GaAs

Physica E 64 (2014) 240–245

Contents lists available at ScienceDirect

Physica E journal homepage: www.elsevier.com/locate/physe

The electrical characterization of ZnO/GaAs heterojunction diode M. Soylu a,n, A.A. Al-Ghamdi b, Omar A. Al-Hartomy b,c, Farid El-Tantawy d, F. Yakuphanoglu b,e a

Department of Physics, Faculty of Sciences and Arts, Bingol University, Bingol, Turkey Faculty of Science, Department of Physics, King Abdulaziz University, PO 80203, Jeddah 21589, Saudi Arabia c Department of Physics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia d Department of Physics, Faculty of Science, Suez Canal University, Ismailia, Egypt e Department of Physics, Faculty of Science, Firat University, Elazig 23169, Turkey b

H I G H L I G H T S

G R A P H I C A L

A B S T R A C T

We have fabricated Al/ZnO/p-GaAs heterostructure diode by sol–gel method. The current–voltage characteristic of Al/ZnO/p-GaAs shows diode-like behavior. AFM images indicate that the ZnO films are formed from the nano-fiber particles. It is evaluated that electrical performance of Al/ZnO/p-GaAs can be controlled by ZnO.

art ic l e i nf o

a b s t r a c t

Article history: Received 11 July 2014 Accepted 1 August 2014 Available online 7 August 2014

The electrical characteristics of sol–gel synthesized n-ZnO/p-GaAs heterojunction were reported. The values of barrier height and ideality factor for n-ZnO/p-GaAs heterojunction diode were determined to be 0.61 eV and 1.83, respectively. The I–V characteristics of the heterojunction diode exhibit a non-ideal behavior. The ideality factor which is greater than unity was attributed to the series resistance, interface states and interfacial layer. The modified Norde's function combined with conventional forward I–V method was used to obtain the parameters including the series resistance and barrier height (BH). The capacitance–voltage (C–V) measurements were performed in the range of 100 kHz to 1 MHz. The interface distribution profile (Dit) as a function of bias voltage was extracted from the C–V and Gadj–V characteristics. The interface state density of n-ZnO/p-GaAs diode is of the order of 1013 eV 1 cm 2. Also, the I–V characteristics of n-ZnO/p-GaAs heterojunction diode were investigated in the temperature range of 293–393 K. & 2014 Elsevier B.V. All rights reserved.

Keywords: Semiconductors Nanofabrications Electronic transport

1. Introduction The practical semiconductor device applications are based on metal–semiconductor (MS) junction in microelectronic integrated circuits (IC) [1–6]. These applications are consisted of space solar cell, heterojunction bipolar transistors, microwave field effect transistors,

n

Corresponding author. Tel.: þ90 426 2160012; fax: þ 90 4262132580. E-mail address: [email protected] (M. Soylu).

http://dx.doi.org/10.1016/j.physe.2014.08.001 1386-9477/& 2014 Elsevier B.V. All rights reserved.

phototransistors, photodiodes, radio-frequency detectors, polariton laser, and quantum confinement devices. The interface between the metal and semiconductor affects the reliability and the performance of a Schottky contact. The many efforts have been devoted to understanding the transport mechanism of the Schottky barrier diodes (SBDs). In last few decades, the metal–semiconductor interfaces, particularly in electronic devices have attracted heavy interest. ZnO has an n-type conductivity that can be attributed to the intrinsic defects such as oxygen vacancies [7,8]. Furthermore, ZnO is one of the attracting photonic materials for devices such as ultraviolet (UV)

M. Soylu et al. / Physica E 64 (2014) 240–245

photodetectors, laser diodes (LDs) and light emitting diodes (LEDs) due to wide band-gap (3.37 eV) and large exciton binding energy (60 meV) [9–11]. Photodetectors working in the UV range have interesting capabilities for military and commercial applications such as ozone layer monitoring, flame detection and space communications. Si based detectors do not sensitive to the wavelength located in the UV range due to the narrow band-gap energy (only 1.2 eV) of Si. Thus, the performance of Si photodiodes is not satisfactory in the UV range. The photoresponse time of ZnO-based photodetectors has improved with the advent of optoelectronic devices including wide direct-bandgap materials. In the last decade, molecular beam epitaxy (MBE), magnetron sputtering, pulsed-laser deposition (PLD), sol–gel process and metal–organic chemical vapor deposition (MOCVD) are some of methods used to prepare ZnO thin films on various substrates [12–17]. Particularly, the sol–gel method is an alternate way that is extremely low-cost and easy to prepare the large area ZnO thin films [18] and also, spin coating is one of the standard methods for depositing sol–gel, nanocomposite or polymer coatings onto flat substrates (silicon wafers, glass plates for displays, sensor substrates, etc.). The preparation of the new metal–semiconductor contacts based on ZnO semiconductor plays a key role in device applications. In this work, ZnO/p-GaAs heterojunction structure was obtained by spin coating of ZnO on p type GaAs substrate. The some properties of the ZnO/p-GaAs heterojunction diode were analyzed by the I–V and C–V measurements.

