Nano Res

1

Graphene-GaN Schottky diodes

Seongjun Kim1, Tae Hoon Seo2, Eun-Kyung Suh1, Keun Man Song3, Myung Jong Kim2, and Hyunsoo Kim1()

Nano Res., Just Accepted Manuscript • DOI 10.1007/s12274-014-0624-7

http://www.thenanoresearch.com on November 4, 2014

© Tsinghua University Press 2014

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Nano Research

DOI 10.1007/s12274-014-0624-7

1

Graphene-GaN Schottky

TABLE OF CONTENTS (TOC)

Graphene-GaN Schottky diodes

Seongjun Kim1, Tae Hoon Seo2, Eun-Kyung Suh1, Keun

Man Song3, Myung Jong Kim2 and Hyunsoo Kim1,*

1. Chonbuk National University, Republic of Korea

2. Korea Institute of Science and Technology, Republic of

Korea

3. Korea Advanced Nano Fab Center, Republic of Korea

The electrical characteristics of graphene-GaN Schottky diodes with

excellent rectifying behavior are presented, i.e., the Schottky barrier

height of 0.90 eV and 1.240.13 eV as determined by thermionic

emission and barrier inhomogeneity model.

Provide the authors’ website if possible.

Author 1, http://psdl.jbnu.ac.kr/

2

Graphene-GaN Schottky diodes

Seongjun Kim1, Tae Hoon Seo2, Eun-Kyung Suh1, Keun Man Song3, Myung Jong Kim2, and Hyunsoo Kim1()

1 School of Semiconductor and Chemical Engineering, Semiconductor Physics Research Center, Chonbuk National University, Jeonju

561-756, Republic of Korea 2 Soft Innovative Materials Research Center, Korea Institute of Science and Technology, Jeonbuk 561-905, Republic of Korea 3 Korea Advanced Nano Fab Center, Suwon 443-700, Republic of Korea

Received: day month year / Revised: day month year / Accepted: day month year (automatically inserted by the publisher)

© Tsinghua University Press and Springer-Verlag Berlin Heidelberg 2011

ABSTRACT The electrical characteristics of graphene Schottky contacts formed on undoped GaN semiconductor were

investigated. Excellent rectifying behavior with a rectification ratio of ~107 at 2 V and a low reverse leakage

current of 1.010−8 A/cm2 at −5 V were observed. The Schottky barrier height, as determined by the thermionic

emission model, Richardson plots, and barrier inhomogeneity model, were 0.90, 0.72, and 1.240.13 eV,

respectively. Despite the predicted low barrier height of ~0.4 eV at graphene-GaN interface, the formation of

excellent rectifying characteristics with much larger barrier height is attributed to the presence of a large number

of surface states (1.21013 states/cm2/eV) and the internal spontaneous polarization field of GaN, resulted in a

significant upward surface band bending or a bare surface barrier height as high as of 2.9 eV. Using the S

parameter of 0.48 (measured from the work function dependence of Schottky barrier height) and the mean barrier

height of 1.24 eV, the work function of graphene in Au/graphene/GaN stack could be approximately estimated

to be as low as 3.5 eV. The obtained results indicate that graphene is a promising candidate for use as a Schottky

rectifier in the GaN semiconductors with n-type conductivity.

KEYWORDS Graphene, GaN, Schottky diode, Schottky barrier height, Fermi level pinning

Introduction

Two-dimensional hexagonal carbon array, also known

as graphene, has been extensively studied for

application as an active or passive layer in electronic

and optoelectronic semiconductor devices due to its

outstanding physical and optical characteristics,

including high intrinsic electron mobility, quantum

electronic transport, low optical absorption, and good

chemical and mechanical stability [1−14]. In particular,

Nano Res DOI (automatically inserted by the publisher)

Review Article/Research Article Research Article

Address correspondence to Hyunsoo Kim, hskim7@jbnu.ac.kr

3

good electrical conductivity and excellent optical

transparency across the entire spectrum of

wavelengths of graphene made it a promising

candidate for use as a transparent contact in

optoelectronic devices such as solar cells [15−18] and

light-emitting diodes (LEDs) [19−27].

Very recently, a number of studies focusing on the

application of graphene p-contacts in GaN-based

LEDs have been reported by several groups [22−27].

