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Enhanced thermionic emission and low 1/f noise in exfoliated graphene/GaN Schottky barrier diode Ashutosh Kumar, Ranjit Kashid, Arindam Ghosh, Vikram Kumar, and Rajendra Singh ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.5b12393 • Publication Date (Web): 10 Mar 2016 Downloaded from http://pubs.acs.org on March 15, 2016

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ACS Applied Materials & Interfaces

Enhanced thermionic emission and low 1/f noise in exfoliated graphene/GaN Schottky barrier diode Ashutosh Kumar,ξ,δ,* Ranjit Kashid,§ Arindam Ghosh,§ Vikram Kumar,δ,£ and Rajendra Singhξ,δ,*

ξ

Department of Physics, Indian Institute of Technology Delhi, New Delhi-110016, India

δ

Nanoscale Research Facility, Indian Institute of Technology Delhi, New Delhi-110016,

India §

Department of Physics, Indian Institute of Science, Bangalore, Karnataka-560012, India

£

Centre for Applied Research in Electronics, Indian Institute of Technology Delhi, New

Delhi-110016

KEYWORDS: GaN, graphene-semiconductor interface, Schottky barrier diodes, currentvoltage characteristics, low frequency noise, inhomogenous Schottky barrier.

*Address correspondence to [email protected], [email protected]

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Abstract Temperature dependent electrical transport characteristics of exfoliated graphene/GaN Schottky diodes are investigated and compared with conventional Ni/GaN Schottky diodes. The ideality factor of graphene/GaN and Ni/GaN diodes are measured to be 1.33 and 1.51, respectively, which is suggestive of comparatively higher thermionic emission current in graphene/GaN diode. The barrier height values for graphene/GaN diode obtained using thermionic emission model and Richardson plots are found to be 0.60 eV and 0.72 eV, respectively, which are higher than predicted barrier height ~ 0.40 eV as per Schottky-Mott model. The higher barrier height is attributed to hole doping of graphene due to graphene-Au interaction which shifts the Fermi level in graphene by ~ 0.3 eV. The magnitude of flicker noise of graphene/GaN Schottky diode increases up to 175 K followed by its decrease at higher temperatures. This indicates that diffusion currents and barrier inhomogeneities dominate the electronic transport at lower and higher temperatures, respectively. The exfoliated graphene/GaN diode is found to have lower level of barrier inhomogeneities than conventional Ni/GaN diode, as well as earlier reported graphene/GaN diode fabricated using chemical vapor deposited graphene. The lesser barrier inhomogeneities in graphene/GaN diode results in lower flicker noise by two orders of magnitude as compared to Ni/GaN diode. Enhanced thermionic emission current, lower level of inhomogeneities and reduced flicker noise suggests that graphene-GaN Schottky diodes may have the underlying trend for replacing metal-GaN Schottky diodes.


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1. INTRODUCTION Graphene, a two-dimensional carbon material, has attracted great research interest in last few years due to its unique properties like high electrical conductivity, ultra-high mobility, and high optical transparency, making it a promising material for future high-speed electronics, optoelectronics and photovoltaics.1-4 Due to high electrical conductivity and zero bandgap, graphene is analogous to a metal at the metal-semiconductor (MS) interface, which suggests that graphene-semiconductor (GS) junctions may have the underlying trend for replacing conventional MS junctions. The GS junctions allow the investigation of electrical transport mechanism at the interface of 2D and 3D materials with zero and definite band gap, respectively. Also, the GS junctions are advantageous over conventional MS junctions due to the possibility of tuning of Fermi level of graphene and hence it's work function by chemical doping5, 6 or electrostatic gating.7-9 Several researchers have reported that a Schottky contact is formed between graphene and various semiconductors like Silicon (Si),10-13 Silicon Carbide (SiC),11,

14

Gallium Arsenide (GaAs)11 and Gallium Nitride (GaN).11,

15, 16

Accordingly

graphene-based Schottky contacts have been employed in various applications like solar cells,17-19 barristors,20 photo-detectors,21,

22

and sensors23. When compared to other

semiconductor materials, GaN has the advantages like high breakdown fields, high electron saturation velocities and chemical and radiation hardness.24, 25 In earlier reports, metals like Nickel (Ni),26-29 Platinum (Pt),28 and Palladium (Pd)28 have been used to fabricate Schottky contacts on GaN. However, diffusion of the metal into semiconductor at elevated temperatures enhances the tunneling of the carriers across the barrier, causing a decrease in thermionic emission current, i.e. lowering of the barrier and hence restricts the hightemperature operation of the device. Recently, Tongay et. al.16 found graphene/GaN Schottky barriers to be thermally stable on prolonged annealing up to 900 K for two days which suggests that use of graphene as a Schottky contact on GaN can solve the problem of device