2. Experimental details In this study, p-GaAs (1 0 0)-doped with Zinc (Zn) was used as substrate. The GaAs wafer was cleaned with methanol, acetone and trichloroethylene. After, the wafer was thoroughly washed with deionized water (418Mohm.cm), followed by drying under high purity (99.9%) dry N2 gas. The native oxide on the wafer was removed by etching in sequence with acid solutions (H2SO4:H2O2:H2O¼3:1:1) for 60 s, and (HCI:H2O¼ 1:1) for another 60 s. Again, the wafer was thoroughly washed with de-ionized water (418Mohm.cm), followed by drying under high purity (99.9%) dry N2 gas. The ohmic contact to the p-type GaAs wafer backside was deposited by thermal evaporation of high purity (99.999%) indium metal in the pressure of 2 10 5 Torr. The GaAs wafer with indium back contact was thermally treated at 370 1C for 6 min in N2 atmosphere. Sol–gel method was employed for preparation of undoped ZnO sample. Zinc acetate hexahydrate, deionized water and monoethanolamine were used as the starting material, the solvent and stabilizer, respectively. Zn2 þ and monoethanolamine were used in equal concentrations. In order to a homogeneous sol, the solution was mixed with a magnetic stirrer at 65 1C for 2.5 h and then remained in air for 24 h aging. The thin film of ZnO was formed on the front surface of the GaAs by spinning (non-vacuum process) at 1000 rpm, for 1 min. The ZnO thin film was heated to 470 1C for 3 min in a tube furnace. Contacts with a diameter of approximately 2 mm of Al were formed on undoped ZnO films by thermal evaporation method through a molybdenum mask at vacuum ambience of E3.4 10 5 mbar pressure. A diagram of the diode structure is shown in Fig. 1.

Fig. 1. A schematic cross-section of the Al/ZnO/p-GaAs structure.

241

The measurements were performed using KEITHLEY 4200 semiconductor characterization system. The two terminal cables of Source Measure Unit1 (SMU-1) and Source Measure Unit2 (SMU-2) were united to a home made specially designed holder for a point contact. The temperature dependent measurements were controlled by means of a temperature controller (Lakeshore 331) with sensitivity better than 70.1 K.

3. Results and discussion 3.1. The current–voltage characteristics of the Al/ZnO/p-GaAs heterojunction diode In order to investigate the morphology of the ZnO film, atomic force microscopy (AFM) (Park System XE-100E) was used. Fig. 2 shows two (2D) dimensional and inset: three (3D) dimensional AFM images of the ZnO film. The AFM results show that the ZnO films are formed from the nanofibers. The surface roughness of undoped ZnO film by means of a PARK system AFM XEI software programming was determined to be approximately 42.32 nm. The current–voltage (I–V) characteristics were measured to obtain the effective values of the diode parameters. Fig. 3 shows the current–voltage characteristics of ZnO/GaAs/In heterojunction diode. As seen in Fig. 3, the diode shows a rectifying characteristic with relatively low reverse current of 9.15 10 6 A at reverse bias of VR ¼ 1.0 V. The current increases exponentially in low applied voltages. The current flow for V IRs 43kT/q, can be analyzed by the following relation [1,19,20]: qðV IRs Þ I ¼ I o exp ð1Þ nkT where, I 0 is the reverse saturation current given by: ! qΦI V I 0 ¼ AAn T 2 exp b kT

ð2Þ

where q is the electronic charge, V the definite forward biasing voltage, A the contact area, An the effective Richardson constant, k the Boltzmann's constant, T the absolute temperature, ΦIb V the barrier height and n is the ideality factor. The values of ΦIb V and n

Fig. 2. AFM images of nano fiber ZnO thin film.

242


In Norde method, the series resistance is given as: Rs ¼

kTðγ nÞ ; qI o

ð5Þ

The Rs value for the diode was found to be 431.0 Ω. There is a good agreement between the Rs values obtained from Rs ¼ ∂V/∂I relation and the Norde function. It is evaluated that the series resistance is a parameter intended to limit the amount of current for this structure.

