Politecnico di Milano

Scuola di Ingegneria Industriale e dell’InformazioneCorso di Laurea Magistrale in Engineering Physics

Dipartimento di Fisica

ELECTRICAL AND OPTICAL

CHARACTERIZATION OF

GRAPHENE/GERMANIUM SCHOTTKY

JUNCTIONS

Supervisor: Prof. Giovanni ISELLACo-supervisors: Eng. Luca ANZI

M.S. Andrea BALLABIO

Master thesis by:Alessandra FERRARI Matr. 837660

Academic Year 2015–2016

Abstract

After its discovery in 2004 by Geim and Novolosev (Nobel Prize in Physics in2010), graphene has been the most studied material. It exhibits extraordinaryproperties, such as very high mobility, large current-carrying capability, greatflexibility, scalability and transparency, which make it be suitable for electronicapplications.

In the last five years systematic investigation have focused on the graphene/semiconductor Schottky junctions. Since studies are still at an early stage, afully accepted theory that models such a junction does not exist yet, althoughSchottky theory well describes it in first approximation.

In this work the electrical and optical characteristics of graphene/germaniumjunctions are discussed. Different substrates have been employed: heavily dopedepitaxial germanium, low-doped epitaxial germanium, a low-doped bulk germa-nium. A proper Schottky behavior is observed, when low-doped germanium isemployed. Measured barrier heights are about 0.40-0.53eV.

Once electrical characteristics are proven to be good, samples are opticallymeasured. Thanks to the optical properties of graphene, graphene/germaniumdiodes can be used as photodetectors. Absorption in graphene is only about2-3% in the near-infrared and visible spectral range, therefore it acts like atransparent carrier collector. Carriers are photogenerated inside the semicon-ductor and injected into graphene. When working in standard photodiodemode, i.e. when bias is applied between anode and cathode, responsivity ofthe graphene/germanium junctions is verified to lay in the standard germaniumspectral range. An enhancement in responsivity should be expected when a biasacross graphene is applied. This phenomenon, called Quantum Carrier Rein-vestment, has been reported only in a single publication (Liu et al., 2014, ACSNano) and has not been reproduced yet, so the reason why it is not here verifiedis still an open issue.

i

Sommario

Sin dalla sua scoperta nel 2004 da parte di Geim e Novolosev (Premi Nobelin fisica nel 2010), il grafene è stato il materiale più studiato degli ultimi diecianni. Esso possiede infatti proprietà straordinarie, come l’alta mobilità, l’abilitàdi trasportare alte correnti, la scalabilità e trasparenza, che lo rendono adattoper applicazioni elettroniche.

Negli ultimi cinque anni sono stati effettuati studi sistematici sulle giun-zioni Schottky grafene/semiconduttore. Questi studi sono quindi ancora nellaloro fase iniziale, pertanto al momento non esiste ancora una teoria completache modellizzi tale giunzione, sebbene essa sia ben descritta in prima approssi-mazione dalla teoria Schottky.

In questo lavoro sono discusse le caratteristiche elettriche e ottiche di giun-zioni grafene/germanio. Diversi substrati sono stati impiegati: germanio epitas-siale altamente drogato, germanio epitassiale poco drogato e germanio bulk pocodrogato. Un corretto andamento rettificante è stato osservato con substrati digermanio poco drogato. Le altezze di barriera ottenute sono circa 0.40-0.53eV.

Una volta verificata la correttezza delle caratteristiche elettriche, i campionisono stati misurati otticamente. Grazie alle proprietà ottiche del grafene, i diodigrafene/germanio possono essere impiegati come fotorivelatori. L’assorbimentonel grafene è solo del 2-3%, pertanto esso si comporta come un raccoglitore diportatori trasparente nel range spettrale del visibile e del vicino IR. I portatorisono quindi fotogenerati all’interno del semiconduttore e trasportati nel grafene.La responsivity delle giunzioni grafene/germanio si trova all’interno del rangespettrale standard dei fotorivelatori di germanio, quando il dispositivo lavoracome fotodiodo convenzionale, ovvero quando il bias è applicato tra anodo ecatodo. Ci si aspetterebbe un aumento nella responsivity se il bias venisseapplicato attraverso il grafene. Questo fenomeno, chiamato Quantum CarrierReinvestment, è riportato in un solo articolo (Liu et al., 2014, ACS Nano) e non

ii

è ancora stato riprodotto. La ragione per cui la sua presenza non sia stata quiriscontrata è ancora, pertanto, una questione aperta.

Acknowledgments

I would like to thank my supervisor prof. Giovanni Isella for the amazing op-portunity of working in the Silcon Germanium Epitaxy group in the L-NESSlaboratory and for being a mentor in these months. A greatful thanks goes toAndrea Ballabio and Dr. Jacopo Frigerio for introducing me in the research lab-oratory and for their constant help. For the collaboration with the NanoscaleDevice group I would like to thank Prof. Roman Sordan, Dr. Marco Fioccoand Luca Anzi. Finally I would like to thank all the members of the L-NESSlaboratory, in particular Marco Leone, Mario Lodari and Luca Esposito.

Thanks to all my friends for making things easier with laughs and talks, youare a constant inspiration for me. Thanks to Federico for always being by myside.

The final and most special thanks goes to my family for always giving mestrength, love and support.

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Contents

Contents I

List of Figures III

List of Tables VIII

1 Introduction 1

2 Graphene Schottky diode 32.1 Schottky junction . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1.1 Fermi level pinning . . . . . . . . . . . . . . . . . . . . . . 92.2 Graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 Model of the graphene-semiconductor junction . . . . . . . . . . 142.4 Photodetector application of graphene Schottky diode . . . . . . 17

3 Sample fabrication 203.1 Back ohmic contact . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.1.1 Epitaxial germanium . . . . . . . . . . . . . . . . . . . . . 203.1.2 Bulk germanium . . . . . . . . . . . . . . . . . . . . . . . 22

3.2 Graphene wet transfer . . . . . . . . . . . . . . . . . . . . . . . . 233.3 GrOnGe18 series . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.3.1 GrOnGe18A using optical lithography . . . . . . . . . . . 253.3.2 GrOnGe18B using EBL . . . . . . . . . . . . . . . . . . . 27

3.4 GrOnGe17 series . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.5 GrOnBulkGe sample . . . . . . . . . . . . . . . . . . . . . . . . . 31

4 Electrical measurements 324.1 Fitting models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

I

4.2 Test sample: Pt/Ge Schottky barrier . . . . . . . . . . . . . . . . 344.3 Graphene/germanium Schottky diode . . . . . . . . . . . . . . . 39

4.3.1 GrOnGe18 series . . . . . . . . . . . . . . . . . . . . . . . 394.3.2 GrOnGe17 series . . . . . . . . . . . . . . . . . . . . . . . 404.3.3 GrOnBulk sample . . . . . . . . . . . . . . . . . . . . . . 46

5 Photocurrent measurements 535.1 Measurement setup . . . . . . . . . . . . . . . . . . . . . . . . . . 535.2 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . 54

6 Conclusions 62

A LEPECVD 64

B Scanning Electron Microscope (SEM) for EBL 66

C Reactive Ion Etching (RIE) 68

Bibliography 69

List of Figures

2.1 Band diagrams before and after contact. (a) high-work-functionmetal and n-type semiconductor, (b) low-work function metal andn-type semiconductor, (c) high-work-function metal and p-typesemiconductor, (d) low-work function metal and p-type semicon-ductor. Source : figure from Ref. [1] . . . . . . . . . . . . . . . . 4

2.2 Schematic view of when a metal and a n-type semiconductorplaced in contact. In the semiconductor a depletion layer w isformed as a consequence of the preservation of thermal equilib-rium. Ei is the built-in electric field. Source : figure from Ref.[2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.3 Potential energy of a Schottky barrier in a n-type semiconductor.Source : figure from Ref.[3] . . . . . . . . . . . . . . . . . . . . . 5

2.4 Effect of the image force in lowering the barrier height. Source :

figure from Ref. [4]. . . . . . . . . . . . . . . . . . . . . . . . . . 62.5 Effect of the ideality factor n on the behaviour of J as a function

of the applied voltage V. Source : figure from Ref.[3] . . . . . . . 82.6 I-V characteristics of a Schottky diode for progressively high car-

rier concentrations. (a) N ≤ 1017cm−3, thermoionic-emissiondominates, (b) N ' 1018 − 1019cm−3, thermoionic-field tunnel-ing dominates, (c) N ≥ 1019cm−3, field-emission tunneling dom-inates. Source : figure from Ref. [5]. . . . . . . . . . . . . . . . . 8

2.7 Electric circuit that includes both series resistance and shunt re-sistance (Rp, parallel resistance) . . . . . . . . . . . . . . . . . . 9

2.8 Tayloring of the metal wavefunction inside the semiconductor,which gives rise to Metal Induced Gap States MIGS. Source :

figure from Ref. [1] . . . . . . . . . . . . . . . . . . . . . . . . . . 10

III

2.9 (a) Honeycomb lattice in graphene. Lattice is made of two tri-angular sub-lattices, whose primitive vectors are a1 and a2 re-spectively. a=0.142nm is the distance between two carbon atomsSource : figure from “Graphene nanoelectronics and nanofabrica-tion” lecture handouts, held by prof. Roman Sordan in Politec-nico di Milano. (b) Graphene band structure. Conduction andvalence bands touch at the six Dirac points K and K’. Source :

figure adapted from Ref. [6] . . . . . . . . . . . . . . . . . . . . . 112.10 Effect of an applied bias on the Fermi level in graphene. The

assumption is that at zero bias the Fermi level is exactly at theDirac point. Under forward bias EF is shifted downwards and thiseffect is very small. Under reverse bias EF is shifted upwards.Source : figure from Ref. [2] . . . . . . . . . . . . . . . . . . . . . 14

2.11 Band scheme of the working principle of a graphene-semiconductorjunction as photodetector. e-h pairs are generated in the semi-codnuctor depletion region and flow in graphene under the appli-cation of a reverse bias. Source : figure adapted from Ref. [7] . . 17

2.12 Responsivity of the device working in high-gain configuration(left) and in photodiode mode (right). Source : figure from Ref. [8] 18

3.1 Ohmic behaviour tested for 100nm Ni evaporated on n-Si at dif-ferent annealing times. No deviations from ohmic behavior isobserved. Differences arise only in the values of the resistances. . 22

3.2 Effect of annealing of 90nm of AgSb on top of Ge n=8e16. (a)Without thermal annealing no proper ohmic contact is formed.(b) I-V characteristics after thermal annealing. No substantialdifference is observed between the two thermal treatments. . . . 23

3.3 Thermal annealing on Ge n=2e15. A further annealing of 5 min-utes at 450°C is required in order to obtain a proper ohmic contact. 24

3.4 Main steps of graphene wet transfer. (a) Graphene is grown ona copper foil by CVD. (b) PMMA is used to protect grapheneon one side while graphene on the other side is removed throughoxygen plasma. (c) Copper etchant removes copper foil. (d)Graphene is stuck to PMMA and it is rinsed in water. (e)Graphene fishing. Sample is placed in water below graphene.The sample is then dried in an inclined plane and hot baked for5 minutes at 160°C. . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.5 Scheme of pads and contacts of sample GrOnGe18A . . . . . . . 253.6 Main steps in optical lithography (a) and EBL (b). Source : figure

adapted from “Graphene nanoelectronics” lecture handouts, heldby prof. Roman Sordan in Politecnico di Milano. . . . . . . . . . 26

3.7 Effect on ohmic nichel contacts after rinsing sample in HF. Thebehaviour is still ohmic, the resistance value is increased. . . . . 27

3.8 Scheme of GrOnGe18B sample. Many structure combinationsare tested with L = 150µm−300µm−450µm and H = 150µm−300µm− 450µm. . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.9 (a) Scheme of GrOnGe17A and GrOnGe17B. (b) Different paddimensions and distances between the two pads are tested. . . . . 29

3.10 (a) Scheme of GrOnGe17C, GrOnGe17D and GrOnBulkGe sam-ples. (b) Tested distances between pads L = 10µm − 20µm −30µm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.1 Scheme of test sample Pt/Ge Schottky junction. . . . . . . . . . 344.2 Pt/Ge junction at different semiconductor dopings. Contribution

of the series resistance is already removed by plotting the currentas a function of the effective voltage. . . . . . . . . . . . . . . . . 35

4.3 Linear fitting performed in order to determine series and parallelresistances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.4 (a) Results of the fitting in the case of highly doped germaniumsubstrate. The blue curve represents the raw data. The redcurve represents the diode curve obtained by plugging the fittedparameters in equation 4.1. (b) Semilogarithmic plot of Pt/Gen=8e16. The two red points represent the range of the linearfitting performed in order to extrapolate Isat and n. . . . . . . . 37

4.5 Boxplots of the barrier height and ideality factor n in the Pt/GeSchottky diodes. The red crosses represents outliers. . . . . . . . 38