Jo et al. [22] demonstrated the first GaN-based LEDs

fabricated with transparent graphene p-contact.

However, the forward voltage obtained was very

large in the study, which was due to a poor graphene

Ohmic contact to p-GaN associated with the large

work-function mismatch between graphene (G=4.5

[28−30]4.6 eV [31−33]) and the p-GaN (~7.5 eV),

namely, the expected Schottky barrier height (B) was

as high as of ~3.0 eV according to the Schottky-Mott

theory. Accordingly, Chandramohan et al. [23] showed

that the specific contact resistance of graphene contact

formed on heavily Mg-doped p-GaN was as large as

~101 Ωcm2. To overcome this poor p-Ohmic contact, a

hybrid-type contact combining graphene with

indium-tin-oxide islands [24], Au nanoparticles [25],

Ag nanowires [26], and Ag nanocluster [27] were

introduced by our groups.

On the one hand, thermally stable rectifying

behavior was also observed for the graphene contact

formed on n-type GaN by Tongay et al. [33, 34],

suggesting that the graphene on n-GaN be a

promising candidate for the Schottky rectifiers.

Indeed, this finding is strange considering that the B

expected to form at graphene/n-GaN interface is as

low as ~0.4 eV due to the small work-function

difference between graphene and n-GaN, implying

that the graphene contact to n-GaN should produce

poor rectifying behavior. Furthermore, the

experimentally obtained B of 0.74 eV [33, 34] was

even larger than the predicted value. These

inconsistent results indicate that, for the successful

development of graphene integrated GaN-based

semiconductor devices, the electrical characteristics

and carrier transport mechanism of graphene-GaN

contact should be thoroughly investigated. However,

in-depth comprehensive studies on this subject are

still lacking.

In this study, we investigated the electrical

characteristics and carrier transport mechanism of the

graphene contact formed on undoped GaN. For this

purpose, first, we focused on the fabrication of reliable

Schottky diodes by transferring the synthesized

graphene onto the GaN wafer, followed by oxygen

plasma etching to define accurate active region.

Indeed, it is worth noting that, according to the

previous studies [34−36], the active region of the

graphene Schottky contact was too large (e.g.,

10002000 m2) [34] to extract reasonable Schottky

parameters, since current crowding can occur as a

result of the limited conductivity of graphene. More

importantly, the active region of previous studies

could not be clearly defined due to the use of a

window-frame structure, where the transferred

graphene would be lying on the bottom GaN surface

and the top side of window-frame structure

simultaneously, i.e., the boundary of active region

cannot be clearly defined. Meanwhile, our fabrication

method was developed to solve these problems. In

addition, previously [33, 34], the fabricated Schottky

diodes were solely analyzed by the thermionic

emission (TE) model. However, the obtained ideality

factor (n) of 2.9 was much larger than the unity,

indicating that the obtained B of 0.74 eV might be

incorrect due to the use of inadequate conduction

model. In this regard, we attempted to analyze the

Schottky diodes by using TE, activation energy plots,

and barrier inhomogeneity model based on the

measured current-voltage-temperature (I-V-T) data.

Experimental

For this study, 4.5-μm-thick undoped GaN wafers,

which were grown on sapphire substrates by metal-

organic chemical vapor deposition system (MOCVD),

were used. The Hall-effect measurements of GaN

wafer showed an electron concentration (N) of

3.11016 cm-3 and a Hall mobility () of 297 cm2/V-s.

For the fabrication of Schottky diodes, first, the

graphene which was formed on 25-μm-thick Cu foil

by CVD method was transferred to the GaN wafers by

using polymethyl methacrylate (PMMA) sacrificial

4

layer. Note that, prior to the graphene transfer, the

surface of GaN wafers were cleaned with acetone,

isopropyl alcohol, H2SO4:HCl (1:1) solutions, a

buffered oxide etchant, and deionized water. The

detailed synthesis of graphene by CVD method and

transfer techniques can be found elsewhere [24−27, 36]

(also shown in Fig. S1 in the Electronic

Supplementary Materials, ESM). The surface

morphology, physical and optical properties of

graphene transferred to GaN wafers were measured

using an atomic force microscope (AFM), Raman

spectroscopy (excited with a 514 nm-line of an Ar ion

laser), X-ray photoelectron spectroscopy, and UV/VIS

spectrometer.