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degradation at high temperatures. They attributed device sustainability at higher temperatures to the thermal stability of carbon-carbon bonds and less diffusion of contaminates across the interface. Therefore, graphene/GaN Schottky barrier junctions could potentially be applicable to high-temperature operations of metal-semiconductor field effect transistor (MESFET), high electron mobility transistors (HEMT) and UV photodetectors. Therefore, investigating electrical characteristics of graphene/GaN Schottky barrier diodes can be considered as the important area of research for employing graphene in the semiconductor industry. There are only a few reports on the use of graphene as Schottky contact on GaN. Tongay et. al.11, 16 investigated electrical transport properties of graphene/GaN Schottky barrier diodes with and without annealing and found barrier height and ideality factor close to 0.70 eV and 2.9, respectively at room temperature with no significant degradation at higher annealing temperatures. Kim et. al.15 reported Schottky barrier height to be 0.90 eV using thermionic emission model for graphene/GaN Schottky diode and attributed it to spontaneous polarization and a large density of surface states in GaN. In these reports, electrical transport properties from room temperature to higher temperatures are reported where current transport is governed by thermionic emission. In contrast, the electrical transport at low temperature is mainly governed by other processes such as thermionic field emission, field emission, generation-recombination etc. So far detailed investigations/observations of electrical properties at lower temperatures are not reported in the literature. The low-temperature characteristics are likely to give more insight into current transport mechanism at graphene/GaN interface. Also, in all of above reports on graphene/GaN Schottky barriers authors have used chemical vapor deposition (CVD) prepared graphene. Although, CVDgrown graphene layers on other substrates offer a promising method to produce large area graphene, but there are various sources of disorders in CVD graphene like structural defects, lattice defects and grain boundaries resulting from growth process. These sources can


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significantly affect the device parameters such as barrier height, ideality factor, rectification etc.10,

30, 31

On the other hand, graphene layers produced by mechanical exfoliation are

reported to be highly crystalline with high electron and hole mobilities and almost negligible defects.32, 33Therefore, unlike the use of CVD grown graphene where barrier properties are likely to be affected by graphene growth parameters, use of exfoliated graphene for fabricating Schottky contacts can give devices with more reliable barrier parameters. Low frequency noise (1/f) or flicker noise spectroscopy is an excellent technique for studying the GS interface which is different from conventional MS interface due to unique properties of graphene like two-dimensional nature, zero energy band gap, uncommon energy dispersion for charge carriers and metallic conductance.3, 34, 35 The tuning of a number of layers in graphene i.e. from mono-layer to multi-layers allows the comparison of surface and volume contribution to 1/f noise.34 It is well accepted that origin of 1/f noise in different materials and devices can vary i.e. mobility fluctuations or number density fluctuations.3, 36, 37 The magnitude of 1/f noise is very crucial for any electronic device as it can mix up with phase noise and can degrade the performance of device at high-frequency communications. Therefore, for employing a new material system for practical applications, the origin, and magnitude of 1/f noise need to be investigated in detail. For this reason, 1/f noise properties of graphene/GaN Schottky contacts are crucial for the integration of two important materials (graphene and GaN) into the technological application. To the best of our knowledge, 1/f noise behavior of graphene/GaN Schottky diode is not reported so far. It is already demonstrated that 1/f noise behavior of Schottky diodes is directly related to interface quality, i.e. the existence of barrier inhomogeneities at interface and density of interface states.27, 38 Therefore 1/f noise measurements are important from technological as well as scientific point of view as substantial information about electronic transport at graphene/GaN interface can be achieved. 5 ACS Paragon Plus Environment


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Here, we present the fabrication of graphene/GaN Schottky diodes by selective transfer of exfoliated graphene on GaN. The graphene/GaN interface is characterized by current-voltage (I-V) and low-frequency noise (1/f) measurements in the temperature range of 80-300 K. 2. EXPERIMENTAL METHODS GaN epitaxial films ( 1 cm × 1 cm × 3.5 μm) grown over c-sapphire by metal-organic chemical vapour deposition technique are used. The epitaxial films are unintentionally doped with electron carrier concentration of 3 × 10 cm obtained from Hall measurements (Ecopia Hall measurement set-up-5000) at 300 K. Before graphene transfer and any metallization, samples are cleaned using standard procedures.26 Four layer Ohmic contact pads of Ti/Al/Ni/Au in the thickness ratio of 20/100/20/100 nm are deposited using e-beam evaporation at a base pressure of 3 × 10 mbar. Rapid thermal annealing of the Ohmic contacts is performed at 800°C for 60 sec to enhance the diffusion of Ti into GaN yielding good quality Ohmic contacts. In the next step, vertical strip of SiO2/Cr/Au with dimensions 1 cm × 2 mm and thickness of 50/5/50 nm is deposited using rf sputtering technique. Here, SiO2 is used to provide electrical isolation between Cr/Au and GaN to avoid the formation of Cr/Au Schottky contact on GaN. A number of graphene flakes are exfoliated from bulk kish graphite using standard micromechanical exfoliation method on 285 nm SiO2/Si substrate. The single layer graphene flakes exfoliated from the same bulk kish graphite have been used to fabricate high mobility devices which are reported elsewhere.39,

40

Before transferring graphene flake on GaN,

Raman measurements (LabRAM HR Horiba Jobin Yvon) are performed on various flakes to identify a number of layers, with the excitation wavelength of 532 nm. The spot size of the laser beam used for Raman measurements is around 0.7 µm. Fig. 1(a) shows Raman spectrum of graphene flake used for fabrication of Schottky contact. The deconvolution of 2D peak with single Lorentzian line shape confirms the monolayer nature of graphene. The full width 6 ACS Paragon Plus Environment

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at half maxima of 2D band is found to be ~24.8 cm-1. As exfoliated monolayer graphene was transferred on GaN in such a way that one side of the graphene is in contact with GaN while other with Au (schematically shown in Fig. 1(b)). For selective transfer of graphene flake, we have followed the method reported earlier.40,