4.6 Current voltage characteristics of the GrOnGe18 series. No properrectifying behavior is observed. . . . . . . . . . . . . . . . . . . . 39

4.7 Fitting of sample GrOnGe18A. . . . . . . . . . . . . . . . . . . . 404.8 Current-voltage characteristic of sample GrOnGe17B. . . . . . . 414.9 Current-voltage characteristics of GrOnGe17C and GrOnGe17D

before graphene etching. Both curves show a good rectifyingbehavior. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.10 (a) Linear fitting perfomed on sample GrOnGe17D L = 10µm, inorder to determine series and parallel resistance values. (b) Semilogarithmic plot of the current-voltage characteristic of GrOnGe17DL = 10µm. The red rectangles represents the voltage range lim-its, where linear fitting is performed. . . . . . . . . . . . . . . . . 43

4.11 I-V curves of sample GrOnGe17D (L = 30µm) before and aftergraphene etching. . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.12 Boxplots of the fitted parameters barrier height and n in GrOnGe17Dafter graphene etching. . . . . . . . . . . . . . . . . . . . . . . . . 46

4.13 Current-voltage characteristics in graphene/germanium wafer sam-ple. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.14 Fitting applied on graphene/Ge wafer diode. . . . . . . . . . . . 484.15 Boxplots of the barrier height and the ideality factor n in graphene/Ge

wafer diode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.16 Current voltage characteristics in graphene/Ge wafer junction

and GrOnGe17D. . . . . . . . . . . . . . . . . . . . . . . . . . . . 504.17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.1 Experimental setup. . . . . . . . . . . . . . . . . . . . . . . . . . 545.2 Photocurrent measurement setup. Vpb represents voltage applied

between the top electrode and the back contact. Vpp is the voltageapplied between the two front pads. . . . . . . . . . . . . . . . . 55

5.3 Responsivity in (a) graphene/epitaxial Ge junction at an appliedbias Vpb = −0.66V and (b) graphene/wafer junction at Vpb =

−0.9V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.4 Responsivity of sample GrOnGe17D L = 30µm (a) and L =

30µm (b). Applied bias in both configurations is -0.66V. . . . . . 565.5 Responsivity of sample GrOnGe17D L = 20µm. Applied bias in

both configurations is -0.66V. . . . . . . . . . . . . . . . . . . . . 575.6 Responsivity in graphene/Ge wafer sample at an applied bias of

-2V. The measured structure is (a) 3.1, L = 20µm and (b) 1.4L = 10µm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5.7 Photocurrent measured as a function of the applied bias betweenthe two front pads (red curve) and between a front pad and theback (blue curve). . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.8 Photocurrent measured in graphene/epitaxial Ge diode as a func-tion of the applied pad-pad bias Vpp at λ = 1300nm. . . . . . . . 59

5.9 (a) Responsivity in graphene/Ge wafer junction (device 1.4, L =

10µm) at different applied pad-pad biases. Back contact is leftfloating. (b) Current as a function of the applied pad-pad voltageVpp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.10 Responsivity in graphene/Ge wafer sample (device 1.4, L = 10µm)when working int he conventional photodiode mode (a) and whenboth biases are applied (b). . . . . . . . . . . . . . . . . . . . . . 61

A.1 Scheme of the LEPECVD chamber. Source: figure adapted fromRef. [9] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

B.1 (a) Electron beam impinges on the substrate. A is the area tobe exposed. (b) Electron beam (primary electron) impinges onthe sample. Electrons inelastically scatter in forward directionand secondary electrons (SE) are generated. SE are actually re-sponsible for resist exposure. Less frequently electrons can beelastically back scattered (BSE). Source : images from “Graphenenanoelectronics” lecture handouts, held by prof. Roman Sordanin Politecnico di Milano. . . . . . . . . . . . . . . . . . . . . . . . 67

C.1 Scheme of RIE. Source : figure adapted from Ref. [10] . . . . . . 68

List of Tables

4.1 Medians of the fitted parameters in samples Pt/Ge . . . . . . . . 384.2 Median values of parameter in samples where graphene is not

etched around each structure. . . . . . . . . . . . . . . . . . . . . 424.3 Median values of parameters in sample GrOnGe17A according

to the different pad dimensions. The number of measurementsperformed for each case is displayed in squared brackets. . . . . . 44

4.4 Median values of the saturation current and the ideality factor nin sample GrOnGe17D. The case where graphene is not etchedaround each structure is compared to the one where each struc-ture is isolated from each other. . . . . . . . . . . . . . . . . . . 45

4.5 Medians of the fitted parameters in GrOnGe17D after grapheneetching. In squared brackets the number of tested devices is shown. 46

4.6 Median values of the fitted parameters in graphene/germaniumwafer Schottky junction. In squared brackets the number oftested pad combination is shown. . . . . . . . . . . . . . . . . . . 47

4.7 Difference between epitaxially grown germanium and a germa-nium wafer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

VIII

Chapter 1

Introduction

Thanks to its properties such as very high mobility, large current-carrying ca-pability, great flexibility, scalability and transparency, graphene is a suitablematerial for electronic applications [11, 12, 13, 14].

In the last five years systematic investigation have focused on the graphene/semiconductor Schottky junctions . Since studies are still at an early stage, afully accepted theory that models such a junction does not exist yet, althoughSchottky theory well describes it in first approximation.

Thanks to its optical properties graphene is also suitable for optical ap-plications. In particular the fact that it is transparent (graphene absorptionbecomes important at IR radiation) makes graphene/germanium diode suitablefor photodetection applications. In the responsivity range of germanium (upto 1550nm), graphene acts therefore as a transparent carrier collector, whilephotocarriers are generated inside the germanium and injected into grapheneby the application of a reverse bias.

The aim of this thesis is to electrically and optically characterize a graphene/germanium Schottky diode. Three different substrates are investigated: heavilydoped epitaxial germanium, low-doped epitaxial germanium and low doped bulkgermanium, which corresponds to further optimization steps of the devices.

This thesis is organized in four main chapters. First a theoretical overviewabout Schottky model and its adjustments due to the presence of grapheneis discussed. Fabrication methods are then presented. Devices are electri-cally characterized and the presence of a proper rectifying behavior is verified.Diode parametres (Rs, Rp, Isat, barrier height, n) are determined by fittingthe current-voltage characteristics through a MATLAB function coded for this

1

work. Once the formation of a proper Schottky junction is verified, samples areoptically investigated. The aim of these optical measurements is first to checkthe potential use of these devices as photodectors and then the verification ofthe presence of absence of the Quantum Carrier Reinvestment effect predictedby Liu et al. [8].

Chapter 2

Graphene Schottky diode

In this chapter Schottky diode theory is presented. First a standard metal-semiconductor junction is considered, since it can explain in first approximationthe current-voltage behavior of graphene-semiconductor junction. Further ad-justments to the Schottky theory are however needed due to the presence ofgraphene. They are presented in section 2.3. Finally its application as photode-tector is discussed.

2.1 Schottky junction

When a metal is in contact with a semiconductor, different situations may ariseaccording to the type of doping of the semiconductor, the metal work functionand the respective positions of the two Fermi levels, which are shown in figure2.1. Let us consider an ideal Schottky barrier formed with a n-type semicon-ductor and a high-work-funcion metal. In order to preserve thermal equilibriumthe Fermi level of the semiconductor must be aligned to that of the metal, thusleading to a net charge flow. After contact formation, electrons flow from thesemiconductor to the metal and therefore a depleted region is created in thesemiconductor at the interface with the metal. In the metal then there mustexist a thin layer of positive space charges balancing the electrons accumulatedin the metal thus fulfilling charge conservation [1]. These two layers of oppositecharge can be seen as a parallel plate capacitor. The electric field there formedEi opposes to the motion of charges from the semiconductor to the metal. Ei

is called built-in electric field (see figure 2.2).

3

Figure 2.1: Band diagrams before and after contact. (a) high-work-functionmetal and n-type semiconductor, (b) low-work function metal and n-type semi-conductor, (c) high-work-function metal and p-type semiconductor, (d) low-work function metal and p-type semiconductor. Source : figure from Ref. [1]

Figure 2.2: Schematic view of when a metal and a n-type semiconductor placedin contact. In the semiconductor a depletion layer w is formed as a consequenceof the preservation of thermal equilibrium. Ei is the built-in electric field.Source : figure from Ref. [2]

Figure 2.3: Potential energy of a Schottky barrier in a n-type semiconductor.Source : figure from Ref.[3]

If uniform distribution within the space charge region is assumed, Poisson’sequation holds and the existence of parabolic energy barrier within the depletionregion is predicted:

Φ(x) =q2Nx2

2εsε0(2.1)

where N is the ionized donor concentration, εs the static dielectric constant ofthe semiconductor and ε0 is the permittivity in vacuum. Let w be the depletionlayer width, x is therefore comprised between 0 and w (figure 2.3). The depletionlayer width depends on the energy band bending, according to

Eb = Φb − Φs − qV =q2Nw2

2εsε0(2.2)

where Φb is the barrier height, Φs is the energy between the Fermi level of thesemiconductor and the conduction band edge, V is the applied voltage [3].

As shown in figure 2.3 there exist three main mechanisms that contribute toconduction across the Schottky barrier [3]: thermionic emission, thermionic-fieldemission and field-emission.

The first who derived a mathematical theory for thermionic emission wasBethe [15] under the assumption qφb kT . Using Maxwell-Boltzmann statis-tics he related the forward current If , that is the one experienced under for-ward bias, and the reverse current Ir, under reverse bias. Forward bias reducesthe band bending, thus the barrier height experienced by carriers in the semi-conductor is also reduced. Electrons are then more likely to flow inside themetal (forward flux). Under reverse bias however the barrier height remains

Figure 2.4: Effect of the image force in lowering the barrier height. Source :figure from Ref. [4].

unchanged.

If = Ir exp

(qV

kT

)(2.3)

Ir ≡ AA∗T 2 exp

(−qΦbkT

)(2.4)

where A∗ is the Richardson constant of the semiconductor, A is the active areaof the device, k is the Boltzmann constant (k = 1, 38 · 10−23JK−1) and φb isthe Schottky barrier height. The total current is therefore:

I = If − Ir = Ir

(exp

(qV

kT

)− 1

)(2.5)

which is the ideal diode equation. Ir is also known as the saturation current.Usually an ideality factor n is also included in the formula 2.5 in order to

take into account non ideal effects, i.e. image force lowering. Due to image force,band bending is not truly parabolic and the real value of the barrier height islower than the one predicted in the ideal case. As shown in figure 2.4, the barrierheight is lowered by both the external applied electric field and the potentialof the image force [4]. When an electron is at a distance x from the metal, apositive charge is induced in the metal at a distance -x from the interface. Thetwo charges are then attracted and the image force is given by

F =−q2

4πε0εs (2x)2 =

−q2

16πε0εsx2(2.6)

and the work done to move an electron from infinity to its final position x is

W =

ˆ x

∞Fdx =

−q2

16πε0εsx(2.7)

The total potential is given by the sum of two contributions: the potential dueto the image force and the one due to the external applied electric field E

Ψtot = Ψimage−force − q |E|x =−q

16πε0εsx− q |E|x (2.8)

This equation has its maximum value for dΨtot/dx = 0, from which the position

and the barrier lowering are derived xm =√

q16πε0εs|E| and ∆Φ =

√q|E|

4πε0εs

[4]. So starting from zero bias ∆Φ will increase or decrease according to theapplied bias. In forward bias ∆Φ reduces causing an increase in the barrierheight. Therefore the current density J will increase less rapidly with V thanthe ideal case. In reverse bias, vice versa, E increases causing ∆Φ to increase.The barrier height is in this case lowered, so current does not saturate at theideal saturation current density (equation 2.4) but it gradually increases withthe applied reverse bias. A factor n called ideality factor is used in order totake into account all these non-ideal effects. The Schottky diode equation thenbecomes

I = Ir

(exp

(qV

nkT

)− 1

)(2.9)

where n is a positive integer number and it is equal to 1 in the ideal case. Inequation 2.9 the non-ideality, considered with parameter n, only affects the curveshape in forward bias, which is a fairly good approximation when thermionicemission dominates.

As seen in equation 2.1, band bending also depends on the doping of the semi-conductor. When doping increases, the barrier width is reduced and thermionic-field emission tunneling is enhanced [3]. This also causes the diode ideality factorn to deviate from unity (figure 2.6). In this situation the diode n-value shouldalso appear in the reverse flux term, thus leading to a modification of the diodeequation 2.9

I = Ir

exp

(qV

nkT

)− exp

[(1

n− 1

)qV

kT

](2.10)

when n is equal to 1 equation 2.10 again reduces to the ideal diode equation 2.5.Other deviations from ideality are to be ascribed to the contributions of the

series and shunt resistance [16]. The actual circuit scheme is shown in figure

Figure 2.5: Effect of the ideality factor n on the behaviour of J as a function ofthe applied voltage V. Source : figure from Ref.[3]

Figure 2.6: I-V characteristics of a Schottky diode for progressively high carrierconcentrations. (a) N ≤ 1017cm−3, thermoionic-emission dominates, (b) N '1018 − 1019cm−3, thermoionic-field tunneling dominates, (c) N ≥ 1019cm−3,field-emission tunneling dominates. Source : figure from Ref. [5].