The Schottky diodes were fabricated by using the

conventional photographic technique and oxygen

plasma etching, as illustrated in Fig. 1. For example,

first, using an e-beam evaporator, a ~10-nm-thick Au

layer was deposited on the graphene for enhanced

current spreading. The circular pattern of the

Schottky contact with a diameter of 100 μm was

defined by conventional photolithographic technique,

followed by wet etching (HCl:HNO3=3:1) for 10 sec to

remove the Au layer, and then oxygen plasma etching

in an inductively-coupled plasma reactive ion etching

system to remove the graphene. Ti/Au (50 nm/50 nm)

Ohmic contacts were then deposited on the exposed

GaN layer. Finally, a Cr/Au (30 nm/250 nm) layer was

deposited on top of the Schottky region for the

formation of a probing contact pad having the

diameter of 50 m (see the inset of Fig. 3). The

Schottky diodes were evaluated using a parameter

analyzer (HP4156A) and a variable temperature probe

station in darkroom conditions. Note that the probe

station was equipped with a vacuum chamber (<

2102 Torr) to suppress the undesirable reaction of

graphene with the ambient atmosphere.

Results and discussion

Figure 2 show the Raman spectra of graphene

transferred to GaN/sapphire substrates. Typical G

band and 2D band peaks of graphene were observed

at the wave number of 1586 and 2682 cm-1, which are

associated with the LO and TO modes of the graphite

honeycomb lattice vibration generating at the Γ point

of the Brillouin zone and two inelastic electron-

phonon scattering events involving opposite

momenta, respectively [37−39]. At around 1350 cm-1,

D band peak was also observed, indicating that the

elastic electron-phonon scattering caused by defects,

wrinkles, and disorders in the graphitic material or

edges of graphene occurred. Consistently, as shown in

the inset of Fig. 2(a), the AFM surface images revealed

the presence of a few wrinkles and white spots. It is

known that the wrinkles form at the atomistic defect

lines (e.g., step edges of Cu terraces) of Cu foils during

growth of graphene by CVD [40]. In addition, the

white spots may originate from the residual chemical

contaminants such as PMMA. Due to these possible

defects or disorder of graphene, D band peak

appeared. However, it is worth noting that, except

these defects, the graphene is quite flat and uniformly

transferred on GaN surface

To further investigate the chemical components,

XPS measurement was also performed for the bare

GaN and graphene-GaN samples, as shown in Fig.

2(b). The survey XPS spectra showed that the

chemical components and their relative peak

intensities of both samples are nearly the same except

C 1s peak, i.e., the C 1s intensity of bare GaN was

negligibly small, while that of graphene-GaN sample

was large. Figure 2(c) shows the C 1s peak of both

samples, where the deconvolution of C 1s exhibited

the presence of C-C, C-O, and C=O bonds. Besides C-

C bond for the graphene, the presence of C-O and

C=O bonds is attributed to PMMA residue [41].

Indeed, the PMMA contaminants may hinder the

formation of sound graphene-GaN junction, as this

will also relate to the electrical characteristics..

Figure 1 Fabrication procedure of graphene-GaN Schottky

diodes.

5

In the Raman spectra, note that the full width at half

maximum (FWHM) of 2D peak was 30.8 cm-1,

indicating that the graphene is a mono layer [42]. In

addition, 2D/G peak intensity ratio was 1.65, which is

also indicative of mono-layer graphene because it

exceeds 1.0 [25]. The evidence of mono-layer

graphene was further confirmed by the excellent

optical transmittance (see Fig. S2 in the ESM). For

example, at the wavelength of 350600 nm, the

integrated transmittance of graphene transferred on

GaN sample relative to bare GaN was as high as 97 %,

which is consistent with the fact that the mono-layer

graphene has 2.3 % optical absorption [3].

Figure 3(a) shows the semi-logarithmic I-V

characteristics of a graphene-GaN Schottky diode at a

measurement temperature of 300 K (under dark

condition); a top-view optical microscopy image of

the diodes is provided in the inset. Excellent rectifying

behavior with a rectification ratio as high as 1.1107 at

2.0 V was observed. In addition, the reverse leakage

current measured at 5 V was as low as 1.0108 A/cm2,

which is even lower than the previous result [34].