41

Prior to graphene transfer, open circuit

resistance is observed between Au pad and Ohmic contact. After the selective transfer of the graphene, an electrical connection is itself established between graphene-Au and grapheneGaN. The current-voltage (I-V) measurements are performed in a variable temperature cryostat from 300 to 80 K at a base pressure of 10-2 mbar using Keithley semiconductor characterization system (SCS-4200) and temperature controller (Cryo-con model 32). The low-frequency noise measurements are performed in the temperature range of 80-300K with a frequency range between 1 and 100 Hz at a battery-generated current of 0.1 µA. More experimental details about low-frequency noise measurement technique are reported in our earlier works.26, 27, 42 3. RESULTS AND DISCUSSION 3.1 Electrical characteristics of Gr/GaN Schottky diodes Current transport across MS interface in forward bias condition in a good quality Schottky contact is governed by thermionic emission (TE). The relative dominace of TE over other transport mechanism like thermionic-field emission (TFE) and field emission (FE) is determined by comparing characterstic energy with k (k is Boltzmann constant and T

the absolute temperature). For TE, is smaller than k while it is larger than k for FE.

The value of is comparable to k for TFE. The is calculated from doping concentration, Nd in the semiconductor as43 =

qh 4π ∗

(1)



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Here q is the charge on an electron, h the Planck’s constant, = 9.5ϵ ) the permittivity of

the GaN and ∗ = 0.22m ) is the electron effective mass.26, 27 From Eq. 1, is calculated

to be 3 meV at room temperature. The smaller value of in comparison to k at room temperature indicates TE as dominant transport mechanism at room temperature.

In order to compare the electrical properties of graphene/GaN (Gr/GaN) diodes with the conventional GaN Schottky diodes, Ni/GaN diodes of 1 mm diameter and Ni thickness of 40 nm are also fabricated on GaN epitaxial film obtained from same GaN wafer. For comparison, the processing conditions for this diode like cleaning procedures, Ohmic contacts and their thermal treatment etc. are kept identical to Gr/GaN diode. The I-V characteristics of Gr/GaN and Ni/GaN Schottky diodes at 300 K are shown in Fig. 2(a) with inset showing the forward biased characteristics on expanded scale. According to thermionic emission theory, electron transport in a Schottky diode across MS interface can be explained using the following equations43 # = #$ [&

where

'

() *+,

#$ = 0A∗ 2 & '

− 1]

(2)

3(456 +,

(3) where 78 is zero bias Schottky barrier height, 9 the ideality factor, V the applied voltage, A* is the effective Richardson’s constant (~26.8 Acm-2K-2 for GaN).26 According to SchottkyMott model, Schottky barrier height is equal to 7: − ; ?BCDE F) − CDEG1 − &HI −=@ A ⁄>)KL

(4)

where @ A = @ − #M$ is the effective voltage drop across the diode. The 9 versus V plot as shown in Fig. 2(b), has a maximum at 0.09 V indiating the existence of surface states, as earlier observed in GaN15, 45, InP46 and GaAs47. This behavior is similar to work by Kim et. al.15 on Gr/GaN diode fabricated using CVD graphene where they observed a bell-shaped behavior for voltage dependent 9 with maximum at 0.08 V. By assuming equilibrium between surface states and GaN, density of surface states at Gr/GaN interface, NOP can be estimated as15 NOP =

O 9 − 1) < − 2 2 Q= = R

(5)

here O is assumed as permittivity of free space, Q the thickness of oxide later at interface,

assumed as 1 nm and R is the depletion width. Using Eq. 5 and expression of 9 @ ), voltage

dependent NOP is plotted as a function of S − = 7T − =@ A ) in Fig. 2(c), hence NOP @) for

Gr/GaN diode lies in the range of ~1013 states/cm2/eV. As shown in Fig. 2(c), NOP @) falls

after ~0.55 eV which indicates that deep level states are located around 0.55 eV below the



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conduction band . This matches with deep level observed at Ec-0.6 eV in GaN due to Nitrogen antisites.45 Kim et. al15. and Pirkle et. al.48 reported that defects created during transfer of graphene or the foreign molecules attached to graphene significantly affect the barrier parameters by enhancing the density of surface states at Gr/GaN interface. To differentiate the contribution coming from the graphene, we calculated the NOP from electrical behavior of Schottky contacts formed on same GaN epitaxial film using conventional metals like Ni and W. The NOP is found to be ~3 × 10 2 &@ U2 which is lower as compared to surface states calculated from I-V measurements of Gr/GaN Schottky diode ( 1 ×

10 &@ U2 ). The calculations of NOP is shown in the supporting information. Higher NOP in Gr/GaN diode is consistent with the evolution of D peak only in the Raman spectra of

graphene/GaN which will be discussed later in the manuscript. However, we wish to mention that ideality factor of 1.33 for Gr/GaN diode suggests limited role of contaminations in our work. The reported values of work function values of Ni and free standing graphene are 5.1 eV29, 49 and 4.5 eV,6,

50, 51

respectively and electron affinity of GaN is 4.1 eV26,

29, 49

. Therefore,

according to Schottky-Mott model, theoretically predicted values of Schottky barrier height for Ni/GaN and Gr/GaN SBDs should be approximately close to 1.0 and 0.4 eV, respectively. For Ni/GaN diode, obtained barrier height is lower whereas it is higher for Gr/GaN diode than theoretically predicted barrier height. Barrier heights values (obtained from I-V measurements) lower than predicted values for conventional M/GaN (M=Ni, Pd, Pt, Au) have been already reported in previous studies.26-29, 52 This is mainly due to the existence of barrier inhomogeneities and nature of I-V measurement which gives lowest barrier height.26, 29, 38 Therefore, we expect barrier height close to or lower than 0.4 eV for Gr/GaN Schottky diode. However, in the present study, barrier height comes out to be 0.60 eV which is higher than predicted barrier height (as per Schottky-Mott model) and this needs to be understood in 10 ACS Paragon Plus Environment