Figure 2.7: Electric circuit that includes both series resistance and shunt resis-tance (Rp, parallel resistance)

2.7. The series resistance Rs becomes important at high forward voltages and itincludes the resistances of the contacts in the device, i.e. back contact, contactbetween metal-semiconductor, contact between the probe and the metal. It hasthe effect of lowering the voltage effectively applied to the diode.

Veff = V −RsI (2.11)

Considering Current Kirchoff’s Law, equation 2.9 becomes

I = Id + Ip = Ir

[exp

(q (V −RsI)

nkT

)− 1

]+V −RsIRp

(2.12)

Series resistance can be extrapolated by a linear interpolation of the I-Vcurve at high forward biases. Ideally its value should be zero. Shunt resistancerepresents a parallel path where leakage current flows at the sample surface[16]. Ideally Rp is infinite and it is computed by linearly fitting the reverse biasregion.

2.1.1 Fermi level pinning

From equation 2.2 and neglecting image force lowering, one would say thatthe Schottky barrier height (SBH) only depends on the metal, semiconductorand their respective Fermi levels. In the metal a work function φ is definedas the difference between the vacuum level and the Fermi level of the metal,ΦM = Evac−EF . In the semiconductor the Fermi level depends on the doping,so it is more useful to define the electron affinity χ as the difference between

Figure 2.8: Tayloring of the metal wavefunction inside the semiconductor, whichgives rise to Metal Induced Gap States MIGS. Source : figure from Ref. [1]

the vacuum level and the bottom of the conduction band, χSC = Evac − EC .From these two definitions one would expect that the Schottky barrier heightdepends on the respective position of the two Fermi levels. According to theSchottky-Mott rule [17, 18] the barrier height at zero bias is

φ0B = ΦM − χSC (2.13)

valid for a n-type semiconductor.What is experimentally observed [19] instead is that there is no substan-

tial change in barrier height with different metals and the same semiconductor.There is then no strong dependence of the SBH on the metal work function[20]. This phenomenon is called “Fermi level pinning”. When an interface be-tween metal and semiconductor is established, the interface states are not sim-ply formed by the superposition of the charge distribution of the two surfacesconsidered separately. Surface properties substantially change because of theinteraction of the two surfaces. As shown in figure 2.8, metal wave-functionexponentially decays inside the semiconductor. This fact induces the presenceof surface states, whose energy lies in the semiconductor band gap. These statesare then called Metal Induced Gap States (MIGS) and they are responsible forthe pinning of the Fermi level at the metal-semiconductor interface [1].

Recently graphene was employed as an intermediate layer between semicon-ductor and metal. Experimental results showed that the presence of a graphenelayer between gold and n-type germanium actually led to Fermi level depinning[21].

(a) (b)

Figure 2.9: (a) Honeycomb lattice in graphene. Lattice is made of two triangu-lar sub-lattices, whose primitive vectors are a1 and a2 respectively. a=0.142nmis the distance between two carbon atoms Source : figure from “Graphene nano-electronics and nanofabrication” lecture handouts, held by prof. Roman Sordanin Politecnico di Milano. (b) Graphene band structure. Conduction and valencebands touch at the six Dirac points K and K’. Source : figure adapted from Ref.[6]

2.2 Graphene

Graphene was discovered by Geim and Novolosev in 2004 [11], who won theNobel Prize in physics in 2010.

Graphene is a 2D material made of carbon atom arranged in a hexagonalhoneycomb structure, as shown in figure 2.9a. Carbon atoms are hybridized sp2.Therefore each atom forms three σ bonds, that give rise to a planar structureand one half-filled π bond in the perpendicular direction. Owing to the strongcovalent bonds, graphene has an extraordinary mechanical strength [22, 23]. Thehexagonal lattice can be considered as made of two interpenetrating triangularsub-lattices A and B.

The conduction and valence bands touch at six points in the reciprocal space,i. e. at the Dirac points K and K’ (figure 2.9b). Graphene is a zero-band gapsemiconductor, then it is classified as semi metal. The total wave function isgiven by the superposition of the wave function of lattice A and that of latticeB (notation refers to figure 2.9a).

|Ψ (k, r)〉 =∑ΨA (k) exp (jk · rAi) |φ (r− rAi)〉

+∑ΨB (k) exp (jk · rBi) |φ (r− rBi)〉

(2.14)

By solving Schrödinger equation HΨ = EΨ in tight binding approximation

[24] we get [0 −γf(k)

−γf∗(k) 0

][ΨA

ΨB

]= E(k)

[ΨA

ΨB

](2.15)

where γ is the hopping energy (γ=2.8eV) and f(k) =∑3i=1 exp(jk · ui), k is

a vector of the reciprocal space. By solving the eigenvalue equation 2.15, it ispossible to obtain the following expression for the energy

E(k) = ±γ |f(k)| (2.16)

|f(k)| =

√√√√1 + 4 cos

(3

2aky

)cos

(√3

2akx

)+ 4 cos2

(√3

2akx

)(2.17)

a is the distance between two carbon atoms a = 0.142nm (figure 2.9a).The two signs of equation 2.16 correspond to two bands, one for the con-

duction band (the empty π∗) and the other for valence band (π). The bandstructure for graphene is shown in figure 2.9b [25]. In the neighborhood of theDirac points the energy dispersion is linear

E(k) = ~vF |k−K| (2.18)

where vF ≈ 106ms is Fermi velocity. In the neighborhood of the Dirac pointsit is therefore possible to evaluate the function f(k) by considering its Taylorexpansion f(k) ≈ 3

2a (kx + jky). The new Hamiltonian is

H = ~vF

[0 kx − jky

kx + jky 0

]= ~vFσ k (2.19)

with σ = (σx, σy), where σx and σy are the Pauli matrices in the x- and y-direction, and ~vF = 3aγ

2 . Equation 2.19 has the same form of the Dirac-Weyl Hamiltonian. At the Dirac points therefore electrons behave as relativisticparticles [12]. They travel at constant speed vF , which is 1/300 of the speed oflight in vacuum. This phenomenon is at the basis of the interest in high-speedelectronics applications of graphene.

Another important feature of graphene is its extremely high mobility [14]due to the absence of back scattering at low-energy excitations near the Diracpoints. The absence of back-scattering in graphene is a direct consequence of

the form of its wavefunction near the Dirac point K [14]

Ψ (k) =

[ΨA

ΨB

]=

1√2

[exp

(− iθk2

)± exp

(iθk2

)] (2.20)

where θk = arctan(qxqy

)and q = k − K is the momentum measured from

the Dirac point K. Since electrons along +kx and -kx have orthogonal wave-functions, they have no probability of being scattered back. The mobility forgraphene on SiO2/Si substrate is ∼ 1÷ 1.5 · 104cm2V −1s−1 and for suspendedgraphene it is ∼ 2 · 105cm2V −1s−1 [26].

For a two-dimensional system, it is possible to derive a relationship betweenthe carrier density n and the position of the Fermi level EF [27, 2]. The numberof states between q and q+dq is

N(q)dq =2πqdq(2πL

) (2πW

) · 2 · g (2.21)

where A = LW is the area of the sample and g = 2 in graphene, the factor 2takes into account spin degeneracy. By introducing the dispersion relation 2.18,the above equation becomes N(q)dq = N(E)dE = 2A EdE

π(~vF )2. The density of

states per unit energy and unit area is

D(E) =N(E)

A=

2

π (~vF )2 |E| = D0 |E| (2.22)

From the approximation n =´∞0D(E)f(E)dE ≈ 1

π

(EF

~vF

)2, which holds

only at T = 0K and where f(E) is the Fermi function, the relationship betweenn and EF is obtained

EF = ∓ h

2√πvF√n (2.23)

where the signs + and - correspond to n and p-type graphene respectively.The position of the Fermi level in graphene can be controlled by either

doping the material [28] (even ambient impurities dope graphene) or by gatingit through an applied bias [29]. This feature can be exploited in the graphene-semiconductor junction, in order to tune the barrier height and the rectifyingproperties [2].

Figure 2.10: Effect of an applied bias on the Fermi level in graphene. Theassumption is that at zero bias the Fermi level is exactly at the Dirac point.Under forward bias EF is shifted downwards and this effect is very small. Underreverse bias EF is shifted upwards. Source : figure from Ref. [2]

2.3 Model of the graphene-semiconductor junc-

tion

An exhaustive theory of the graphene-semiconductor Schottky junction doesnot exists to-date [2], although some attempts to explain the phenomenon havebeen made.

S.Tongay et al. [30] proposed a modification to the thermionic emissiontheory in order to take into account the variation of the Fermi level in graphenedue to an applied bias. In the case of a conventional metal-semiconductorinterface, the charges induced in the metal by the semiconductor are negligible,as a consequence of the high density of states in the metal. In the case ofgraphene the effect of induced charges is instead no longer negligible.

Let us consider that the Fermi level is at the Dirac point when there is noapplied bias and let us take into account the interface between graphene and a n-type semiconductor (fig. 2.10). Under forward bias the Fermi level in grapheneEF shifts downwards since a smaller number of charges is required to mirrorthe positive charges formed in the depletion layer of the semiconductor. Viceversa under reverse bias the depletion layer in the semiconductor increases andso does the number of negative charges in graphene, thus leading to an upwardshift of the Fermi level in graphene. This bias-dependence has to be included inthe diode equation (eq. 2.9) by considering the following expression of the totalbarrier height

eΦb = eΦ0b + e∆Φb (V ) = eΦ0

b −∆EF (V ) (2.24)

where Φ0b is the zero-bias Schottky barrier height and ∆Φb (V ) is the correction

to the barrier height at fixed voltage V. It is possible to notice from figure 2.10that the change in the graphene Fermi energy is opposite to the change in theSchottky barrier height, e∆Φb (V ) = −∆EF (V ). From equation 2.23 we obtain

∆EF = ∓ h

2√πvF√|ninduced (V )| (2.25)

where ninduced is the charge induced by the application of a bias V. As an exam-ple let us take into account the interface between graphene and germanium withND ≈ 2 · 1017 C

cm3 . The depletion layer in the semiconductor can be predictedto be w ≈ 60nm. Therefore the charge induced at the interface graphene-germanium is ninduced ≈ NDw ≈ 1.2 · 1010 C

cm2 . According to equation 2.25ninduced causes a significant shift in the graphene Fermi level of ∆EF ≈ 0.1eV .

The total charge density in graphene is given by the sum of its initial dopingn0 and ninduced. ninduced is supposed to be opposite to the variation of charge inthe depletion layer caused by the application of bias and the charge density perunit area in the depletion layer is Qd = eNDw, where w is the depletion layer

width w =

√2εsε0

(Vbi+V−

kBT

e

)eND

[4]. So the total charge density of graphene is

ngraphene = n0 + ninduced = −

√2εsND

(Vbi − V − kBT

e

)e

(2.26)

where ND is the density of ionized donors, which is considered constant through-out the depletion width of the semiconductor. Vbi is the built-in potential, whichcan be computed through the analysis of the capacitance-voltage characteristics

[4]. At zero bias ∆EF = 0, ngraphene = n0 = −

√2εsND

(Vbi−

kBT

e

)e .