3.2. Capacitance–voltage characteristics of the Al/ZnO/p-GaAs heterojunction diode

Fig. 3. Current–voltage characteristics of an Al/ZnO/p-GaAs Schottky barrier diode.

were calculated from the intercept and the slope of the forward bias ln(I) vs. voltage (V) plot, respectively. The values of ΦIb V and n were obtained to be 0.61 eV and 1.83, respectively. The ideality factor, which is higher than unity, may relate to the presence of recombination current arising from traps. The I–V characteristics of the Al/ZnO/p-GaAs diode exhibit a non-ideal behavior due to the nanocrystalline nature of the ZnO film and the presence of surface states. It should take into account also the recombination via deep levels. The higher ideality factor implies that the current transport mechanism of the studied device could not be explained by thermionic emission (TE) only and could be due to presence of secondary transport mode at the interface. The high ideality factor is indicative of a tunnelingdominated current mechanism and might be attributed to factors such as incomplete contact filling of ZnO rod arrays and the high density of defect states at the interface, [21–24]. The surface state density, which is high enough can control the barrier height in ZnO/GaAs structure, leading to the high value of n [2,25]. The deviation from linearity of I–V characteristics can be due to the series resistance and interfacial layer. The series resistance Rs for the diode can be calculated using Rs ¼∂V/∂I relation. The Rs value was calculated to be 432 Ω. Furthermore, the diffusion potential value of 0.787 V for the device was determined from the forward bias I–V plot in Fig. 3. There are several ways to estimate the series resistance. The modified Norde method is expressed as [26] FðV Þ ¼

V 0 kT IðVÞ n 2 q A AT γ

Fig. 5 shows the C–V curves of the Al/ZnO/p-GaAs heterojunction diode at various frequencies. It is seen that capacitance characteristics exhibit 20% dispersion between 1 MHz and 100 kHz, across the reverse bias region. The C–V curves show peak at positive voltages and then, the peaks disappear with increasing frequencies. The maximum points in the forward C–V plots may be related to the presence of reordering of the interface states and the molecular restructuring, and series resistance. There are interface states in equilibrium with the p-GaAs at the interface. The interface states can follow the alternating signal (a.c.) at lower frequencies compared to the higher frequencies. From here, it is explained the physical origin of the excess capacitance at low frequency. This is meaningful if the time constant is too long to permit the charge to move in and out of the states in response to an applied signal. The capacitance of depletion layer in a Schottky

Fig. 4. Plot of F(V) vs voltage of an Al/ZnO/p-GaAs Schottky barrier diode.

ð3Þ

where γ is the integer (dimensionless) greater than n. Fig. 4 shows the plot of F(V) vs. voltage for the diode. The F(V) has a minimum point and thus, the barrier height is written as follow: Φb ¼ FðV 0 Þ þ

V 0 kT ; q γ

ð4Þ

where F(Vo) is the minimum point of F(V) function. From the F(V)–V plot, the barrier height was found to be 0.65 eV. The obtained barrier height is lower than that of Al/p-GaAs Schottky diodes [27,28]. The result indicates that nanostructured ZnO thin film can be changed the barrier height of metal/p-GaAs diodes, providing an important modification of interface states [29–33].

Fig. 5. The forward and reverse biasing of C–V characteristics of the Al/ZnO/p-GaAs structure for various frequencies at room temperature.


243

barrier diode can be written as [34]: 1 C

2

¼

2ðV bi þ VÞ

ð6Þ

qεs εo A2 N a

where Na is the density of acceptor impurity atoms, V bi the built-in voltage, V the applied voltage and εs is the static dielectric constant, equal to 13.1 for p-GaAs [3], εo ¼ 8:85 10 14 F/cm. Fig. 6 shows the reverse bias 1/C2–V plot of Al/ZnO/p-GaAs diode measured at 1 MHz frequency. The non-linear behavior of the curve is attributed to the presence of interface states. The diffusion potential at zero bias (the built-in voltage) was determined to be 0.766 V from an extrapolation of the linear C 2 V plot to the V-axis. This value is in close agreement with the value of 0.787 V obtained from the forward bias I–V plot in Fig. 3. The N a is determined from the slope of C 2 vs. V curve and can be obtained from the expression given below " # 2 1 Na ¼ ð7Þ qεs εo A2 dðC 2 Þ=dV The BH ðΦCb V Þ found from capacitance is expressed as: kT Nv 1 þ ln ; ΦCb V ¼ V bi þ q Na