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detail. The barrier heights higher than predicted are also observed by previous authors as Tongay et. al.11, 16 and Kim et. al.15 reported barrier height values of Gr/GaN Schottky diode to be 0.72 and 0.90 eV, respectively by assuming thermionic emission model. Tongay et. al.16 analyzed the thermal stability of Gr/GaN diodes and did not discuss the observation of higher barrier height than predicted whereas Kim et. al.15 attributed higher barrier height to a large number of interface states and spontaneous polarization of GaN. It is important to note that both of these authors used CVD graphene for fabricating Schottky diodes where a large number of interface states are expected due to the growth and transfer induced disorders which in turn affects the barrier parameters. Therefore, we used exfoliated graphene to avoid the impact of growth induced defects on barrier parameters. Our experimental finding of observing lower barrier height for exfoliated graphene diode in comparison to reported CVD graphene diode is supported by experimental work of Parui et. al.10 on graphene/Si diodes where they observed lower barrier height for exfoliated graphene diode (0.69 eV) in comparison to CVD graphene diode (0.84 eV). In conventional metal/semiconductor diodes, the work function of the metal is assumed to be constant and is bias independent as the movement of electrons between metal and semiconductor do not alter the work function of the metal due to the high density of states in metals. In the present work, graphene is in contact with GaN as well as Au, thus, movement of electrons due to graphene-GaN or graphene-Au interactions could alter the Fermi level position in graphene i.e. work function of graphene due to low density of states in graphene, hence can possibly change the barrier height of Gr/GaN diode. The Fermi level lies at ~4.23 eV in the GaN epilayer (Nd=3×1016 cm-3) in our work calculated using V = 2.6 × 10 X for

GaN which gives V − Y = >⁄= )CZ V ⁄ ) = 0.13 eV, and electron affinity of GaN, ; =

4.1 eV. Due to lower work function of GaN (~4.23 eV) with respect to single layer graphene ~ 4.5 eV,6, 50, 51 graphene-GaN interaction is expected to result in upward shift of the Fermi 11 ACS Paragon Plus Environment


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level i.e. electron doping in graphene. Zhong et. al.53 also reported that graphene forms a selfadaptive contact on GaN and graphene-GaN interaction resulted in electron doping in graphene. The Fermi level shift due to graphene-GaN interactions can be obtained by calculating the charge transfer between graphene and GaN.43, 53 The Fermi level shift due to graphene-GaN interaction in present work is calculated to be ~0.04 eV. For detailed calculation of Fermi level shift due to graphene-GaN interaction, see supporting information. As graphene is also in contact with the Au, therefore Fermi level shift due to graphene-Au interaction is also calculated. It is well known that Fermi energy of free-standing graphene coincides with the conical points but in a real situation, adsorption of graphene on metal surfaces shifts the Fermi level of graphene.54 The graphene is adsorbed differently on different metal surfaces. For example, graphene is chemisorbed on Co, Ni, Pd whereas physisorption of graphene occurs on metals surfaces of Al, Pt, Au etc. The chemisorption of graphene on surfaces like Co, Ni, Pd causes strong perturbation in graphene bands leading to the destruction of conical points while physisorption of graphene on Al, Au, Pt results in weaker interaction, which maintains the conical structure and results only in Fermi level shift causing electron or hole doping in graphene.54, 55 The upward or downward shift of the Fermi level depends upon work function of the free-standing graphene and clean metal surface. If work function of the clean metal surface (WM) is greater than the work function of freestanding graphene (WG), then electrons move from graphene to metal and results in hole doping in graphene. In a similar way, WM< WG results in electron doping in graphene. So physisorption of graphene on metals like Al, Ag (work function of metal is lower than graphene) results in electron doping in graphene while physisorption on Au, Pt (work function of the metal is higher than graphene) results in hole doping in graphene. In present work, one side of graphene is lying on Au while other is in contact with GaN. Due to work function difference between Au and graphene in present work, electrons move from graphene 12 ACS Paragon Plus Environment

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to Au and hence result in hole doping in graphene. As the density of states in graphene is too small in comparison to Au, so any shift required for equilibrating Fermi levels takes place entirely in graphene. The Fermi level shift due to graphene-Au interaction is calculated in the similar way as mentioned earlier54, 55 and comes out to be ~0.31 eV. The calculations are given in supporting information. The downward shift of Fermi level in graphene due to graphene-Au interaction in our work is consistent with the existing reports on Fermi level shift due to graphene-metal interactions.54-57 Therefore, Fermi level in graphene shifts upwards due to graphene-GaN interaction by ~ 0.04 eV whereas graphene-Au interaction results in the downward shift by ~0.31 eV. The interaction of graphene with GaN and Au and corresponding Fermi level shifts are schematically shown in Fig. 3(a). Thus, Fermi level shift in graphene is dominated by the graphene-Au interaction in present work and shifts downwards. The graphene-GaN band alingement is shown in Fig. 3(b). The downward shift of Fermi level due to graphene-Au interactions explains the discrepancy between observed barrier height (0.60 eV) and theoretically predicted barrier height (~0.4 eV) in present work. As discussed earlier, higher NOP for Gr/GaN in comparison to conventional diodes suggests defects created during transfer process. As reported in existing literature, Raman measurements of the graphene can be used to estimate defect density in graphene as well as nature of doping in graphene.9, 58, 59 Therefore, a graphene flake is exfoliated from the same bulk kish graphite and transferred onto SiO2/Si substrate. For a statistical distribution, Raman measurements are performed at 20 random locations. Next, the same graphene flake is transferred on GaN and Raman measurements are carried out again at 20 random locations. The averaged Raman spectrum for graphene/SiO2 and graphene/GaN is plotted in Fig. 4(a). The D, G and 2D peaks positions corresponding to graphene as observed in Fig. 4(a) are plotted on expanded scale in Fig(s). 4(b), (c) and (d), respectively. As shown in Fig. 4(d), the 13 ACS Paragon Plus Environment


