Plasmonically enhanced light absorption in graphene nanoribbons

Master Erasmus Mundus in Photonics Engineering, Nanophotonics and Biophotonics Europhotonics MASTER THESIS WORK Infrared Plasmons and Photocurrent in Graphene Achim Wößner Supervised by Prof. Frank Koppens (ICFO - Institut de Ciències Fotòniques) Presented in Barcelona, on 6th September 2012 Registered at Infrared Plasmons and Photocurrent in Graphene Master Thesis of Achim Wößner at ICFO - The Insitute of Photonic Sciences Reviewer: Prof. Frank Koppens (ICFO) Second Reviewer: Prof. Uli Lemmer (KIT) Advisor: Dr. Marko Spasenovi´ c (ICFO) Duration: 1. April 2012 – 6. September 2012 I herewith declare, that the present thesis is original work written by me alone and that I have indicated completely and precisely all aids used as well as all citations, whether changed or unchanged, of other theses and publications. Ich versichere wahrheitsgem¨ aß, die Arbeit selbstst¨ andig angefertigt, alle benutzten Hilfsmittel vollst¨ andig und genau angegeben und alles kenntlich gemacht zu haben, was aus Arbeiten anderer unver¨ andert oder mit Ab¨ anderungen entnommen wurde. Achim W¨ oßner Abstract Light absorption plays a crucial role in both optical detectors and photovoltaics. In order to improve the light absorption properties of materials different measures can be taken. This thesis considers light absorption of graphene in the mid infrared region of the electromagnetic spectrum. A numerical study of light absorption and of localized plasmons in nanostructured graphene is presented and discussed. We show that for nanostructured graphene in the mid infrared region of the spectrum light absorption can increase significantly due to plasmon resonances. We perform photocurrent measurements in graphene in the mid infrared region of the spectrum. We show the first proof of concept measurements showing photocurrent in the midinfrared from simple graphene devices. We find a photodetection responsivity of 10−4A/W in unpatterned graphene in the mid-infrared. Keywords: Graphene, Nanoribbons, Plasmonics, Photocurrent, Mid-Infrared Contents 1 Introduction 1 2 Background 3 2.1 GrapheneProperties ........................... 3 2.1.1 Conductivity in the Random-Phase Approximation . . . . . . 5 2.1.2 Graphene Light Absorption . . . . . . . . . . . . . . . . . . . 7 2.1.3 Photon Absorption . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 GraphenePlasmons............................ 9 2.2.1 Graphene Plasmon Dispersion Relation . . . . . . . . . . . . . 9 2.2.2 Localized Graphene Plasmons . . . . . . . . . . . . . . . . . . 10 2.2.3 RelaxationTime ......................... 11 2.3 Photocurrent ............................... 12 2.3.1 Mechanisms of Photocurrent Generation . . . . . . . . . . . . 12 3 Plasmon Simulations 15 3.1 Graphene Nanoribbons . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.2 SingleRibbon............................... 16 3.3 MobilityVariation ............................ 21 3.4 WidthVariation.............................. 23 3.5 Fermi Energy Variation . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.6 DistanceVariation ............................ 29 3.7 Conclusions ................................ 31 4 Infrared Photocurrent 33 4.1 ActiveArea ................................ 33 4.2 Characterization of the Devices . . . . . . . . . . . . . . . . . . . . . 33 4.3 Measurements............................... 37 4.3.1 Setup ............................... 37 4.3.2 Device(1)............................. 40 4.3.3 Device(2)............................. 45 4.4 Conclusion................................. 47 5 Outlook 49 5.1 Simulations ................................ 49 5.2 Experiments................................ 49 Bibliography 53 i 2. Background constant and τis the relaxation time of the carriers. The relaxation time takes into account losses due to impurities, defects and scattering in a phenomenological way and can be extracted from the dc mobility of graphene [38]. Assuming zero temperature, which is a good approximation for doped graphene where EFkBT and a Fermi energy high enough such that the interband channel in Eq. 2.1 becomes negligible. Eq. 2.3 describes the interband transitions, which produce losses for energies higher than 2EF. In this term Θ is the Fermi-Dirac distribution function. The conductivity is derived using the local environment [15] . The limit of the structure size below which the RPA breaks down due to quantum effects is around 10 nm [39]. Therefore it is assumed that the RPA also holds for the nanostructured graphene under investigation. The frequency dependent permittivity, or dielectric function, of graphene can then be calculated using [40]: ε(ω) = 1 + iσ(ω) ε0ω(2.4) Figure 2.3: Real (solid curves) and imaginary (dashed curves) parts of the conductivity of doped graphene as a function of energy. The middle of the kink for each of the Fermi energies is at 2EF. For high transition energies the conductivity reaches a constant value of e2/4¯h. From [15]. Fig. 2.3 shows the real parts (solid curves) and imaginary parts (dashed curves) of the conductivity of doped graphene as a function of energy. The zero conductivity for low transition energies is due to Pauli blocking which will be explained later. The middle of the kink for each of the Fermi energies is at 2EF. For high transition energies the conductivity reaches a constant value of e2/4¯h. 6 2.1. Graphene Properties One can show that the constant conductivity over this large frequency range leads to a constant absorption of the graphene layer. For this one needs to consider the incident photon flux of a laser with the electric field ~ E, which shines perpendicular on a graphene sheet of unit area to be Wi=c/4π|~ E|. The light absorbed by the graphene sheet can be shown to be Wa=σ|~ E|=e2/4¯h|~ E|[41]. One finds that the absorption is P=Wa/Wi=πe2/¯hc =πα which is the universal absorption constant of graphene. This broadband constant absorption, which is only dependent on the fine structure constant α=e2/¯hc ≈1/137, can be explained by the fact that graphene has a gapless dispersion relation and by its two dimensional nature [41]. 2.1.2 Graphene Light Absorption Fig. 2.4 (a) shows a microscope image of an area that is partly covered with single layer graphene and bilayer graphene. A scan along the yellow line clearly shows that single layer graphene absorbs 2.3% of the incoming light and bilayer graphene around twice as much. This absorption for only a single atomic layer is remarkably high. Figure 2.4: (A) Microscope image of an area which is partly covered with graphene and bilayer graphene. A scan along the yellow line showing the intensity transmittance of white light is shown. The inset shows the sample design which is a 20-µm-thick metal structure that has several apertures of 20, 30, and 50 µm in diameter with graphene placed over them. (B) The open circles show the transmittance spectrum of graphene. The inset shows the transmittance for multilayer graphene. The frequency independent absorption of 2.3% is remarkably large for a single atom thick material and can be expressed in terms of the fine structure constant α. From [41]. Fig. 2.4 (b) depicts that the absorption of graphene for a wide frequency range is constant and only determined by the fine structure constant. This shows experi7 2. Background mentally that the universal absorption constant of graphene. 