la-

bel “hb” stands for hot bands and is explained in the text.

Oxygen related defects in silicon

discrete centres ( 1 ≤ n ≤ 16 ) have been resolved by IR measurements, with n increas-

ing with annealing time [Wagner 1989, Götz 1992]. Each centre is a shallow helium

like double donor according to effective-mass-theory ( EMT ), that gives rise to sharp

electronic absorption lines from the ground state ( 1s ) to the excited states ( 2p0, 2p±l/h,

3p0 etc. ). They appear in the range of ( 533 – 350 )cm−1 at 4.2K where the donors are in

their neutral charge state. If the annealed silicon also contains acceptors such as boron,

it will be partially compensated. The singly ionised centres, TDD+n, give rise to elec-

tronic transitions in the range ( 1170–580 )cm−1, see figure 4.3 [Wagner 1989].

In EPR the TDD+n centres cause the so called NL8 spectrum, consisting of four

strongly overlapping lines corresponding to a C2v-symmetry. The NL8 spectra show

progressively shifting g-values and decreasing anisotropy with increasing annealing

temperature. The observations are attributed to the simultaneous presence of overlap-

ping, unresolved resonance lines due to adjacent TDD+n species [Muller 1978] [Dirksen

1999]. ENDOR measurements reveal the presence of 17O in diffused samples contain-

ing a high concentration of this isotope with nuclear spin of I=5/2 and a quadrupole

moment, whereas 16O and 18O show no nuclear spin [Michel 1989]. The results show an

Fig. 4.3 FTIR spectrum of Cz-silicon after 12hours heat treatment at 450°C. The

absorption lines are due to electronic transitions of singly ionised TDD+n.

Oxygen related defects in silicon

increasing intensity of the ENDOR transitions with increasing n, providing evidence

that the number of O atoms incorporated also increases. The same authors revealed a

highly anisotropic structure of the TDDs with a line of O atoms along a [110] direction.

The structure of the core is still a matter of controversial debate, as can be outlined by

the following two citations. A model by Deák et al. indicates that a mobile interstitial Si

atom is trapped and forms dative bonds with two trivalent Oi atoms in the donor core

[Deák 1992]. However, first principles calculations by Chadi imply that vacancies or

self-interstitials can not be present in the core [Chadi 1996]. A model of the TDD

atomic structure as proposed by Deák is shown in figure 4.4 [Deák 1992].

A recent model for the formation kinetics of the TDDs demonstrates the sequential dis-

sociation of early species of oxygen clusters in favour of the creation of higher species

that show increasing stability with increasing size ( increasing n ) [Götz 1998]. This

model supposes that no further loss of Oi should appear as the re-arrangement of the

TDD towards larger clusters takes place. The model also implies that a TDDn centre is

transformed into a TDD(n+1) centre by the addition of two O atoms ( a dimer ), rather

than one atom, to one end of the oxygen chain aligned along the [110] direction. Such

growth must be responsible for the unusual sequential changes of the measured ionisa-

tion energies Ei of the individual TDDn [Götz 1992]. The Ei decreases with a “staircase

structure” [Götz 1992] as n increases, implying the existence of two types of centres.

Fig. 4.4 Atomic model of the core structure of the TDDs as proposed by Deák. Un-

perturbed lattice positions are marked by small grey circles. Besides elec-

trons present in bonds and lone pair orbitals, two electrons are in a delocal-

ised orbital so that the complex is a shallow double donor [Deák 1992].

Oxygen related defects in silicon

High resolution EPR and ENDOR measurements of the NL8 spectrum have confirmed

that adjacent members have alternating C2v ( orthorhombic I ) and CS ( monoclinic I )

symmetries, as n increases to n+1 [Dirksen 1999]. It follows that the extra Oi atom ( or

O2 dimer ) must be added sequentially to alternate ends of the existing chain or that the

core structure is re-located due to local diffusion jumps. A simulation of an angular de-

pendence for NL8 EPR spectra is given in figure 4.5.

A strong enhancement of the TDD formation has been found by Brown et al. after ex-

posing the Cz-silicon specimen to H plasma during the heat treatment cycle [Brown

1988]. By means of high resolution FTIR measurements Newman et al. proved that hy-

drogen is not incorporated in the TDD [Newman 1996]. As a possible conclusion of

both findings an enhanced oxygen diffusion in the presence of hydrogen during heat

treatment has to be assumed.

Finally, due to the results of very specific approaches to IR absorption lines of TDDn

centres a bi-stability of the TDD1 and TDD2 has been postulated [Hallberg 1996] but

could not be supported and analysed in EPR.

Fig. 4.5 Calculated EPR angular dependence of A-centre-, NL8- and NL10-spectra

for a fixed microwave frequency ( νMW=9.5GHz ) and g-tensors as given in

table 4.1. The sample was rotated in a [11

]-plane. The numbers in the

pattern of the A-centre indicate the six centre orientations of the C2v sym-

metry of the defect.

Oxygen related defects in silicon

4.3 Shallow Thermal Donors

Next to the NL8 spectra further resonances labelled NL10 can be found in EPR if the

heat treatment around T=450°C is significantly prolonged. The NL10-centres are related

to “Shallow Donor Centres”, STDn, seen in IR absorption measurements in the range of

( 150-300 )cm−1 [e.g. Gregorkiewicz 1988]. The spectra of NL10 are less anisotropic

compared to the ones of NL8 ( figure 4.4 ). The centres were first detected by photo-

thermal ionisation ( PTIS ) and absorption spectroscopy of Cz-Si preannealed in oxygen

gas and then heated at T≤500C°. The donor ionisation energies of ( 30−40 )meV corre-

spond to the values predicted by effective mass theory ( EMT ), thus STDs are shal-

lower that TDDs. ENDOR spectra of 29Si demonstrate that the extended [110] structure

of the NL10 defects is similar to that of NL8 centres, a similarity also observed for the

17O ENDOR [Ammerlaan 1996, Spaeth 1996].

Several groups of these single donors depending on further impurities involved in the

STDs are known. At least three families can be distinguished by the elements contrib-

uting to the formation of the STDn. For STD(Al)n it has been shown with ENDOR that

an aluminium atom ( 27Al, ( 100% : I=5/2 ) is incorporated in the core of the defect

[Gregorkiewicz 1988, Meilwes 1993]. Further, the structure of the NL10 in Al-doped

silicon alternates between C2v ( orthorhombic ) and CS ( monoclinic ) symmetry for

adjacent species as it does for TDD+n.

For a second family of STD, labelled STD(H)n, the incorporation of hydrogen (H) is

revealed by a shift of IR absorption lines towards lower energies ( ~0.1cm−1 ) when H is

replaced by deuterium ( D ) in the preannealing process [Newman 1998]. The frequen-

Defect Spin g1||[001] g2||[110] g3||[-111]

NL8 a½1.99991 1.99323 2.00091

NL10 a½1.99959 1.99747 1.99957

A-centre b½2.0029 2.0096 2.0019

Table 4.1 Values of the g-factor for relevant oxygen-related paramagnetic defects as

given by a) Muller et al. [Muller 1978] and b) Bemski [Bemski 1959].

Oxygen related defects in silicon

cies of the IR absorption lines are different from those recorded of STD(Al)n and the

change in ionisation energy Ei when passing from 1≤n≤5 for STD(H)n is only ~50% of

that for the shallow donors incorporating Al. The incorporation of hydrogen in silicon

during crystal growth is proven by the identification of several IR absorption lines of as-

grown samples [McQuaid 1994] with the known STD(H)(1-3) in hydrogenated samples.

Further, Martynov et al. found H-related ENDOR resonances in Al-doped samples al-

though the specimen had not been H-doped deliberately [Martynov 1995].

Several further shallow donors gives rise to IR absorption lines that are grouped to the

family STD(X)n where the element or elements participating in the defect are not clear

yet. Their transition frequencies are nearly indistinguishable from those gained by PTIS

of samples doped with nitrogen (N) during crystal growth or preannealed in N2 atmos-

phere. Still there is no direct evidence to identify X with nitrogen and it is suggested

that vacancies diffusing from Si3N4 surface layers with a concentration of approx.

1014cm−3 during nitridation are involved in the STD(X)n [Newman 1996].

Alternatively, these vacancies can be caused by radiation damage [Watkins 1965]. The

IR spectroscopy results are very close to those of STD(H)n yet a small but reproducible

shift proves a different origin.

4.4 Radiation defects with participation of oxygen

The most prominent oxygen related defect occurring only after electron- or γ-irradiation

of silicon crystals is a vacancy-oxygen complex labelled A-centre [Watkins 1959, Bem-

ski 1959]. Its electronic structure was studied with ENDOR by van Kemp et al. [van

Kemp1986]. The singly negative charged paramagnetic state ( V−O )− shows an ortho-

rhombic symmetry and is stable in n-type silicon. In figure 4.5 a simulation of an angu-

lar dependence is given. The excited neutral triplet state of the A-centre, ( V−O )0*, with

an electron spin S=1 is called SL1-centre. It can only be detected after and during illu-

mination with above-band-gap light. It is created by the recombination of free charge

carriers at the ( V−O ) complex. The SL1-centre is easily detected in EPR as well as in

EDEPR.

Oxygen related defects in silicon

It has been shown recently that the formation of STD can be increased strongly by elec-

tron irradiation of the silicon samples and thus creation of radiation defects prior to an-

nealing [Markevich 1998].

Fig. 4.6 Model for the Si-A centre depicting it as a vacancy trapped at an interstitial

oxygen atom.

Oxygen related defects in silicon

Magnetic resonance studies of shallow donors in silicon

Chapter 5

Magnetical and optical studies of

shallow thermal donors in hydrogen-

ated Cz-Si crystals

Three species of a shallow donor family ( D1−D3 ) have been observed previously by

means of infrared absorption measurements in hydrogenated Czochralski-grown Si-

crystals [Markevich 1994]. They appear after irradiation with fast electrons and subse-

quent annealing in the temperature range of ( 300−550 )°C.

In this chapter the results of an optical ( FTIR ) and magnetic resonance study ( EPR,

EDEPR, ENDOR ) of the D1−D3 shallow donors are presented. Hydrogen incorpora-

tion into the D1 and D2 centers is found by the observation of resonance lines due to

hyperfine ( hf ) interactions of an unpaired electron with the 1H and 2H nuclei in

ENDOR spectra. Parameters of the hf-tensor are determined from the analysis of angu-

lar dependencies of the ENDOR lines. The observed EPR and ENDOR signals are

compared with those due to Si-NL10(H) shallow thermal donors published previously

and possible atomic structures and formation mechanisms of the defects are discussed.

Magnetic resonance studies of shallow donors in silicon

5.1 Introduction

In order to introduce the family of shallow donor centres forming with the participation

of hydrogen, STD(H)n, the published data presented in chapter 4 are summarised. Upon

heat treatment of oxygen-rich silicon at approx. 470°C two oxygen related defect cen-

tres show distinguishable absorption lines in FTIR and PTIS. The centres labelled TDD

and STD develop after annealing times of t §K DQGW >10h, respectively. The STDs

appear with absorption bands in the range of ( 300−150 )cm−1 and corresponding ioni-

sation energies of ( 34−40 )meV [e.g. Navarro 1986]. After such heat treatments of Cz-

Si two defect centres are found in EPR as well, and are called NL8 for t §K DQG

NL10 for t >10h, respectively. The oxygen incorporation in the centres has been proven

by ENDOR [Gregorkiewicz 1987][Michel 1989].

Several features ( e.g. formation kinetics ) indicate an identification of the TDDs, found

in FTIR, with the NL8 defects and of the STD with the NL10 centres [e.g. Newman

1996]. The labelling of the centres is sketched in table 5.1.

The defects occurring after prolonged annealing ( t >10h ) can be divided into several

families depending on the additional doping of the Si. Each of them is specified by a

distinctive set of absorption lines in FTIR. Three families of STDs have been estab-

lished so far: the STD(H) ( incorporating hydrogen ), the STD(Al) ( incorporating alu-

minium ), and the STD(X) ( incorporation of nitrogen or lattice vacancies ). The impu-

rities incorporated in the centres have been detected using FTIR and ENDOR [Newman

1998][Martynov 1995][Meilwes 1993]. In recent years the strong effects of hydrogen in

silicon have triggered intense studies of hydrogen related defect centres, such as the

STD(H). The participation of hydrogen in this defect was proven by isotopic shifts of

electronic absorptions after exchanging hydrogen by deuterium [Newman 1996]. An

enhanced formation of STDs after hydrogenation of nominally nitrogen- and alumin-

ium-free Cz-Si was found [Martynov 1995].