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full width at half maxima of 2D peak (fitted using single Lorentzian line shape) of graphene/SiO2 comes out to be ~ 27 cm-1 which cofirms monolayer nature of graphene. The statistical distribution of G and 2D peak positions are plotted in Fig. 4(e)-(h). The G peak position is almost same whereas 2D peak shifts slightly to a lower wave number in graphene/GaN in comparison to graphene/SiO2. In Fig. 4(b), no D peak in graphene/SiO2 suggests good quality of graphene whereas D peak centered around 1365 cm-1 in graphene/GaN indicates presence of defects due to graphene-GaN interaction or transfer process. The broadening of G and 2D in graphene/GaN spectra in comparison to graphene/SiO2 is due to defects created during transfer process which resulted in higher NOP in Gr/GaN diode. The defect density in graphene lying on GaN can be calculated from the intensities of G peak and D peak as58 Z] U2 ) =

1.8 ± 0.5) × 1022 #] c e #d `ba

(6)

where #] and #d are the intensities of the D and G peaks and `a (in nanometers) is the excitation laser wavelength (532 nm in present work). Note here that above relation for calculating defect density in graphene is valid only if point defects are separated by a distance, g] ≥ 10 nm. Therefore, before calculating the Z] , g] is calculated using58 g2]

Z

2)

# j b ] ) = 1.8 ± 0.5 × 10 `a c e #d

(7)

using #] ⁄#d =0.85 from averaged Raman spectrum of graphene/GaN as shown in Fig. 4(a), the g] lies between 11-14 nm which is greater than 10 nm. The defect density calculated in

graphene lying on GaN is calculated to be ~ (1.4 − 2.4) × 10 U2 . This is comparable to the defect density in pristine graphene on SiO2 as reported by Wang et. al.59 The low defect density suggests that quality of the graphene is not degraded on transferring to GaN which resulted in the formation of a good quality Schottky contact between graphene and GaN.


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The Raman shifts in the G and 2D peaks can be used to estimate type and level of doping in graphene. Das et. al.9 reported that n-type (p- type) doping in graphene can shift the 2D peak to lower (higher) wave number. The 2D peaks fitted by single Lorentzian peak fitting are observed at 2672.3 cm-1 and 2669.9 cm-1 for graphene/SiO2 and graphene/GaN, respectively as presented in Fig. 4(d). The error bars in the fitting are ~0.1 cm-1.

The respective

histograms are shown in Fig. 4(g) and 4(h). The small shifting of 2D peak to lower wave number by ~ 2 cm-1 indicates slight electron doping of graphene due to graphene-GaN interaction. This small shift is consistent with the observation of slight electron doping in graphene due to graphene-GaN interaction which shifted the Fermi level upwards by 0.04 eV obtained by considering the charge transfer between graphene and GaN. To further understand nature of electrical transport at Gr/GaN interface, we performed I-V characteristics in the temperature range of 80 to 300 K and compared it with the conventional Ni/GaN Schottky diode. Figs. 5 (a) and (b) show I-V characteristics on the semi-log scale for Gr/GaN and Ni/GaN Schottky diodes, respectively. The values of η and 78 for Gr/GaN and Ni/GaN Schottky barrier diodes calculated using Eq. (2) and (3) are shown in Fig.5(c) and (d), respectively. Another factor that can significantly affect the barrier height values is Richardson coefficient. For barrier height calculation, we have assumed theoretical value of Richardson coefficient to be 26.8 Acm-2K-2 while the reported values of Richardson coefficient are significantly lower than theoretical values due to inhomogeneous nature of barrier and interface states.15 Another way to calculate barrier height is by l

plotting ln 'nmo - vs rn. From Eq. 3, CZ c

#$ 78 e = CZ 00∗ ) − 2 >

(8)



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l

The plot between ln ' mo - and n

rn

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should be linear with slope equal to 78 , but the plot is not

linear as shown in Fig 6(a). This discrepancy is due to the temperature dependence of ideality factor which is not included in Eq. 8. On incorporating η in Eq. 8, CZ c l

The plot between ln ' mo- and n

urn

#$ 78 ∗) e = CZ 00 − 2 9>

(9)

is now linear as shown in Fig. 6(b) with 78 equals to 0.72

eV. As per implicit assumption of this method, 78 should not vary with temperature.

However, as shown in Fig. 5(c), dependence of 78 on temperature contradicts this assumption and suggests that barrier inhomogeneities model is needed to explain this

behavior.38, 60According to this model, barrier height of an inhomogeneous Schottky contact follows a Gaussian distribution given as26, 29, 38 }}}}} 78 − 78 )2 v 78 ) = exp |− ~ 2y should yield a straight line with intercept and slope giving }}}}} 78 and y< , respectively.