Therefore under reverse bias and considering ninduced n0, the equation2.25 becomes [14]

e∆Φb (VR) = −∆EF (VR) = ~vF√π

[√|ngraphene| −

√|n0|

]= ~vF

√π[√|n0 + ninduced| −

√|n0|

]≈ −1

2~vF√πn0

ninducedn0

= −1

2~vF√π

(ngraphene − n0)√|n0|

(2.27)

The bias-dependence of SBH (equation 2.24) is included in the diode equa-tion 2.9

J(V ) = A∗T 2 exp

(−eΦ

0b + e∆Φb (V )

kBT

)[exp

(eV

kBT

)− 1

](2.28)

where the expression of ∆Φb is derived from equations 2.26 and 2.27. Thebarrier height is therefore

Φb (V ) = Φ0b−

∆EF (V )

e= Φ0

b−a

(√Vbi − V −

kBT

e−√Vbi −

kBT

e

)(2.29)

where a = h4√πvF

√εsND

2en0. From equation 2.29 it is possible to notice that when

V = 0, i.e. when no bias is applied, Φb (V ) = Φ0b . Therefore equation 2.29

could be exploited in order to extrapolate the barrier height at different appliedbiases, while Φ0

b can still be evaluated by the forward bias current at V = 0.D. Sinha and J. U. Lee [31] proposed another approach for explaining the

diode characteristics using Landauer formalism. The Landauer transport equa-tion for the density of current J is [32]

J = − eτ

ˆ +∞

−∞T (E)D (E) (fg − fs) dE (2.30)

where fg and fs are the Fermi functions of graphene and semiconductor respec-tively, τ−1 is the injection rate from the contact to the graphene and fromgraphene to the semiconductor, D (E) = D0 |E| is the density of states ingraphene near the Dirac point (equation 2.22). T (E) is the transmission prob-ability over the zero-bias barrier height, we assume that in rectifying conditiononly carrier with energies greater than the Schottky barrier height are trans-mitted, the others are reflected. A further assumption valid under rectifyingcondition is that E −EF ≈ E −EFs > Φ0

b kT , with reference to figure 2.10.Therefore Fermi distribution can be approximated by Boltzmann distribution

1(exp

E−EFgkT +1

) ≈ exp(−E−EFg

kT

). Equation 2.30 becomes

J =e

τD0 (kT )

2

(Φ0b

kT+ 1

)exp

(−Φ0

b

kT

)(exp

(EFkT

)− exp

(EFskT

))(2.31)

Since EF −EFs = −eV , equation 2.31 is formally identical to the ideal diodeequation 2.5, therefore it is possible to obtain an expression for the Richardson

Figure 2.11: Band scheme of the working principle of a graphene-semiconductorjunction as photodetector. e-h pairs are generated in the semicodnuctor deple-tion region and flow in graphene under the application of a reverse bias. Source :figure adapted from Ref. [7]

constantA∗ =

e

τD0k

2

(Φ0b

kT+ 1

)(2.32)

This formula explains the experimentally observed very low value for Richard-son constant in graphene-semiconductor junction [31].

2.4 Photodetector application of graphene Schot-

tky diode

Graphene also exhibit remarkable optical properties [33], which make G/S junc-tion suitable for photodetection applications when working under reverse bias.Optical absorption mainly takes place in the semiconductor, while grapheneacts like a transparent carrier collector. Absorption in graphene becomes im-portant in the infrared spectral region1. In figure 2.11 the working principleof a graphene Schottky diode working as photodetector is shown [2]. In thedepletion layer of semiconductor electron-hole pairs are generated by photonsimpinging onto the diode. Photo-generated carriers are injected into graphene

1In the near-infrared and visible spectral range, light transmittance T does not depend onfrequency. At normal incidence, transmittance can be expressed as [34, 35] T = (1 − 0.5πα)2 ≈1−πα ≈ 0.977, where α is the fine structure constant α = e2

4πε0~2c. A single layer of suspended

graphene has an absorption of 2.3%, which is about 50 times higher than, for example, in GaAsat λ = 1550nm.

Figure 2.12: Responsivity of the device working in high-gain configuration (left)and in photodiode mode (right). Source : figure from Ref. [8]

by the built-in potential and they will contribute to photocurrent. The fastrecombination time in graphene, of the order of picoseconds [36], is not an is-sue. Lifetime of photo-carriers is indeed related to the probability of being backinjected into the semiconductor. If the intrinsic recombination time in the semi-conductor is very low, recombination rate of photo-generated carriers τ r can befurther reduced.

F. Liu and S. Kar [8] obtained a very high responsivity (up to 107 AW ). De-vices used and their responsivities are shown in figure 2.12. When working inhigh-gain mode, i.e. when bias is applied to the two front electrodes, there is agreat gain in responsivity with respect to the standard photodiode mode case.The fact that the shapes of the two responsivities are similar shows that most ofthe photo-generated carriers originate in the semiconductor and are injected ingraphene. Contribution of photocarrier generated in graphene is then negligible.

The high responsivity obtained under high-gain mode is due to the QuantumCarrier Reinvestment mechanism (QCR) [8]. Carriers are injected in grapheneand they contributes to photocurrent until they are back injected in the semi-conductor. Since transit time τ t in graphene is very small, a single carrier isreinvested many times before it recombines in the semiconductor, thus lead-ing to an enhancement in responsivity. It is therefore possible to define thequantum gain (QG) as the external quantum efficiency2 times the number of

2EQE (External Quantum Efficiency) is defined as the number of carriers produced perphoton.

EQE =Iph/e

Φinwhere Iph is the photocurrent, Φin is the incoming photon flux.

reinvestments of each hole

QG = EQE ·(τ rτ t

)(2.33)

Transit time in graphene is defined in the diffusion transport model

τ t =L

vd=

L2

µV(2.34)

where L is the distance between the electrodes, vd the drift velocity, μ themobility in graphene and V is the applied bias. The photocurrent responsivityRI is therefore defined as

RI =IphPin

= EQEe

hντ r

(µV

L2

)(2.35)

where Pin is the incident optical power.

Chapter 3

Sample fabrication

In this chapter the fabrication methods are discussed. At the beginning opticallithography was used to fabricate graphene/Ge Schottky diodes, but it wasthen replaced by Electron Beam Lithography (EBL) in order to obtain smallerstructures, which are more suitable in photodetection applications.

Different sample series are here presented, which correspond to improvedoptimization steps. Graphene transfer and EBL lithography are performed bycollaborators of the Nanoscale Device Group, in the L-NESS laboratory. LEP-ECVD growths are carried out by the Silicon and Germanium Epitaxy group,in L-NESS. Samples series are divided according to the substrate used: heavilydoped epitaxial germanium, lightly doped epitaxial germanium and Ge wafers.

3.1 Back ohmic contact

The first issue to be addressed is the formation of a back ohmic contact. It canbe quite easily achieved with highly-doped semiconductors, where field-emissiondominates (chapter 2). With low-doped semiconductors, the formation of anohmic contact may become an issue.

3.1.1 Epitaxial germanium

Two substrates are made by growing germanium on a silicon substrate (ρ =

0.001Ωcm) via Low-Energy Plasma-Enhanced Chemical Vapour Deposition (LEP-ECVD, see appendix A). Epliayer with two different n-type doping have beenused for this work:

20

• n = 3 · 1018cm−3. The series will be called graphene on germaniumGrOnGe18

• n ≈ 2 · 1017cm−3. The series will be called graphene on germaniumGrOnGe17

In both cases the epilayer-thickness is approximately 1.5µm.Before deposition the n-type Si substrate is RCA cleaned1 and rinsed in

hydrofluoric acid in order to remove native oxide and passivate the surface (hy-drogen passivation) to prevent the oxidation before the loading in the loadlockchamber.

After the epitaxial growth an ohmic contact is formed at the back side ofthe Si substrate by e-beam evaporation of 100nm nickel and annealing at 400°Cfor 5 minutes. In e-beam evaporation electrons are thermionically generatedby heating a filament inside a vacuum chamber at about 10−6mbar. Electronsare accelerated by a 12kV bias towards the target material which is molten orsublimated depending on its melting temperature. The atomic beam formedprecipitates into solid state when getting the target sample, thus creating a thinfilm on the sample.

As shown in fig. 3.1 different annealing times are tested. However no de-viations from the ohmic behavior is observed. The only difference is in theresistance values.

Annealing time [s] Resistance [Ω]

30 3.7960 4.61150 3.78300 3.44

It is important to notice that the resistance values reported in the tableabove do not refer to the values of the contact resistances. In order to test theohmic behavior of the contact a metallic mask made of four pads is used. A two-probe system is used in order to measure the current-voltage characteristics ofthese test samples. Resistances are obtained by linear fitting the curves. Since

1The RCA cleaning consists of two chemical etch steps, in order to remove both organicand ionic contaminants:

1. NH3 : H2O2 : H2O, 1 : 1 : 5, (400ml:400ml:2l) for 10 minutes at 75°C

2. HCl : H2O2 : H2O, 1 : 1 : 5, (400ml:400ml:2l)The chemical volumes are intended with the concentrations: NH3 28%, H2O2 31%, HCl 37%.

-0.5 0 0.5

Voltage [V]

-0.1

-0.05

0

0.05

0.1

Cu

rre

nt

[A]

Ni 30s annealed

Ni 60s annealed

Ni 150s annealed

Ni 300s annealed

Figure 3.1: Ohmic behaviour tested for 100nm Ni evaporated on n-Si at differentannealing times. No deviations from ohmic behavior is observed. Differencesarise only in the values of the resistances.

the same mask is employed in all test samples, the geometry is the same. Theresistance values can therefore be used in order to compare the relative effect ofthe different annealing times.

3.1.2 Bulk germanium

The substrate is a crystalline germanium sample 1.5cm x 1.5cm. The firstissue to be addressed is the formation of an ohmic contact with a low-dopedsemiconductor. Two different dopings are tested. 90 nm of AgSb (Ag with1% Sb) are evaporated on Ge n = 1 · 1018cm−3, n = 8 · 1016cm−3 and Gen = 2 · 1015cm−3. It is possible to notice that for doped Ge n = 8 · 1016cm−3

a thermal annealing at 400°C for 300 seconds guarantees the formation of anohmic contact (R ≈ 6Ω), as shown in figure 3.2. A further annealing at 450°Cfor 300 seconds does not provide any substantial difference. In the case of low-doped Ge (n = 2 · 1015cm−3) a further annealing at 450°C for 300 seconds isrequired (Figure 3.3). Resistance is in this case about 20Ω. An annealing at400°C for 5 minutes provides the formation of an ohmic contact also in the caseof Ge n = 1 · 1018cm−3, with a resistance R ≈ 6.5Ω.

In this case Ge n = 8 · 1016cm−3 is used to ensure the formation of a goodSchottky barrier with Graphene. Native oxide is removed by hydrofluoric acid.

-1 -0.5 0 0.5 1

Voltage [V]

-3

-2

-1

0

1

2

3

Curr

ent [m

A]

90nm AgSb on Ge n=8e16 No annealing

(a)

-1 -0.5 0 0.5 1

Voltage [V]

-100

-50

0

50

100

Curr

ent [m

A]

AgSb on Ge n=8e16

Annealing 400°C 5 minutes

AgSb on Ge n=8e16

Annealing 400°C+450°C

5 minutes

(b)

Figure 3.2: Effect of annealing of 90nm of AgSb on top of Ge n=8e16. (a)Without thermal annealing no proper ohmic contact is formed. (b) I-V charac-teristics after thermal annealing. No substantial difference is observed betweenthe two thermal treatments.

Back contact is made by evaporation of 90nm AgSb (Ag with 1% Sb) andannealed at 400°C for 5 minutes.

3.2 Graphene wet transfer

Graphene is grown by Chemical Vapour Deposition CVD on two sides of acopper foil. A PMMA (Polymethyl-methacrylate) layer is spin coated on topof a graphene covered side. Graphene on the other side is removed by usingoxygen plasma. Then copper is removed using a copper etchant. Grapheneis now stuck to the PMMA, it is left floating in deionized water in order toremove all residual impurities and to exploit the straightening effect of the watersurface. Graphene is made adhere to the substrate by placing the sample inwater under graphene. This process is called graphene fishing. Then the samplewith graphene and PMMA on top is left on an inclined plane in order to removethe remaining water. The sample is baked on a hot plate at 160°C for 5 minutesin order to further promote graphene adhesion on the substrate. PMMA isremoved through a solvent such as acetone or NEP (N-Ethylpyrrolidone). Abasic procedure scheme is shown in figure 3.4.

-1 -0.5 0 0.5 1

Voltage [V]

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Curr

ent [m

A]

90nm AgSb on Ge n=2e15

No annealing

(a)

-1 -0.5 0 0.5 1

Voltage [V]

-40

-30

-20

-10

0

10

20

30

Curr

ent [m

A]

90nm AgSb on Ge ne=2e15

Annealing 400°C 5 minutes

(b)

-1 -0.5 0 0.5 1

Voltage [V]

-50

0

50

Curr

ent [m

A]

90nm AgSb on Ge n=2e15

Annealing 400°C+450°C 5 minutes

(c)

Figure 3.3: Thermal annealing on Ge n=2e15. A further annealing of 5 minutesat 450°C is required in order to obtain a proper ohmic contact.

Figure 3.4: Main steps of graphene wet transfer. (a) Graphene is grown on acopper foil by CVD. (b) PMMA is used to protect graphene on one side whilegraphene on the other side is removed through oxygen plasma. (c) Copperetchant removes copper foil. (d) Graphene is stuck to PMMA and it is rinsedin water. (e) Graphene fishing. Sample is placed in water below graphene. Thesample is then dried in an inclined plane and hot baked for 5 minutes at 160°C.

3.3 GrOnGe18 series

3.3.1 GrOnGe18A using optical lithography

Substrate preparation is described in section 3.1.1, in this case epitaxial ger-manium is n-doped with n = 3 · 1018cm−3. Four oxide pads are created ongermanium using optical lithography, see fig. 3.5. The presence of oxide padsis crucial in order to create a proper contact with graphene. Without oxide,current would directly flow from the front metal contact to germanium, thus no

Figure 3.5: Scheme of pads and contacts of sample GrOnGe18A

Figure 3.6: Main steps in optical lithography (a) and EBL (b). Source : fig-ure adapted from “Graphene nanoelectronics” lecture handouts, held by prof.Roman Sordan in Politecnico di Milano.

