Numerical Determination of Schottky Barrier Height of Nickel/n-Type Gallium Nitride Diodes Formed on

Journal of Modern Mathematics Frontier Volume 3 Issue 2, June 2014 doi: 10.14355/jmmf.2014.0302.01

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Numerical Determination of Schottky Barrier Height of Nickel/n-Type Gallium Nitride Diodes Formed on Free-standing Substrates Kazuhiro Mochizuki*1, Akihisa Terano2, Takashi Ishigaki3, Tomonobu Tsuchiya4, Tomoyoshi Mishima5, Naoki Kaneda6 Central Research Laboratory, Hitachi, Ltd.

1, 2, 3, 4

1-280 Higashi-koigakubo, Kokubunji, Tokyo, 185-8601 Japan Cable Materials Research Laboratory, Hitachi Metals, Ltd.

5, 6

3550 Kidamari, Tsuchiura, Ibaraki, 300-0026 Japan kazuhiro.mochizuki.fb@hitachi.com; 2akihisa.terano.qm@hitachi.com; 3takashi.ishigaki.ug@hitachi.com; 4tomonobu.tsuchiya.ct@hitachi.com; 5tomoyoshi.mishima.ja@hitachi-metals.com; 6naoki.kaneda.je@hitachimetals.com *1

Received 23 January, 2014; Revised 3 March, 2014; Accepted 15 March, 2014; Published 20 June, 2014 © 2014 Science and Engineering Publishing Company

Abstract To validate the condition for applying thermionic emission (TE) theory when depletion-layer width is larger than carrier mean free path, Schottky barrier height qΦB of reported nickel/n-type gallium-nitride diodes was numerically determined. The forward-current/voltage characteristics of diodes on free-standing substrates were precisely reproduced by qΦB of 0.98 eV. Although this qΦB is consistent with the reported value (0.99 eV) determined from capacitance-voltage measurement, it is 0.05 eV higher than the reported value (0.93 eV) determined from TE theory.

This discrepancy indicates that qΦB of GaN Schottky barrier diodes needs to be determined not by analytically but by numerically fitting the experimental data.

Keywords Schottky Barrier Height; Nickel; Gallium Nitride; Free-Standing Substrate; Simulation

Introduction Gallium nitride (GaN) is an attractive material for not only its high-frequency but also power-electronics applications. Its high breakdown electric field of 3.75 MV/cm, which is about ten times that of silicon, makes it ideal for power devices. GaN-based power devices are usually fabricated on substrates such as sapphire, silicon carbide, and silicon. These substrates cause high-density (108 to 1010 cm-2) dislocations in heteroepitaxially grown GaN. Free-standing GaN

substrates are thus expected to open the way to explore the intrinsic performance of GaN. The main advantage of GaN for power-device applications is very low resistance of a drift region that is designed to support a high voltage. It favors the development of high-voltage unipolar devices that have much higher switching speed than bipolar devices. Schottky-barrier diodes (SBDs), formed by making a rectifying metal contact to the GaN drift region, are thus one of the key unipolar devices for power applications. So far, several SBDs (made of GaN and its related alloys) have been fabricated on freestanding GaN substrates.

As for metal contacts on n-type semiconductors, current transport is mainly due to electrons. Since electron mobility μ is controlled by scattering, electron mean free path λ can be given by λ = (μ / q) (3 k T m*)1/2,

(1)

where q is elementary charge (1.6×10-19 C), k is Boltzmann’s constant, T is absolute temperature, and m* is electron effective mass. Under a forward-bias condition, the electrons in the neutral region of an ntype semiconductor exceed depletion-region width W, which is given by W = {2 ε [Vbi – V – (k T / q)] / (q ND)}1/2,

(2)