2.1.3 Photon Absorption Fig. 2.5 depicts the mechanism of both photon absorption and Pauli blocking in graphene. The dispersion relation is referred to as Dirac cone. Photons can only make vertical transitions as their momentum is too small to give momentum to the electrons in order to change their momentum and therefore make non-vertical transitions. Figure 2.5: Sketch of the mechanism of Pauli blocking in graphene. EFshows the Fermi energy of the graphene. ¯hω shows the energy of the photon. (a) Photons with an energy smaller than 2 |EF|cannot be absorbed by graphene due to Pauli blocking. (b) Photons with an energy bigger than 2|EF|get absorbed by the graphene. (c) Photons with an energy smaller than 2 |EF|cannot be absorbed by graphene due to Pauli blocking. Fig. 2.5 (a) shows that photons with an energy smaller than 2 |EF|cannot be absorbed by graphene. This is because the photon energy is not high enough to excite an electron from the valence to the conduction band. Fig. 2.5 (b) shows a photon with an energy bigger than 2 |EF|where a photon can excite an electron from the valence band to the conduction band and therefore create an electron-hole pair. This means that for a photon with an energy ¯hω > 2|EF|free carriers can be created which is a necessary condition for a photovoltaic photoresponse. Fig. 2.5 (c) depicts the case where Fermi energy of the graphene is too high and therefore there are no free states for an electron to be excited from the valence band to the conduction band due to the Pauli exclusion principle, hence also the name Pauli blocking [42]. The principle of Pauli blocking in graphene has already been applied to use graphene as a saturable absorber for building a graphene based modelocked laser [43]. 8 2.2. Graphene Plasmons 2.2 Graphene Plasmons While an absorption of 2.3% is a lot for a material that is only one single atom thick, in terms of absolute absorption the value is rather small. In order to increase the absorption of graphene it is possible to use plasmons. Plasmons are collective oscillations of electrons at the surface of a conductor, and can be excited by photons. Graphene plasmons promise many interesting features which are explained in the following section. 2.2.1 Graphene Plasmon Dispersion Relation In order to find the plasmon dispersion relation of a two dimensional layer of graphene one needs to solve Maxwells equations with the appropriate boundary conditions [13]. For graphene with a dielectric on one side and air on the other, one finds that: ε pεk2 0−k2 P +1 pk2 0−k2 P =−4πσ(ω) ω(2.5) Here εis the dielectric constant of the dielectric. For the limit of the non retarted regime, i.e. ω/c =k0 |kP|, Eq. 2.5 simplifies to: kP≈iω ε+ 1 4πσ(ω)(2.6) Plugging the frequency dependent conductivity from Eq. 2.2 into Eq. 2.6 leads to the following dispersion relation for graphene plasmons in highly doped graphene: kP≈¯h2 4e2EF(ε+ 1) ω2+iωτ−1(2.7) We can clearly see a quadratic dependence of the real part of the plasmon wave vector on ω. From this equation one finds for the relation between the surface plasmon wavelength and the free space wavelength: λP≈λ0αEF EP 4 εr+ 1 (2.8) The plasmon wavelength is λP,α= 1/137 is the fine structure constant, λ0is the free space wavelength of light, EP= ¯hω0is the plasmon energy and εrthe relative permittivity of the substrate. One can see that the plasmon wavelength only depends on the Fermi energy EFof the graphene layer, on the plasmon energy EP and on the relative permittivity of the substrate. These parameters, especially the Fermi energy and the plasmon energy can be easily controlled from the outside and therefore the plasmon wavelength can be controlled using external parameters. This formula shows that the plasmon wavelength in graphene is by about a factor of α smaller than the free space wavelength, which makes graphene an excellent material for tight confinement of light. 9 2. Background The losses of surface plasmons can then be calculated using the following formula [13]: Re {kP} Im {kP}=ωτ =2πcτ λ0 (2.9) One can see that for the losses of the graphene plasmon both the intrinsic relaxation time τand the excitation frequency of the plasmon are relevant. Figure 2.6: Dispersion diagram of a surface plasmon mode in graphene for a Fermi energy of EF= 0.5 eV. Furthermore the intraband and interband transitions are shown in green and red. From [15]. Fig. 2.6 shows the dispersion relation of graphene plasmons. One has to note that graphene plasmons are only long lived excitations in a regime where neither interband nor intra-band transitions are possible (white region on the left of Fig. 2.6) [44]. 2.2.2 Localized Graphene Plasmons Localized plasmons in graphene nanostructures possess slightly different properties than surface plasmons and can behave similar to two-level systems at resonance with the frequency of the incoming electromagnetic field. This section compares the absorption behavior of localized graphene plasmons with the absorption behavior of atoms interacting with an electromagnetic field. In order to understand the absorption properties of graphene plasmons one can look at the polarizability of the nanostructure. The polarizability is a measure of how the nanostructure responds to an external electromagnetic field. It was found that the polarizability of graphene nanodisks is well described by a Lorentzian lineshape as [45, 46]: α(ω) = 3c3κr 2ω2 0 1 ω2 0−ω2−iκω3/ω2 0 (2.10) where ω0is the plasmon frequency, κris the radiative contribution to the decay rate and κis the total decay rate. The decay rate of a of the plasmon is related to the 10 2.2. Graphene Plasmons plasmon relaxation time by κ= 1/τP. One can then calculate the extinction cross section for incident light parallel to the disk using σext = (4πω/c) Im {α(ω)}. This gives: σext(ω) = 6πc2κrκω41 ω4 0(ω2 0−ω2)2+κ2ω6(2.11) From Eq. 2.11 of the absorption one finds that the maximum extinction cross section at resonance, i.e. ω=ω0, of the graphene plasmon on a graphene nanodisk is: σext =3λ2 0 2π κr κ(2.12) where λ0is the wavelength of the plasmon resonance, κis the total decay rate and κrthe radiative decay rate. Typically the total decay rate is much bigger than the radiative decay rate [46]. It is important to note that even though all the formulas above are for graphene nanodisks in principle they are also valid for graphene nanoribbons, as long as the polarization of the incident light is parallel to the surface and the short axis of the nanoribbon. The maximum absorption cross section of a two level atom with the incident light on resonance with the transition energy and the ground and excited states having the same statistical weight, can be described using the formula [47]: σabs =3λ2 0 2π κr κ(2.13) where λ0is the resonance wavelength of the transition, κis the total decay rate and κrthe radiative decay rate.. By comparing extinction cross section of a localized graphene plasmon in Eq. 2.12 with the absorption cross section of an atom at resonance in Eq. 2.13 it becomes clear that the maximum extinction cross section of a graphene plasmon and the maximum absorption cross section of a two level atom have the same analytical expression. The difference is the decay rate of a a localized plasmon and an atom. A localized plasmon has typical total decay rates of 1012 1/s and an atom has typical decay rates of 1081/s. 2.2.3 Relaxation Time The intrinsic relaxation time, or also scattering time, of graphene takes into account the losses due to impurities, defects and scattering in a phenomenological way. If the excitation frequency is below the inter-band transition frequency and below the optical phonon branch (¯hω < 0.2 eV) one can neglect both inter-band transitions and electron-phonon interactions. Therefore the scattering time τcan then be estimated from dc conductivity measurements [1, 38]. The relaxation time in graphene can be calculated using: τ=1 ev2 F µEF(2.14) 11 2. Background where µis the dc mobility of the graphene, EFis the Fermi energy, ethe elementary charge and vF≈c/300 the Fermi velocity in graphene [48]. A moderate mobility of µ= 10000 cm2/Vs gives a relaxation time of τ≈10−12 s for EF= 1 eV and τ≈10−13 s for EF= 0.1 eV. In silver the relaxation time is 10−14 s. This shows that plasmons in graphene can be up to two orders of magnitude longer lived than plasmons in silver for typical carrier mobilities of graphene. This fact makes graphene an ideal candidate for replacing traditional metals, such as silver and gold, in the field of plasmonics. 