FTIR EPR

t §K TDD ⇔NL8

t >10h STD ⇔NL10

Table 5.1 Formation conditions and labelling of the corresponding heat treatment

centres detected by optical and magnetic resonance methods.

Magnetic resonance studies of shallow donors in silicon

Two models describing the STDs(H) have been presented so far. In one model an in-

complete passivation of the NL8 is claimed resulting in a single donor centre NL10(H) /

STD(H) instead of a double donor [Martynov 1995]. A theoretical study yielded a Ci-H-

2Oi complex with a single donor character [Ewels 1996]. Several arguments and ex-

perimental findings support the latter model rather than the former one and will be dis-

cussed later.

A new family of shallow thermal donors was found occurring after hydrogenation and

electron-irradiation of Cz-Si and subsequent heat treatment in the range of

( 300−500 )°C [Markevich 1994][Hatakeyama 1997]. The centres labelled D1−D3 show

enhanced formation kinetics compared to the conventional STDs(H). The advantages in

studying the D1−D3 species compared to the STD(H)n centers are worth mentioning.

Usually several different species of the STD(H) family give rise to very similar EPR

and ENDOR signals simultaneously, very much complicating the analysis of the EPR

and ENDOR spectra [e.g. Gregorkiewicz 1988]. However, for the irradiated Si:O,H

samples, it is possible to choose the annealing conditions such that only one particular

donor species dominates the spectra. This provides a good opportunity for structural

studies of one particular species.

Samples for this study were prepared from n-type (N(P)=5·1015 cm−3) Czochralski-

grown silicon with a resistivity of ρ=1 Ωcm and cut to dimensions of 3·3·15mm3. The

oxygen concentration was estimated by FTIR absorption measurements to be

9.5·1017cm−3. The carbon concentration was under the detection limit of the optical ab-

sorption method (≤ 1·1016 cm−3). Hydrogen (deuterium) was introduced into the samples

by heat-treatments in H2 ( D2 ) gas at 1200°C for 1h, terminated by quenching. Irradia-

tion with fast electrons ( 3MeV ) was performed at room temperature with a flux of

2·1016cm−2 . The samples were subsequently placed in an evacuated quartz ampoule

filled with argon and heat treated in the range of ( 100-500 )°C. Isochronal annealing

procedures were performed with 50°C steps for 30min each. Before optical and EPR

measurements the samples were etched with CP4 ( HNO3 : CH3COOH : HF ) at 60°C in

order to remove damaged surface layers and to obtain polished surfaces.

Magnetic resonance studies of shallow donors in silicon

5.2 Electronic properties of the shallow donors D1−D3

A typical infrared absorption spectrum of a hydrogenated, irradiated and annealed

( 400°C / 30min ) sample is shown in figure 5.1. Two strong absorption lines arising

from the primary dopant phosphorous are detected. Further, absorption lines due to

three shallow donor centres are seen, which are called D1, D2 and D3 [Markevich

1994]. The subscript index (0, ± ) indicates the orbital quantum number. The indices are

applied for shallow states of defect centres which can be described by effective-mass-

theory ( EMT ). For further information the reader is referred to textbooks like [Alonso

1988].

To gain information about the formation of the D1-D3 heat treatment centres samples

with various preparations have been studied. In figure 5.2 infrared absorption spectra of

hydrogenated Cz-Si crystals are shown, which were either heat-treated at 470°C for 10

hours ( spectrum a) ) or electron irradiated and subsequently annealed at 470°C for 0.5

and 3 hours ( spectra b) and c)), respectively. The spectra were measured at 10K with a

resolution of 0.5cm−1. Several donor absorption lines are observed in the range of

( 180−250 )cm−1. These lines are due to electronic transitions of heat treatment centres

[Newman 1998]. It is found that the positions of some lines coincide in all samples

studied.

Particularly, the lines due to donors labelled D2 and D3 in irradiated samples are at the

Fig. 5.1 FTIR spectrum of n-type Cz-Si after hydrogenation, electron-irradiation and

subsequent annealing at 400°C for 30min.The sample was measured at 10K.

Magnetic resonance studies of shallow donors in silicon

same positions as the corresponding lines in the spectrum of the non-irradiated sample

( 204.3 and 246.9 cm−1 for D2 and 198.3 and 241.2 cm−1 for D3 ). These wave numbers

are the same as those cited for the STD(H)2 and STD(H)3 centers by Newman [1998].

In table 5.2 the absorption line positions and the corresponding ionisation energies are

listed for the D1−D3 centres. The values for D2 and D3 are compared with those ob-

tained by Newman et al. for the STD(H)2 and 3 [Newman 1998]. The good agreement

between the values confirms previous suggestions about the identity of the D2 and D3

donors and two centers of the STD(H) family [Markevich 1998][Newman 1998].

In figure 5.3 a study of the relation between the temperature of the heat treatment and

the development of the Dn centres is shown. The results were obtained after isochronal

( 30min ) annealing of a hydrogenated and electron irradiated Cz-Si sample. The sample

was measured with FTIR after each annealing step, starting at 275°C for 30min. The

annealings were carried out with a temperature increased by 50°C each time. The pro-

cedure was continued up to a final temperature of 550°C. Depicted in figure 5.3 are the

Fig. 5.2 Infrared absorption spectra ( T=10 K ) of the following hydrogenated Cz-Si

samples: a) heat-treatment at 470°C for 10h, b) and c) electron irradiation at

room temperature ( F = 2·1016 cm−2 ) followed by anneals at 470°C for 0.5

and 3 h, respectively. The numbers ( 1−7 ) indicate the number of the donor

species of the STD(H)n family, according to [Newman 1998]. The Dn indi-

cate the donors according to [Markevich 1994].

Magnetic resonance studies of shallow donors in silicon

intensities of the absorption lines due to 1s→2p± electronic transitions as listed in table

5.2. The development of the individual species of this shallow donor family can easily

be traced. Each donor can be prepared with a maximum intensity at one specific tem-

perature.

Remarkable are the comparable signal intensities of D1 and D2 indicating an equal con-

Transition D1 D2 D3 STD(H)2STD(H)3

1s→2p0 (cm−1) 249.7 204.3 198.3 204.2 198.2

1s→2p± (cm−1) 291.7 246.9 241.2 246.8 241.1

Eb (meV) 42.6 37.0 36.3 37.0 36.3

Table 5.2 Absorption line positions of the shallow donor centres D1−D3 investigated

in this work compared to those published for STD(H)2 and 3 previously

[Newman 1998].

Fig. 5.3 Development of the intensities of the 1s→2p± electronic transitions appear-

ing at the absorption line positions listed in table 5.1. The sample was hy-

drogenated, electron-irradiated, and isochronally ( 30min ) annealed with

50°C temperature increments. FTIR measurements were carried out after

each annealing step. In the graph the absorption intensities are given for the

corresponding annealing temperatures indicated on the abscissa.

Magnetic resonance studies of shallow donors in silicon

centration of these centres. Only the D3 centre is formed with a reduced concentration

compared to D1 and D2.

The necessity of both the hydrogenation and electron irradiation for the accelerated and

increased formation of the Dn donors is underlined by the FTIR spectra presented in

figure 5.4. They were recorded from samples that all had been annealed at 400°C for

30min as a final preparation step. The temperature was chosen in order to create both

donors D1 and D2. The preceding preparation for sample a) was annealing at 1000°C in

an inert gas ambience and electron irradiation, whereas sample b) was hydrogenated at

1000°C only. In both spectra a) and b) absorption lines due to electronic transitions of

the primary dopant 31P are also detected. Only after a preparation procedure including

hydrogenation ( 1000°C ), electron irradiation and final annealing new absorption lines

due to the shallow thermal donors D1 and D2 arise. This strongly indicates the incorpo-

ration of hydrogen in the atomic structure of the Dn family. An incorporation of inter-

stitial atoms, created by the irradiation of the sample, can be assumed tentatively from

the FTIR results.

Fig. 5.4 Development of the infrared absorption line intensities of D1 / D2 and 31P

electronic transitions. All samples were finally annealed at 400°C for

30min. The precedent preparation was a) annealing in inert ambience at

1000°C and electron irradiation, b) hydrogenation at 1000°C, and c) hydro-

genation at 1000°C and electron irradiation.

Magnetic resonance studies of shallow donors in silicon

5.3 EPR investigation of the shallow donors D1−D3

The infrared absorption measurements presented above reveal that the D1−D3 centers

develop sequentially upon isochronal annealing of irradiated Si:O,H samples in the

temperature range ( 275−550 )°C. The concentration of D1 centers reaches a maximum

value at about 350°C and then decreases upon annealing at higher temperatures. After

annealing at about 450°C the concentration of D1 is negligible, while the D2 species is

the dominant one. Treatments at higher temperatures lead to a decrease of the D2 con-

centration with the simultaneous growth of the concentration of the D3 centers. To trace

this development of the Dn centres by EPR is one of the intentions of the following

section.

For all donors Dn a dependence of the EPR spectra on illumination of the sample is

found. The feature is illustrated for the D1 centre in figure 5.5 as an example. Only a

weak D1 EPR signal is detected next to 31P resonances when the sample is cooled to

measurement temperature ( 10K ) in the dark. Upon white light illumination of the sam-

ple at 10K the D1 EPR resonance strongly increases ( figure 5.5 b) ). This intensity re-

mains when the light is turned off for the following measurements ( c) ).The signal can

only be suppressed by heating the sample to ( 50−60 )K, followed by cooling to meas-

urement temperature in the dark. Such changes in the signal intensity of the D1 centre

had been observed previously with FTIR as well [Markevich 1994]. The results of EPR

and FTIR reveal that the strong EPR signal is related to a metastable shallow donor state

of the D1 centre. When the centre is cooled to the measurement temperature in the dark,

the centre is transformed into the singly negatively charged stable state. Both the ab-

sorption of transitions in FTIR and the D1 EPR resonance line disappear. However, it is

possible to recreate the FTIR lines and the EPR signal by illumination of the sample at

low temperatures ( 6−10 )K. No new EPR lines appear when the sample is cooled in the

dark. Hence, the electrons at the (D1)− state are paired.

Figure 5.6 shows the development of the EPR spectra, measured at 10 K, upon isochro-

nal ( 30min ) annealing of a hydrogenated and electron-irradiated Cz-Si sample. The

same sample as used of the FTIR study presented in figure 5.3 is taken. Weak EPR sig-

nals are observed in the field range ( 323−324 )mT after annealing at 300°C ( figure 5.6,

spectrum 1 ). According to their g-factor the signals are fingerprints of the radiation-

induced A-centre ( see chapter 4 ). After annealing at 350°C these signals are not ob-

served any more, but the resonance line seen in figure 5.6 ( spectrum 1 ), situated cen-

Magnetic resonance studies of shallow donors in silicon

trally between the two lines due to 31P is strongly enhanced. This intense EPR signal

with a nearly isotropic g-factor of 1.9987 arises from the shallow donor D1.

Heat treatment of the irradiated crystals at temperatures higher than 350°C results in a

transformation of the D1 to the D2 centers. This leads to the transformation of the iso-

tropic EPR signal observed after annealing at 350°C to another one, the shape of which

Fig. 5.5 Development of the intensity of the shallow donor resonance D1 upon illu-

mination of the sample before/during measurement. The spectra have been

recorded subsequently with the sample a) cooled in the dark to 10K, b) with

subsequent illumination at 10K, and c) illumination turned off at 10K. In the

range of ( 349−350 )mT traces of the A-centre induced by irradiation of the

sample appear in spectrum b). The sample was hydrogenated, electron-

irradiated and subsequently annealed at 350°C for 30min prior to the above

measurements. The spectra have been measured in X-band for B

||[110].

Magnetic resonance studies of shallow donors in silicon

is characteristic for the defects with orthorhombic-I symmetry, C2v point group ( figure

5.6, spectra 3-5 ). The decrease in the concentration of the D2 centers and the appear-

ance of the shallower D3 donors after annealing at 500°C leads to changes of the EPR

signals.

The isotropic behaviour of the D1 signal and the orthorhombic-I symmetry of the D2

centre are confirmed by EPR measurements in K-band. The corresponding spectra are

presented in figure 5.7.

On the basis of a slightly decreased spectral range of the D3 resonance lines compared

to those of D2 a more isotropic g-tensor can be assumed. Recalling the results of the

FTIR measurements it is found that the D3 donor is not created with a concentration as

Fig. 5.6 Development of EPR spectra upon 30-min isochronal annealing of a hydro-

genated Cz-Si sample which was irradiated with fast electrons ( 2.0·1016

cm−2 ). Last annealing temperature, [°C] 1:300; 2:350; 3:400; 4:450; 5:500.