The variations of 78 with 1⁄2> for Gr/GaN and Ni/GaN Schottky barrier diodes are shown in Figs. 7(a) and (b) where two linear regions are observed for both the diodes which indicate different level of barrier inhomogeneities in different temperature ranges. The existence of double Gaussian distribution of local barrier heights in M/GaN (M=Ni, Pt, Pd, Au ) Schottky barrier diodes is also reported by various authors.26, 28, 29, 52, 61 From the intercept and slope of

two linear regions (shown in Fig. 7(a) and (b)), }}}}} 78 and y< for Gr/GaN diode are calculated to

be 0.79 eV and 100 meV in 300-150 K, and 0.59 eV and 70 meV in 150-80 K, respectively.

}}}}} Similarly, for Ni/GaN diode, respective values of 7 8 and y< comes out to be 1.24 eV and

138 meV in 300-150 K and 0.76 eV and 77 meV in 150-80 K. The lower value of y< in 300-

150 K suggests more homogenous nature of Gr/GaN diode as compared to Ni/GaN diode. In addition, Gr/GaN diode in present study is more homogenous as compared to CVD graphene/GaN diode reported by Kim et. al.15 where y< is reported to be 130 meV. The lower

values of y< in temperature range 150-80 K in comparison to 300-150 K suggest more

homogenous nature of both the diodes on lower temperature side. As level of noise and its behavior (Lorentzian or 1/f) is directly linked to the barrier inhomogeneities, noise variation with temperature is expected to be different in different temperature ranges and will be disussed in next section of the manuscript. 3.2 Variation of 1/f noise of Gr/GaN Schottky diodes with temperature For further understanding the electronic transport at Gr/GaN interface, noise measurements are carried out. A forward current of 0.1 µA is applied across the diode at each measurement



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temperature and spectral power density of voltage fluctuations ) is recorded which is then

converted into current fluctuations l ) using the relation26, 27, 62 l =

'

l

− M< -

=

'

un

ll

)

2

(12)

The variation of l with frequency at various temperatures is shown in Fig. 8 where a single noise spectrum is the average of 160 spectra (At each temperature, measurements are repeated for four times and during single measurement an average of 10 noise spectra is taken). In the temperature range 80-300 K, l varied as with varying between 0.90 and 1.25 (see Fig. 9(a)) which confirms 1/f behavior of l at Gr/GaN interface. The 1/f behavior

in entire temperature range is due to inhomogenous nature of Gr/GaN interface.60,

63

According to one of the recent reports, an inhomogeneous charge distribution is created along the graphene sheet due to random charge impurities at graphene/substrate interface making Gr/GaN interface inhomogeneous.64 Also, temperature dependent I-V characteristics revealed inhomogeneous nature of Gr/GaN interface. The two main processes giving rise to current fluctuations are: the random capture and emission of electrons at interface states and inhomogenous nature of Gr/GaN interface.38, 42, 63 The former process modulates the total charge at interface, thus modulating the 78 which leads to the noise. In addition, current varies exponentially with the barrier height (Eq. 2 and 3), therefore small barrier height fluctuations due to inhomogeneous nature of graphene/GaN interface results in significant noise. Madenach et. al.63 explained 1/f noise properties by considering random trapping and de-trapping of carries and inhomogeneous nature of MS interface. They found noise behavior in an electrically homogenous barrier y$ = 0) where all interface states are assumed at same

energy or having a distribution in energy, to be Lorentzian type (at lower frequency' ≪ -,

~constant while at ' ≫ -, ∝ o where is the time constant). For an inhomogeneous

barrier y$ ≠ 0), the 78 follows a distribution with depending exponentially on 78 . Thus


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any distribution in 78 leads to a distribution time constants which deviates the Lorentzian spectra towards 1/f noise.60,

63

Therefore, in present work, 1/f nature of l confirms the

inhomogenous nature of Gr/GaN interface which is consistent with variation of 78 with temperature as mentioned earlier in the manuscript. The temperature dependence of l at = 10 Hz is shown in Fig. 9(b) where l first increases with temperature from 80 to 175 K and decreases afterwards. The three widely accepted models to explain variation of 1/f noise with temperature are Hsu’s,65, 66 Luo’s67 and barrier inhomogeneities models.38, 60, 63 The noise variation with temperature in present work is not according to Hsu’s model as it predicts noise to be independent of temperature. This nonapplicability of Hsu’s model is expected as it considers that traps states are uniformely distributed in energy and space which does not hold for Schottky barriers based on GaN.68 Also, Hsu’s model does not consider the barrier inhomogeneities at metal-semiconductor interface which is not applicable for GaN diodes as revealed from electrical measurments in present work. In GaN based Schottky diodes, interface states which are distrbitued nonuniformly and inhomogeneities severely affect the current transport across the interface, and hence noise.26, 27 Therefore, one has to look for other noise models like Luo’s and barrier inhomogeneities model which predicts noise to be increasing and decreasing fucntions of temperatures, respectively. According to barrier inhomogeneities model, noise should reduce as temperature increases due to the inhomogeneous nature of Gr/GaN interface. However, this is not observed on lower temperature range (80-175 K) where noise increases with increase in temperature (see Fig. 9(b) ). This is due to the departure from thermionic emission at lower temperatures and contributions from other mechanisms like diffusion currents which causes 9 to increase, 78 to decrease with decrease in temperature.28,

29, 42

Therefore, the

increase of noise in 80-175 K is due to the presence of diffusion currents which is in agreement with Luo’s model of 1/f noise. As temperature increases, noise behavior is 19 ACS Paragon Plus Environment