2.3 Photocurrent This section explains the different mechanisms which can lead to a photocurrent in graphene. Different origins of the photoresponse were shown to exist in graphene illuminated by a laser in the visible region of the electromagnetic spectrum [49, 50] 2.3.1 Mechanisms of Photocurrent Generation Three different mechanisms are though to contribute to photocurrent in graphene: Bolometric Effect The bolometric effect is an effect in which the incident electromagnetic radiation increases the local temperature of the graphene. The change of temperature then changes the resistance of the graphene which produces a photocurrent for a graphene device with an applied bias. One can confirm the bolometric effect by measuring the temperature dependence of the photocurrent. The bolometric coefficient can then be extracted [50]. This effect can only be seen for a biased graphene device and is therefore not considered to be relevant for the conducted experiments. Thermoelectric Effect For generating a thermoelectric photocurrent the laser spot creates a temperature gradient in the device. This creates a thermoelectric current. Typically in experiments a p-n junction is used to produce a Seebeck effect which then turns into a photocurrent [49, 51, 52]. Photovoltaic Effect For the photovoltaic effect photo-excited electrons and holes are separated and then pulled into opposite directions by the built-in electric field due to the work function mismatch at the graphene gold interface or by applying an external electric field. Fig. 2.7 shows a sketch of how a photocurrent can be seen in unbiased graphene devices. The Fermi energy is depicted by the dashed line and is the same throughout the whole device because there is no bias electric field applied to the contacts. The energetic position of the Fermi level in the device is governed by the gold contacts, because of their large amount of charge carriers, through so called Fermi level pinning [53]. 12 2.3. Photocurrent The solid black line is a sketch of the band diagram of the graphene. As it can be seen a p-n-p junction is formed within the graphene device. As the electrostatic potential φ∝ −Eband it becomes clear that a bending in the band structure at the contacts of the graphene gold interface leads to a built in electric field at these contacts. Charge carriers that are created within this region are separated by the electric field. S D + p n p Δϕ { Laser - Figure 2.7: Sketch of the mechanism that is responsible for a photovoltaic photocurrent at a graphene metal interface. The dashed line shows the Fermi energy and ∆φdescribes the pinning of the Fermi level. Both source (S) and drain (D) contacts are made of gold. Laser light is impinging on the interface between graphene and a contact and creating an electron hole pair. Due to the potential difference between the contact and the graphene a current can flow. Adapted from [53]. Charge carriers that are created in the middle where the band is flat do not feel any electric field and therefore can only move by diffusion. With a typical carrier relaxation time of 0.1 picoseconds and a typical mobility of µ= 10000 cm2/Vs the diffusion length can be calculated using ld=pkBTµτ/e, where eis the elementary charge and kBT= 25 meV at room temperature. One then finds that the diffusion length in graphene with this properties is around 50 nm. This shows that diffusion is a negligible effect for the generation of photocurrent for graphene samples with a typical mobility. For graphene on boron nitride or suspended graphene with much higher mobilities [27, 28, 29], and therefore also a possibly longer lifetime of the charge carriers, one can imagine that photocurrent due to diffusion starts playing a role. 13 3. Plasmon Simulations In this chapter simulations of graphene nanoribbons with different parameters and properties are shown and analyzed. First graphene nanoribbons and their manufacturing process are introduced. After this the general setup of the simulation and the parameters used are explained and justified. Afterwards the simulation results for a single graphene ribbon in free space are shown and explained. After that the change of the plasmonic resonance by changing various parameters of the graphene ribbons, such as their mobility, size and Fermi energy, is investigated. Thereafter the resonance of multiple graphene ribbons and their coupling is investigated. Finally the implications of the obtained results onto designing samples for a successful experiment for showing plasmonic resonances are discussed. 3.1 Graphene Nanoribbons Graphene nanoribbons are nanostructured graphene sheets with a specific width and length, where the width is typically tens of nanometers and the length tens of micrometers. For multiple nanoribbons there is one additional parameter, which is the distance between the ribbons. The easiest way to define graphene nanoribbons is electron beam lithography [54, 55]. For electron beam lithography the minimum width obtainable is limited by the resolution of the electron beam process, but it is typically god enough to get widths which are desired within this thesis. Other techniques, such as scanning tunneling microscope lithography [56], unzipping carbon nanotubes [57, 58] or nanoscale cutting [59] exist to create very narrow nanoribbons with properties different from bulk graphene. Figure 3.1: Schematic of a graphene nanoribbon with a width wand a length l. The nanoribbons which are simulated in this thesis have a much smaller width than length, i.e. wl. A typical width is 60 nm and a typical length are tens of micrometers. Fig. 3.1 depicts a schematic of a graphene nanoribbon with a width of w, also referred to as short axis, and a length l, also referred to as long axis. The nanoribbons under consideration have a much smaller width than length, with a width of typically 60 nm and a length of tens of micrometers. Edge effects are not relevant for the 15 3. Plasmon Simulations absorption for an increase of mobility is visible. As Eq. (2.8) predicts there is no dependence of the resonance frequency on the carrier mobility of the graphene. 0 10000 20000 0 1 0 2 0 M a x i m u m A b s o r p t i o n ( % ) M o b i l i t y ( c m 2/ V s ) (a) Maximum absorption 0 10000 20000 0 1 2 3 4 5 6 7 F W H M ( T H z ) M o b i l i t y ( c m 2/ V s ) (b) FWHM Figure 3.7: Maximum absorption and FWHM extracted from Fig. 3.6 for different mobilities. (a) Increasing maximum absorption for an increasing mobility is shown. The black dashed line shows a linear fit of the maximum absorption. (b) Decreasing FWHM with an increasing mobility. The black dashed line shows a fit of FWHM ∝1/µ. Fig. 3.7 (a) depicts the increasing maximum absorption with an increase of the mobility. The black dashed line shows a linear fit of the maximum absorption. According to Eq. 2.9 the losses in graphene are proportional to ωτ. As the frequency stays constant with a change of mobility the losses are proportional to τwhich is proportional to µ. Therefore we find that the losses of plasmon and therefore its maximum absorption of the graphene ribbon are linearly dependent on the graphene mobility. In Fig. 3.7 (b) we find that the FWHM of the plasmon resonance peak decreases with increasing mobility, which means that the decay rate of the plasmon resonance decreases. This behavior is expected as the graphene plasmons have a longer lifetime with increasing graphene mobility. Therefore one can see that for an increasing mobility the resonance wavelength of the plasmon stays constant while the FWHM decreases. It was shown that the plasmon quality factor follows qualitatively the behavior Q≈ω0τ[15]. The definition of the quality factor is Q=ω0/FWHM. Therefore combining the two formulas of the qualitative behavior and the definition of the quality factor we find that FWHM ∝1/τ and as shown in Eq. 2.14 τ∝µ and therefore we find that FWHM ∝1/µ which is the fit we used for the FWHM in Fig. 3.7 (b). 