The spectra were measured in X-band at 10 K for B

|| [110]. The spectra are

normalised to the equal intensity of the signal due to 31P.

Magnetic resonance studies of shallow donors in silicon

high as that of D1 or D2. Attempts to prepare D3 as the dominant shallow donor failed.

This is in good agreement with findings by Newman [Newman 1998]. The IR absorp-

tion spectra presented there show as well a weak STD(H)3. Because of the low concen-

tration and the strongly overlapping EPR signals no further investigation of the D3 cen-

tre was performed.

Figure 5.8 shows an angular dependence of the positions of four D2 EPR lines upon

rotation in a )011( -plane. The solid lines represent the best fit to the data assuming that

the lines are due to a defect with orthorhombic-I symmetry. The principal values of the

g-tensor are determined from the fit as g1||[ 101 ] = 1.99952, g2||[110] = 1.99722 and

g3||[001] = 1.99982 ( ∆gn=±0.00005, obtained from EDEPR, section 5.4 ). These values

are close to those usually quoted for NL10 centers (g1 = 1.99957, g2 = 1.99747 and g3 =

1.99959, ∆gn=±0.00004 ) [Muller 1978], but there is a small difference. The values of

the D2 centre indicate a somewhat bigger anisotropy of this centre compared with the

NL10 centers, with above values of g-tensor. The reason of this small difference is

probably the higher value of the ionisation energy of the D2 centre compared to those of

other species of the STD(H) family. According to Sieverts [Sieverts 1983] an increased

Fig. 5.7 Angular dependent K-band EPR spectra at 8K of a P-doped Cz-Si sample

after hydrogenation, electron-irradiation and annealing at 450°C for 30min.

The detected resonances appear upon illumination and are attributed to the

shallow donor centre D1 and D2, respectively.

Magnetic resonance studies of shallow donors in silicon

ionisation energy of a shallow donor results in a larger anisotropy of the corresponding

EPR signal. In table 5.3 the g-values obtained for D2 in this work are compared with

those presented for NL10(H) in literature.

gxx gyy gzz symmetry

δψφ

Refs.

D2 1.99952 1.99722 1.99982 rhombic-I 0 0 45 this work

NL10(H) 1.99957 1.99747 1.99959 rhombic-I 0 0 45 Muller 1978

Table 5.3 Principal values of the g-tensor of the shallow donor centres D2

( ∆gn=±0.00002 ) investigated in this work compared to those published for

NL10(H) ( ∆gn=±0.00004 ) centres previously [Muller 1978]. The high ac-

curacy of the D2 g-values is achieved by the 72GHz EDEPR measurements.

The angle δ is between the z-axis of the tensor and a [001] direction.

Fig. 5.8 Angular variation of the EPR lines due to D2 centres for rotation in a

( 011 )-plane. The angle “0” corresponds to B

||[001]. The solid lines are

calculated for a defect with S = 1/2, C2v symmetry. The principal values of

the g-tensor are listed in table 5.3.

Magnetic resonance studies of shallow donors in silicon

5.4 EDEPR investigation of the shallow donor D2

The EPR resonance lines due to the D2 shallow donor are overlapping strongly in the

spectra measured in X-band (∼9GHz) and even in K-band (∼25GHz). In order to resolve

them, higher microwave frequencies have to be utilised. Since a microwave bridge to

detect the microwave absorption in a conventional EPR experiment was not available

for frequencies higher than 25GHz, EDEPR as described in chapter 2 was used to real-

ise measurements in V-band (∼72GHz).

Fig. 5.9 EDEPR spectra of an electron-irradiated Si:O,H sample annealed at 450°C,

measured at 10K using a microwave frequency and power of 72.2GHz and

150mW, respectively The sample was illuminated with white light in order

to create excess charge carriers and the EPR effect was detected monitoring

a resistivity increase of the sample when applying a constant current of 6µA.

The numbers 1-4 represent the centre orientations corresponding to the or-

thorhombic-I symmetry ( figure 4.4 ). The tensor orientation is given in ta-

ble 5.3. The contributions to the spectra by resonances due to the radiation-

induced SL1 defect are indicated.

Magnetic resonance studies of shallow donors in silicon

In figure 5.9 EDEPR spectra of an electron-irradiated Si:O,H sample after annealing at

450°C are shown. The angular positions for B

||[110] and B

||[001] have been chosen to

demonstrate the increased separation of the individual resonance lines of the D2 centre

between the 31P-lines. The latter dominating lines are due to the hyperfine splitting of

the sample’s phosphorous doping and can be used as g-factor calibration markers as

their SHF parameters have been determined precisely [Feher 1959].

Indicated in figure 5.9 is the labelling of the individual lines of the orthorhombic-I D2

centre. The analysis of the angular dependence measurements yielded the same g-tensor

values already determined by fitting of the K-band data, but the precision of the values

could be enhanced. It is noted that successful measurements of the shallow donor D1

Fig. 5.10 Angular dependent EDEPR spectra of a P-doped Cz-Si sample after hydro-

genation, electron-irradiation and annealing at 450°C for 30min. The domi-

nant lines are caused by the primary dopant 31P. In the range of

( 2571.5−2574.5 )mT four resonance lines of the D2 centre appear. Addi-

tionally, traces of the radiation induced SL1-centre contribute to the spectra.

The microwave frequency of 72.2GHz was square-wave amplitude modu-

lated with 30dB/500Hz. No microwave resonator was used and the sample

was illuminated with white light at T=6K.

Magnetic resonance studies of shallow donors in silicon

were carried out as well. The spectra show again the isotropic character of the centre

studied in K-band already and are not presented here again therefore.

In figure 5.10 more spectra of the V-band EDEPR angular dependence are shown. It is

noted that EDEPR investigations with microwave frequencies as high as 72GHz have

not been are reported in the literature so far. Tests with a W-band microwave source

( 95GHz ) were successful for the dominant 31P-lines depicted in figure 5.9. Unfortu-

nately, only very weak traces of the D2 centre could be revealed due to limited micro-

wave power ( <80mW ).

More details about the EDEPR features and a discussion about the mechanism allowing

to measure EDEPR of the donor centres are presented in chapter 6.

5.5 EPR investigation of shallow donor interaction with 29Si nuclei

When taking a closer look at the spectra presented in figure 6.5 two additional, weak

resonance lines can be detected next to those being caused by the 31P atoms and the D1

centre. As the lines appear symmetrically about the D1 resonances it is tempting to as-

sign them to satellite lines, arising from hyperfine interaction of the unpaired electron

with 29Si nuclei. The 29Si is present with a natural abundance of 4.7% ( I=1/2 ). In order

to study these satellite lines in detail measurements with increased integration time were

performed.

Figure 5.11 presents a D1 EPR spectrum which was recorded after cooling in the dark.

It was subtracted from one recorded after previous illumination of the sample at low

temperatures. Two satellite lines around the central line are clearly detectable in the

inset. The ratio of the integrated area under the satellite lines to the total integrated area

of all three lines is ( 4.7±0.2 )%. This value is in good agreement with one expected for

one 29Si-atom. From the angular dependence of the D1 satellite lines an isotropic hyper-

fine interaction with a= (58±1)MHz is derived. The results obtained from angular and

power dependent measurements of the D1 satellite lines are presented in figure 5.12.

Similar 29Si satellite lines with an intensity of (5.6±0.2)% were observed for the D2

centre.

Magnetic resonance studies of shallow donors in silicon

Fig. 5.11 X-band EPR spectrum of a hydrogenated, electron irradiated and finally

annealed ( 350°C/ 30min ) Cz-Si sample. Further details are given in the

text.

Centre Preparation

( °C / h )

Satellite-

Ratio ( % )

( MHz )

( meV )

D1 H /e− / (350/0.5) 4.7 58 42.6

D2 H /e− / (450/0.5) 5.6 70 37.0

NL10(H) H / (470/50) 5.3 71 ( 34−40 )a

NL10(Al) Al-doping /(460/100) 1.7 52 −

Table 5.4 Values for the integrated area ratio of the satellite lines ( ±0.2%) and the

hyperfine splitting ( ±1MHz ) listed with the preparation procedure and the

corresponding ionisation energy of the shallow donor centres. The values

for the ionisation energies for NL10(H) (a) are taken from [Navarro 1986].

Magnetic resonance studies of shallow donors in silicon

A further Cz-Si sample was hydrogenated and annealed for 50h. The preparation gave

rise to intense NL(H) resonances. Also for this sample a hyperfine splitting of the shal-

low thermal donor centre is observed for the first time. The data obtained are given in

table 5.4. The intensity of the EPR satellite lines of 5.3% indicates an identification with

Fig. 5.12 a) Power dependence of the of the D1 29Si-satellite lines. The circles give

the ratio of the integrated area under the satellite lines to the total integrated

area under all three lines in dependence on the microwave power. b) The

angular dependence of the hyperfine splitting of the D1 29Si-satellite lines

for a rotation in the ( 011 )-plane is shown. The angle “0” corresponds to

||[001].

Magnetic resonance studies of shallow donors in silicon

a hyperfine interaction with one 29Si nuclei again. However, the splitting constant a for

the D2 and NL10(H) centres is larger than that obtained for D1.

Finally, an Al-doped ( p-type ) Cz-Si sample, annealed for 100h at 460°C was exam-

ined. The sample was originally prepared by Meilwes and the incorporation of alumin-

ium in the NL10 centre proven with ENDOR [Meilwes 1993]. The NL10(Al) defect had

been studied in detail and resonance lines due to 31P in the nominally phosphorous free

silicon had been observed by Meilwes. However, in the present study the NL10(Al)

satellite lines were detected for the first time upon increased signal integration. The

NL10(Al) EPR spectrum is shown in figure 5.13. For the hyperfine splitting a value of

( 52±1 )MHz is determined, which is significantly smaller compared to those found for

the centres studied so far. Further, the intensity ratio of the satellite lines ( 1.7% ) is too

small to be explained by a 29Si hyperfine interaction of the NL10(Al) centre. The find-

ings are discussed in a later section.

It can be concluded from the investigation of the shallow donor hyperfine lines that a

prominent interaction of the unpaired electron of the defect with one neighbouring or

interstitial Si-atom is observed.

Fig. 5.13 X-band EPR spectrum of a Al-doped Cz-Si sample after annealing at 460°C

for 100h. In spite of a nominally phosphorous free Si starting material traces

of 31P are observed.

Magnetic resonance studies of shallow donors in silicon

5.6 ENDOR investigation of the shallow donors D1 and D2

The precedent EPR measurements have already revealed strong similarities between the

D1/D2 donors appearing after hydrogenation, electron irradiation and annealing and the

NL10(H) donors reported in literature. In order to reveal the atomic structure of the Dn-

species and to find additional arguments for their identification with the hydrogen in-

corporating donors NL10(H), ENDOR measurements have been carried out. Figure 5.14

shows ENDOR spectra in the frequency range of ( 14.8−15.2 )MHz for an electron-

irradiated Si:O,H sample which was annealed at 350°C and had a strong EPR signal due

to the D1 centre.

Prominent resonance lines are observed in the spectra. The lines are positioned symmet-

rically around the nuclear frequency of free hydrogen and depict the hyperfine interac-

Fig. 5.14 ENDOR spectra of an electron-irradiated Si:O,H sample annealed at 350°C,

measured at 7K with illumination of the sample with white light. A micro-

wave frequency of 9.8GHz and frequency-modulation of the rf-field was

used. Indicated is the position of the frequency of the free hydrogen nucleus

calculated for a static magnetic field of B=352mT. Three spectra for the

main crystallographic orientations are given.

Magnetic resonance studies of shallow donors in silicon

tion between the unpaired electron and a hydrogen nucleus. Thus, hydrogen incorpora-

tion into the D1 donor is proven. Apparent changes in the spectra upon rotation of the

sample with respect to the static magnetic field ( “characteristic“ as opposed to “distant“

ENDOR ) are observed showing that the hydrogen atom takes a characteristic position

within the structure of the centre.

A deconvolution of the ENDOR spectra was performed assuming various symmetries of

the defect. Due to the nuclear spin I=1/2 of the hydrogen two sets of resonance lines

have to be used, placed symmetrically around the frequency of a free hydrogen nucleus.