Schottky junction between graphene and germanium would be formed. 100nmSiO2 are evaporated on top of germanium. The positive resist AZ9260 is spincoated for 60 seconds at a speed of 3800rpm reached with an acceleration of500rpm/s. This spin coating allows to have 4.6μm thick resist layer. The sam-ple is then baked on a hot plate for 2 minutes at 110°C. The purpose of thepre-exposure bake is to remove all the solvent, so that the photoresist layerbecomes dry and solid [37]. The sample is exposed by UV light (λ = 365nm)using Karl Suss MA56 mask aligner. The resist dose is 850 mJ

cm2 . After exposure,it is developed with AZ726 Developer for 3 minutes and 30 seconds. Then oxideis etched using BOE (Buffer Oxide Etch), which is a mixture of a bufferingagent ammonium fluoride NH4F and HF for 7 seconds. The effect of HF on theohmic contact is evaluated on a test sample. As shown in fig. 3.7 no deviations

-0.4 -0.2 0 0.2 0.4

Voltage [V]

-0.1

-0.05

0

0.05

0.1

Cu

rre

nt

[A]

Ni contact

Ni contact after HF

Figure 3.7: Effect on ohmic nichel contacts after rinsing sample in HF. Thebehaviour is still ohmic, the resistance value is increased.

from the linear ohmic behavior is observed, although there is a change in theresistance value from 3.44Ω to 7.95Ω.

Graphene is wet transferred (see sect. 3.2) and it is etched around the padsaccording to fig. 3.5. The etching pattern is created by another lithographystep using a positive resist. Graphene is etched with Reactive-Ion Etching (RIE,see appendix C) at a pressure of 100mTorr with oxigen plasma at 50W for 25seconds.

Electrodes are created on top of the oxide pads by using a negative resistAZ2035, which is spin coated for 60 seconds at a speed of 2500rpm reached withan acceleration 500rpm/s. Resist height is about 3.6µm. Then it is baked for 1minute at 110°C and exposed using the mask aligner (resist dose is 80 mJ

cm2 ). Itis again baked for 1 minute at 110°C after exposure and then developed usingAZ726 Developer for about 1 minute. Contacts are made of an adhesion layerof 3nm Ti and 100nm Au. Lift-off is performed using AZ100 Remover for abouttwo hours at 70°C.

3.3.2 GrOnGe18B using EBL

For this type of sample the same substrate as GrOnGe18A is employed. Asshown in figure 3.8, structures are made of two pads of different sizes: oneside is 150μm and the other side H is 150μm, 300μm, 450μm. The distances L

Figure 3.8: Scheme of GrOnGe18B sample. Many structure combinations aretested with L = 150µm− 300µm− 450µm and H = 150µm− 300µm− 450µm.

between the two pads are 150μm, 300μm and 450μm.Fabrication is performed with Electron Beam Lithography (see appendix B).

In order to create the oxide pads, positive resist PMMA is spin coated on thesubstrate. The sample is exposed using a suitably modified SEM (ScanningElectron Microscope). 100nm of SiO2 is evaporated and then lifted-off withacetone over-night. Graphene is then wet transferred (see sect. 3.2) and etchedwith 25s oxygen plasma at 50W with RIE in a squared area around the padsof 700μm side. With another lithography step using the same positive resistPMMA, the contacts made of 3nm Ti and 100nm Au are evaporated, thenlifted-off with acetone over-night.

3.4 GrOnGe17 series

Fabrication is performed with Electron Beam Lithography using the substratewith n-type germanium n ≈ 2 · 1017cm−3 described in section 3.1.1. In a singlesample 1cm x 1cm 25 structures each made of two pads are fabricated. Theoxide pads are made of aluminum, whose native oxide is exploited in order tocreate an insulator pad. Two layers of PMMA are spin coated on the samplewith thickness of 120nm and 80nm respectively, then baked for 5 minutes at160°C. The bottom PMMA layer has lower density than the top one. In thisway the top layer suffers less from exposure and development than the other andgeometry is better preserved. Exposure was made by EBL. 30nm of aluminumare evaporated and then lifted-off in acetone for about 5 hours.

Graphene is wet transferred (see sect. 3.2). Two layers of PMMA are spin

(a)

(b)

Figure 3.9: (a) Scheme of GrOnGe17A and GrOnGe17B. (b) Different paddimensions and distances between the two pads are tested.

coated on the sample. After exposure 100nm Au are evaporated and lifted-offin acetone for about 5 hours, in order to obtain the two top electrodes. Fourdifferent samples in this series are fabricated, whose different characteristics willbe discussed in detail:

GrOnGe17A This sample is made with the procedure described above. Padsdimensions and their respective distances are shown in figure 3.9a. Grapheneis not etched around each structure. Therefore it is not possible to know theexact active area of the Schottky diode, since all the structures are connectedwith each other. In figure 3.9b the tested structures are shown.

GrOnGe17B Insulator pads are made of 100nm SiO2 instead of aluminum.Graphene is not etched around each structure. Pads dimensions and their re-spective distances are the same as shown in figure 3.9a.

(a)

(b)

Figure 3.10: (a) Scheme of GrOnGe17C, GrOnGe17D and GrOnBulkGe sam-ples. (b) Tested distances between pads L = 10µm− 20µm− 30µm .

GrOnGe17C Sample is made according to the above procedure. Grapheneis not etched. Each structure is made of two pads having a rectangular shape150μm x 300μm, and their respective distances L are 10μm, 20μm, 30μm (figure3.10).

GrOnGe17D Sample is made with the procedure described above. Eachstructure is made of two pads having a rectangular shape 150μm x 300μm, andtheir respective distances L are 10μm, 20μm, 30μm. Sample scheme is shown infigure 3.10, with the difference that the structures with distance between padsL=150μm are not fabricated. Graphene is etched around each structure exceptfor the ones with a pad-pad distance of 20μm because of exposure problems. Inorder to etch graphene two PMMA layers are spin coated on the sample with atotal thickness of about 160nm and the structure is exposed by electron beam.RIE is employed with 25 seconds of oxygen plasma at a radio frequency of 50W,pressure is 100mTorr.

3.5 GrOnBulkGe sample

A germanium wafer with a doping n = 8 · 1016cm−3 is employed as substrate.Cleaning procedure and formation of the back ohmic contact is discussed insection 3.1.2. Pad structure and fabrication are the same as described inGrOnGe17D. Graphene is etched around pads according to figure 3.10.

Chapter 4

Electrical measurements

In this chapter the fitting methods for the determination of the diode parameters(Rs, Rp, Isat, barrier height and n) from the current-voltage diode characteris-tics, are discussed. Depending on the semiconductor doping the current-voltagecharacteristics should or should not take into account the thermionic-field emis-sion term, as discussed in section 2.1. Fitting is therefore performed by codingtwo different MATLAB functions. The reliability of the fitting is first testedon a conventional metal-semiconductor Schottky diode and then it is applied tothe graphene Schottky diodes.

4.1 Fitting models

As discussed in chapter 2.1, the first issue to be addressed is the determinationof the two resistances Rs and Rp. The knowledge of these two resistances allowsone to determine the effective voltage and current applied to the diode.

The contribution from the series resistance becomes important at high volt-age, i.e. for voltages greater than 0.3V [16]. Rs is determined by a linear fittingof the diode curve for V ≥ 0.8V . The MATLAB function polyfit(x , y ,N ) re-ceives as input the variables x and y, which in this case are voltage and currentof the diode respectively, and the polynomial degree of the fitting curve. Withthe same function also Rp is determined by a linear fitting of the small signalregion in reverse bias. In this case the fitting is performed for voltages in therange −0.2 ≤ V ≤ −0.1.

Two different fitting methods are used depending on the semiconductor dop-

32

ing. For this purpose I coded two different MATLAB functions.

Method 1: heavily doped semiconductors. For heavily-doped semicon-ductors the thermionic-field emission term has to be included in the diode char-acteristics. In practice when the values of the two resistances are determined,they are used in order to obtain the effective voltage and current across thediode: Veff = V − RsI and Ieff = I − V−RsI

Rp. The “corrected” curve is then

least squared fitted according to the characteristic

Ieff = Isat

exp

(qVeffnkT

)− exp

[(1

n− 1

)qVeffkT

](4.1)

Isat and n are determined by using a MATLAB function lsqcurvefit , whichtakes as input the curve to be fitted and the model function that fits it. It thenperforms the fitting via least squares approximation. The value of the barrierheight is derived from equation

Isat ≡ AA∗T 2 exp

(−qΦbkT

)(4.2)

where A is the active area of the device, A∗ is the Richardson constant of thesemiconductor, A∗ = 143 A

cm2K2 for n-type germanium 100. Since measure-ments are performed at room temperature T is considered equal to 300K.

Method 2: low-doped semiconductors. In the case of low-doped semi-conductor the diode characteristics is

I = Isat

[exp

(e (V −RsI)

nkT

)− 1

](4.3)

and under the assumptions that V RsI and that the exponential term is bigenough it can be expressed as

ln (I) = ln (Isat) +e

nkTV (4.4)

Saturation current and the n parameter are therefore determined by a linear fit-ting of the semi logarithmic plot in forward bias. The n parameter is evaluatedby the slope of the linear fitting, according to equation 4.4, while ln (Isat) cor-responds to the intercept of the linear curve at V = 0. The fitting range needsto be chosen accurately, so that the two approximations assumed in equation

Figure 4.1: Scheme of test sample Pt/Ge Schottky junction.

4.4 hold: V RsI and exp(e(V−RsI)

nkT

) 1. The value of the barrier height is

derived from equation 4.2. In equation 4.3 parallel resistance is assumed to bebig enough to consider Ieff = I − V−RsI

Rp≈ I. The validity of this assumption

is discussed in section 4.2.

4.2 Test sample: Pt/Ge Schottky barrier

A conventional metal-semiconductor junction is used in order to test the reliabil-ity of the fitting procedures discussed above. The Schottky junction is made bythe interface between platinum and a germanium wafer. Germanium is n-typedoped and three different dopings are tested: n ≈ 1018cm−3, n = 8 · 1016cm−3

and n = 2 · 1015cm−3. The formation of an ohmic contact is discussed in detailin section 3.1.2. For germanium n ≈ 1018cm−3 and n = 8 · 1016cm−3, 90nmof AgSb are evaporated and annealed at 400°C for 5 minutes. For germaniumn = 2 · 1015cm−3 a further annealing at 450°C for 5 minutes is required. Schot-tky junction is formed by e-beam evaporation of 4nm of platinum on top ofgermanium, covering an area of 6.4 x 5.4 mm2. Electrodes on top of Pt (figure4.1) are made of 10nm of titanium, which forms an adhesion layer, and 100nmof Au plus 200nm of Al.

In figure 4.2 the effect of semiconductor doping on the diode characteristicsis shown. In those plots the current is displayed as a function of the effectivevoltage Veff = V − RsI. The effect of the series resistance on the diode curveis in this way removed. For highly doped semiconductors (n ≈ 1018cm−3)the characteristic strongly deviates from the rectifying behavior in reverse bias.In this case thermionic-field emission cannot be neglected so the first fittingmethod has to be employed. The characteristics of Ge n = 8 · 1016cm−3 and

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2

Voltage [V]

-0.02

-0.01

0

0.01

0.02

0.03

0.04

Cu

rre

nt

[A]

Pt/Ge Schottky junctions

Ge n=2e15

Ge n=8e16

Ge n=1e18

Figure 4.2: Pt/Ge junction at different semiconductor dopings. Contribution ofthe series resistance is already removed by plotting the current as a function ofthe effective voltage.

n = 2 · 1015cm−3 show instead a good rectifying behavior, so the second fittingmethod is applied.

Series resistance is measured by linear fitting the diode curve from 0.4V inthe case of Ge n ≈ 1018cm−3, since measurements are performed in the range−0.5 ≤ V ≤ 0.5. In the case of Ge n = 8 · 1016cm−3 and n = 2 · 1015cm−3, thevoltage range extends up to 2V, so the linear fitting is performed for V ≥ 1.5V .Parallel resistance is found by a linear fitting in the region −0.2 ≤ V ≤ −0.1

(figure 4.3).Figure 4.4a shows the application of the first fitting method. The reliability

of the fitting is validated by comparing the experimental data (yellow curve)and the curve plotted by plugging in equation 4.1 the fitted parameters Rs, Isatand n (blue curve).

Figure 4.4b shows the semi logarithmic plot of Pt/Ge n = 8 · 1016cm−3.The linear fitting is performed in the voltage range between the two red squarepoints. In this region the model assumptions can be considered valid. ForV = 0.12V , RsI ' 5 · 10−3and exp

(e(V−RsI)

nkT

)≈ 85, and for V = 0.18V ,

RsI ' 1.7 · 10−2 and exp(e(V−RsI)

nkT

)≈ 500, so the assumptions V RsI and

exp(e(V−RsI)

nkT

) 1 hold.