Such findings indicate that the graphene/GaN

junction was soundly constructed.

The forward I-V curves should be analyzed using

the appropriate conduction model, which can be

determined depending on the N value of GaN and

temperature (T), i.e., E00/kT<0.5 for TE, 0.5<E00/kT<5 for

thermionic field emission, and E00/kT>5 for field

emission [43, 44]. Here, k is the Boltzmann constant

and E00 is the tunneling parameter, which is given by

E00=qh/4(N/m*s)1/2, where q is the electronic charge, h

is the Planck constant, m* is the effective electron mass,

and εs is the dielectric constant of GaN. The

calculation for our sample showed that E00/kT=0.09,

indicating that the TE model is appropriate to use.

Under the condition that V 3kT/q, the general diode

equation by TE is given by [45]:

1exp0

nkT

qVII (1)

where I0 is the saturation current. Here, I0 is given by:

kT

qTAAI Bexp2**

0 (2)

where A is the Schottky contact area and A** is the

Richardson constant (26.4 A/cm2K2) [46]. Over a

voltage range of 0.10.5 V, the theoretical fits of the

forward I-V curves using Eqs. (1) and (2) revealed that

I0=9.81014 A, n=1.32, and B=0.90 eV. It is noted that

the obtained n value is much smaller than the

previously reported value of 2.4, indicating that the

Figure 2 (a) Raman spectra of graphene transferred to

GaN/sapphire substrates. The inset shows 20×20 μm2 AFM image

of graphene. (b) Survey XPS spectra and (b) C1s peaks of bare

GaN and graphene-GaN samples.

6

Schottky parameters obtained by the I-V method are

much more accurate and reliable than those in

previous works [33, 34].

However, the obtained n value is larger than the

unity, which may be attributed to GaN surface states

originating from native crystal defects [47, 48],

interfacial layers [49, 50], barrier inhomogeneities [43,

44], residual chemical contaminants [34], and to the

effect of series resistances (Rs) [51]. Indeed, the Rs has

a significant influence on the I-V curve in the high

voltage range exceeding 0.6 V, revealing a saturated

behavior. According to the Norde plots as shown in

the Fig. S3 of the ESM, the Rs was estimated to be as

high as 7600 K, while the reference Schottky diode

fabricated with thick Ni contact exhibited the Rs of

26.1 K. Despite the use of the same wafers and

process except Schottky contact, the extremely large

Rs value of graphene-GaN diode is attributed to the

low electrical conductivity of graphene, as will be

further discussed in details (with and without

illumination). The obtained n value of 1.32 is, however,

thought to be unaffected by the Rs since it was

estimated in the low voltage range of 0.10.5 V (note

that the forward I-V curve showed a very evident

conduction regimes below and above the critical

forward voltage of ~0.6 V).

Instead, other origins associated with the GaN

surface states are thought to induce the large n value.

Specifically, the interface quality of graphene-GaN

could be analyzed using the voltage dependence of n

value, i.e.,

kT

qV

JLogd

dV

kT

qn

exp1

(3)

where V' is the effective applied voltage, i.e., V'=VIRs

(Fig. 3b). In Fig. 3b, note that the n value has a bell-

shaped behavior with its maximum at around 0.08 V,

which is indicative of the presence of surface states, as

reported in the GaAs [52], InP [53], and GaN [54].

Assuming that these surface states are in equilibrium

with the GaN, the surface states density (Ds) can be

estimated according to

Wqn

qtD s

i

is 22

)1(

(4)

where i and ti are the permittivity and thickness of

the interfacial layer and W is the depletion width.

Here, i and ti , which are unknown parameters, were

assumed to be the permittivity of free space and 5 Å ,

so as to compare our obtained Ds value with those of

Cowley and Sze [55, 56], Schmitz et al. [57], and

Arulkumaran et al [58]. Using Eq. (4) and the n(V)

Figure 3 (a) The I-V characteristics of a graphene Schottky diode

fomed on GaN; a top-view optical microscopy image of the

fabricated diodes is shown in the inset. (b) n versus V, and (c) Ds

vs. EC−E plots.