ð8Þ

where Nv (¼8.34 1018 cm 3) is related to the effective density of states in the valence band for p-GaAs at 300 K. The values of N a and V bi are obtained from the slope and the intercept of the extrapolated C 2–V lines with the V axis, respectively. Then, the value of ΦCb V is determined by using Eq. (8). The barrier height ΦCb V fp-GaAs diode was found/p-GaAs diode was found to be 0.724 eV. ΦCb V is higher than ΦIb V at room temperature. The discrepancy in barrier height values estimated using the C–V and I–V methods may be originated from the presence of an intervening insulating layer, surface contamination, edge leakage currents, deep impurity levels, image-force lowering, quantum mechanical tunneling and instrumentation problems [1,34–37]. A non-linear behavior is observed in the capacitance–voltage curve because of the formation of insulator layer between the metal and semiconductor, the density of interface states and series resistance. Non-linear regime in the conductance–voltage and capacitance–voltage curves of ZnO/p-GaAs diode is eliminated by the following equations [38–40], C adj ¼

½G2m þ ðωC m Þ2 C m a2 þ ðωC

2

mÞ

Gadj ¼

½G2m þðωC m Þ2 a ; a2 þ ðωC m Þ2

ð9Þ

where a ¼ Gm ½G2m þ ðωC m Þ2 Rs ;

Fig. 7. The voltage dependent curves of Gc at different frequency of the Al/ZnO/p-GaAs Schottky diode.

ð10Þ

Fig. 6. The reverse bias C 2–V characteristic of the Al/ZnO/p-GaAs structure at 1 MHz frequency.

Fig. 8. The variation of the series resistance of the Al/ZnO/p-GaAs structure as a function of bias voltage for various frequencies at room temperature.

where the Cm and Gm symbols are the measured conductance and capacitance at any given voltage, respectively. ω is the angular frequency. Figs. 7 and 8 show the Gadj V and Rs V measurements, respectively. In addition, the frequency-series resistance relation from the C–V–f and Gadj–V–f measurements is given as: Rs ¼

Gma G2ma þ ðωC ma Þ2

ð11Þ

The variance in the Rs values with applied bias voltage is given in Fig. 8. The series resistance reaches the peak value at about 0.20 V depending on the frequency. It starts to drop when the frequency further increases. The particular distribution density of interface states was found in relation to the voltage and frequency of Rs. The Gadj–V characteristics are parallel with the C–V characteristics in the same bias range. Such behavior of C–V and Gadj–V characteristics may be sensitive to particular distribution of the interface state density (Dit). The change in Rs is dominant in the depletion and accumulation regions. The interface states affect the charge transport mechanism between the semiconductor and the metal. The density of the interface states is possible to estimate with the capacitance– voltage measurements. The capacitance of the interfacial layer and the depletion region constitutes a series. The interface state density is estimated using Hill's method [41], which is an useful way to calculate the density of interface states (Dit). According to

244


Fig. 9. Interface state density profile of Au/ZnO/p-GaAs diode.

Hill's method, the density of interface states is written as: Dit ¼

2 ðGm =ωÞmax qA ½ðGm =ωÞmax C ox Þ2 þ ð1 C m =cox Þ2

ð12Þ

where Gm and Cm are the measured conductance and capacitance, which are taken into account for the peak values, respectively. Cox is the capacitance of the oxide layer. The interface state density was determined to be 1013 eV 1 cm 2. The Dit values calculated from Gadj V plots for the diode are shown in Fig. 9. As seen in Fig. 9, the Dit values decrease with increasing frequency and then, indicate a minimum and again increase with frequency. The change in the interface states may be originated from the restructuring or reordering. Also, this behavior is attributed to the various interface states with different life times. Fig. 10(a) and (b) also shows the I–V characteristics of ZnO/GaAs/Al diode at various temperatures and plot of Vth vs. T. The current values increase for both forward and reverse biases as the temperature increases. Threshold voltage, Vth is defined as the point where the current starts to increase in the forward bias direction. The threshold voltage (Vth) response of the ZnO/GaAs/Al diode shows a linearity and decreasing trend as the temperature increases, from 0.325 V at 293 K to 0.289 V at 393 K. Furthermore, the rectifying feature of I–V characteristics remains unchanged. The values of n and BH determined from the slope and the intercept of the forward bias In(I) vs. voltage (V) plot according to thermionic emission (TE) theory are shown as a function of temperature in Fig. 11. As can be seen in Fig. 11, the zero-bias barrier height increases, while the ideality factor decreases with increasing temperature. Since the current transport mechanism in the MS junction is a temperature-dependent process, electrons can exceed the lower barriers at low temperatures. Thus, the carrier transport will be provided by charges flowing through the patches with a larger ideality factor and lower barrier height. With the increasing temperature, more and more electrons will have enough energy to overcome the higher barrier [35,42]. The threshold value for an ideal Schottky diode is expected to decrease as the temperature increases. In common, the threshold voltage– temperature coefficient (TCVth) is expressed as [43]: TCV th ¼