Measurements are performed with a two-probe system on every combination

-0.5 0 0.5

Voltage [V]

-0.04

-0.02

0

0.02

0.04

0.06

Cu

rre

nt

[A]

Diode curve Pt/Ge n=e18

Series resistance fitting

Parallel resistance fitting

Figure 4.3: Linear fitting performed in order to determine series and parallelresistances.

of Schottky contact and ohmic contact (as a reference see figure 4.1). Resultsare shown in table 4.1. It is possible to notice that the parallel resistance is ofthe order of kΩ in the case of Ge n = 8 · 1016cm−3 and Ge n = 2 · 1015cm−3,thus the approximation Ieff = I − V−RsI

Rp≈ I assumed in the second fitting

method can be considered valid. In the case of Ge n ≈ 1018cm−3 the valueof the parallel resistance is ∼ 100Ω and so for the sake of precision the leastsquare fitting in the second method is performed considering the correction ofthe parallel resistance on the effective voltage.

From figure 4.2 one would say that the on-state of the diode, which is re-flected in the value of the barrier height, would be at lower voltages for Gen ≈ 1018cm−3 than for Ge n = 8 · 1016cm−3 and Ge n = 2 · 1015cm−3. Intable 4.1 it is possible to notice that the barrier height values are higher for Gen ≈ 1018cm−3. This over estimation of the barrier height could be due to anoverestimation problem in the first fitting method.

Results for the barrier height and the n parameter are also displayed as boxplots (figure 4.5). The red line shows the median and inside the blue box thedispersion results within the first and the third quartile. Saturation current isdetermined according to the applied method and barrier height by equation 4.2.

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2

Effective voltage V-RsI [V]

-0.04

-0.02

0

0.02

0.04

0.06

0.08

Cu

rre

nt

[A]

Pt/Ge n=1e18

Experimental curve

Fitting

(a)

-1.5 -1 -0.5 0 0.5 1

Voltage [V]

10-8

10-6

10-4

10-2

100

Cu

rre

nt

[A]

Pt/Ge n=8e16

0.12V

5.85e-4A

0.18V

2.2e-3A

(b)

Figure 4.4: (a) Results of the fitting in the case of highly doped germaniumsubstrate. The blue curve represents the raw data. The red curve representsthe diode curve obtained by plugging the fitted parameters in equation 4.1. (b)Semilogarithmic plot of Pt/Ge n=8e16. The two red points represent the rangeof the linear fitting performed in order to extrapolate Isat and n.

Sample Rs[Ω] Rp[Ω] Isat[A] Φb[eV] n

Ge n ≈ 1018cm−3 5.21 134.46 2.11 · 10−3 0.61 1.36Ge n = 8 · 1016cm−3 8.05 1241.81 3.02 · 10−5 0.61 1.53Ge n = 2 · 1015cm−3 13.10 2847.25 5.32 · 10−5 0.594 1.52

Table 4.1: Medians of the fitted parameters in samples Pt/Ge

Ge n=1e18 Ge n=8e16 Ge n=2e15

0.59

0.595

0.6

0.605

0.61

0.615

0.62

Barrier height in Pt/Ge Schottky diodes

(a)

Ge n=1e18 Ge n=8e16 Ge n=2e15

1.35

1.4

1.45

1.5

1.55

1.6

1.65

1.7

Ideality factor n in Pt/Ge Schottky diodes

(b)

Figure 4.5: Boxplots of the barrier height and ideality factor n in the Pt/GeSchottky diodes. The red crosses represents outliers.

-2 -1 0 1 2

Voltage [V]

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02C

urr

ent [A

]GrOnGe18A

(a)

-1 -0.5 0 0.5 1

Voltage [V]

-3

-2

-1

0

1

2

3

Curr

ent [A

]

×10-4 GrOnGe18B

(b)

Figure 4.6: Current voltage characteristics of the GrOnGe18 series. No properrectifying behavior is observed.

4.3 Graphene/germanium Schottky diode

In this section the main results obtained with graphene/germanium Schottkyjunctions are presented. The first fabricated samples, the GrOnGe18 series, didnot show any proper rectifying behavior. The main cause was ascribed to theuse of a too heavily doped germanium substrate. The use of a lower dopedsemiconductor, in the GrOnGe17 series, as a substrate greatly improved thedevice response.

4.3.1 GrOnGe18 series

The first fabricated samples, the GrOnGe18 series, do not show any properrectifying diode characteristic (figure 4.6). Because of the almost absent rectify-ing behavior in reverse and the high semiconductor doping, the fitting method1 is employed (figure 4.7). Results on such characteristics do not seem to bereliable due to the quite “broad” characteristics. Moreover the value for thebarrier height is about 0.9eV both in GrOnGe18A and GrOnGe18B. Results aretherefore not comparable to those obtained in literature (barrier height 0.45eV[38]).

The main cause of this characteristics could be ascribed to the use of sucha heavily doped semiconductor (Ge n = 3 · 1018cm−3). In fact quite similarbehaviors are obtained in both processed samples (figure 4.6).

The use of Ge n = 3 · 1018cm−3 as a substrate is then abandon in favor of

-1 -0.5 0 0.5 1 1.5

Voltage [V]

-5

0

5

10

Cu

rre

nt

[A]

×10-3

Corrected curve

Experimental curve

Figure 4.7: Fitting of sample GrOnGe18A.

a lower doped semiconductor, as it will be discussed in section 4.3.2. A nonrectifying characteristic is however obtained also in the sample GrOnGe17B,where the oxide pads are made of e-beam evaporated SiO2. A further factorthat affects the current-voltage characteristic could therefore be the use of SiO2

as oxide pads. The resulting current-voltage characteristic is shown in figure4.8. The fabrication of SiO2 oxide pads is abandoned in favor of aluminum,which provides a better response.

4.3.2 GrOnGe17 series

For the fabrication of GrOnGe17 samples, epitaxial germanium n ≈ 2·1017cm−3

is employed as a substrate. Three main samples are described in this section. Inone single sample 1cm x 1cm there are 25 structures, each is made of two padsof different dimensions and different respective distances (for details see section3.4). Graphene is transferred upon the whole the sample. As a consequence insamples where graphene is not etched around each structure it is not possible todistinguish among the different structures, since they are all connected. Dataanalysis for samples GrOnGe17A and GrOnGe17C only provides informationabout series resistance, parallel resistances, saturation current and the idealityfactor n. Barrier height cannot be derived according to this fitting method, sincethe active area of the device is unknown. GrOnGe17D sample is electricallymeasured both before and after graphene etching.

-1 -0.5 0 0.5 1

Voltage [V]

-1

-0.5

0

0.5

1

1.5

2

Cu

rre

nt

[A]

×10-3 GrOnGe17B

Figure 4.8: Current-voltage characteristic of sample GrOnGe17B.

The current-voltage characteristic (see as an example figure 4.9) shows arectifying behavior and is therefore well described by equation 4.3. The fittingis indeed performed according to the second method described in section 4.1.Series resistance and parallel resistance are determined by linear fitting thecurrent-voltage curve for V ≥ 0.8V and −0.4 ≤ V ≤ −0.2 respectively. Anexample of the performed fitting is shown in figure 4.10a. The linear fitting ofthe semi logarithmic plot is performed in the region, which is limited by thetwo red squares. It is possible to show that within this region the two modelassumptions hold. The chosen voltage range is 0.12 ≤ V ≤ 0.2 [V]. In the sampleGrOnGe17D for example at V=0.12, current is I = 2.491 · 10−4A (figure 4.10b)and the series resistance is Rs = 30Ω. The condition V RsI is satisfied sinceRsI ≈ 7.5 · 10−3V and exp

(e(V−RsI)

nkT

)≈ 100, where n is assumed n ≈ 1. For

V=0.2V, RsI ≈ 0.017V and exp(e(V−RsI)

nkT

)≈ 1000.

Pads in sample GrOnGe17A have instead different dimensions: 9 pads havedimensions 150μm x 150μm, 8 are 150μm x 300μm and 2 are 150μm x 450μm.Electrical measurements are performed applying a voltage on every pad andgrounding the back ohmic contact. Values in table 4.2, where the median valuesare reported, do not take into account this difference in dimensions. In table 4.3the median values of the fitted parameters in sample GrOnGe17A are computedby taking into account the differences in pad dimensions. It is possible to noticethat no substantial difference arises, except for the series resistance in the case

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4

Veff

-2

0

2

4

6

8

Curr

ent [A

]

×10-3 GrOnGe17C

(a)

-1 -0.5 0 0.5

Voltage [V]

-0.01

0

0.01

0.02

0.03

0.04

Curr

ent [A

]

GrOnGe17D Before graphene etching

(b)

Figure 4.9: Current-voltage characteristics of GrOnGe17C and GrOnGe17Dbefore graphene etching. Both curves show a good rectifying behavior.

Sample Rs[Ω] Rp[Ω] Isat[A] n

GrOnGe17A [19] 163.56 1574.45 1.48 · 10−5 5.08GrOnGe17C [37] 79.61 1071.54 4.84 · 10−5 3.76

GrOnGe17D No etching [37] 11.83 1079.73 1.02 · 10−4 3.74

Table 4.2: Median values of parameter in samples where graphene is not etchedaround each structure.

-1 -0.5 0 0.5 1

Voltage [V]

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

Cu

rre

nt

[A]

Experimental curve

Series resistance fitting

Parallel resistance fitting

(a)

-1 -0.5 0 0.5 1

Voltage [V]

10-8

10-6

10-4

10-2

100

Cu

rre

nt

[A]

GrOnGe17D after graphene etching

V=0.2V

I=5.648e-4

V=0.12V

I=2.491e-4A

(b)

Figure 4.10: (a) Linear fitting perfomed on sample GrOnGe17D L = 10µm, inorder to determine series and parallel resistance values. (b) Semi logarithmicplot of the current-voltage characteristic of GrOnGe17D L = 10µm. The redrectangles represents the voltage range limits, where linear fitting is performed.

Pad dimensions Rs[Ω] Rp[Ω] Isat[A] n

150μm x 150μm [9] 167.14 1975.10 1.11 · 10−5 5.34150μm x 300μm [8] 162.12 1411.59 2.20 · 10−5 4.95150μm x 450μm [2] 202.78 1251.69 3.54 · 10−5 5.09

Table 4.3: Median values of parameters in sample GrOnGe17A according to thedifferent pad dimensions. The number of measurements performed for each caseis displayed in squared brackets.

150μm x 450μm where however the statistical population is not significant.In samples GrOnGe17C and GrOnGe17D all the pads have the same di-

mensions 150μm x 300μm. Table 4.3 shows that no substantial improvementarises in the series resistance values, when electrodes have a smaller area. Onthe other side the use of bigger pad area improves measurement stability in theprobe station.

In sample GrOnGe17D, graphene is etched around each pad in post-processing.The difference between the two current-voltage curves is shown in figure 4.11,where contribution from the series resistance is already subtracted by plottingthe current as a function of the effective voltage. Differences may arise becauseof the different active areas, in particular in GrOnGe17D the active area of thedevices is A = 300µm × L, where L is the inter pad distance and L = 30µm

in the example shown in figure 4.11. When graphene is not etched, it is notpossible to estimate the active area of each device. However in this case it isintuitively larger than the one measured after graphene etching. A bigger arearesults in more current flowing in the diode, since diode current is linearly pro-portional to the area of the device (see equation 4.3). It is possible to observethis effect in figure 4.11. Another difference may arise as a consequence of thefurther lithography step, which is required in order to etch graphene aroundeach structure. This may cause a further doping in graphene, which is verysensible to chemical impurities and it may result in a different position of theFermi level in graphene. In table 4.4 median values of the saturation current andthe ideality factor n are shown. No difference arises in the n parameter, whilesaturation current is slightly larger in the case where graphene is not etched.

In figure 4.12 and table 4.5 results of the fitting for sample GrOnGe17D aftergraphene etching are shown. Results are displayed according to the respectivedistance between the two pads. Fourteen devices have an inter-pad distance ofL = 30µm and twelve of L = 10µm, their active areas are therefore 300μm x

-1 -0.5 0 0.5

Voltage [V]

-0.01

0

0.01

0.02

0.03

0.04

0.05

Cu

rre

nt

[A]

GrOnGe17D before etching

GrOnGe17D after etching

Figure 4.11: I-V curves of sample GrOnGe17D (L = 30µm) before and aftergraphene etching.

Sample GrOnGe17D Isat n

Before graphene etching [38] 1.02 · 10−4 3.74After graphene etching L = 10µm [12] 8.31 · 10−5 3.81After graphene etching L = 30µm [14] 7.33 · 10−5 3.85

Table 4.4: Median values of the saturation current and the ideality factor nin sample GrOnGe17D. The case where graphene is not etched around eachstructure is compared to the one where each structure is isolated from eachother.