7

values, the bias voltage dependence of Ds, i.e., Ds(V)

could be obtained according to the relation of

ECE=BqV', as shown in Fig. 3c. Note that the Ds(V)

values are in the range of ~1013 states/cm2/eV, which

are consistent with the reported values (~1-21013

states/cm2/eV) for the conventional contacts formed

on GaN [57, 58]. Particularly, the Ds(V) showed a bell-

shaped behavior with its maximum at around ~0.8 eV,

indicating that the deep-level states locates 0.8 eV

below the conduction band (EC) edge. Indeed, this

position is slightly larger than the commonly

observed level of EC0.6 eV associated with nitrogen

antisites (NGa) [54], while it corresponds to the level of

0.73 and 0.89 eV observed in n-GaN grown on SiC [59].

Meanwhile, as suggested in the literature [54], the

deep-level states might originate from the interfacial

oxide generated during the process step, which

should be further investigated. Based on our findings,

the n value larger than unity is primarily due to the

deep-level states of GaN associated with native

defects. As observed in the XPS spectra, the PMMA

contaminant might be also responsible for the large n

value. For example, Pirkle et al. [41] showed that the

effective removal of PMMA residue could increase 2

times higher average mobility of graphene-based field

effect transistors. The influence of PMMA

contaminant on the n value, however, seemed to be

small in the study considering that the n value of

reference Schottky diode fabricated with Ni contact

(no PMMA contaminant) was 1.22 (Fig. S4 of the ESM).

Note that for the measurements of B using the I-V

method, the Richardson constant A** was assumed to

be 26.4 A/cm2K2, which is a theoretical value.

However, the uncertainty in A** may cause errors in

the estimation of B. Therefore, to obtain

experimental values of both A** and B, activation

energy plots were generated using I0 values measured

at various temperatures between 300400 K, as shown

in Fig. 4. The lower inset shows the typical forward I-

V curves of Schottky diodes obtained at 300, 340, and

380 K. The theoretical fits of ln(I0/AT2) vs 1000/T data

using a rewritten form of Eqs. (1) and (2), i.e., so-called

Richardson plots having the expression [45]:

kT

qA

AT

I B

**

2

0 lnln (5)

yielded a ΦB value of 0.72 eV and an experimental A**

value of 1.36102 A/cm2K2. Note that the ΦB value

obtained by the Richardson plots is slightly lower

than the ΦB obtained by the I-V method, but the

experimental A** is much lower than the theoretical

value. Indeed, a large discrepancy between the

experimental and theoretical A** values has frequently

been observed for Schottky contacts in GaN systems

[55, 60]. Such differences are attributed to abnormal

carrier transport at the contact/GaN interface.

Furthermore, the ΦB value obtained by the I-V method

increased with temperature (see the inset of Fig. 4),

which is in contrast to the implicit assumption of the

Richardson plot method that the barrier height should

be independent of temperature [45]. Consequently,

the large n and small A** that were obtained and the

temperature-dependent ΦB value suggest that a more

appropriate model should be used to explain the

carrier transport at the graphene-GaN interface.

Recent studies have shown that one of the most

reasonable ways to explain carrier transport in a

contact-GaN system is to use the barrier

inhomogeneity [43, 44] and/or a thermionic field

emission model [49, 61, 62]. In our studies, the barrier

inhomogeneity model was applied, since a positive

temperature coefficient of ΦB is a distinctive feature of

the presence of inhomogeneous barriers [43, 44, 62,

63], i.e., carriers can flow through the local shallow

Figure 4 Activation energy plots of the Schottky diodes obtained

over a temperature range of 300−400 K. The upper inset shows

the ΦB values vs. temperature, and the lower inset shows the

typical forward I-V curves obtained at 300, 340, and 380 K.

8

barrier at relatively low temperatures (due to the low

thermal energy of carriers), resulting in a reduced

mean barrier height and vice versa. In this model, the

barrier height can be assumed to have a Gaussian

distribution with a mean barrier height (ΦB,m) and a

standard deviation (σ), i.e., [43, 44]:

kT

qTT

2)0()(

2

mB,B

. (6)

From a linear fit of the ΦB(T) data using Eq. (6), the

value of ΦB,m at 0 K could be estimated to be 1.24 eV

with σ=0.13 eV, as shown in Fig. 5. It is noted that the

value of σ is in agreement with the value obtained for

a conventional metal contact formed on GaN [62, 63].