22 3.4. Width Variation This section clearly shows that high quality graphene with a high mobility is essential for doing experiments with graphene nanoribbons. Not only does the magnitude of the absorption increase strongly with the mobility but also the FWHM of the absorption resonance decreases which allows for much easier detection of the absorption peak due to the graphene plasmon for high quality graphene samples. 0 10000 20000 0 500 1000 1500 Q f a c t o r ( a . u . ) M o b i l i t y ( c m 2/ V s ) Figure 3.8: The quality factor of the plasmon for different mobilities of the graphene extracted from a Lorentzian fit of the absorption profiles in Fig. 3.6. A linear increase of the quality factor with increasing mobility is shown. The black dashed line shows a linear fit of the quality factor. Fig. 3.8 depicts the quality factor Q=ω0/FWHM of the plasmon resonance increasing for an increasing mobility. The black dashed line shows a linear fit of the quality factor with increasing mobility. This means that for an increasing mobility of the graphene one can expect the plasmon excitation to be longer lived. The linear scaling behavior can be found using Q≈ω0τ[15]. We then simply use the definition of the relaxation time from section 2.2.3 and from there we see that τ∝µ. As we have seen before the resonance wavelength does not depend on the mobility and therefore we find that the quality factor scales linear with the mobility, i.e. Q∝µ, which exactly the behavior also found for our numerical simulations of the mobility dependence of the plasmon resonance. From these simulations of different mobilities of the graphene it becomes clear that a high mobility is crucial for experiments with graphene nanoribbons. Not only does the maximum absorption increase with increasing mobility but also the lifetime of the plasmon oscillation. For low quality graphene samples with low mobility it becomes increasingly harder to see the plasmon resonance in experiments because both the maximum absorption and the quality factor decrease with decreasing mobility. 3.4 Width Variation In this section the dependence of the plasmon resonance wavelength on the width of the graphene ribbon is investigated. For the plasmon resonance dependence on 23 3. Plasmon Simulations the variation of the width of the ribbon, a ribbon with a graphene mobility of µ= 5000 cm2/Vs and a Fermi energy of EF= 0.3 eV is simulated. The width of the ribbon is varied from 30 to 150 nm in steps of 30 nm. 4 5 6 7 8 9 1 0 0 2 4 6 8 1 0 1 2 1 4 1 60 . 3 1 0 . 2 5 0 . 2 1 0 . 1 8 0 . 1 6 0 . 1 4 0 . 1 2 w = 3 0 n m P h o t o n E n e r g y ( e V ) A b s o r p t i o n ( % ) W a v e l e n g t h ( µ m ) w = 3 0 n m w = 6 0 n m w = 9 0 n m w = 1 2 0 n m w = 1 5 0 n m Figure 3.9: The absorption spectrum of graphene nanoribbons as a function of the width of the graphene ribbons. An increasing absorption maximum and an increasing resonance wavelength for an increasing width of the ribbon is visible. The parameters used for the simulation are a variable width of the nanoribbon from 30 to 150 nm, a Fermi energy of EF= 0.3 eV and a mobility of µ= 5000 cm2/Vs. Fig. 3.9 depicts the dependence of the absorption spectrum of the graphene nanoribbons for different widths of the ribbons. The trend of an increasing resonance wavelength for bigger widths of the nanoribbons is clearly visible. Furthermore an increase in the maximum absorption of nanoribbons is visible. This increase in absorption magnitude is mainly due to the bigger size of the graphene nanoribbons as a normalization by the width of the ribbons shows. The peaks with a smaller magnitude towards the lower wavelength range correspond to the higher order plasmon modes of the graphene nanoribbons. 24 3.4. Width Variation 0 40 80 120 160 0 4 8 1 2 C e n t r a l w a v e l e n g t h ( µ m ) W i d t h ( n m ) (a) Central wavelength 0 40 80 120 160 0 1 2 F W H M ( T H z ) W i d t h ( n m ) (b) FWHM Figure 3.10: Central wavelength and FWHM extracted from Fig. 3.9. (a) The central wavelength of the plasmon resonance scales with λ0∝√wand a fit for this behavior is shown by the black dashed line. The central wavelength of a nanoribbon with a width of 15 nm is added. (b) The FWHM of the plasmon resonance for different widths of the nanoribbons stays constant as the decay rate in first approximation only depends on the material properties of graphene. The FWHM of a nanoribbon with a width of 15 nm is added. Fig. 3.10 (a) depicts the increasing central wavelength of the plasmon resonance for an increasing width of the nanoribbon. From Eq. (2.8) one finds that λ0∝√λP. Knowing that the width of the graphene ribbon needs to be a multiple of the plasmon wavelength [67] one can deduce that λ0∝√w[66]. The fit of the central wavelength in Fig. 3.10 (a) shows that this simple deduction of the dependence of the resonance wavelength on the width is correct and can also be seen in the numerical simulations used in this thesis. Furthermore this behavior has been shown experimentally by Ju et al. [68] for plasmons in the THz frequency range and is a characteristic of two dimensional electron systems [33]. Fig. 3.10 (b) shows the FWHM of the plasmon resonance for different widths of the nanoribbon. The FWHM of the plasmon resonance stays constant over all the sizes simulated. This is equivalent to a constant decay rate for the different widths of the graphene ribbons. We find this to match with previously published theory for the Fermi energy used in this simulation [46]. 25 3. Plasmon Simulations 0 40 80 120 160 0 100 200 300 400 500 Q f a c t o r ( a . u . ) W i d t h ( n m ) Figure 3.11: The quality factor of the plasmon for different widths of the nanoribbon. The quality factor clearly decreases for an increasing width of the ribbon. The black dashed line shows a fit of Q∝1/√w. Fig. 3.11 depicts the quality factor Q=ω0/FWHM of the plasmon resonance for widths of the nanoribbons. The black dashed line shows a decrease of the quality factor for an increasing width of the nanoribbon. The decrease follows Q∝1/√w. This means that for an increasing width of the nanoribbon the number of plasmon oscillations before the plasmon decays is deceasing. From these simulations show that the width of the nanoribbons has to be chosen according to the specific experimental requirements. While an increasing width gives a higher absolute absorption because of the higher filling factor of the ribbon compared to the incoming laser beam, the quality factor of the plasmon oscillation decreases for an increasing width. Furthermore for experiments the resonance frequency of the plasmon cannot be arbitrary because of the laser one wants to use for the experiment. Therefore one should choose a width of the ribbon which gives a resonance approximately in the middle of the accessible wavelength range. But keep in mind that not only the width but also the Fermi energy in the nanoribbon plays an important role for the resonance frequency of the plasmon as you will see in the next section. 3.5 Fermi Energy Variation In this section the effect of a change of the Fermi energy of the graphene, or in other words a change of the Fermi energy, on the plasmon resonance is investigated. For the plasmon resonance dependence on the variation of the Fermi energy a 60 nm wide ribbon with a graphene mobility of µ= 5000 cm2/Vs is simulated. 