1 dV th V th dT

Fig. 11. Temperature dependences of experimental BH and n values obtained from current vs. voltage characteristics of Al/ZnO/p-GaAs device between 293 and 393 K.

ð13Þ

and the threshold voltage as a function of temperature is given by: V th ðTÞ ¼ V th ðT 0 Þ½1 þ TCV th ðT T 0 Þ

Fig. 10. (a) I–V curves of Au/ZnO/p-GaAs diode at different temperatures (b) the forwardbias threshold voltage Vth as a function of temperature, respectively.

ð14Þ

where TCVth ¼1 corresponds to the ideal case. The threshold voltage temperature coefficient for the ZnO/p-GaAs diode was found to be 4.178 eV. The temperature dependent threshold

voltage for the Al/GaN-nanowire Schottky contact is attributed to the thermal expansion coefficient of Al, which is larger compared to that of GaN [44]. The density of gap states, which result from the oxygen vacancies in ZnO tends to ionize at high temperature, leading an increase in the free-carrier density [45]. Thus, the values of the forward and reverse bias current increase as the temperature increases.


4. Conclusions The electrical properties of Al/ZnO/GaAs heterojunction were investigated by means of I–V, C–V and Gadj–V measurements. The Al/ZnO/p-GaAs structure exhibits a rectifying behavior. The AFM images show that the ZnO films are formed from the nanofibers. It was found that the forward and reverse bias (C–V–f) and Gadj–V–f) characteristics of the Al/ZnO/p-GaAs structure were quite sensitive to frequency, especially at relatively low frequency. The interface state density of the Al/ZnO/p-GaAs diode was of the order of 1013 eV 1 cm 2. The threshold voltage (Vth) response of the ZnO/ GaAs/Al diode shows a linearity and decreasing trend as the temperature increases, from 0.325 V at 293 K to 0.289 V at 393 K. Acknowledgements The present study is a result of an international collaboration program between University of Tabuk, Tabuk, Saudi Arabia and Firat University, Elazig, Turkey. The authors gratefully acknowledge the financial support from the University of Tabuk, Project number 4/1433. References [1] S.M. Sze, Physics of Semiconductor Device, second ed., John Wiley & Sons, New York, 1981. [2] E.H. Rhoderick, R.H. Williams, Metal-Semiconductor Contacts, second ed., Clarendon Press, Oxford, 1988. [3] A. Neamen Donald, Semiconductor Physics and Devices, Boston, Irwin, 1992. [4] J. Singh, Semiconductor Devices, Basic Prenciples, John Wiley & Sons, New York, 2001. [5] M.C. Petty, M. Bryce, An Introduction to Molecular Electronics, Oxford University Press, NewYork, 1995. [6] C. Joachim, M.A. Ratner, Molecular Electronics, American Chemical Society, Washington D.C, 1997. [7] T.M. Barnes, J. Leaf, S. Hand, C. Fry, C.A. Wolden, J. Appl. Phys. 96 (2004) 7036. [8] H. Kato, M. Sano, K. Miyanoto, T. Yao, Jpn. J. Appl. Phys. 42 (2003) L1002. [9] Y.I. Alivov, E.V. Kalinina, A.E. Cherenkov, D.C. Look, B.M. Ataev, A.K. Omaev M.V. Chukichev, D.M. Bagnall, Appl. Phys. Lett. 83 (2003) 4719. [10] S. Liang, H. Sheng, Y. Liu, Z. Huo, Y. Lu, H. Shen, J. Cryst. Growth 225 (2001) 110.