Thus spectra consisting of 2·12, 2·7 and 2·4 ENDOR lines for triclinic, monoclinic-I and

orthorhombic-I symmetry, respectively, were simulated. The simulation was performed

Fig. 5.15 Comparison of the ENDOR line positions as determined by fit and simula-

tion, assuming a triclinic symmetry, with the corresponding, integrated

ENDOR spectra. With (*) the number of ENDOR lines coinciding at each

data point of an orientation is given. Data points and spectra are shown for

the main crystallographic orientations and one additional orientation

(°+ 70]001[||B

) . The latter angle is chosen to depict the largest width of

the spectrum.

Magnetic resonance studies of shallow donors in silicon

for all ( 10 ) ENDOR spectra recorded upon rotation in the range of ( 0−90 )° with 10°

steps. The obtained correlation coefficient for the deconvoluted spectra was 98%, 91%

and 82% for triclinic, monoclinic-I and orthorhombic-I symmetry, respectively. Thus,

triclinic symmetry was chosen.

To confirm the choice of the triclinic symmetry the ENDOR spectra with differential

line shapes were integrated and compared to the ENDOR line positions determined by

fit and simulation. In figure 5.15 four examples of such a comparison are shown. The

three angles ]110[],111[],001[||B

 have been chosen as for these orientations several of

the total 2·12 lines coincide. The pattern of the positions where the lines coincide is

characteristic for a triclinic symmetry of the defect centre. Further, the results for the

angle °+ 70]001[||B

 are shown, as for this orientation the largest width of the spectrum

is detected. It is noted that the numbers (*) indicate the quantity of ENDOR lines coin-

ciding for each data point for a certain sample orientation. Thus, the numbers represent

the signal strength of each data point. Especially for the orientation ]001[||B

 the com-

position of the ENDOR spectrum is obvious. The signal intensity of the integrated

spectrum can be described by 2:1:1:2 ( left to right ). The double intensity is caused by

the two adjacent resonance lines whereas only one is responsible for the single intensity

detected at the inner side of each ENDOR branch.

A further detail is noted for a later discussion of the anisotropic hf parameters b and b´.

From the spectrum ]110[||B

 the smallest gap between the two ENDOR branches can be

determined ( 18kHz ) whereas for °+ 70]001[||B

 a largest width of the overall spectrum

( 148kHz ) can be found.

In summary, the triclinic symmetry of the defect can be assumed to be the correct one.

Resulting from the triclinic symmetry it can be stated that only one hydrogen atom is

incorporated in the defect. Further consequences of these results are discussed in a later

section.

In figure 5.16 the solid lines represent the results of a computer calculation of the

ENDOR angular dependence using triclinic symmetry with the following parameters of

the hyperfine interactions a=88kHz, b=±40kHz and b´=±20kHz, given with an accu-

racy of ±5%. The z-axis of the tensor is pointing along [110]±3° direction. The orienta-

tion of the hf tensor is shown in figure 5.17 in a more detailed way and the orientation

of the z-axis in the atomic structure of the defect is explained in figure 5.20. In figure

5.16 the positions of ENDOR lines for four sample orientations relative to the magnetic

field, determined by fit and simulation of the respective spectra, are given as well

Magnetic resonance studies of shallow donors in silicon

The hf interactions are given in terms of the isotropic hyperfine (hf) constant a and the

anisotropic hf constants b and b’ which are related to the principal values of the usual hf

tensor Ax´x´, Ay´y´, Az´z´ by:

a=( A

x´x´ + Ay´y´ + Az´z´ ) / 3

b=( A

z´z´ – a ) / 2

b´=(A

x´x´ – Ay´y´ ) / 2

The absolute signs of the hf constants cannot be determined experimentally. However,

the isotropic and anisotropic hf constants show opposite signs. The choice of a negative

Fig. 5.16 Calculation of the angular dependence of the D1-hydrogen-ENDOR pre-

sented in figure 5.14. A triclinic symmetry with the hyperfine-constants

a=88kHz, b=±40kHz and b´=±20kHz was assumed (±5%). Experimental

data points for the main crystallographic orientations and one additional ori-

entation ( °+ 70]001[||B

) are inserted. The latter angle is chosen to depict

the largest width of the spectrum.

Magnetic resonance studies of shallow donors in silicon

value for the isotropic part a can be explained by a spin polarisation process which is

described by [Carrington 1967]. The anisotropic parts of the tensor, b and b´, can be

explained by a point dipole-dipole interaction. The parameters a, b and b´ are discussed

later in more detail.

To obtain information about the field-gradient at the site of the hydrogen nucleus this

atom has to be exchanged by one with a nuclear spin of I=1, i.e. having a quadrupole

moment. For this reason samples were prepared with deuterium ( I=1 ) instead of hy-

drogen during the gas heat treatment cycle. An irradiated sample, finally heat treated at

350°C to create the D1 centre, has revealed EPR features identical to those investigated

before with the hydrogen incorporation. No ENDOR lines in the frequency range

( 14.8−15.2 )MHz have been observed in this sample. However, new lines in the fre-

quency range of ( 2.1−2.4 )MHz occur. An ENDOR spectrum of the deuterium-doped

sample with D1 centers is given in figure 5.18(a). Three prominent resonance lines

placed symmetrically around the nuclear frequency of free deuterium are observed. The

spectrum was analysed with respect to further ENDOR lines which should appear sym-

metrically around these, but all other signals can only be explained by the high noise

level of the spectrum.

Fig. 5.17 Orientation of the hf tensor (x´, y´, z´) according to the transformations nec-

essary to successfully calculate the ENDOR angular dependence assuming

triclinic symmetry. “S” indicates the intersection line between the (x, y)-

and the (x´, y´)- plane.

Magnetic resonance studies of shallow donors in silicon

For the parameters of the hf tensor of the deuterium-ENDOR it has to be considered that

the exchange of hydrogen by deuterium does not change the symmetry of the defect.

However, to simulate the recorded spectrum the ratio of gn(H)/gn(D)= 0.1535 of the nu-

clear g-factors of hydrogen (gn=5.585) and deuterium (gn=0.857) has to be considered.

Hence, the hf constants found for the corresponding hydrogen ENDOR spectra have to

be downscaled by this factor, leading to a=13kHz, b=±6kHz and b´=±3kHz with an

accuracy of ±5%. In figure 5.18(b) a stick spectrum calculated with the downscaled hf

Fig. 5.18 In (a) the ENDOR spectrum of an electron-irradiated, deuterium-enriched

Si:O sample, annealed at 350°C ( D1(D) centre ). The sample was measured

with illumination with white light. A microwave frequency of 9.8GHz and

frequency-modulation of the rf-field was used. The frequency of the free

deuterium nucleus, calculated for a static magnetic field of B=352.2mT, is

indicated. The stick spectra in (b) and (c) are explained in the text.

Magnetic resonance studies of shallow donors in silicon

parameters is given. It is obvious that the recorded spectrum cannot be explained suffi-

ciently by this calculation. A quadrupole interaction of deuterium has to be taken into

account with Q[001]=64kHz additionally. This leads to a satisfactorily description of the

D1-deuterium ENDOR spectrum as can be seen by the stick spectrum in figure 5.18(c).

The tensor of the hf interaction was assumed to be the same as used to calculate the D1-

ENDOR angular dependence. However, to explain the D1-deuterium ENDOR spectrum

for ]001[||B

 with a quadrupole interaction the z-axis of the quadrupole tensor and thus

the field gradient was assumed to be aligned along [001]. A relative strong deuterium

ENDOR signal as depicted in figure 5.18 was only detected for ]001[||B

. Attempts to

detect deuterium signals for further orientations of the sample failed, thus the orienta-

tions of the tensors cannot be verified and remain speculative.

To obtain information about the incorporation of hydrogen into another species of the

Dn family, ENDOR measurements were performed using a specimen annealed at 450°C

thus leading to the creation of D2 centers. The respective spectrum is given in figure

5.19. The ENDOR lines are again placed symmetrically around the hydrogen frequency

but a reduced width of the pattern compared to that shown in figure 5.14 occurs. This

indicates a smaller hf interaction of the unpaired electron with one hydrogen atom in

this case. There are apparent changes in the spectra upon rotation of the samples in

(011 ) plane with respect to the magnetic field direction, but strong overlapping of the

individual resonance lines makes the determination of positions of the lines extremely

difficult. Nevertheless, a calculation of the ENDOR angular dependence with triclinic

a ( kHz ) b ( kHz ) b´( kHz ) Q[001]( kHz )

D1 ( hydrogen ) 88 ±40 ±20 −

D1 ( deuterium ) 13 ±6±3±64

D2 ( hydrogen ) 75 ±25 ±5−

Table 5.5 Calculated values for the hf interaction constants. The error of the hf values

is within ±5% for D1-hydrogen and D1-deuterium. For D2 the error is esti-

mated to be within ±15%. The value for the quadrupole interaction q is cal-

culated with a certainty of ±20%. For all three defects the same tensor ori-

entation was assumed.

Magnetic resonance studies of shallow donors in silicon

symmetry of the D2 tensor reveals the hf parameters as given in table 5.5. Since the

resolution of the D2 spectra was very low the only appropriate way was to assume the

lowest symmetry possible, being triclinic. Therefore, the same tensor orientation as for

the D1-hydrogen and the D1-deuterium sample was used.

5.7 Discussion

Two models of the atomic structure of the STD(H) centers have been proposed so far.

On the basis of similarities in arrangements of oxygen and silicon atoms for the STD(H)

and oxygen-related thermal double donors ( TDD ) and a sequential formation of these

defects, an identification of the STD(H) / NL10(H) centre as a singly passivated state of

the TDDs in its neutral charge state was suggested [Martynov 1995]. According to an-

other model, carbon atoms play an important role in the appearance of the STD(H)

Fig. 5.19 ENDOR spectra of two electron-irradiated, Si:O,H samples, annealed at

350°C (D1) and 450°C (D2), respectively. The samples illuminated ith

white light during measurement. A microwave frequency of 9.8GHz and

frequency-modulation of the rf-field was used.

Magnetic resonance studies of shallow donors in silicon

centers and a (C-H)i-O2i structure was proposed as a core of the STD(H) family [Ewels

1996].

The former model is not consistent with several experimental observations. Particularly,

STD(H) centers are found to be stable up to 500°C [Newman 1998], while, according to

deep level transient spectroscopy measurements, passivated TDDs dissociate at about

200°C [Weber 1996]. It appears that the results of the presented infrared absorption

measurements are not consistent with this model either. The concentration of TDDs is

found to be negligible ( ≤1013cm−3 ) in hydrogenated irradiated Cz-Si samples after

short-time ( t=30min ) anneals at ( 350−450 )°C, while the concentration of D1 and D2

centers exceeds 1015cm−3 in the samples. It seems to be extremely unlikely that TDDs in

concentration exceeding 1015cm−3 can be formed so fast and then be passivated by hy-

drogen during short-time treatments of irradiated Si:O,H samples at ( 350-450 )°C. To

achieve a TDD concentration of 1015cm−3 at these temperatures anneals for at least

t ≥ 60min are necessary.

A closer look at the results of the NL10 H-ENDOR presented by Martynov et al. [Mar-

tynov 1995] shall be taken. The authors investigated Cz-Si samples that had been

treated with hydrogen prior to annealing at 470°C for various periods. Equal to the D1

and D2 investigations of this work they performed angular dependent ENDOR meas-

urements for a rotation of the sample in a )011( -plane. The data are given with the

principal hf values combined with the respective orientation cosines. For comparability

they have been transformed to the a, b and b´ format, used in this work and are given in

table 5.6. Martynov et al. fitted the NL10(H) ENDOR angular dependence using two

similar hf tensors of triclinic symmetry. Thus, the spectra are described by 48 resonance

lines altogether, giving a high degree of freedom for the fitting of the spectra and hence

reducing the reliability of the fit. The tensor orientation given by Martynov does not

allow any alignment of one of the tensor axes with an orientation of the silicon lattice

and no atomic model of the NL10(H) is given. Both can most probably be explained by

the low signal-to-noise ratio of the spectra recorded by Martynov. Only one spectrum of

the NL10(H) ENDOR has been published by the author. A comparison of this with the

spectra recorded in this study reveals a higher signal-to-noise ratio of the latter. Gener-

ally speaking, the results obtained in this work can be regarded with a higher degree of

certainty.

Magnetic resonance studies of shallow donors in silicon

It is apparent from table 5.6 that Martynov did not observe a change of the sign for the

isotropic and anisotropic hf parameters. However, it will be shown later that this change

is partly characteristic for the atomic model of the NL10(H).