Consequently, the resulting schematic band diagram

of graphene contact to GaN can be drawn as shown in

the inset of Fig. 5.

According to the barrier inhomogeneity model, the

voltage dependence of ΦB can be also estimated based

on the temperature dependence of n value, namely [54,

64, 65],

baB

kT

q

nV

21

1

, (7)

where a and b are the voltage coefficients that are

used in the relations of B,m= B,m0 + aV and σ2=

σ20+bV (here, the subscript “0” denotes a zero bias).

The linear regression fit of the experimental data

using Eq. (7) yielded that a =0.58 and b = 17 mV. The

positive signs of a and b indicate that the mean

barrier height B,m and the standard deviation σ

increase with increasing bias voltages.

Considering that the large fluctuation of the barrier

height (or large value) was reported to be largely

due to the GaN surface states associated with crystal

defects in studies, the carrier transport at the

graphene-GaN interface is also expected to be

influenced by the surface states of GaN. Accordingly,

the ΦB,m of 1.24 eV obtained by using the barrier

inhomogeneity model was found to be much larger

than the ΦB of 0.90 eV obtained by using the I-V

method. This is due to the fact that the ΦB obtained

using the I-V method mainly reflects the lowest

barrier height of local shallow patches, while ΦB,m

reflects the average value of the fluctuating barriers as

shown in the inset of Fig. 5. To verify the obtained ΦB,m

value, we performed capacitancevoltage (C-V)

measurements of the diodes, since the ΦB,m value is

equivalent to the ΦB value obtained using the C-V

method (due to the fact that the lateral potential

fluctuations of the barrier height do not influence the

C-V characteristics) [66]. However, we could not

obtain reliable C-V data for graphene-GaN diodes. In

keeping with this, Tongay et al. [33] also showed that

reliable C-V measurements for graphene-GaN and

graphene-SiC were not available due to the high Rs

values of wide-band-gap semiconductors, while the

C-V measurements gave reasonable information for

graphene-GaAs and graphene-Si. This indicates that,

consistently, the large Rs value of our diodes impede

the reliable measurement of C-V data. This requires

further study.

According to the Schottky-Mott theory [45], i.e.,

B,m=GGaN, where ΦB,m=1.24 eV and GaN is the

electron affinity of GaN (4.1 eV), G is obtained to be

5.34 eV. This estimated G is much larger than the

reported value of 4.5 [28−30] −4.6 eV [31−33]. One

possible explanation for such a discrepancy is the

tuning of G value caused by the doping effect

associated with charge transfer (due to the presence

of an interface dipole layer) between graphene and

metal [28−30] and/or metal contact induced charge

inhomogeneity [67−69]. Song et al. [30] summarized

the practical G value under various metals based on

the C-V analysis of metal-graphene-oxide-

semiconductor capacitors, e.g., G under Pd and Au

was ~4.62 eV, G under Cr/Au bilayer was ~4.3 eV, and Figure 5 Plots of ΦB vs. 1000/T. The inset shows the schematic

band diagram of graphene-GaN interfaces with inhomogeneous

Schottky barriers.

9

G under Ni was ~5.0 eV. Note that, although the G

was shown to change significantly depending on the

contact metals, there are no metals reaching our

estimated G value of 5.34 eV. In addition, for the

graphene under Au, the G difference between the

estimated value (5.34 eV) and the reported one (4.62

eV) is as high as 0.72 eV, indicating that this

explanation in terms of G tuning is somewhat

limited.

Another possible explanation is the pinning of the

surface Fermi level (EF) of GaN that is associated with

surface states, namely, Bardeen model. Indeed, this

model becomes more practical in GaN

semiconductors due to the presence of strong

spontaneous polarization field (Psp) built from the Ga-

terminated surface (Ga-polarity surface) toward the

bulk direction [70−72] as shown in the upper inset of

Fig. 6. For example, under the presence of Psp, the

electron carriers are readily transported to the Ga-face

side and are subsequently trapped at the surface

states, i.e., the surfaces are negatively charged,

inducing a compensating positive charge near the

GaN surface (or the formation of induced electric

dipoles) and hence causing upward surface bending.