0.395

0.4

0.405

0.41

0.415

0.42

0.425

0.43

0.435

Barrier height in GrOnGe17D

(a)

3.3

3.4

3.5

3.6

3.7

3.8

3.9

4

Ideality factor n in GrOnGe17D

(b)

Figure 4.12: Boxplots of the fitted parameters barrier height and n inGrOnGe17D after graphene etching.

Sample Rs[Ω] Rp[Ω] Isat[A] Jsat

[A

cm2

]Φb[eV ] n

L = 10µm [12] 30.78 3952.07 8.31 · 10−5 2.77 0.40 3.81L = 30µm [14] 28.56 3820.41 7.33 · 10−5 0.78 0.43 3.89

Table 4.5: Medians of the fitted parameters in GrOnGe17D after grapheneetching. In squared brackets the number of tested devices is shown.

30μm and 300μm x 10μm respectively.

4.3.3 GrOnBulk sample

In this sample a germanium wafer is used as a substrate, whose doping isn = 8 · 1016cm−3. The better quality of this substrate with respect to theepitaxially grown germanium used in GrOnGe17 series is reflected in the devicecharacteristic. Figure 4.13 shows as an example the characteristic of the devicewith inter pad distance L = 30µm. The second fitting method is applied, whichis suitable because of the rectifying behavior in reverse bias. The same fittingranges as in sample GrOnGe17 can be applied, since the model approximationsstill hold (figure 4.14). In order to extrapolate the value of the parallel resis-tance a linear fitting is performed in the voltage range −0.4 ≤ V ≤ −0.2, whilethe voltage range V ≥ 0.8V is fitted in order to obtain the value of the seriesresistance. Currents in forward bias are however so high that in many cases thecompliance, which is set at 100mA, is reach at V = 0.8V . In this case the linear

-1 -0.8 -0.6 -0.4 -0.2 0 0.2

Vefe

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

Cu

rre

nt

[A]

Graphene/Ge wafer Schottky diode

Figure 4.13: Current-voltage characteristics in graphene/germanium wafer sam-ple.

Device Rs[Ω] Rp[Ω] Isat[A] Jsat

[A

cm2

]Φb[eV] n

L = 10µm [12] 5.11 33397.25 9.55 · 10−6 0.32 0.45 1.69L = 20µm [13] 4.82 31488.72 9.12 · 10−6 0.15 0.47 1.67L = 30µm [13] 5.01 36823.12 9.30 · 10−6 0.10 0.48 1.66L = 150µm [10] 4.82 22082.39 7.28 · 10−6 0.02 0.53 1.64

Table 4.6: Median values of the fitted parameters in graphene/germanium waferSchottky junction. In squared brackets the number of tested pad combinationis shown.

fitting is performed in the range V ≥ 0.6V . The validity of the fitting on thesemi logarithmic plot is tested. An example is here presented in figure 4.14b bytaking into account measurement on the right pad of structure 1.4 (L = 10µm):

• V RsI, for V = 0.12V RsI ≈ 1.16 · 10−3V and for V = 0.2V RsI ≈6.678 · 10−3V

• exp(e(V−RsI)

nkT

) 1, where n is assumed ≈ 1. exp

(e(V−RsI)

nkT

)≈ 100 for

V = 0.12V and exp(e(V−RsI)

nkT

)≈ 1700 for V = 0.2V .

In table 4.6 and in figure median values of the sample are shown accordingto the distance between pads. The main differences between the structures

-1 -0.5 0 0.5 1

Voltage [V]

-0.05

0

0.05

0.1C

urr

en

t [A

]

Series resistance fitting

Parallel resistance fitting

(a)

-1 -0.5 0 0.5 1

Voltage [V]

10-8

10-6

10-4

10-2

100

Cu

rre

nt

[A]

Graphene/Ge wafer junction

V=0.12V

I=1.633e-4A

V=0.2V

I=9.377e-4A

(b)

Figure 4.14: Fitting applied on graphene/Ge wafer diode.

0.46

0.48

0.5

0.52

0.54

Barrier height in graphene/Ge wafer diode

(a)

1.45

1.5

1.55

1.6

1.65

1.7

1.75

Ideality factor n in graphene/Ge wafer diode

(b)

Figure 4.15: Boxplots of the barrier height and the ideality factor n ingraphene/Ge wafer diode.

arises in the value of the saturation current density, which decreases as L andso the active area increases. This fact is also reflected in the barrier heightvalue, which vice versa increases as L increases. No variation in the value of theideality factor n are instead observed.

A comparison between this sample and GrOnGe17D, where graphene isetched, is of interest (see table 4.7 and figure 4.16). Germanium wafer hascertainly a better quality with respect to epitaxially grown germanium. Thisinfluences the values of the fitted parameters, which are closer to their idealvalues in the case of graphene/Ge wafer junction. The value of the parallelresistance is much higher and therefore closer to its infinite value in the idealcase in the Graphene/Ge wafer. Also the ideality factor n is reduced in Gewafer and it is closer to its ideal value =1. The saturation current density isstrongly reduced and this property can be exploited in photodetection applica-tions in order to obtain a lower dark current. With reference to figure 4.16, itis possible to notice how much the n parameter influences the forward part ofthe current-voltage characteristics. Actually both the barrier height and the nparameter influences the forward-bias characteristic. In this case however thebarrier heights are found to be similar (0.43eV for epitaxial Ge and 0.48eV forGe wafer), while the n parameter is 3.83 in graphene/epitaxial Ge diode and1.66 in graphene/Ge wafer diode. Results are also shown as box plots in figure4.17.

A proper rectifying behavior is obtained in devices where a low-doped ger-

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4

Veff

[V]

0

0.02

0.04

0.06

0.08

0.1C

urr

en

t [A

]Ge LEPECVD

Ge wafer

Figure 4.16: Current voltage characteristics in graphene/Ge wafer junction andGrOnGe17D.

Device Rs[Ω] Rp[Ω] Jsat

[A

cm2

]Φb[eV] n

Epitaxial Ge [26] 29.37 3923.86 1.03 0.43 3.83Ge wafer [48] 4.86 31458.80 0.13 0.48 1.66

Table 4.7: Difference between epitaxially grown germanium and a germaniumwafer.

Epitaxially grown Ge Ge wafer

10

20

30

40

50

60

Series resistance

(a)

Epitaxially grown Ge Ge wafer

0

2

4

6

8

10

×104 Parallel resistance

(b)

Epitaxially grown Ge Ge wafer

0

0.5

1

1.5

2

2.5

3

3.5

Saturation current density

(c)

Epitaxially grown Ge Ge wafer

0.46

0.48

0.5

0.52

0.54Barrier height

(d)

Epitaxially grown Ge Ge wafer

1.5

2

2.5

3

3.5

4

Ideality factor n

(e)

Figure 4.17

manium is employed (both epitaxial Ge and Ge wafer). These two samples,GrOnGe17D and graphene/Ge wafer junction, are also optically characterized.Results are discussed in the next chapter.

Chapter 5

Photocurrent measurements

Two samples (graphene/epitaxial Ge junction and graphene/Ge wafer junction)have been optically investigated. First their possible use as photodetectors ischecked. Further measurements aim to provide the presence of the QuantumCarrier Reinvestment effect discussed in chapter 2.4. The reason why no QCRis not observed in these devices is still an open issue.

5.1 Measurement setup

The photocurrent measurement setup is shown in figure 5.1. Light source isprovided by an incandescence lamp coupled with a monochromator (Oriel In-strument, Cornestone 260). In order to get rid of higher order harmonic wave-lengths a filter (850-2750nm) is placed at the lamp output. Light then impingeson a lens and it is focused on a mirror, that directs light downward towards thesample. The sample lies on an horizontal plane. In order to apply a bias tothe device, a two-probe system is employed. The back contact is attached on acopper plate by using silver paste and it is grounded or left floating accordingto the measurement. Bias is applied by a transimpedence amplifier, which alsoconverts the photocurrent signal into a voltage signal. Signal can be now readby an oscilloscope and it is sent to a lock-in amplifier (EG&G 5808 two-phaselock-in analyzer). The lock-in receives as an input also an AC reference signalfrom the chopper, whose frequency must be the same as the signal frequency.The chopper, which rotates at a frequency of 391Hz, is therefore placed betweenthe lamp and the monochromator.

53

Figure 5.1: Experimental setup.

A calibration is performed by using a Ge biased photodetector (Thorlabs,DET50B). The photodetector responsivity is provided by manufacturer. It ispossible to determine the effective power impinging onto the sample by dividingthe detected photocurrent by the responsivity of the photodetector.

5.2 Experimental results

Two samples are optically investigated: graphene/epitaxial germanium (GrOnGe17D)and graphene/Ge wafer junction. First their operation as a "conventional"Schottky barrier photodetector is checked. A reverse bias is applied betweenthe front pad and the back (Vpb in figure 5.2). In this configuration the deviceis said to work in photodiode mode. In figure 5.3 the responsivities obtainedin the two diodes are shown. These plots are not to be intended in absolutevalues. The real responsivity value should take into account the power densitythat effectively impinges onto the device Power[W ]

DetectorArea[cm2] . The plotted valueshould therefore be rescaled according to R = Rplotted

Adetector

Adevice. Since it is not

so easy to precisely determine the effective illuminated area in both the pho-todetector and the device, data here presented are not rescaled according to thisarea factor. The shape of the responsivity is however reliable. It is possible to

Figure 5.2: Photocurrent measurement setup. Vpb represents voltage appliedbetween the top electrode and the back contact. Vpp is the voltage appliedbetween the two front pads.

1300 1350 1400 1450 1500 1550 1600 1650

Wavelength [nm]

0

1

2

3

4

5

6

7

Responsiv

ity [A

/W]

×10-4

(a)

1400 1500 1600 1700 1800

Wavelength [nm]

0.5

1

1.5

2

2.5

3

Responsiv

ity [A

/W]

×10-3

(b)

Figure 5.3: Responsivity in (a) graphene/epitaxial Ge junction at an appliedbias Vpb = −0.66V and (b) graphene/wafer junction at Vpb = −0.9V .

1300 1350 1400 1450 1500 1550 1600 1650

Wavelength [nm]

0

1

2

3

4

5

6

7R

esp

on

siv

ity [

A/W

]×10

-4

(a)

1300 1350 1400 1450 1500 1550 1600 1650

Wavelength [nm]

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Re

sp

on

siv

ity [

A/W

]

×10-5

Pad-Back

Pad-Pad

(b)

Figure 5.4: Responsivity of sample GrOnGe17D L = 30µm (a) and L = 30µm(b). Applied bias in both configurations is -0.66V.

notice from figure 5.3 that the responsivity in graphene/epitaxial Ge diode dropsdown at 1550nm, which corresponds to the direct gap of germanium (0.8eV). Ingraphene/Ge wafer instead the spectrum extends at longer wavelengths becauseof indirect transitions in Ge.

Other measurements are performed by applying a bias between the two frontpads (Vpp in figure 5.2) while the back contact is left floating. This measure-ment configuration should provide evidence of the presence or the absence ofthe Quantum Carrier Reinvestment phenomenon discussed in chapter 2.4. Thequantum gain

QG = EQE ·(τ rτ t

)(5.1)

is in this configuration proportional to the ratio between the recombinationtime from graphene to semiconductor and the transit time τ t = L

vd= L2

µV . Thetransit time can be estimated considering, as an example, a mobility in grapheneµ ∼ 1000 cm

2

V ·s , an applied bias of the order of 0.1V and the distance betweenpads L = 10µm. The value obtained within these approximations is τ t ∼ 10−8s.The recombination time depends on the substrate used. For epitaxially grownGe τ r ∼ 10−9s [39]. In graphene/epitaxial Ge junction therefore transit time iscomparable, or even lower, to the recombination time. The order of magnitudein responsivity is expected to be the same in the two configurations. Figure5.4 shows the responsivity obtained in a structure where distance between padsis L = 30µm, the applied bias is -0.66V. Power impinging on the sample at1350nm is about ∼ 1 · 10−4W . In sample GrOnGe17D graphene is not etched

1300 1350 1400 1450 1500 1550 1600 1650

Wavelength [nm]

0

0.02

0.04

0.06

0.08

0.1

Re

sp

on

siv

ity [

A/W

]

Pad-Back

Pad-Pad

Figure 5.5: Responsivity of sample GrOnGe17D L = 20µm. Applied bias inboth configurations is -0.66V.

around the structures with length L = 20µm. In this case an estimation for thetransit time is not possible, since it is not possible to predict the current pathfrom one electrode to the other. In general in graphene/epitaxial Ge diodes noQCR effect is present as expected.