Although the isotropic parts a of the hf tensor are very similar for all three ENDOR

studies compared in table 5.6, significant differences are obvious regarding the aniso-

tropic parts b and b´. The question arises which of the two centres D1 or D2 the Mar-

tynov NL10(H) can be compared to. The comparison of the values for b and b´ indicates

an identification of the D2 with the NL10(H), and further arguments can be found. To

conventionally create the NL10(H) defect in a concentration sufficient for ENDOR

Martynov had to anneal the samples for 20h at least. For annealing periods as long as

this it is known that multiple species of the NL10(H) are created. Their resonances are

super-positioned in the spectra, but it is known that they show a decreasing anisotropy (

see chapter 4 ). The latter fact explains the low values for the anisotropic hf parameters

b and b´, whereas the value for the isotropic part a remains similar for all presented

samples.

It has been shown by FTIR and EPR at the beginning of this chapter that the preparation

a (kHz) b (kHz) b´(kHz)

(°)

(°)Refs.

D1 ( H ) 88 ±40 ±20 90 45 26 this work

D2 ( H ) 75 ±25 ±5904526this work

84.6 15.2 14.8 75 30 55

NL10 ( H )

80.6 15.0 11.4 70 35 50

Martynov

(1995)

Table 5.6 The values for the D1 ( ±5% ) and D2 (

±15% ) hf interaction constants

yielded in this work and those presented by [Martynov 1995] are compared.

A triclinic symmetry of the defect was assumed in each case. Martynov et

al. presented their data with the principal hf values associated to the direc-

tion cosines. Thus, the values had to be transformed to the a, b, b´ format

used in this work. The data were arranged in such a way that the z-axis of

the hf tensor is oriented along the direction of the largest hf interaction. No

value of the error of the hf constants is given by Martynov.

Magnetic resonance studies of shallow donors in silicon

method of hydrogenation, electron-irradiation and annealing used in this study provides

the facility to prepare the first species of NL10(H) selectively. Hence, from a compari-

son of the hf parameters and the preparation methods of the samples it can be concluded

that an identification of the Martynov NL10(H) with the D2 of this work is most likely.

As a consequence, it can be stated that with the D1 defect the first species of the

NL10(H) has been studied with ENDOR in this study for the first time.

In this study several arguments have been found to support the (C-H)i-O2i structure,

originally suggested by Ewels et al. [Ewels 1996] . An atomic model of the NL10(H)

defect is shown in the figures 5.20 and 5.21. The Ci atom is placed slightly above the

( 011 )-plane in which next to the Si lattice atoms the two Oi are located. The Hi is

bonded to the Ci in a [ 011 ] direction. The Si atom bonded to the Ci in the [ 100 ] direc-

tion is attached to two further Si atoms on regular lattice sites, but lacks bonding of its

fourth electron. The silicon pz orbital with the unpaired electron is aligned along the

Fig. 5.20 Atomic model of the core structure of STD(H) on the basis of the calcula-

tions by Ewels et al. [Ewels 1996]. The position of the hydrogen is deter-

mined from ENDOR investigations in this study. The numbers in the figure

indicate the bond lenghts in Å. In figure 5.21 the central part of the model

( bordered by the dashed lines ) is shown in a different orientation.

Magnetic resonance studies of shallow donors in silicon

[110] direction. From the calculated Kohn-Sham eigenvalues Ewels et al. estimated a

high spin density in the silicon pz-orbital and concluded a single shallow donor level of

the defect [Ewels 1996]. It is noted that Ewels obtained his results from calculations of

clusters with 151 atoms. Since the cluster size is small the calculated spin densities are

significantly higher compared those predicted by effective-mass-theory ( EMT ). Fur-

ther, no absolute values for the spin densities were given by the authors.

In the following paragraphs results of this work and considerations are presented which

support the (C-H)i-O2i model of the core structure of the shallow thermal donors.

The enhanced formation of STD(H)n centres in irradiated samples can be considered as

an indirect evidence for the carbon-related model of the STD(H). According to this

model, the formation of the STD(H) donor core requires the appearance of interstitial

carbon atoms ( Ci ) in Cz-Si crystals. The main mechanism of their appearance is known

to be the interaction of silicon self-interstitials ( ISi ) with substitutional carbon atoms

( CS ) [Watkins 1965]. The concentration of the CS is typically at least 5·1015 cm−3 in

Cz-silicon crystals [Series 1982].

Fig. 5.21 Atomic model of the core structure of STD(H) on the basis of the calcula-

tions by Ewels et al. [Ewels 1996] and the results of this work. In compari-

son to figure 5.20 the atomic model has been rotated for 90° about the [001]

direction and only the central part of figure 5.20 ( bordered by the dashed

lines there ) is shown.

Magnetic resonance studies of shallow donors in silicon

The creation of silicon self-interstitials and consequently Ci in non-irradiated Cz-Si

samples upon annealing at about 450°C is believed to be associated with the process of

oxygen aggregation [Newman 1990]. As the Ci are effectively formed due to the inter-

action of radiation-induced ISi with CS, the enhanced formation of shallow donor centers

in irradiated Cz-Si:H samples can be easily explained assuming that the STD(H) species

incorporate a Ci-H unit.

The calculated value for the hf constant of the free hydrogen atom is 1420.4MHz. Esti-

mating the ratio of this value to the one observed in the ENDOR experiments

( a=88kHz ) leads to an extremely small unpaired spin density in an hydrogen 1s or-

bital ( ~6·10−5 ). The hydrogen atom is therefore in a diamagnetic charge state. Because

of a well defined hf tensor orientation it is bonded to a lattice or interstitial atom. How-

ever, the small unpaired spin density of the hydrogen cannot come from this bond. It is

well possible that the hydrogen is placed next to a Ci, forming ( C−H )i. A theoretical

interpretation of the hydrogen hf interaction with its characteristic opposite signs of the

isotropic and anisotropic part can be given for this model.

The negative sign of the isotropic part of the hf tensor can be explained by a spin-

polarisation process between the 2pz-orbitals of the interstitial carbon atom and the 1s-

orbitals of the bonded hydrogen [e.g. Carrington 1967]. It is known from aromatic radi-

cals that the odd electron occupies a molecular π orbital delocalised over the carbon

atom framework of the molecule. This orbital, formed by an overlap of the carbon 2pz

atomic orbitals, has a node in the plane of the molecule, where the ring hydrogen atoms

are. However, the unpaired spin density of the 1s orbitals necessary for the observed

hyperfine splittings can not be explained by this configuration yet. It has to be consid-

ered that the exchange forces between the electrons couple together the spins of the

electrons in the C−H bond and the

electrons in the ring. With molecular orbital theory

the coupling can be explained by assuming an isolated >C−H fragment with one

elec-

tron, occupying the carbon 2pz orbital, perpendicular to the plane of the three trigonal

bonds. Considering the two electrons forming the

C−H bond, the fragment can be

drawn as shown in figure 5.22.

In approximation of a perfect pairing one would consider the structures a) and b) to be

equally important. Taking into account the interaction between the

and

systems,

structure a) is slightly preferred because of the favourable exchange interaction between

the

electron and the carbon

electron, whose spins are parallel. The spins in the C−H

Magnetic resonance studies of shallow donors in silicon

bond are therefore polarised slightly. If the odd electron has spin

, there is slight

excess

spin in the carbon

orbital and corresponding excess

spin in the hydrogen

1s orbital. This gives rise to a negative isotropic proton splitting. It is noted that

spin

in the carbon pπ orbital induces

spin at the proton. For this reason the spin density at

the proton and the hyperfine coupling constant are both negative.

A value of aH= −23.04G for the

proton splitting for an unpaired spin density of 100%

in the carbon pz orbital is known for methyl radicals ( –CH3 ) [e.g. Carrington 1967].

For a reduced spin density the splitting constant is consequently lowered. The hf split-

ting constant derived from the hydrogen ENDOR measurements of the shallow donor

centre D1 in this work can be written as aH,exp.= −0.00315G (a=88kHz, table 5.5 ).

The resulting ratio of aH/aH,exp= 0.0014 or 0.14% indicates a very low spin density in

the carbon pz orbital. This corresponds nicely with the findings of Ewels et al. whose

calculations revealed a negligible spin density on both the carbon and hydrogen atom

for the favoured (C-H)i-O2i structure for STD(H) [Jones 2000].

It is noted that the spin polarisation process described above is not exactly accurate for

the atomic model of the shallow donors as presented in figure 5.20/5.21. The process

explained by Carrington is based on a hydrogen atom being regularly bonded to a car-

bon atom [Carrington 1967]. In the present case of the (C-H)i-O2i structure the Hi is

bonded to a Ci and no further electrons of this are unpaired. More exact, the unpaired

electron of the (C-H)i-O2i structure is located in the pz orbital of the Si atom which is

bonded along a [ 100 ] direction to the Ci. Thus the spin polarisation process takes part

between the unpaired electron of the Si atom and the hydrogen atom via the carbon

Fig. 5.22 Atomic orbital models of the two electron configurations of the

bond for a

C−H fragment.

Magnetic resonance studies of shallow donors in silicon

atom. The process is known as “superexchange”.

In EPR an isotropic interaction of 29Si nuclei with the Dn centres of a=(60−70)MHz

was observed. With an isotropic hf splitting constant of 4594MHz [Morton 1977]for a

3s silicon orbital with 100% spin density, a ratio of both the observed and the maximal

interaction of 1.3·10−2 is calculated. The value represents the spin density at the silicon.

It can be assumed that a spin density of about one order of magnitude less is induced at

the site of the carbon. This results in a spin density of 1.3·10−3 in the carbon orbitals, a

value which is in excellent agreement with the one obtained from the ENDOR analysis

above ( 0.14% or 1.4·10−3 ).

For the silicon atom equal spin densities can be assumed as well in the 3s- as in the 3p-

orbital. The spin density value of 1.3·10−2 obtained above leads to an anisotropic hf in-

teraction which would detectable as an angular dependence of the observed interaction

with the 29Si nuclei. With an anisotropic interaction value of about 114MHz [Morton

1977] for the silicon 3p orbital the angular variation of the 29Si satellite positions would

be of about 1MHz. However, this variation is below the resolution of the experiments

performed in this study.

With the result of 0.14% spin density in the carbon pz orbital a valuable information is

given to consider the point dipole-dipole interaction, leading to the anisotropic hf inter-

action constant b. This can be calculated as bH= 95.625 gn/RB3 where RB is the distance

between the neighbour nucleus and the defect centre ( in atomic units ) [Spaeth 1992].

Assuming a C−H bond length of R= 1.2Å and a g-factor of the hydrogen nucleus of

gn= 5.58569 a hf constant of bH= 61.46MHz is obtained. Scaling this value by the factor

obtained for the carbon pz-orbital 0.14% results in bH= 46kHz, being in excellent

agreement with the experimentally obtained data of bH,exp= 40kHz.

An explanation of the smaller hf interactions for the D2 centre compared with those for

the D1 can be found considering the decreased ionisation-energy of D2 to D1 centers

and thus the lower localisation of the paramagnetic electron on the hydrogen atom.

As a summary of the above sections about the hf interaction constants it can be noted

that an excellent agreement of the observed hf parameters with those gained by theoreti-

cal considerations is found. The “superexchange” process can explain the orientation of

the hf tensor with its z-axis parallel ]011[ as well.

Magnetic resonance studies of shallow donors in silicon

The EPR investigation of the hyperfine interactions of the Dn centres with 29Si nuclei

reveals that one silicon atom is taking a prominent position in the defect structure. This

result corresponds nicely to the results obtained from calculations by Ewels et al., who

find a very low spin density on the interstitial atoms ( Ni for STD(X) and Ci for

STD(H) ) but a significant one on the nearest Si-atom. In this work this hf interaction

has been observed for NL10(H) prepared only by hydrogenation and annealing for the

first time. The observation of the satellite lines in both the Dn and NL10 centres pro-

vides a further argument to identify the Dn and the NL10(H) centers.

Martynov et al. observed weak hydrogen-related ENDOR lines in nominally H-free

samples which had been doped with Al [Martynov 1995]. The finding was astonishing

as no indications had been presented earlier about an incorporation of H in the NL(Al)

defect structure. No model of the defect has been presented by the authors and the con-

nection of the Al-atoms with the hydrogen remained unclear. With respect to the alleged

observation of hf interaction of NL10(Al) centres with 29Si nuclei an explanation con-

sistent with all experimental findings and suggested defect models can be found. The

decisive argument is the low ratio of the integrated area under the satellite lines com-

pared to the integrated area under all lines of only 1.7%. The result clearly indicates that

the central line ascribed to the NL10(Al) is not causing the satellite lines. The central

line is most probably a superposition of the EPR lines of NL10(Al) and a weaker reso-

nances arising from NL10(H). The following considerations can explain the formation

of NL(H). After prolonged annealing of the Al-doped sample NL10(Al) is formed with

high concentrations. The large number of defects gives rise to further interstitial atoms

such as carbon which is generally present in the Cz-Si samples. It has been proven that

in addition hydrogen is an omnipresent contamination in the samples. Both elements

give rise to low concentrations of the NL10(H) of Dn centres after prolonged annealing.