26 3.5. Fermi Energy Variation E F = 0 . 1 e V E F = 0 . 2 e V E F = 0 . 3 e V E F = 0 . 4 e V E F = 0 . 5 e V 4 6 8 1 0 1 2 0 2 4 6 8 1 0 1 2 1 4 1 60 . 3 1 0 . 2 1 0 . 1 6 0 . 1 2 0 . 1 0 P h o t o n E n e r g y ( e V ) A b s o r p t i o n ( % ) W a v e l e n g t h ( µ m ) Figure 3.12: The absorption spectrum of graphene nanoribbons as a function of the Fermi energy of the graphene. The parameters used for the simulation are a variable Fermi energy of the nanoribbon from 0.1 to 0.5 eV, a width of 60 nm and a mobility of µ= 5000 cm2/Vs. The resonance wavelength decreases for increasing Fermi energy and the maximum absorption increases. In Fig. 3.12 the absorption spectrum for different Fermi energies of the graphene is shown. A change of the Fermi energy results both in a shift of the resonance wavelength of the plasmon and a change in the absorption. An increase of the maximum absorption for increasing Fermi energy is visible. The other effect is a decrease in the resonance wavelength for increasing the Fermi energy of the graphene. 27 3. Plasmon Simulations 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 4 8 1 2 1 6 EF ( e V ) C e n t r a l w a v e l e n g t h ( µ m ) 0 4 8 1 2 1 6 M a x i m u m a b s o r p t i o n ( % ) (a) Central wavelength and max. absorption 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 1 2 3 4 F W H M ( T H z ) EF ( e V ) (b) FWHM Figure 3.13: Maximum absorption, central wavelength and FWHM extracted from Fig. 3.12. (a) A decreasing central wavelength for increasing Fermi energy is shown. The fit of the central wavelength shows a λ0∝1/√EF dependence of the central wavelength which is shown by the black dashed line. Furthermore a increasing maximum absorption for increasing Fermi energy is depicted. (b) Decreasing FWHM with an increasing Fermi energy. The black dashed line shows a fit of FWHM ∝1/EF. Fig. 3.13 (a) shows the decreasing central wavelength for an increasing Fermi energy. This can be explained using the basic plasmon equation. We set the plasmon wavelength in Eq. (2.8) constant. This is a reasonable assumption, as the plasmon wavelength for the zero order mode of the plasmon is half the width of the graphene ribbon and the width of the graphene ribbon is kept constant in these simulations. We then rearrange the formula and finds that λ0∝1/√EF. The fit of the central wavelength in Fig. 3.13 (a) shows exactly this behavior and therefore shows that the simulation of the Fermi energy dependence of the plasmons gives good results in accordance with the analytical formula for plasmons in graphene. The scaling law of λ0∝1/√EFis a signature of massless Dirac fermions [35, 68]. Fig. 3.13 (b) shows the FWHM of the resonance peaks of the plasmons decreasing with an increase of Fermi energy, which means that the decay rate of the graphene ribbons decreases. One can easily find that the scaling of the FWHM should follow the law FWHM ∝1/EF. This is due to the plasmon quality factor scaling with Q≈ω0τand the definition of the quality factor which is Q=ω0/FWHM. Combining these two formulas one finds that FWHM ∝1/τ. As shown in section 2.2.3 τ∝EFand therefore we find that FWHM ∝1/EF, which is the black dashed line fit in Fig. 3.13 (b). We find this to be consistent with previously published theory [46]. 28 3.6. Distance Variation 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 200 400 600 800 Q f a c t o r ( a . u . ) EF ( e V ) Figure 3.14: The quality factor of the plasmon for different Fermi energies of the graphene. The black dashed line shows a fit of Q∝E3/2 F. Fig. 3.14 shows the quality factor of the plasmon oscillations for the different Fermi energies that have been simulated. It is interesting to note that the quality factor of the plasmon oscillation increases with the proportionality of Q∝E3/2 F. This can be shown simply by the definition of the quality factor and the proportionality of its components. The quality factor is defined to be Q=ω0/FWHM. As we have shown before ω0∝1/λ0∝√EFand FWHM ∝1/EF. Plugging in those proportionalities into the definition of the quality factor one easily finds the proportionality of Q∝E3/2 F. From this simulations it can be seen that one can change both the resonance wavelength of the plasmon and the absorption at the resonance wavelength by changing the Fermi energy of the graphene. As explained in section 2.1 one can change the Fermi energy of graphene by just applying a voltage to the backgate of the graphene device. This feature of graphene therefore makes up for a very interesting property of the graphene plasmons as their resonance behavior can be changed just by changing a voltage. This means that one could create electrically changeable infrared absorbers. Furthermore it is interesting to note that one can drastically change the quality factor of the plasmon oscillations by changing the Fermi energy of the graphene. 3.6 Distance Variation In this section the simulation of multiple ribbons using periodic boundary conditions is discussed and the results obtained from the simulations are evaluated. Fig. 3.15 shows a sketch of the simulation parameters for the distance dependent simulations. For the following simulations the width wof the graphene ribbons was constant and the distance dbetween the graphene ribbons was varied. The other parameters, i.e. Fermi energy and mobility were also kept constant. 29 3. Plasmon Simulations w E k Graphene d d GrapheneGraphene Figure 3.15: Sketch of the distance dependent simulation of multiple graphene ribbons. For the simulations the distance dbetween the ribbons was varied and their width w, their Fermi energy and mobility were kept constant. For the simulation of the distance dependence of the plasmon resonance 60 nm wide ribbons with a mobility of µ= 5000 cm2/Vs and a Fermi energy of EF= 0.3 eV were used. The simulations were made using periodic boundary conditions. 0 100 200 300 400 0 1 0 2 0 3 0 4 0 5 0 M a x i m u m a b s o r p t i o n ( % ) D i s t a n c e ( n m ) (a) Maximum absorption 0 100 200 300 400 7 8 9 1 0 C e n t r a l w a v e l e n g t h ( µ m ) D i s t a n c e ( n m ) (b) Central wavelength Figure 3.16: Maximum absorption and central wavelength as a function of the distance between the graphene ribbons. For the simulations 60 nm wide ribbons with a mobility of µ= 5000 cm2/Vs and a Fermi energy of EF= 0.3 eV were used. Fig. 3.16 (a) depicts the distance dependence of the maximum absorption at the plasmon resonance frequency of the graphene nanoribbon array. A clear nonlinear increase of the maximum absorption for smaller distances between the nanoribbons can be seen. This nonlinearity is due to the coupling between the ribbons that becomes stronger for a decreasing distance between the ribbons. 30 3.7. Conclusions In Fig. 3.16 (b) the distance dependence of the resonance wavelength of the nanoribbon array can be seen. Here the increasing coupling strength between the nanoribbons is even more visible and one can see a strong change in the plasmon resonance wavelength starting for distances smaller than 100 nm between the ribbons. From these distance dependent simulations it becomes apparent that when designing an experiment with graphene nanoribbons one not only has to take the width and the Fermi energy into account but also the separation between the ribbons. A large separation between the ribbons guarantees a unperturbed plasmon resonance wavelength of the nanoribbon array, but at the same time does not give the maximum achievable absorption. From the simulations we find that decreasing the distance gives a strong increase in absorption which is desirable. Decreasing the distance between the graphene ribbons even more should lead to a decrease in absorption, but has not been quantified for this thesis, as smaller distances between the ribbons are not realistically achievable experimentally. Using the simulations one can predict the change in resonance wavelength and therefore design the other parameters of the nanoribbons such that the resonance wavelength falls into the desired range for the experiment. 