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dominated by inhomogeneies at interface as carriers have sufficient thermal energy to surmount the barrier, which limits the diffusion currents effects. Also, dominance of barrier inhomogeneities is likely to be more on higher temperatures in comparison to lower temperatures as y$ is more in 300-150 K as compared to 150-80 K. Therefore, above 175 K, barrier inhomogeneities dominate diffusion currents causing noise to decrease with increase in temperature. Therefore, variation of 1/f noise with temperature in Gr/GaN diode suggests the presence of two different transport mechanisms in higher (300-150 K) and lower temperature (150-80 K) ranges. 3.3 Low 1/f noise in Gr/GaN in comparison to Ni/GaN Schottky diodes The level of 1/f noise is very crucial for any electronic device and researchers have reported various strategies to reduce its level.3, 27, 69, 70 Therefore, we compared the level of 1/f noise in Gr/GaN diode with Ni/GaN diode. The noise measurement at 300 K for Gr/GaN diode is already shown in Fig. 8 which is re-plotted in Fig. 10 along with l of Ni/GaN Schottky

diode. The l of Ni/GaN Schottky diode also exhibited dependence with = 1.29, which confirms 1/f nature of noise due to inhomogenous nature of Gr/GaN interface. The l of

Gr/GaN diode is found to be about two orders lower than l of Ni/GaN diode. As mentioned

earlier, y< is lower for Gr/GaN diode in comparison to Ni/GaN diode in temperature range

300-150 K. The value of y< indicates the level of inhomogeneity in the barrier height, and is directly linked to the number of local Schottky barriers which contribute to conduction.63. The lower values of y< for Gr/GaN as compared to Ni/GaN diodes indicate lesser inhomogeneity at Gr/GaN interface, i.e. lesser number of barriers take part in conduction mechanism. This results in reduced level of 1/f noise in Gr/GaN diode as compared to Ni/GaN diode.

CONCLUSIONS 20 ACS Paragon Plus Environment

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In summary, we have fabricated graphene/GaN Schottky barrier diodes using the exfoliated graphene. Current-voltage and low frequency noise measurements are performed to investigate and understand electrical transport in exfoliated Gr/GaN Schottky diode. The electrical behavior of Gr/GaN diode is compared with Ni/GaN diode where enhanced thermionic emission is observed in former as compared to later. The higher barrier height of Gr/GaN Schottky diode, 0.6 eV instead of theoretically predicted value of 0.4 eV is explained by calculating the Fermi level shift in graphene due to graphene-GaN and graphene-Au interactions. The graphene-Au interaction resulted in downward Fermi level shift ~ 0.31 eV in graphene whereas an upward shift of ~ 0.04 eV is obtained due to graphene-GaN interaction. The higher Fermi level shift in graphene due to graphene-Au interaction increases the barrier height by ~ 0.3 eV and explains the discrepancy between predicted and experimentally observed barrier height of Gr/GaN Schottky diode. From Raman measurments of graphene on GaN, a small shift of 2D peak towards lower wave number also indicates slight electron doping in graphene due to graphene-GaN interaction. The barrier inhomogeneities model is employed in both the diodes where Gr/GaN is found to be more homogenous as compared to Ni/GaN diode on higher temperature range i.e. above 175 K. Luo’s model is used on lower temperature side to explain increase of noise with temperature whereas decrease of noise with temperature is in accordance with barrier inhomogeneities model with transition temperature close to 175 K. The low frequency noise in Gr/GaN diode is found to be about two orders of magnitude lower than Ni/GaN diode which is due to lower level of barrier inhomogeneities. Our results indicate the potential of graphene as a Schottky contact on GaN for semiconductor devices. ACKNOWLEDGMENTS Ashutosh Kumar (AK) is thankful to Indian Institute of Technology Delhi (IIT Delhi) for senior research fellowship. RK expresses his thanks to University Grant Commission (UGC)