Thus, the low intensity of the satellite lines can be qualitatively explained.

According to ENDOR investigations of the NL10(Al) by Meilwes it was suggested that

the defect consists of a an oxygen chain aligned along a [110] direction and an intersti-

tial Al-atom in the defect core [Meilwes 1993]. The finding of Ali by Meilwes and the

Ci presented in this work as well as by Ewels indicates strongly that the presence of an

interstital atom is essential for the defect structures of NL10(Al, N, H). Particularly, as

Ewels et al. calculated models of shallow donors with an incorporation of an interstitial

nitrogen atom as well. The “labelling” atoms can be made interstitial by irradiation or

prolonged annealing. No evidence is found to support the model of an H-passivated

Magnetic resonance studies of shallow donors in silicon

NL8 centre being responsible for the NL10 resonances. In fact, the “passivation” model

would only explain a single feature found for NL10(H).

So far the incorporation of interstitial carbon in the STD(H)/NL10(H) core structure has

been suggested without having any evidence for this assumption from the experimental

data. To find a prove for the Ci, a sample diffused with a high concentration of 13C

( n(13C)§16cm−3 ) was hydrogenated, electron-irradiated and annealed at 350°C in

order to create the shallow donor D1. The isotope 13C has a nuclear spin of I=1/2 and

should be detectable with ENDOR therefore. Although great efforts have been made to

detect a 13C-ENDOR signal, none has been found. The low spin density at the site of the

carbon may explain why the detection of the 13C failed. Experiments with high resolu-

tion FTIR or Photo Thermal Ionisation Spectroscopy ( PTIS ) are projected since the

change of the isotope leads to a change in the position of the absorption line. Unfortu-

nately, the expected isotope shift is about 0.03cm−1, a value which is close to the maxi-

mum resolution ( 0.01cm−1 ) of the best spectrometers available.

To complete this discussion it is noted that the interstitial carbon atom in the (C-H)i-O2i

model for STD(H)/NL10(H) could be exchanged by an interstitial silicon atom. The

structure of the defect would remain the same, as both atoms can have four bonds ac-

cording to the sp3-hybridisation. According to a detailed estimation even the spin densi-

ties in the Sii-orbitals would be very similar to those for the Ci. However, interstitial

29Si-atoms would give rise to characteristic ENDOR resonances which should be de-

tected symmetrically around the “distant” silicon ENDOR line. According to the natural

abundance ( 4.67% ) of 29Si, the isotope is present in the samples with a ratio of 4.67%

compared to 28Si. Although a sufficient signal-to-noise ratio was achieved by increasing

the integration time for the 29Si-ENDOR measurements, no signals of the isotope were

detected. The failure to observe such 29Si-ENDOR lines contradicts the assumption of

an interstitial Si-atom instead of a Ci in the core of the STD(H)/NL10(H).

All the presented experimental results are consistent with the assignment of the D1, D2

and D3 centres to the STD(H) / NL10(H) family. Electronic properties of the D1 donor

differ from those of the other STD(H)n species, but there is a clear correlation in an-

nealing behaviours of the D1 and D2 centres [Markevich 1996]. D2 donors seem to

grow at the expense of D1 centres. Thus, it appears that the D1 defect represents the

first species of the STD(H) donor family and can be called STD(H)1.

Magnetic resonance studies of shallow donors in silicon

5.8 Conclusions

Direct evidence for the incorporation of one hydrogen atom into the D1 and D2 shallow

donor centres is obtained by the observation of hydrogen-related hyperfine interaction

lines in ENDOR spectra. Well-defined hydrogen-related ENDOR patterns

( „characteristic“ as opposed to „distant“ ENDOR ) are observed showing that a hydro-

gen atom takes a characteristic position within the structure of the centres. From the

hyperfine interactions with 29Si nuclei it is concluded that one silicon atom is incorpo-

rated in a prominent position in the shallow donor centres as well. Evidences for the

identity of D2 and D3 defects and two species from the hydrogen-related STD family

are obtained from the comparison of positions of IR absorption lines due to these cen-

tres. It is argued that the formation of hydrogen-related shallow thermal donors is not

related to the hydrogen passivation of thermal double donor centres. In fact, intrinsic

point defects ( most probably silicon self-interstitials ) play an important role in the

formation of STD(H). With the selective preparation of D1 and the complex investiga-

tion of the donor centre by means of EPR and ENDOR the first species of the hydrogen-

related STD family has been examined for the first time. A unifying model for the STD

or NL10 families, supported by all experimental findings so far, can be been presented

as well.

On the mechanism of EDEPR

Chapter 6

On the mechanism and applicability

of EDEPR

In the chapters 3 and 5 magnetic resonance investigations of various defects in silicon

have been presented. Some of the results could only be obtained by EDEPR ( chapter

3 ) and other studies were improved by this method ( chapter 5 ). Because of the diver-

sity of the studied samples a survey of the method itself and is presented in this chapter.

First, an investigation of the Thermal Double Donors ( TDDs ) with EDEPR is de-

scribed. In this case, however, the method claimed for its sensitivity for small defect

concentrations, failed to provide resonance lines of the TDDs. Further examples of un-

successful EDEPR experiments are presented. The question for the reason of failure

leads to the need to understand the mechanism of EDEPR. Therefore, the mechanism

will be studied on the basis of the successful EDEPR experiments in the later para-

graphs of this chapter.

6.1 Investigation of Cz-silicon after heat-treatment at 470°C

As mentioned before the core structure of the thermal donors is undergoing a controver-

sial discussion for more than three decades, equally for both TDD and STD or NL8 and

NL10, respectively. After the electrical detection of EPR was intensively studied in the

group of Prof. Dr. J.-M. Spaeth by Dr. B. Stich its mechanism and potentialities were

explored. One of the most outstanding advantages was found to be the increased sensi-

tivity regarding the defect concentration in comparison to conventional EPR. This fea-

ture, in principle, opened new possibilities to investigate the core structure of the ther-

On the mechanism of EDEPR

mal donors. This can be explained by the fact that for the investigation of early stages of

oxygen precipitation with low donor concentrations the method of EPR was lacking the

required sensitivity. Conventional EPR requires a minimum number of spins of N≈1011

per cm3 for a linewidth of 1mT [Spaeth 1992]. In comparison to this Stich presented

EDEPR spectra with an estimated spin number of N≈108, leading to the statement of a

sensitivity increase by 3 orders of magnitude [Stich 1997]. Therefore EDEPR was in-

tended to investigate the early stages of TDD.

The preparation and characterisation of early stages of TDD in oxygen-rich silicon is

illustrated first . The results of detailed EDEPR studies and the conclusions drawn from

these results are discussed and a re-interpretation of former findings is presented.

6.1.1 Preparation and FTIR-characterisation of Thermal

Double Donors

For the preparation of samples with TDDs, p-type Cz-silicon starting material was used

with a boron concentration of n(B)=3·1015cm−3 and an oxygen concentration of

n(O)=8.5·1017cm−3. To allow a comparability of the results of this study and those ob-

tained by Stich an identical starting material was chosen [Stich 1997]. Following the

idea of a donor-acceptor recombination process being responsible for EDEPR, the ac-

ceptor behaviour of B in silicon should match the donor characteristic of the TDDs. The

size of the samples was ( 2.5·2.5·8 )mm and their surface was polished by wet chemical

etching with CP4 ( HNO3:CH3COOH:HF ) in order to facilitate reliable optical meas-

urements ( FTIR ).

The growth of silicon crystals takes place at elevated temperatures. During the subse-

quent cooling process of the crystal rod the temperature range where TDDs are created

is passed and consequently oxygen precipitates are formed even though in small con-

centrations. An effective procedure to destroy these thermal donors is to anneal the

specimen in an evacuated ampoule at 770°C for 30min. Control measurements with

FTIR proved the efficiency of this approach in the limits of the detection limit of

n=1·1012cm−3 ( see also spectrum “0min” in figure. 6.1 ). The samples were placed in

evacuated ampoules again and heat treated at 470°C for times ranging from

( 10−300 )min. The concentration of TDDs was investigated with FTIR for each sample

afterwards.

On the mechanism of EDEPR

In figure 6.1 FTIR spectra of samples annealed for ( 0–60 )min are given. The dominant

absorption line at

=1136cm−1 is due to the antisymmetric resonant vibration mode of

interstitial 16O [Hrostowski 1960]. This line is used to determine the 16O concentration

in the crystals. The 16O concentration was estimated to n(O)=5·1017cm−3 and thus the

value given by the manufacturer Wacker-Chemitronic could be verified.

The FTIR spectrum ( “0min” ) of the reference sample which was only preannealed at

Fig. 6.1 FTIR spectra of Cz-silicon samples after annealing at 470°C in an evacuated

ampoule in the range of ( 0−60 )min. All samples had been preannealed at

770°C for 30min in order to destroy thermal donors being possibly present

due to the crystal growth process. The Greek letters have the meaning:

α: antisymmetrical resonant vibrational mode of interstitial 16O,

β: first excited state of the rotational mode of 28Si-16O-28Si,

γ: antisymmetrical resonant vibrational mode of interstitial 18O.

On the mechanism of EDEPR

770°C, reveals no absorption lines of TDDs, demonstrating the effectiveness of the pre-

annealing procedure. The development of the absorption lines due to TDD(1−3) in the

other spectra is easily followed.

The corresponding concentrations of the TDDs are listed in table 6.1. Note, that the sig-

nal intensity of the TDD1 absorption lines decreases after 60min annealing already,

whereas those of TDD2 are at their maximum. With the aim to investigate the first two

stages of TDD the annealing time has to be chosen in the range of ( 15−45 )min. The

achievable concentration of TDD(1-3) would be about n(TDD)§13cm−3 after heat

treatment for 30min.

6.1.2 EDEPR of Cz-Si heat treated at 470°C

In order to investigate the early species of the TDDs we re-measured a sample which

had been prepared by Stich originally [Stich 1997]. This sample was heat treated for

60min at 470°C and the EDEPR spectrum was found qualitatively identical to the one

presented by Stich. The author attributed the detected resonance lines to first species of

TDDs.

In figure 6.2 EDEPR spectra of three samples already introduced in conjunction with

the FTIR results are shown. Two resonances, which could not be found in EPR, are de-

Concentration of TDD (cm−3)

Annealing time TDD1 TDD2 TDD3

0 min - - -

10 min 1 ⋅ 1012 2 ⋅ 1012 -

15 min 1 ⋅ 1013 6 ⋅ 1012 1 ⋅ 1012

30 min 8 ⋅ 1012 1 ⋅ 1013 7 ⋅ 1012

60 min 5 ⋅ 1012 1 ⋅ 1013 8 ⋅ 1012

Table 6.1 Concentration of the TDD in Cz-silicon samples after annealing at 470°C

for times as given, gained by analysis of the absorption lines due to 1s→3p0

ground to excited state electronic transitions.

On the mechanism of EDEPR

tected. The line-shapes are similar to the ones found in the TDD-reference sample of

Stich.

To achieve a sufficient signal-to-noise ratio for the individual spectra in figure 6.2, the

magnetic field range had to be scanned numerous times and 42 spectra were accumu-

lated during about 12h. Thus the resulting spectra are normalised to equal integration

times. Very similar signal amplitudes are obtained, even for the sample that had not

been annealed at all and for which no absorption lines due to TDDs could be detected in

FTIR. Thus, similar spectra and similar signal-to-noise ratios were recorded independ-

Fig. 6.2 EDEPR spectra of Cz-silicon samples annealed at 470°C for ( 0-30-60 ) min

after preannealing at 770°C for 30min. Indicated are the g-values of the

resonances which can be given with a certainty of ∆g=±0.0001. Measure-

ments were performed at 10K with white light illumination of the samples.

A sample current of 5µA, magnetic field modulation of 5kHz / 0.2mT and a

magnetic field step-width of 0.02mT was used.

On the mechanism of EDEPR

ent of the annealing procedure of the samples. Thus, an identification of the resonances

with TDDs has to be doubted.