3.7 Conclusions From the simulations of graphene nanoribbons it can be seen that for designing an experiment to exploit the properties of the graphene plasmons all design parameters have to be taken into account. Especially the right choice of distance between the graphene ribbons has to be made in order to find graphene plasmons with the desired resonance frequency. Here a trade off between high absorption and an unperturbed resonance frequency has to be made. In order to achieve strong resonances and a high field confinement high quality graphene, i.e. with a high scattering time and therefore a high mobility, has to be used. Mechanically exfoliated graphene can be used as it shows mobilities of up to 10000 cm2/Vs. As the simulations have shown this mobility is enough to get sharp resonance peaks and the plasmons can be detected in absorption measurements. Furthermore other methods of increasing the mobility of graphene are known. Especially suspended graphene [27, 28] and graphene on boron nitride [29] are very promising candidates with an extremely high mobility. Because of the small width of the graphene nanoribbons the assumption that the Fermi energy is uniform over the entire width of the ribbon is not necessarily true. Future investigations should take this into account and incorporate theoretical findings of the distribution of the Fermi energy into the simulations [69]. The simulations show that FDTD is a versatile tool for investigating the behavior of plasmons in graphene. The concept of using FDTD simulations for studying the behavior of graphene plasmons can be easily extended to many other parameters 31 4. Infrared Photocurrent the focal position according to the formula d=λ/NA, is 60 µm for light with a wavelength of 6 µm and 100 µm for light with a wavelength of 10 µm. The electronic part of the setup consists of the following parts. The measurements of the photocurrent are done using a current preamplifier (Femto DLPCA-200) which is connected to a lock-in amplifier (Stanford Research Systems SR830 DSP). An optical chopper (Thorlabs MC-2000) is used to modulate the laser beam with a frequency of 209 Hz. The integration time at the lock-in amplifier was set to 100 ms. 6 7 8 9 1 0 0 2 4 6 8 1 0 0 . 2 1 0 . 1 8 0 . 1 6 0 . 1 4 0 . 1 2 P h o t o n E n e r g y ( e V ) P o w e r ( m W ) W a v e l e n g t h ( µ m ) (a) QCL Power Spectrum 6 7 8 9 1 0 4 0 6 0 8 0 100 1200 . 2 1 0 . 1 8 0 . 1 6 0 . 1 4 0 . 1 2 P h o t o n E n e r g y ( e V ) F W H M ( µ m ) W a v e l e n g t h ( µ m ) (b) FWHM of Spot Size Figure 4.5: (a) Output power of the quantum cascade laser as function of the laser wavelength. The dips on the lower wavelength side of the spectrum are due to absorption peaks of atmospheric gases in this frequency range. (b) FWHM of the infrared laser beam at the focus of the sample. The spot size is increasing for an increasing wavelength. The black dashed line shows a linear fit of the FWHM. Fig. 4.5 (a) depicts the output power spectrum of the quantum cascade laser. For lower wavelengths dips in the output power are visible, due to absorption peaks of atmospheric gases in this wavelength range. Fig. 4.5 (b) shows the FWHM of the focused infrared laser spot as a function of the wavelength. The FWHM is increasing for an increasing wavelength. The black dashed line shows a linear fit of the FWHM. The FWHM is measured by doing a two dimensional scan of the photocurrent and extracting the FWHM of the photocurrent which is also the FWHM of the laser spot as the size of the graphene device is much smaller than the spot size of the laser. We use the formula d=λ/NA, with dthe FWHM of the laser spot, λthe wavelength and NA the numerical aperture. The linear fit shown in Fig. 4.5 (b) gives the inverse 38 4.3. Measurements of the numerical aperture, which we find to be 0.069 in this setup. The theoretical maximum NA for this setup with a beam size of 5 mm and a focal length of around 25 mm is 0.1. A real numerical aperture of 0.069 in the setup used is actually a very good result. The focus is found by finding the maximum reflection from the red laser and then leaving the z-position untouched for all the infrared wavelengths. Moreover only one parabolic mirror is used and there is no compensation of any kind for divergence of the beam or for the beam pointing in different directions for different wavelengths. 8 . 1 8 . 2 8 . 3 8 . 4 8 . 5 4 . 7 4 . 8 4 . 9 5 . 0 5 . 1 x P o s i t i o n ( m m ) y P o s i t i o n ( m m ) 2 . 5 3 . 0 3 . 5 4 . 0 4 . 5 5 . 0 5 . 5 6 . 0 R e f l e c t i o n ( a . u . ) Figure 4.6: Reflection image of the sample used. The two gold contact pairs defining the two devices can be clearly seen in the reflection image. The graphene itself is not visible in this reflection image. Fig. 4.6 shows the reflection image of the sample. The reflection image is obtained as explained in the discussion surrounding Fig. 4.4. It is interesting to note that most of the features seen in the microscope image, such as the pieces of graphite, can also be seen in the reflection image. When examining the reflection carefully, one even finds that the multilayer graphene around device (2) slightly decreases the reflection. 39 4. Infrared Photocurrent 4.3.2 Device (1) For the measurements on device (1) the drain is connected to the gold contact on the bottom left and the source to the gold contact on the top left of the reflection image. 0 2 4 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 1 . 2 P h o t o c u r r e n t ( n A ) D u t y C y c l e ( % ) Figure 4.7: Photocurrent dependence on the duty cycle of the laser source. The black dashed line shows a linear fit of the photocurrent. In Fig. 4.7 it can be seen that the photocurrent extracted from the device is found to scale linearly with the incident power. The laser light has a wavelength of 7.69 µm for this measurement which has the highest maximum power of the laser (see Fig. 4.5 (a)). The dependence on the duty cycle is measured by staying at the same position on the sample and gradually increasing the power of the laser by changing its duty cycle. From this we can deduce that for the powers used here nonlinear effects do not play any role for the photocurrent response of the graphene. A linear photocurrent response makes it possible to compare the photocurrents which is measured at different wavelengths of the laser and different powers of those wavelengths by a simple power normalization. 40 4.3. Measurements 8.1 8.2 8.3 8.4 8.5 4.7 4.8 4.9 5.0 5.1 x Position (mm) y Position (mm) -170 -136 -102 -68 -34 0 34 68 102 136 170 Photocurrent (pA) Figure 4.8: Two dimensional map of the photocurrent. The photon energy is ¯hω = 0.149 eV and the wavelength is λ= 8.33 µm. The backgate voltage is set to 10 V. The black dashed lines indicates the outline of the two gold contacts to which the graphene is connected. Fig. 4.8 depicts a two dimensional map of the photocurrent for a photon energy of ¯hω = 0.149 eV or a corresponding wavelength of λ= 8.33 µm. The backgate voltage is set to 10 V in order to see a high photocurrent and therefore have a good signal to noise ratio. The black dashed lines indicate the outline of the two gold contacts to which the graphene is connected. The photocurrent at the two different contacts shows an opposite sign. This is the same behavior that has already been observed for photocurrent in graphene with a visible laser source [72]. This behavior can nicely be explained by the sketch in Fig. 2.7 where a built in electric field at the contact between graphene and gold due to the work function difference leads to carrier separation which is measured as a photocurrent. As it was shown before the spot size of the laser beam at λ= 8.33 µm is 100 µm. The spacing of 32 µm between the two contacts therefore is smaller than the spot size of the infrared laser beam. Therefore when the laser beam center is overlapping maximally with one of the contacts it is also already overlapping with the other contact and the net current which is measured is not the actual current that is 41 4. Infrared Photocurrent generated. This is because the two currents from the two contacts have opposite signs and will appear as a smaller current on the measurement. This is especially important for responsivity calculations as the apparent responsivity is smaller than the actual responsivity of the device. 