Specifically, the degree of surface band bending or the

bare surface barrier height (s) of GaN can be

estimated according to the following equation [56, 73]:

S

qSqq GB

s

1

)( (8)

where S is the S parameter, which is defined as S=

d(B)/d(M). To obtain the S parameter of our samples,

we fabricated Schottky diodes with different work

functions of metals (M) including Pt, Ni, and Cr, and

obtained their B,m values using the barrier

inhomogeneity model as shown in the lower inset of

Fig. 6.

Figure 6 shows the B,m plotted as a function of M,

yielding the S parameter of 0.48. The fact that the S

parameter of our sample is slightly higher than those

reported in the literature (0.385 [57], 0.41 [58]) is

attributed to the better epitaxial quality of GaN film.

Consequently, the bare surface barrier height s could

be estimated to be as high as 2.9 eV, indicating that the

large ΦB,m of graphene is essentially associated with

large upward surface band bending or surface Fermi-

level pinning. Indeed, the Ds could be also estimated

using the obtained S parameter and the Cowley-Sze

model [55], i.e.,

i

is

tSq

SD

2

)1(

,

(9)

yielding that Ds = 1.21013 states/cm2/eV. Note that the

obtained Ds value using S parameter is in good

agreement with reported values (1.6−1.81013

states/cm2/eV) [57, 58] and partly the values obtained

using Eq. (4). Therefore, the large Ds value and the

presence of Psp is expected to pin the surface EF,

causing a deviation from the ideal Schottky-Mott

theory, a significant upward surface band bending

and hence the eventual formation of large barrier

height.

Interestingly, using the B,m vs. M relations with

S=0.48 and ΦB,m=1.24 eV for the graphene-GaN contact,

the G value in the Au/graphene/GaN system could

be inversely estimated to be 3.5 eV (see the

extrapolated line of Fig. 6). This finding is quite

interesting, since we can roughly obtain the G value

in the complicated stack of (Au/Cr)/Au/graphene

/GaN system. However, the obtained G value is

likely to be somewhat under-estimated. This is first

attributed to the limited accuracy of S parameter. For

example, for obtaining more reliable and accurate S

parameter, various Schottky diodes having different

work function of metals, particularly having low

Figure 6 ΦB,m vs. ΦM plots. The upper and lower insets show the

schematic band diagram of bare GaN surface and the ΦB-T

diagram for the Pt, Ni, and Cr Schottky diodes, respectively.

10

work function in the range of 3.54.5 eV, had to be

evaluated. However, we just evaluated three types of

diodes with the large work function in the range of

4.55.6 eV due to the absence of appropriate contact

metals (i.e., due to the near Ohmic behavior by low

work-function contact). Second, the doping effect

associated with the charge transfer at each junction of

GaN-graphene, Au-graphene, and/or Au/Cr/Au-

graphene may tune the G. This is presently under

investigation.

Lastly, it will be instructive to reconsider the

anomalously large Rs value of graphene-GaN diodes.

Figure 7 shows the semi-logarithmic I-V curves of a

graphene-GaN Schottky diode at 300 K, taken with

and without illumination. The illumination source

was the conventional fluorescent lamp (PHILIPS

LIFEMAX TLD 32W/365) placed on the ceiling of the

equipment, i.e., the illumination intensity was

relatively weak and the emission spectrum was broad

(Fig. S5 of the ESM). Note that, despite the weak

illumination intensity, the photocurrent (at reverse

bias voltage) and the open circuit voltage were

observed with illumination, indicating

photoexcitation of carriers and generation of

photocurrent. Indeed, this finding is nearly the same

as that of graphene-Si diodes under reverse bias

condition [35]. However, in our case, the illumination

energy (h, =frequency) was lower than the Eg of

GaN (3.4 eV), i.e., B < h < Eg. This indicates that the

origin of photocurrent is the electrons excited from

the graphene over the barrier into the GaN.