Special care has been taken to study the g-value of the detected EDEPR lines. DPPH

( 2,2-diphenyl-1-pikryl-hydrazyl, g=2.0036 ) was used as a g-factor marker and tests of

the magnetic field stability over a time period of 10h revealed a shift of the DPPH reso-

nance line of only B



∆=( 0.009±0.002mT ). The g-values determined for the two reso-

nance lines in figure 6.2 ( 2.0139 / 2.0044 ) can therefore be given with high precision

( ∆g = ±0.0001 ). Comparing these g-values with those of thermal donors listed in table

4.1 yields no agreement. An identification of the detected lines with TDDs has to be

ruled out consequently.

Recalling the results presented in chapter 3 the dangling bond centre Pbb occurring at a

(100) Si/SiO2 interface is most likely to be the origin of the detected resonances in the

heat-treated samples. This conclusion can be drawn taking into account the sample sur-

faces being a (100)-plane and the very similar g-values obtained for a sample orienta-

tion of B

||[011] in both cases. A characteristic change in line-shape upon rotation of the

sample underlines the identification of the detected resonances with the Pbb centre. The

intensity of the Pbb-resonances shown in chapter 3 was very weak, too.

As the resonances detected in the heat-treated samples presented in this chapter were of

significantly less intensity compared to those presented in chapter 3 no further investi-

gations were performed. Nevertheless, a very important conclusion can be drawn from

the investigations of heat treated silicon presented above. Though two partners, boron

and TDDs, are present in the samples, no resonances due to the TDDs nor boron can be

detected with EDEPR. It implies that either the concentration of donors and / or accep-

tors is not suitable for the detection of a recombination process, or that the mechanism

for EDEPR is not depending on a donor-acceptor recombination at all for these centres.

6.2 Presentation of further EDEPR experiments

To discuss the EDEPR mechanism further, several experiments performed by Stich are

summarised [Stich 1997]. A sample only containing the shallow donor phosphorous

were prepared by Stich and investigated with EPR. This sample showed the expected

two hyperfine resonance lines of the dopant due to I=1/2 of 31P. No EDEPR signal

could be recorded from this sample and it was concluded that the mechanism of EDEPR

would not work with a donor only.

On the mechanism of EDEPR

A further sample was prepared in which the shallow donor 31P was compensated by the

shallow acceptor boron, both being present in the sample with a concentration of

n(P,B)=1·1016cm−3. EPR lines of the 31P could be detected again, but only weak signals

of the 31P hyperfine doublet were recorded with EDEPR. The value obtained for the

conductivity change was only about ∆σ/σ § Â−6. The result was astonishing as ac-

cording to the donor-acceptor recombination mechanism a stronger EDEPR signal was

expected. Surprising was in particular, that both recombination partners were present in

the sample with equal, moderate concentrations.

To extend the range of samples a 31P doped one was diffused with chromium (Cr) to a

concentration of n(Cr) §Â16cm−3. Cr is located as well on interstitial as on substitu-

tional sites in the silicon lattice and shows several donor and acceptor levels. In EPR a

spectrum showing Cri+ resonance lines next to 31P lines with a high signal-to-noise ratio

was recorded. Again, in EDEPR only weak signals of the resonances could be detected.

Summarising the results by Stich and recalling the failure to detect resonances of the

thermal double donors with EDEPR ( previous paragraph ) it has to be asked why

EDEPR performed so badly in these experiments. In particular, as the method is

claimed to be highly sensitive with respect to low defect concentrations and to be

caused by a donor-acceptor recombination, a property found when studying the dan-

gling bonds centres ( Pba and Pbb ).

A straight-forward approach to answer this question would be to assume too low a con-

centration of the donor-acceptor pairs in the samples. Therefore, the concentrations of

the donors and acceptors are compared. The samples presented in the previous para-

graph had a concentration of boron and TDD of n(B)=3·1015cm−3 and

n(TDD)§13cm−3, respectively. Thus, the averaged distance between two donor-

acceptor pairs is determined by the concentration of the boron. It can be derived from

the boron concentration and the number of 1023 atoms per cm3 that one boron atom is

placed amongst 108 silicon atoms. From this density it can be concluded that the dis-

tance between two boron atoms is approximately 100010

38≈lattice parameters. Hence

the distance between a TDD centre and a boron atom is of several 100 of lattice pa-

rameters. The value implies that the donors and acceptors are too far separated from

each other to from D-A-pairs and that a recombination of these is very unlikely. In sili-

con-carbide ( SiC ) it is known that the luminescence based on donor-acceptor recombi-

nation works efficiently for concentrations of ( 1017−1018 )cm−3 of the donors and ac-

ceptors. From the comparison of these values it might be concluded that the concentra-

On the mechanism of EDEPR

100

tion of the TDDs and B is too low to detect donor-acceptor-recombination-based

EDEPR.

The samples prepared by Stich had higher concentrations of 1·1016cm−3 of the donor B

and acceptors 31P and Cr. Thus the distance between the recombination partners is re-

duced and the recombination should be more effective. Indeed weak signals of the do-

nors are detected with EDEPR but the observed magnitude of conductivity change is

still by far too low compared to the predictions of the KSM and/or donor-acceptor re-

combination model.

Although great efforts have been undertaken to achieve a luminescence from crystalline

silicon, no results from Photoluminescence-EPR ( PL-EPR) based on donor-acceptor

recombination have been published so far, even so samples with very high do-

nor/acceptor concentrations up to 1019cm−3 have been studied. This fact together with

the findings presented above can be taken as an evidence that it is not a non-adequate

concentration of the donors/acceptors that inhibits the detection of EDEPR.

In none of the EPR or EDEPR spectra presented in this chapter, resonances of a possi-

bly present shallow dopant boron were detected. It is a generally accepted fact that B

can not be observed in EPR due to a dynamic Jahn-Teller-distortion [Ludwig 1962].

6.3 On the impact of electron-irradiation on the EDEPR signal

In this work and the one by Stich [Stich 1997] several EDEPR experiments have been

presented with samples that had been irradiated with electrons as one of the preparation

steps. The consequence of the irradiation on the recorded EDEPR spectrum was very

much surprising. In figure 6.3 an EDEPR spectrum of a 31P-doped Cz-Si sample, which

had been electron-irradiated and annealed at 460°C is shown.

Next to the resonance lines due to the radiation defect SL1 strong signals of both the 31P

and the TDDs are detected. It is apparent that the radiation defects provide an efficient

recombination channel in which additional donors can be detected as well. A situation

like this in known from optically detected magnetic resonance ( ODMR ) where the

defect providing the recombination channel is opening a “shunt” channel [Spaeth 1992].

As the radiation defects seem to enhance the detection of EDEPR, the reason for their

impact must be considered. In chapter 4 the radiation-induced vacancy-oxygen (V-O)

centre has already been introduced. The neutral (V-O)0 state of the (V-O) centre is not

On the mechanism of EDEPR

paramagnetic. Since the defect can change to a paramagnetic state for two reasons, two

different spectra of the (V-O) can be recorded. In the case of an additional electron be-

ing caught by the (V-O), the defect with S=1/2 is called A-centre and can be described

as the negatively charged state (V-O)− [Watkins 1961]. A second way to transform the

(V-O) to the paramagnetic state is to create excess charge carriers by illumination of the

sample with above-band-gap light. The charge carriers recombine via the neutral (V-O)0

to the neutral excited triplet state (V-O)0* with an electron spin S=1. In this way the (V-

O)0 acts as an recombination centre [Vlasenko 1984]. The (V-O)0* can be detected in

EPR and EDEPR and is called SL1-centre. The neutral triplet state (V-O)0* with spin

S=1 is metastable, since electronic transitions to the singlet ground state are spin-

forbidden. The spin selection rule is 100% valid only as long as no additional orbital

momenta are present in the sample. In reality, however, the orbital momenta of a par-

amagnetic defect are not completely quenched by the electrical crystal field of the lat-

tice. This leads to a weakening of the selection rule and electron-hole recombinations

via a transition of the excited triplet state S=1 to the singlet ground state S=0 are possi-

ble.

Fig. 6.3 EDEPR spectrum of a phosphorous-doped Cz-silicon sample after electron-

irradiation and annealing at 460°C for 60min. The spectrum was recorded in

X-band ( 9.54GHz ) at 10K with white light illumination of the sample. A

sample current of 5µA and magnetic field modulation with 5kHz was used.

On the mechanism of EDEPR

102

It is assumed that the three ms-states of the SL1-centre are equally occupied. Yet the

recombination probability is different for the three states. To facilitate the following

considerations it is assumed that the recombination probability R0 of the triplet state

m significantly larger compared to the one of the other triplet states, 1

and 1−=

m, which are called R+1 and R−1, respectively. Thus, 110 ,−+

>> RRR is as-

sumed. Similar to a donor-acceptor pair recombination the different recombination

probabilities of the ms-states enables the electrical detection of EPR via a spin-

dependent recombination. The triplet states of the recombination centre can be created

by the capture of charge carriers ( created by illumination ) with a generation rate G, but

can be destroyed with the dissociation rate WD when emitting the charge carriers. Due

to the assumed higher recombination probability R0 of the triplet state 0

m, a lower

occupation density of this state compared to the 1±=

m states is found. In the case of

EPR transitions being induced according to the selection rule ∆ms=±1, additional elec-

tron-hole pairs are transferred to the 0=

m state, which leads to an increased number

of recombining charge carriers. The increased recombination results in a conductivity

decrease of the sample and can be detected in EDEPR. In the figures 6.4 and 6.5 the

processes are illustrated.

Fig. 6.4 Schematic illustration of an electron-hole recombination via the triplet state

of the radiation-induced SL1 defect. (V-O)0 is for the singlet ( S=0 ) and (V-

O)0* for the triplet state ( S=1 ) of the SL1. The meaning of the arrows is

explained in the text. Further, “e” is for electrons and “h” for holes.

On the mechanism of EDEPR

For the model presented above it is assumed that the neutral singlet state (V-O)0 cap-

tures a hole from the valence band and an electron from the conduction band. In the

case that the spins of the hole and the electron are parallel, the triplet can be formed.

However, if additional donors like 31P or TDDs are present in the sample, the electron

to form the triplet state of the SL1 can come from the donor level as well. It can be as-

sumed that the (V-O)0 captures a hole from the valence band and changes to paramag-

netic state, similar to an acceptor.

In the case that the donor is in its neutral state due to the capture of an electron, both the

hole from the (V-O)0 state of the SL1 ( the “acceptor” ) and the electron from the donor

can recombine via the triplet state if the spins are parallel. The spin orientation of the

donor can be changed with the microwave with certain probability of the EPR transition

WEPR. With the requirement of parallel spins for the recombination a spin selection rule

is found which explains the detection of the donors with EDEPR. Thus, the EDEPR

detection of the additional donors can be explained by an “amplified” donor-acceptor

pair recombination via the SL1-centre. The recombination of electrons and holes with

he participation of additional donors is displayed schematically in figure 6.6.

Fig. 6.5 Schematic illustration of the singlet, ( S=0 ) and (V-O)0, and the triplet state,

( S=1 ) and (V-O)0*, of the radiation-induced SL1 defect. The R(−1,0,+1) indi-

cate the recombination probabilities from the excited triplet to the singlet

ground state for the corresponding ms .

On the mechanism of EDEPR

104

From the EDEPR investigation sample with radiation defects and TDDs it was meas-

ured that the samples conductivity decrease is about ∆σ/σ § Â−3. The relative sign

and the magnitude of the conductivity change are in good agreement with the values

predicted by the modified donor-acceptor recombination mechanism. For a detailed

explanation of the procedure to determine the values the reader is referred to Stich

[Stich 1997]. Since the SL1 signals could be detected in EPR as well as in EDEPR an

investigation of the power dependence of the signals was performed with both methods.

The results are displayed in figure 6.7. The solid lines have been calculated according to

the formulae presented in chapter 1, equations 1.15 and 1.18, which describe the char-

acteristic EPR and EDEPR power dependencies. The latter is based on the D-A-

recombination model. The amplitude and curve parameters used to calculate the

EDEPR power dependence are C=55 and TR=0.025s, respectively. Both parameters C

and TR are assembled of values of the generation rate ( G ), the dissociation rate ( WD )

and the recombination probabilities Ri of the three ms-states of the triplet. For a detailed

explanation of the parameters C and TR the reader is referred to Stich [Stich 1997]. A

good agreement of the calculated curves with the experimental data is obvious. Seen

Fig. 6.6 Schematic illustration of an electron-hole recombination via the triplet state

of the radiation-induced SL1 defect with an additional donor present in the

sample. (V-O)0 is for the singlet ( S=0 ) and (V-O)0* for the triplet state

( S=1 ). The meaning of the arrows is explained in the text. Further, “e” is

for electrons and “h” for holes.