245

[11] A. Mang, K. Reimann, St. Rübenacke, Solid State Commun. 94 (1995) 251. [12] Y. Zhang, L. Wu, H. Li, J. Xu, L. Han, B. Wang, Z. Tuo, E. Xie, J. Alloys Compd 473 (2009) 319. [13] Y. Lin, D.M. Jiang, F. Lin, W.Z. Shi, X.M. Ma, J. Alloys Compd 436 (2007) 30. [14] S.K. Neogia, R. Ghoshb, G.K. Paulb, S.K. Berac, S. Bandyopadhyay, J. Alloys Compd 487 (2009) 269. [15] L.H. Van, M.H. Hong, J. Ding, J. Alloys Compd 449 (2008) 207. [16] S. Huang, Q. Xiao, H. Zhou, D. Wang, W. Jiang, J. Alloys Compd 486 (2009) L24. [17] S.W. Xue, X.T. Zu, W.L. Zhou, H.X. Deng, X. Xiang, L. Zhang, H. Deng, J. Alloys Compd 448 (2008) 21. [18] K.J. Chen, F.Y. Hung, S.J. Chang, S.J. Young, J. Alloys Compd 479 (2009) 674. [19] A. Astito, A Foucaran, G Bastide, M Rouzeyre, J. Appl. Phys. 70 (1991) 2584. [20] A. Ahaitouf, E. Losson, A. Bath, Solid-State Electron 44 (2000) 515. [21] E. Bacaksiz, S. Aksu, G. Cankaya, S. Yılmaz, I. Polat, T. Kucukomeroglu, A. Varilci, Thin Solid Films 519 (2011) 3679. [22] Y. Ni, Z. Jin, K. Yu, Y. Fu, T. Liu, T. Wang, Electrochim. Acta 53 (2008) 6048. [23] M.C. Jeong, B.Y. Oh, M.H. Ham, J.M. Myoung, Appl. Phys. Lett. 88 (2006) 202105. [24] H.P. Maruska, F. Namavar, N.M. Kalkhoran, Appl. Phys. Lett. 61 (1992) 1338. [25] W. Monch, Rep. Prog. Phys 53 (1990) 221. [26] H. Norde, J. Appl. Phys. 50 (1979) 5052. [27] H. Mazari, Z. Benamara, O. Bonnaud, R. Olier, Mater. Sci. Eng., B 90 (2002) 171–175. [28] G. Myburg, F.D. Auret, W.E. Meyer, C.W. Louw, M.J. van Staden, Thin Solid Films 325 (1998) 181. [29] T.U. Kampen, S. Park, D.R.T. Zahn, Appl. Surf. Sci. 190 (2002) 461. [30] S.R. Forrest, M.L. Kaplan, P.H. Schmidt, J. Appl. Phys. 60 (1986) 2406. [31] F. Yakuphanoglu, J. Alloys Compd. 507 (2010) 184–189. [32] S. Liang, H. Sheng, Y. Liu, Z. Huo, Y. Lu, H. Shen, J. Cryst. Growth 225 (2001) 110. [33] M. Cakar, N. Yildirim, S. Karatas, C. Temirci, A. Turut, J. Appl. Phys. 100 (2006) 074505. [34] A. Van der Ziel, Solid State Physical Electronics, second ed., Prentice-Hall, (NJ: Englewood Cliffs), 1968. [35] (a) R.T. Tung, Phys. Rev. B: Condens. Matter 45 (1992) 13502; (b) R.T. Tung, Mater. Sci. Eng., R 35 (2001) 1–138. [36] C.R. Crowell, Solid State Electron. 20 (1977) 171. [37] W. Mönch, Appl. Phys. Lett. 72 (1998) 1899. [38] E.H Nicollian, A. Goetzberger, Bell Syst. Technol. J. 46 (1967) 1055. [39] I. Dokme, S. Altındal, T. Tunc, I. Uslu, Microelectron. Reliab. 50 (2010) 39. [40] E.H. Nicollian, J.R. Brews, MOS (Metal–Oxide–Semiconductor) Physics and Technology, John Wiley & Sons, NewYork, 1982. [41] W.A. Hill, C.C. Coleman, Solid State Electron. 23 (1980) 987. [42] J.P. Sullivan, R.T. Tung, M.R. Pinto, W.R. Graham, J. Appl. Phys. 70 (1991) 7403. [43] A.G. Milnes, D.L. Feucht, Heterojunctions and Metal–Semiconductor Junctions, Academic Press, New York, 1972. [44] J.R. Kim, H. Oh, H.M. So, J.J. Kim, J. Kim, C.J. Lee, S.C. Lyu, Nanotechnology 13 (2002) 701. [45] P. Feng, Q. Wan, T.H. Wang, Appl. Phys. Lett. 87 (2005) 213111.