In graphene/Ge wafer diode recombination time is τ r ∼ 10−3s τ t, so theQuantum Carrier Reinvestment effect would be expected with τr

τt∝ 10−3

10−8 = 105.Figure 5.6 shows the responsivity obtained in graphene/Ge wafer sample fortwo structures with different inter pad distance L = 10µm and L = 20µm.Measurements are performed at a bias of -2V in both configuarations Vpb andVpp. With respect to the setup shown in figure 5.1, a cylindrical lens is placed atthe monochromator output in order to correct the light beam divergence. Powerimpinging on the sample at 1350nm is about ∼ 6 · 10−5W. Stability is improvedin measurements in figure 5.6b by bonding the chosen structure. In general noenhancement in responsivity is obtained when bias is applied between the twofront pads.

Further considerations can be done by measuring the photocurrent as afunction of the applied bias at a fixed wavelength (figure 5.7). Photocurrentincreases as a function of both Vpb and Vpp. When working in photodiode modephotocurrent seems to reach saturation at high applied voltages. When bias isapplied between the two electrodes, photocurrent keeps increasing as a function

1300 1400 1500 1600 1700 1800

Wavelength [nm]

0

0.02

0.04

0.06

0.08

0.1R

esponsiv

ity [A

/W]

Pad-Back

Pad-Pad

(a)

1300 1400 1500 1600 1700 1800

Wavelength [nm]

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Re

sp

on

siv

ity [

nm

]

Pad-Back

Pad-Pad

(b)

Figure 5.6: Responsivity in graphene/Ge wafer sample at an applied bias of-2V. The measured structure is (a) 3.1, L = 20µm and (b) 1.4 L = 10µm.

of Vpp. This last feature is also checked in graphene/epitaxial Ge diode (figure5.4). The fact that photocurrent increases as a function of the applied bias isan important feature that can be exploited in order to tune the responsivityof the photodetectors [8]. However the intensity of the photocurrent remainscomparable both in the photodiode configuration and if bias is applied betweenthe two front pads.

Responsivity is then measured at different biases in graphene/Ge wafer, butno QCR effect is observed. By plotting the responsivity spectra at differentapplied inter pad biases (figure 5.9a), it is possible to notice that the behavioris not truly symmetric with respect to Vpp. Moreover the different responsivityshapes reflect the complexity of the device under study. As a reference in figure5.9b current is plotted as a function of the applied pad-pad bias.

Liu et al. [8] also pointed out that it is possible to control the QCR pho-tocurrent, i.e. the situation when bias is applied between the two front pads,by applying an additional bias across the graphene/Ge junction. Carriers areindeed photogenerated inside the germanium and injected into graphene. Theirlifetime depends on the probability of being back injected in the semiconductor.Since the Fermi level in graphene depends on the applied bias (chapter 2.3), theapplication of Vpb can be used in order to tune the re-entry barrier of holes. Infigure 5.10 the blue curve represents responsivity of the device when workingin standard photodiode mode. The red curve represents the responsivity whenboth Vpb and Vpp are applied. A little gain (of a factor less than two) between

-1.2 -1 -0.8 -0.6 -0.4 -0.2 0

Voltage [V]

0

1

2

3

4

5

Ph

oto

cu

rre

nt

[A]

×10-6

Pad-Back Vpb

Pad-Pad Vpp

Figure 5.7: Photocurrent measured as a function of the applied bias between thetwo front pads (red curve) and between a front pad and the back (blue curve).

-1 -0.5 0 0.5 1

Vpp

[V]

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Ph

oto

cu

rre

nt

[A]

×10-9

Figure 5.8: Photocurrent measured in graphene/epitaxial Ge diode as a functionof the applied pad-pad bias Vpp at λ = 1300nm.

1400 1500 1600 1700 1800

Wavelength [nm]

0

0.5

1

1.5

2

2.5

3

Re

sp

on

siv

ity [

A/W

]

×10-4

Vpp

=0

Vpp

=-0.1V

Vpp

=+0.1V

(a)

-1 -0.5 0 0.5 1

Voltage [V]

-1.5

-1

-0.5

0

0.5

1

1.5

Cu

rre

nt

[A]

×10-3 Pad-Pad IV curve

(b)

Figure 5.9: (a) Responsivity in graphene/Ge wafer junction (device 1.4, L =10µm) at different applied pad-pad biases. Back contact is left floating. (b)Current as a function of the applied pad-pad voltage Vpp.

1400 1500 1600 1700 1800

Wavelength [nm]

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

Re

sp

on

siv

ity [

A/W

]

Vpb

=-1.5V and Vpp

=0

Vpb

=-1.5V and Vpp

=-0.4

Figure 5.10: Responsivity in graphene/Ge wafer sample (device 1.4, L = 10µm)when working int he conventional photodiode mode (a) and when both biasesare applied (b).

the two configuration is present, however no QCR effect is verified.Different measurement configurations are tested, but none of them provided

the expected Quantum Carrier Reinvestment in graphene/Ge wafer junctions.The reason why it is not verified is still an open issue.

Chapter 6

Conclusions

From the electrical characterization of graphene/germanium Schottky diodes agood rectifying behavior emerges in both graphene/epitaxial Ge and graphene/Gewafer junctions, when low-doped semiconductors are employed (n ∼ 1017cm−3).The MATLAB function coded for this thesis work is proven to provide a reliabledata analysis for the extraction of diode parameters (Rs, Rp, Isat, barrier height,n), when current-voltage characteristics exhibit a good rectifying behavior. Thebetter quality of bulk germanium with respect to the epitaxial Ge is reflectedin the diode parameters (Rs, Rp, Isat, n), which are closer to their ideal valuesin the case of graphene/Ge wafer Schottky junctions. The knowledge of theactive area of the device is compulsory for a correct determination of the diodebarrier height, which is found to be 0.43eV in graphene/epitaxial Ge and 0.48eVin graphene/Ge wafer. Values are comparable to the ones obtained in literature[38, 40].

The two samples, graphene/epitaxial germanium and graphene/Ge waferjunctions, are also optically characterized. Graphene/Ge wafer diode has a lowsaturation current (Jsat = 0.13 A

cm2 in graphene/Ge wafer diode and Jsat =

1.03 Acm2 in graphene/epitaxial germanium diode), this fact makes it more suit-

able for photodection applications, since dark current is reduced. When deviceswork in the conventional photodiode mode, responsivity in graphene/epitaxialGe lies in the conventional germanium spectral range, i.e. at 1550nm photocur-rent is no longer generated. In graphene/Ge wafer the responsivity spectrumis “broader” and it lightly extends to higher wavelengths. This fact may bedue to indirect transitions inside germanium. An enhancement in responsivityshould be expected when an additional bias across graphene is applied. This

62

phenomenon, called Quantum Carrier Reinvestment [8], has been reported onlyin a single publication [8] and not reproduced yet, so the reason why it is nothere verified is still an open issue. Eventually the fact that responsivity increaseswhen the applied bias across graphene increases is an important feature thatcan be exploited in order to tune the responsivity of the photodetectors [8].

Further developments

Further investigations on the samples here described are possible. Measurementsas a function of the temperature, for example, provide an alternative methodfor determining Schottky barrier height. Starting from the equation ln

(I0T 2

)=

ln (A ·A∗) − φb

kT and from the so-called Richardson plot (ln(I0T 2

)as a function

of 1T ), it is possible to determine the barrier height directly from its slope. A

precise value for the active area of the device is here not compulsory, moreoverRichardson plot gives the opportunity for an estimation of the area and theRichardson constant A∗ from the intercept to the y-axis.

Although no QCR (Quantum Carrier Reinvestment) effect is observed, graphene/germanium junctions are proven to be suitable for photodetection applications.Further improvements to these devices are however possible. The first thing tobe exploited is the fact that graphene Fermi level depends on the applied bias.The addition of a gate to the devices may be used in order to tune the Schottkybarrier height. These kind of devices are known as barristors.

A further step in the graphene/Ge photodetector is to use germanium pillarsas a substrate. Germanium is grown on top of an anisotropically patternedsilicon wafer by using LEPECVD technique. The formation of a continuous filmis prevented by the self-limited lateral growth when the growth is performedfar from equilibrium [41]. The fabrication of a Ge photodetector out of thissubstrate was already proven to provide an enhanced spectral sensitivity [42].So it may be interesting to investigate the properties of a graphene/Ge pillarsphotodetector.

Appendix A

LEPECVD

Low-Energy Plasma-Enhanced Chemical Vapour Deposition (LEPECVD) is atechnique used in order to obtain crystalline silicon-germanium films on a siliconsubstrate [43]. Figure A.1 shows the basic scheme of a LEPECVD.

The use plasma in CVD (Chemical Vapour Deposition) technique allows oneto enhance growth rate and to perform deposition at a lower temperature withrespect to standard CVD. In the plasma source, figure A.1, electrons are ther-moionically emitted by a tantalum filament. They ionize a gas of argon, whichflows from the source to the deposition chamber. An arc discharge is kept ata constant pressure of 10−2mbar, with a discharge voltage of 20V [43]. Thisarc allows one to discharge plasma and to have lower energy ions than those ofconventional plasma, i.e. with respect to PECVD techniques. Then by adjust-ing plasma potential and substrate potential, it is possible to avoid substratedamage caused by impinging ions [44] and therefore substrate can be placed inthe region of most intense plasma. Growth rates are therefore enhanced. Dis-charge voltage is very low, although discharge currents are very high (20-70A)[43]. From this fact comes the name Low-Energy Plasma Enhanced CVD.

Primary coil provides a magnetic field that focuses the plasma onto thewafer. The wafer on the other side is heated by a graphite heater. Vacuumis provided by a turbo pump. A ring just below the wafer is where gases areintroduced. For SiGe growth SiH4 and GeH4 are employed. The growth ratesusually vary from 1Å

s to 10nms and they can be controlled by tuning the gasflows inside the chamber or by changing the current in the primary coil and thestrength of the magnetic field.

64

Figure A.1: Scheme of the LEPECVD chamber. Source: figure adapted fromRef. [9]

Appendix B

Scanning Electron Microscope(SEM) for EBL

Scanning Electron Microscope is widely used for the imaging of surfaces on ascale down to 10Å [1]. The basic principle of this imaging technique consists infocussing an electron beam onto the sample and detecting secondary electronsemitted by the sample. The intensity of secondary electrons determines thebrightness of the image.

In Electron Beam Litography (EBL) [45, 37], SEM provides the electronbeam used as radiation source in order to expose the desired structure. EBL isa maskless lithography technique, patterns to be exposed are created by usinga computer software. EBL is more suitable for the fabrication of nanodevicesthan optical lithography, where a Hg arc lamp emitting in the UV is employed,since resolution is limited by wavelength of radiation source.

L-NESS laboratory in Como is provided with SEM Philips (FEI) XL30SFEG. Electrons are emitted by a Field Emission Gun (FEG), where electrontunnelling through a Schottky barrier is enhanced by the application of an elec-tric field. The electron beam has a gaussian spot of diametre d and it is focussedon the sample by a series of magnetic lenses. Electrons impinge onto the sampleand PMMA (Polymethyl-methacrylate) resist is exposed. Primary electron dosedepends on the type of resist, on beam energy and on the development methodsD = Q

s2 = Iτs2 (figure B.1a). Beam current I and therefore beam diameter d

have to be chosen properly, since d also influences the resolution of the system.In this EBL system d is about 2nm with a current I = 21pA. Electrons can

66

(a) (b)

Figure B.1: (a) Electron beam impinges on the substrate. A is the area to beexposed. (b) Electron beam (primary electron) impinges on the sample. Elec-trons inelastically scatter in forward direction and secondary electrons (SE) aregenerated. SE are actually responsible for resist exposure. Less frequently elec-trons can be elastically back scattered (BSE). Source : images from “Graphenenanoelectronics” lecture handouts, held by prof. Roman Sordan in Politecnicodi Milano.

also be scattered back (figure B.1b) and this phenomenon leads to undesiredresist exposure near the edges of the structure, called proximity effect. Thiseffect may become a problem in small structures and it can be avoided either byperforming dose modulation or by correcting structure geometry via software.

Appendix C

Reactive Ion Etching (RIE)

The basic scheme of a parallel plate RIE system is shown in figure C.1 [45]. Oneof the electrodes, the cathode, is connected to a radio frequency source througha capacitance coupling. A gas is inserted inside the chamber. The type of gasdepends on the substrate that has to be etched. In particular sulfur hexafluorideSF6 is used in order to etch silicon, for germanium carbon tetrafluoride CF4 isemployed, while for graphene etching, oxygen is required. The radio frequencysource accelerates some free electrons, which collide with the gas and ionize gasmolecules. Then more free electrons are available, thus creating an avalancheprocess and the plasma is formed. Ions are attracted towards the sample bythe electric field. Sputtering is not however the only etching mechanism. Gasesinjected inside the chamber also chemically reacts with the substrate.

Figure C.1: Scheme of RIE. Source : figure adapted from Ref. [10]

68

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