Distinctive feature of our finding, which is different

from the graphene-Si diodes [35], is much more

pronounced photocurrent under forward bias

condition (> 0.6 V), as shown in the inset. Accordingly,

the Norde plot showed a significantly reduced Rs

value of 140 K with illumination (see Fig. S3 of the

ESM). This finding indicates that, first, the

anomalously large Rs value (7600 K) of graphene-

GaN Schottky diodes is primarily associated with the

electrical conductivity of graphene. Second, the

noticeable photocurrent generated under both reverse

and forward bias condition in spite of very weak

illumination intensity provides the new possibility of

graphene-GaN Schottky diodes to use as a functional

photodetectors. Indeed, this is presently under

investigation.

Conclusions

To summarize, the electrical characteristics and

carrier transport mechanism of graphene Schottky

contacts formed on undoped GaN were analyzed.

Unlike the expected poor Schottky contact, the

fabricated Schottky diodes exhibited excellent

rectifying behavior with a rectification ratio of ~107 at

2 V and a low reverse leakage current of 1.010−8

A/cm2 at −5 V. Based on the I-V analysis with TE

conduction model, the B of 0.90 and n of 1.32 could

be obtained. More reasonably, the barrier

inhomogeneity model applied to the I-V-T data

yielded the mean barrier height B,m of 1.24 eV with

the standard deviation of 0.13 eV. The formation of

excellent graphene-GaN Schottky contact is attributed

to the presence of a large number of surface states of

GaN (1.21013 states/cm2/eV) and the internal Psp,

causing a significant upward surface band bending

up to 2.9 eV and hence the formation of large B at the

GaN/graphene interface. Using the obtained barrier

height and S parameter of 0.48, the work function of

graphene G in Au/graphene/GaN stack could be

approximately estimated to be as low as 3.5 eV. Such

a result indicates that graphene is a potential

candidate for use as a Schottky rectifier.

Acknowledgements

Figure 7 The I-V characteristics of graphene-GaN diodes with and

without illumination. The inset shows linear I-V plot.

11

This study was supported in part by a Priority

Research Center Program through the National

Research Foundation of Korea, funded by the

Ministry of Education, Science and Technology of the

Korean government (2011-0027956) and in part by the

Ministry of Education and National Research

Foundation of Korea(NRF) through the Human

Resource Training Project for Regional Innovation

(2013H1B8A2032197).

Electronic Supplementary Material: Supplementary

material (The detailed synthesis of graphene by CVD

method and transfer techniques, and optical

transmittance result) is available in the online version

of this article at http://dx.doi.org/10.1007/s12274-***-

****-*

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14

Electronic Supplementary Material

Graphene-GaN Schottky diodes

Seongjun Kim1, Tae Hoon Seo2, Eun-Kyung Suh1, Keun Man Song3, Myung Jong Kim2, and Hyunsoo Kim1()

1 School of Semiconductor and Chemical Engineering, Semiconductor Physics Research Center, Chonbuk National University, Jeonju

561-756, Republic of Korea 2 Soft Innovative Materials Research Center, Korea Institute of Science and Technology, Jeonbuk 561-905, Republic of Korea 3 Korea Advanced Nano Fab Center, Suwon 443-700, Republic of Korea

Supporting information to DOI 10.1007/s12274-****-****-* (automatically inserted by the publisher)

INFORMATION ABOUT ELECTRONIC SUPPLEMENTARY MATERIAL.

————————————

Address correspondence to Hyunsoo Kim, hskim7@jbnu.ac.kr

Figure S1 The synthesis of graphene by CVD method and transfer techniques on GaN substrate.

Figure S2 The optical transmittance characteristics of bare GaN and graphene on GaN substrate.

15

Figure S3 Norde function, F(V) versus V of (a) Ni-GaN diode, (b) graphene-GaN diode without illumination, and (c) graphene-

GaN diode with illumination.

16

-6 -4 -2 0 210

-15

10-12

10-9

10-6

10-3

Ni-GaN Schottky diode

I (A

)

V (V)

n = 1.22

B= 1.08 eV

Figure S4 The I-V characteristics of Ni-GaN Schottky diodes.

1.5 2.0 2.5 3.0 3.5 4.0

In

ten

sit

y (

a. u

.)

h (eV)

Figure S5 The luminescence spectrum of the fluorescent lamp.