6 . 0 6 . 5 7 . 0 7 . 5 8 . 0 8 . 5 9 . 0 9 . 5 1 0 . 0 0 1x105 2x105 3x105 4x105 5x105 6x105 0 . 2 1 0 . 1 9 0 . 1 8 0 . 1 7 0 . 1 6 0 . 1 5 0 . 1 4 0 . 1 3 0 . 1 2 P h o t o n E n e r g y ( e V ) U p S w e e p N o r m a l i z e d R e s p o n s i v i t y ( A / W ) W a v e l e n g t h ( µ m ) D o w n S w e e p Figure 4.9: Responsivity of the maximum photocurrent normalized by the active area overlap with the laser spot. Fig. 4.9 shows the responsivity of the maximum photocurrent normalized by the active area overlap with the laser spot. Full two dimensional maps of the photocurrent as the one in Fig. 4.8 are obtained for the different wavelenghts at a backgate voltage of 10 V. The active area in this case is the 4 µm wide overlap of the graphene with the gold contact and the width of the p-n junction of 0.2µm as explained in section 4.1. The power spectrum of the laser is obtained from Fig. 4.5 (a) and the spotsize is obtained from the linear fit in Fig. 4.5 (b) . The two data sets refer to two sweeps of the laser frequency. For the up sweep the laser frequency is changed to the next higher frequency after each full two dimensional scan and for the down sweep the laser frequency is changed to the next lower frequency after each full scan. The different responsivities for the up and down sweep could be due to the fact that the Fermi energy does not stay constant during all the measurements but in fact drifts. The drift of Fermi energy on the timescale of a few hours could be due to reaction of the graphene with humidity or contaminants in air. As shown in Fig. 4.11 the photocurrent strongly depends on the backgate voltage (i.e. Fermi energy). 42 4.3. Measurements 6 . 0 6 . 5 7 . 0 7 . 5 8 . 0 8 . 5 9 . 0 9 . 5 1 0 . 0 0 1x105 2x105 3x105 4x105 5x105 6x105 0 . 2 1 0 . 1 9 0 . 1 8 0 . 1 7 0 . 1 6 0 . 1 5 0 . 1 4 0 . 1 3 0 . 1 2 P h o t o n E n e r g y ( e V ) N o r m a l i z e d R e s p o n s i v i t y ( A / W ) W a v e l e n g t h ( µ m ) U p S w e e p D o w n S w e e p Figure 4.10: Responsivity of the minimum photocurrent normalized by the active area overlap with the laser spot. Fig. 4.10 depicts the responsivity of the minimum photocurrent normalized by the active area overlap with the laser spot. The backgate voltage for all the scans was set to 10 V and the active area here is the 5.5µm wide overlap of the graphene with the gold contact and the width of the p-n junction of 0.2µm. As explained before the laser spot size is bigger than the distance between the two gold contacts in this device. Therefore the maximum photocurrent measured is not the actual maximum photocurrent of the device. This means that the responsivity measured in this device is lower than the actual responsivity of the device. 43 4. Infrared Photocurrent - 1 5 - 1 0 - 5 0 5 1 0 1 5 2 0 - 0 . 2 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 N o r m a l i z e d P h o t o c u r r e n t ( a . u . ) B a c k g a t e V o l t a g e ( V ) P h o t o n E n e r g y : 0 . 1 4 e V 0 . 1 6 e V 0 . 1 9 e V R e s i s t a n c e Figure 4.11: Dependence of the photocurrent on the backgate voltage for three different photon energies of the infrared laser. The blue dashed line shows the normalized backgate dependence of the resistance. Fig. 4.11 depicts the backgate dependence of the photocurrent for different photon energies of the infrared laser. The photocurrent is normalized by its maximum value in order to be able to compare the backgate dependent behavior of the photocurrent for different wavelengths. The blue dashed line shows the normalized backgate dependence of the resistance. It can be seen that the photocurrent does not decrease to zero for higher backgate voltages. The photocurrent is expected to go to zero again for higher backgate voltage than the 22 V up to which we measured here. The reason why the photocurrent is expected to go back to zero is that for higher backgate voltages the Fermi energy of the graphene should increase further and the situation which is depicted in Fig. 2.5 (c) should be reached where carrier excitation is forbidden due to the Pauli exclusion principle. The reason why the backgate voltage has not been increased further in the experiments is because the for high voltages applied to the backgate so called backgate leakage might become a problem. This backgate leakage is a current flowing from the backgate to the drain. For thin SiO2, like the 90 nm used here, the leakage can occur for relatively low backgate voltages. The leakage occurs because of charges from the silicon layer below the dielectric flowing to the gold contacts either through the graphene or directly to the contacts. This behavior is not only undesired it might also destroy the device and therefore one has to be careful when increasing 44 4.3. Measurements the backgate voltage. 4.3.3 Device (2) For the measurements on device (2) the drain was connected to the gold contact on the top right and the source to the gold contact on the bottom right of the reflection image. 8.20 8.25 8.30 8.35 8.40 8.45 4.75 4.80 4.85 4.90 4.95 5.00 5.05 Photocurrent (pA) x Position (mm) y Position (mm) -390 -312 -234 -156 -78 0 78 156 234 312 390 Figure 4.12: Two dimensional map of the photocurrent. The photon energy is ¯hω = 0.161 eV and the wavelength is λ= 7.69 µm. The backgate voltage was set to 20 V. The black dashed lines indicates the outline of the two gold contacts to which the graphene is connected. Fig. 4.12 depicts a two dimensional map of the photocurrent. The photon energy is ¯hω = 0.161 eV, which is in terms of wavelength λ= 7.69 µm. The backgate voltage was set to 20 V in order to see a high photocurrent response. The black dashed lines show the outlines of the two gold contacts to which the graphene is connected. Here the spot size of the infrared laser spot is smaller than the separation between the two contacts. The distance between the two maximum and minimum of the photocurrent in Fig. 4.12 was found to be 114 µm, which is in excellent agreement with the distance between the two contacts extracted from the microscope image. 