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for Dr. D. S. Kothari Postdoctoral Award Scheme. All the authors acknowledge Nanoscale Research Facility (NRF) at IIT Delhi funded by Department of Electronics and Information Technology, Ministry of Communications and Information Technology, Government of India. Corresponding Author(s): *E-mail: [email protected] *E-mail: [email protected] Supporting Information: Electrostatic calculations of Fermi level shifts in graphene due to graphene-GaN and graphene-Au interactions. This material is available free of charge via the Internet at http://pubs.acs.org. Notes: The authors declare no competing financial interest. REFERENCES 1. Castro Neto, A. H.; Guinea, F.; Peres, N. M. R.; Novoselov, K. S.; Geim, A. K. The Electronic Properties of Graphene. Rev. Mod. Phys. 2009, 81, 109-162. 2. Vlassiouk, I.; Polizos, G.; Cooper, R.; Ivanov, I.; Keum, J. K.; Paulauskas, F.; Datskos, P.; Smirnov, S. Strong and Electrically Conductive Graphene-Based Composite Fibers and Laminates. ACS Appl. Mater. Interfaces 2015, 7, 10702-10709. 3. Balandin, A. A. Low-Frequency 1/f Noise in Graphene Devices. Nat. Nanotechnol. 2013, 8, 549-555. 4. Ren, W.; Cheng, H.-M. The Global Growth of Graphene. Nat. Nanotechnol. 2014, 9, 726730. 5. Shi, Y.; Kim, K. K.; Reina, A.; Hofmann, M.; Li, L.-J.; Kong, J. Work Function Engineering of Graphene Electrode via Chemical Doping. ACS Nano 2010, 4, 2689-2694. 6. Chang, J.-K.; Lin, W.-H.; Taur, J.-I.; Chen, T.-H.; Liao, G.-K.; Pi, T.-W.; Chen, M.-H.; Wu, C.-I. Graphene Anodes and Cathodes: Tuning the Work Function of Graphene by Nearly 2 eV with an Aqueous Intercalation Process. ACS Appl. Mater. Interfaces 2015, 7, 17155-17161. 7. Yu, Y.-J.; Zhao, Y.; Ryu, S.; Brus, L. E.; Kim, K. S.; Kim, P. Tuning the Graphene Work Function by Electric Field Effect. Nano Lett. 2009, 9, 3430-3434. 8. Yuan, H.; Chang, S.; Bargatin, I.; Wang, N. C.; Riley, D. C.; Wang, H.; Schwede, J. W.; Provine, J.; Pop, E.; Shen, Z.-X.; Pianetta, P. A.; Melosh, N. A.; Howe, R. T. Engineering UltraLow Work Function of Graphene. Nano Lett. 2015, 15, 6475-6480. 9. Das, A.; Pisana, S.; Chakraborty, B.; Piscanec, S.; Saha, S. K.; Waghmare, U. V.; Novoselov, K. S.; Krishnamurthy, H. R.; Geim, A. K.; Ferrari, A. C.; Sood, A. K. Monitoring Dopants by Raman Scattering in an Electrochemically Top-Gated Graphene Transistor. Nat. Nanotechnol. 2008, 3, 210-215. 10. Parui, S.; Ruiter, R.; Zomer, P. J.; Wojtaszek, M.; van Wees, B. J.; Banerjee, T. Temperature Dependent Transport Characteristics of Graphene/n-Si Diodes. J. Appl. Phys. 2014, 116, 244505.


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Fig. 1

Fig. 1 (a) Raman spectra of exfoliated graphene flake which is selected for device fabrication with embedded figure showing the optical image of the same flake. (b) The schematic of graphene/GaN Schottky diode where the monolayer exfoliated graphene is transferred in such a way that one end of the graphene is in contact with GaN while other with Au.


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Fig. 2

Fig. 2 (a) Current-voltage (I-V) characteristics of Gr/GaN and Ni/GaN Schottky barrier diodes at 300 K with inset showing the forward biased characteristics on expanded scale.(b) shows the η as a function of applied bias while the density of surface states, Dit, as a function of EC-E is shown in (c).



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Fig. 3

Fig. 3 (a) Schematic representation of Fermi level shift in graphene due to graphene-GaN and graphene-Au interactions. (b) The band alignment configuration of graphene-GaN Schottky contact.


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Fig. 4

Fig. 4 (a) shows the average of 20 Raman spectra of same single layer graphene on SiO2 and GaN while (b), (c) and (d) shows the magnified view of the ranges corresponding to D, G and 2D peaks, respectively. The statistical distributions of G peak positions of graphene/SiO2 and graphene/GaN are shown in (e) and (f), respectively whereas (g) and (h) show the statistical distributions for 2D peak positions.



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Fig. 5

Fig. 5 Current-voltage (I-V) characteristics of (a) Gr/GaN and (b) Ni/GaN Schottky barrier diodes on semi-log scale in the temperature range 80-300 K. The values of η and 78 at each temperature calculated using thermionic emission are shown in (c) and (d) for Gr/GaN and Ni/GaN Schottky barrier diodes, respectively. The values of η and 78 are found to be increasing and decreasing with decrease in temperature which indicate existence of barrier inhomogeneities in both the cases.


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Fig. 6

l

Fig. 6 The variation of ln ' mo - with (a) n

rn

l

and (b)

temperature. On incorporating 9 , ln ' mo - versus n

urn

for Gr/GaN diode as a function of

urn

shows linear variation with slope

yielding, 78 = 0.72 eV. Solid line in (b) represents least square fit.



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Fig. 7

Fig. 7 The variation of 78 with 1⁄2> for (a) Gr/GaN and (b) Ni/GaN Schottky barrier diodes. Solid lines represent least square fit. An error of 0.03 eV is expected in the barrier height of Gr/GaN diode due to error in area of the graphene flake. The existence of two linear regions in both the plots indicates the presence of double Gaussian distribution. The lower y< of Gr/GaN in comparison to Ni/GaN in both the temperature ranges suggest lesser inhomogeneities at Gr/GaN interface in comparison to Ni/GaN interface.


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Fig. 8

Fig. 8 The variation of l with frequency of Gr/GaN Schottky barrier diode at (a) 80 K, (b)

100 K, (c) 150 K, (d) 200 K, (e) 250 K and (f) 300 K for # = 0.1 0. 1/f behavior of l in entire temperature range is due to inhomogenous nature of Gr/GaN interface.



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Fig. 9

Fig. 9 (a) The frequency exponent, as a function of temperature. The values of lying between 0.9 and 1.30 confirm the 1/f noise behavior in temperature range of 80-300 K. (b) The variation of l of Gr/GaN diode as a function of temperature at = 10 at a fixed

forward current of # = 0.1 0. With increase in temperature, l first increases followed by a decrease with transition close to 175 K.


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Fig. 10

Fig. 10 Comparison of l of Gr/GaN with Ni/GaN Schottky diode at 300 K. The reduced 1/f noise in Gr/GaN diode is attributed to lower level of inhomogeneities at Gr/GaN interface.



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