On the mechanism of EDEPR

together with the fact that both the sign and the magnitude of the observed conductivity

change can be predicted correctly ( explained in detail by [Stich 1997] ), three argu-

ments have been found to prove the proposed donor-acceptor recombination model to

be correct.

6.4 On the mechanism responsible for the EDEPR detection of Pba

and Pbb

So far the mechanism responsible for the EDEPR detection of Pb-centres has been dis-

cussed controversially in the literature. In this study the EDEPR signals of Pba and Pbb

correspond to a decrease of the sample conductivity of approx. ∆σ/σ =7·10−4. The de-

crease of the conductivity is in agreement with both the Lépine-model and the donor-

acceptor ( D-A )-pair recombination mechanism by Stich [Stich 1997]. However, the

magnitude of the conductivity change can only be explained by the latter model. For the

Fig. 6.7 Microwave power dependence of the TDD+ signal of the sample presented

in figure 6.3. The spectra were recorded at T=10K in X-band for both EPR

and EDEPR and the sample was illuminated each time. Magnetic field

modulation was used with 100kHz and 5kHz, respectively. The solid lines

are calculated according to equations 1.15 and 1.18, respectively.

On the mechanism of EDEPR

106

D-A-recombination mechanism donors and acceptors have to be present in the sample.

From the g-factor values obtained for Pba and Pbb which are higher than that of the free

electron ( 2.0023 ), it can be concluded that both Pba and Pbb act as donors. As the sam-

ples were prepared from p-type ( boron ) FZ-silicon boron can be assumed to be the

corresponding acceptor. Thus both partners for recombination are present in the sample.

A study of the power dependence reveals a further argument for the applicability of the

D-A recombination mechanism. In figure 6.8 the observed signal intensities of the

dominant line of the Pba centre in dependence of the microwave power are shown. Ad-

ditionally, a curve calculated with equation 1.15 is inserted in the figure. Equation 1.15

describes the power dependence of an EDEPR signal according the D-A mechanism. A

good agreement of the curve with the experimental data points is found. The power de-

Fig. 6.8 Microwave power dependence of the Pba EDEPR signal of a sample im-

planted with Mo with 7MeV. The sample is presented in detail in chapter

figure 3. The spectra were recorded at T=10K in X-band EDEPR and the

sample was illuminated during the measurement. Magnetic field modulation

was used with 100kHz and 5kHz, respectively. The solid lines are calculated

according to equations 1.15 and 1.18, respectively.

On the mechanism of EDEPR

pendence has been calculated with values of C=380 ( amplitude parameter ) and

TR=0.04s ( curve parameter ). The parameter C limits the maximum value of the calcu-

lation is therefore dependent on the signal intensity of the experiment. It is noted that

the parameter TR, which is responsible for the shape of the curve, is very similar for the

calculated dependencies in the figures 6.7 and 6.8. This indicates that the recombination

efficiency for both defect systems the SL1-centre and the dangling bonds are similar.

Hence, a further argument is found to support the assumption that a donor-acceptor re-

combination process is responsible for the EEPR detection of the dangling bonds.

From SDR measurements by Henderson et al. it was concluded that the dangling bonds

on the trivalent Si-atoms act as centres for electron-hole recombination processes

[Henderson 1984]. As the recombination results in a conductivity change in a surface-

near region of the sample, the Pb centres can be detected with EDEPR. The suggested

SDR mechanism is developed upon the Lépine model but lacks the correct evaluation of

the magnitude of the SDR effect. The model predicts an SDR effect of ∆σ/σ =10−6 [Lé

pine 1972] whereas Henderson et al. observed ∆σ/σ =10−4. The authors could not ex-

plain the derivation of ∆σ/σ between experiment and theory.

With the predicted power dependence, the sign and the magnitude of the conductivity

change, three arguments can be found to support the D-A-recombination model for the

EDEPR detection of Pba and Pbb. However, the validity of the mechanism remains

somewhat speculative.

6.5 Peculiarities of EDEPR

Figure 6.9a depicts an EPR spectrum of an electron-irradiated p-type ( boron-doped )

Si-sample. The resonance line near 330mT ( g=2.0699 ) represents an iron contamina-

tion of the sample, which is known to be a interstitial centre in silicon [Ludwig 1962]. It

can be regarded as the dominant peak in the EPR spectra whereas it is not detectable in

the EDEPR spectrum in figure 6.9b. The phenomenon can be explained by the fast re-

combination behaviour of the iron. Its recombination time is shorter compared to the

spin-flip-rate for a spin-dependent transition. The available microwave power is not

high enough to induce sufficient spin transitions during the recombination time.

On the mechanism of EDEPR

108

As an essence of figure 6.9 it has to be kept in mind that the applicability of EDEPR has

to considered carefully. Defect centres detected in EPR may not be detectable in

EDEPR as the mechanism for the two techniques appears to be a different one.

6.6 Conclusions

Summarising the results of this chapter it can be concluded that EDEPR is a qualitative

method for the spectroscopy of point defects in semiconductors. For low defect concen-

trations and moderate donor-acceptor recombination times the methods provides spec-

tral information and signal-to-noise ratios equal to those obtained by EPR. For selected

Fig. 6.9 EPR (a) and EDEPR (b) X-band spectrum of an electron irradiated p-type

Si-sample with a strong Fe-contamination at B~330mT. The Fei0-signal can

be detected in EPR only.

On the mechanism of EDEPR

defect systems, EDEPR can be more sensitive with respect to the spin concentration per

cm3 by up to 4 orders of magnitude. The method is especially suitable for state-of-the-

art thin layers and surface/interface defects. The EDEPR signals of point defects can be

strongly increased by irradiation of the sample, as the radiation defects act as “shunts”

which are known from ODMR. The recombination via the triplet state of the radiation-

induced SL1-centre provides an efficient channel to detect additional shallow donors as

well. It can be estimated that if the recombination time of a defect is comparable to the

spin-lattice relaxation time a strong EDEPR signal should be observed.

On the mechanism of EDEPR

110

111

Summary

The simultaneous detection of two dangling bond centres at and below a (100) Si/SiO2

interface is reported for the first time. It is noted that the detected dangling bond centre

Pba is very similar to the Pb0 defect reported in the literature. The Pb0 centre is related to

implantation damage below the Si/SiO2 interface, leading to dangling bonds within the

bulk material. Assuming a positive identification of Pba with Pb0 the result underlines

the observation that the Pb0 centre is generated by particle radiation. However, the iden-

tification of the Pba centre found here with the known Pb0 centre must remain somewhat

uncertain.

The more anisotropic Pbb centre can be attributed to dangling bonds at the (100) Si/SiO2

interface, occurring after annealing or low energy particle implantation. The Electrical

Detection of Electron-Paramagnetic Resonance ( EDEPR ) signal of the Pbb centre can

be increased by annealing in an oxygen containing atmosphere. The Pbb centre has been

detected for the first time due to the increased sensitivity and low noise figure of low

temperature EDEPR measurements.

Angular dependent EDEPR spectra of the dangling bond centres Pba and Pbb have been

recorded with improved spectral resolution and signal-to-noise ratio. The calculation of

the angular dependence reveals a threefold symmetry of both defects. It can be con-

cluded that the dangling bonds are aligned along a [111] direction in the crystal. The Pba

centres are thought to be due to silicon vacancies in the bulk created by radiation dam-

age leaving the [111] dangling bond at one neighbour. The radiation damage is also

believed to stabilise the vacancies against diffusion.

Shallow thermal donors which were prepared according to a recently developed proce-

dure, comprising hydrogenation and electron-irradiation prior to annealing, were inves-

tigated with optical and magnetic resonance spectroscopy. Thus, three species ( D1-D3 )

of these shallow donors can be created selectively by choosing a specific temperature in

the range of (300−500)°C for the annealing step. The electronic properties of the Dn

Summary

112

were determined by means of Fourier Transform Infrared Absorption ( FTIR ) meas-

urements. Evidence for an identification of D2 and D3 with two species of hydrogen-

related shallow thermal donors ( STD(H) ) reported in the literature was found from the

FTIR data. It is shown that the D1 is a precursor or the first species of the STD(H), un-

discovered before.

EPR studies of the Dn centres revealed an isotropic ( g = 1.9987 ) D1 signal upon rota-

tion of the sample and orthorhombic-I symmetry for D2 centres ( gx,y,z = 1.99952,

1.99722, 1.99982, ∆g = ±0.00002 ). The high accuracy of the g-values was obtained

from EDEPR spectra recorded with V-band microwaves ( 72GHz ). The g-values of the

D2 are very similar to those of the oxygen precipitate NL10 presented in the literature

and an identification of the Dn with the early species of the NL10 is suggested. Hyper-

fine ( hf ) lines of D1 and D2 due to an interaction of the unpaired electron with 29Si

nuclei ( nuclear spin I=1/2 ) are observed. From the intensity ratio of the hf lines to the

central line ( § ) the incorporation of one silicon atom in the defect structure of the

Dn is concluded. Similar hf interactions are observed for NL10 defects with the incor-

poration of hydrogen, NL10(H), and aluminium, NL10(Al) for the first time.

The detection of the individual Dn centres with both methods FTIR and EPR provides a

clear link between the STD(H) and the NL10(H) centres, reported in the literature sepa-

rately from measurements of FTIR and EPR, respectively.

From an Electron-Nuclear Double Resonance ( ENDOR ) study of D1 centres prepared

with hydrogen ( deuterium ), the incorporation of one hydrogen ( deuterium ) atom in

the D1 defect is found. The angular dependence of the ENDOR spectra can be under-

stood assuming a low symmetric ( triclinic ) hf tensor of the hydrogen atom. From the

hf interactions observed in ENDOR a very low spin density at the site of the hydrogen

is derived. A comparison with published data reveals that with the investigation of the

D1 centre the first species of the STD(H) / NL10(H) has been studied for the first time.

An atomic model for the STD(H) centre had been presented previously on the basis of

theoretical calculations. All experimental findings of this study support the suggested

(C-H)i-Sis-O2i structure. Furthermore, as an interstitial site for the Al-atom in NL10(Al)

was suggested in a previous study, a similar atomic model with the (C-H)i exchanged by

an Ali can be proposed for the NL10(Al).

Finally, the results of the EDEPR measurements carried out for this thesis have been

summarised. A previously suggested donor-acceptor pair ( DAP ) recombination model

for the mechanism of EDEPR was used to explain the recorded spectra. An investiga-

Summary

tion of the characteristic microwave power dependence of the EDEPR signals and both

the sign and the magnitude of the conductivity change support the assumption. Further,

indications were searched for to explain an amplification of EDEPR signals after irra-

diation of silicon samples with electrons. It is concluded that by the creation of the ra-

diation-induced defect SL1, which appears upon illumination of the sample, an efficient

recombination channel is provided via the triplet state of the SL1. This recombination

channel can be “used” similar to a “shunt” known from Optically Detected Magnetic

Resonance by other defects in the sample and their EDEPR signal can be significantly

increased.

Further it is shown that a variation of the modulation techniques for the detection of

EDEPR can improve both the signal-to-noise ratio of the detected signals and the spec-

tral resolution in the case of several overlapping resonance lines. The spectral resolution

of EDEPR was further enhanced by the use of high microwave frequencies in a modi-

fied high-field spectrometer. EDEPR measurements with frequencies as high as 72GHz

are reported for the first time.

Summary

114

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Mein besonderer Dank gilt Herrn Prof. Dr. J.-M. Spaeth für die freundliche Aufnahme

in seine Arbeitsgruppe. Kritische Diskussionen waren stets ergebnisorientiert und

brachten die entscheidenden Hinweise zur Deutung der experimentellen Daten.

Herrn PD Dr. S. Greulich-Weber danke ich für die Einführung in die magnetischen Re-

sonanzmethoden und seine stete Hilfe bei experimentellen Problemen aller Art.

Ich danke Herrn Dr. habil. S. Schweizer für seine Hilfe, die auch über fachliche Pro-

bleme hinaus stets freundschaftlich war.

Ich danke allen, die für eine vortreffliche Infrastruktur im Fachbereich sorgten,

für das Rechnernetz Herrn Dr. Ch. Hoentzsch,

für die mechanische Werkstatt Herrn F. Risse,

für die Versorgung mit Kältemitteln Herrn Dr. F. Lohse und Herrn J. Pauli und

für das Kristallzuchtlabor mit Herrn D. Niggemeier und Herrn R. Winterberg.

Dank gilt allen Mitgliedern des Institutes für die gute Zusammenarbeit und ein hervor-

ragendes Arbeitsklima.