45 4. Infrared Photocurrent The responsivity normalized by the active area is found to be 2 ·10−4A/W. As for the measurements with device (1) the signs of the photocurrent at the two contacts have opposite sign. 0 50 100 150 200 250 0 5 1 0 1 5 2 0 P h o t o c u r r e n t ( p A ) P o s i t i o n ( µ m ) B a c k g a t e V o l t a g e ( V ) - 6 0 0 - 4 0 0 - 2 0 0 0 200 400 600 2 0 4 0 R e s i s t a n c e ( k O h m ) Figure 4.13: Backgate dependence of the photocurrent. The photon energy is ¯hω = 0.161 eV which corresponds to a wavelength of λ= 7.69 µm. The photocurrent was measured for different backgate voltages with a cut from one contact to the other. The plot on the right shows the backgate dependence of the resistance of the device. Fig. 4.13 shows the backgate dependence of the photocurrent with a cut from one contact of the device to the other for one wavelength on device (2). The plot on the right shows the backgate dependence of the resistance of the device. The photon energy is ¯hω = 0.161 eV which corresponds to a wavelength of λ= 7.69 µm. The backgate voltage has been not decreased further because the device starts leaking for a backgate voltage smaller than 0 V because the device showed leakage. The backgate voltage was not increased any further than 22 V in order to not damage the device. As for device (1) the strong increase of the photocurrent occurs for backgate voltages above the Dirac point of the device. A very weak photocurrent can be seen for low backgate voltages that switches sign around 10 V backgate voltage. The switch of sign can be explained by the graphene going through the flatband condition. This means that the band bending as seen in Fig. 2.7 goes from the p-n-p junction which is sketched in this figure to a flatband. For this flatband there is no built-in electric field which leads to no photocurrent in 46 4.4. Conclusion this case. Further increasing the backgate voltage will result in a n-p-n junction and therefore an inverted sign of the current. This has already been seen for photocurrent from visible radiation [72]. Further increasing the backgate voltage leads to an increasing photocurrent. Increasing the backgate voltage even further one should see that the photocurrent starts to decrease due to Pauli blocking in the graphene, which is not the case here, probably because the backgate voltage was not increased to a high enough value. The backgate voltage has not been increased further in order not to risk damaging the device. 4.4 Conclusion The experiments show that we can get photocurrent at the gold graphene interface from a mid infrared laser source. We are able to show a photocurrent for the whole spectral range of our laser and are able to characterize the responsivity in the mid infrared of our device. A dependence of the photocurrent on the Fermi energy of the graphene is shown for different wavelenghts. The photocurrent from infrared radiation is shown to scale linear with the incident power, as one would expect for the powers used in this thesis. The responsivity of the photocurrent for device (1) is found to be around 10−5A/W for a broad spectrum which is about one to two orders of magnitude smaller than the photocurrent responsivity of graphene found for visible irradiation [49, 72, 20]. This is explained by the size of the laser beam being bigger than the distance between the two contacts. Due to this the maximum photocurrent measured is not the maximum photocurrent of the device but rather the maximum photocurrent given the destructive interference between the opposite currents of the two contacts. The photocurrent shows a strong dependence on the backgate voltage. For a backgate voltage higher than the backgate voltage of the Dirac point a strong increase in photocurrent is visible which peaks and then starts declining again. The strong increase of the photocurrent could be due to the electric field at the gold graphene interface increasing because of the increasing doping in the graphene and the decrease of the photocurrent for higher backgate voltages due to absorption of photons being reduced because of Pauli blocking. In device (2) the responsivity is found to be around 10−4A/W which is comparable to responsivities found for visible irradiation [49, 72, 20]. The higher value of the responsivity compared to device (1) is because the two regions of positive and negative photocurrent are nicely separated and the absolute maximum and minimum of the photocurrent are measured. This result shows that for accurate photocurrent experiments in the infrared it is important to use devices with a separation between the contacts which is larger than the spot size of the laser beam. 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Applied Physics Letters 91, 163513 (2007). 56 Acknowledgements First of all I would like to thank Frank for the great opportunity of working on the new and exciting field of graphene plasmonics for my master thesis in such an excellent environment as ICFO. Thanks for always having an open ear to problems coming up during the experiments and simulations and thanks for pushing me further when needed. Also I would like to thank Marko for the awesome supervision and great help during my thesis at ICFO, both during and after work. Then I would like to thank Michela for working with me on the lab, helping and working many hours trying to align mirrors and turn knobs and then the same thing all over again because something turned, got touched or the translation stage had to be moved. Thanks to my office partners Gabriele and Fabio for the good time in the office and the nice chats when I was not in the lab and you were not in the cleanroom (which rarely happened). Thanks also to the rest of the group, Klaas, Louis, Ivan and Kevin for the fun times both during work hours and during the free time. The group is really extraordinary being both very productive and hard working and still very nice and cool people. I hope you will continue publishing in such great journals as you have been in the past and I surely hope that the fun and excitement for your work never vanishes. My next block of thanks goes to all the people that studied with me for the past two years in the Europhotonics program in no particular order: Alek, Lazar, Lara, Kevin, Vacys, Bruno, Judith, Gabriele, Moritz, Maria, Duc, Radwan, Tan, Arko, George, Waiz, Yibing, Wei, Valentina and Mohamed. Even though our classes and professors were not always the best I still would say that we had an awesome time during our master and learned a lot about optics, photonics and life. I remember, and also lots of times don’t remember, many wonderful nights in Marseille, eating, drinking and laughing. Thanks to all of you the dorms in Alice Chatenoud were only half as bad and even the loss of a car was not that tragic anymore. I will never forget our trips to different parts of France. And even though all of us came from very different countries we were still able to connect and become friends. It was a great pleasure meeting every single one of you. I hope to see all of you at many different places in the future. But for sure we will all meet at the 1st of October 2015, the official Europhotonics reunion date. Thanks to Pau for translating my abstract into Catalan and Spanish, it is really appreciated. An dieser Stelle auch vielen Dank an all meine Freunde in Deutschland, die ich ¨ uber die letzten zwei Jahre mit Sicherheit viel zu sehr vernachl¨ assigt habe. Danke an alle die ich auch heute noch meine Freunde nennen kann, obwohl ich dann doch nur mal alle paar Monate ein paar S¨ atze von mir h¨ oren lasse. Danke f¨ ur all die unvergesslichen Erinnerungen und auch Danke ¨ ur die Erinnerungen die dann doch schon wieder vergessen sind. Danke, dass ihr mich immer wieder in die Realit¨ at zur¨ uck holt und mir zeigt wie sch¨ on es doch in der Heimat sein kann. Ihr seid zu 57 Viele um euch hier alle einzeln aufzuz¨ ahlen aber ich bin mir sicher, ihr wisst wer ihr seid. Vielen Dank auch an Mama und Papa, Conny und Karl-Heinz, daf¨ ur, dass ihr mir das alles erm¨ oglicht habt. Ohne eure moralische und finanzielle Unterst¨ utzung w¨ are aus meinem Studium mit großer Sicherheit nichts geworden. Danke f¨ ur alles. Vor allem, dass ihr immer an mich geglaubt habt und mir alle Freiheiten gegeben habt die ich gebraucht habe. Die Arbeit widme ich meiner Oma Elisabeth, die das Ende leider nicht mehr mitbekommen hat. Danke f¨ ur alles! To all of you I want to say: Thank you! And I hope to meet every single one of you again in the future.