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where Vbi is a built-in potential, and ε and ND are, respectively, dielectric constant and net donor density of the n-type semiconductor. When W is smaller than λ, which is the case with silicon SBDs, thermionic emission (TE) is the controlling current-conduction mechanism. In the case of GaN SBDs, on the other hand, W tends to be larger than λ (Fig. 1); for example, W = 8 λ when ε = 10.4×8.85×10-14 F/cm, Vbi – V – (k T / q) = 0.5 V, ND = 1×1016 cm-3, T = 300 K, m* = 0.24×9.1×10-31 kg, and μ = 1000 cm2/Vs. According to Rhoderick, thermionic emission (TE) theory “merely requires that the electron density at the top of the barriers is in equilibrium with the bulk of the semiconductors, and this can be the case even if the electrons make many collisions in negotiating the depletion region.” It is unobvious, however, whether seven collisions (in the case of W = 8 λ) can be regarded as “many collisions.” Numerical analysis is thus considered to be indispensible for determining Schottky barrier height, qΦB, of GaN SBDs.

and with μ of 600 cm2/Vs (ND = 1×1016 cm-3). It was known that μ strongly depeded on carrier compensation, which was observed in n-type GaN on GaN substrates when ND was below 5×1016 cm-3. As shown by the solid circles in Fig. 2, compensation ratio r of the two MOVPE layers described above corresponded to about 0.90. According to Suda et al., μ was about 1000 cm2/Vs when ND was 7.6×1015 cm-3, which corresponded to an r of 0.60 (open circle in Fig. 2). This low r may be attributed to their crystal-growth technique, i.e., hydride vapor-phase epitaxy (HVPE).

The JF-VF characteristics of GaN SBDs in the case of electrons having the least number of collisions when negotiating the depletion region were used in this study to numerically determine qΦB.

FIG. 2 CARRIER-CONCENTRATION DEPENDENCE OF ELECTRON MOBILITY The dotted and dashed lines are taken from Chin et al, 1994.

Solid circles: fitted data for Hashimoto et al., 2007 and Mochizuki et al., 2011; open circle: fitted data for Suda et al., 2010.

FIG. 1 SCHEMATIC BAND DIAGRAM OF FORWARD-BIASED GALLIUM NITRIDE SCHOTTKY-BARRIER DIODE qΦB: Schottky-barrier height; EC: energy of conduction-band minimum; EV: energy of valence-band maximum; W: depletion-layer width; λ: electron mean free path.

In 2001, electrical characteristics of GaN SBDs were numerically investigated by Shelton et al.; however, the substrates they assumed were sapphire, and μ was tentatively assumed to be 350 cm2/Vs. In 2011, the present authors fabricated GaN SBDs by using layers grown by metal-organic vapor-phase epitaxy (MOVPE) on GaN substrates. And they fitted their measured forward-current-density (JF)/forward-voltage (VF) characteristics and those reported by Hashimoto et al., respectively, with μ of 750 cm2/Vs (ND = 5×1015 cm-3)

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FIG. 3 GaN SCHOTTKY-BARRIER DIODE REPORTED BY SUDA ET AL., 2010

Simulation of SBDs GaN SBDs (ND = 7.6×1016 cm-3) fabricated on GaN substrates were simulated in reference to the cylindrical coordinate system by using the drift-

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diffusion and thermionic-emission models in a commercial device simulator. A schematic of the GaN SBD reported by Suda et al. is shown in Fig. 3. The thickness of the HVPE substrate was assumed to be the mean value reported in Suda et al., 2010. In the simulation, cathode-contact resistance was neglected (Mochizuki et al., 2011). Note that both substrate thickness and contact resistance have little influence on JF/VF characteristics as long as JF is less than 1 A/cm2.

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thermionic field emission (TFE), instead of the equation for TE, because of a high electric field at the metal/semiconductor interface: JTFE = (A* T q ħ E / k) [π / (2 m* k T)]1/2 × exp {-ΦB, TE + (q ħ E)2 / [24 m* (k T)2 ]/(k T)}, (3) where A* is the effective Richardson constant (28.9 A/cm2K2), ħ is reduced Planck’s constant, and E is electric field at the meal/semiconductor interface. Here, E is given by

SBD Forward Electrical Characteristics The error bars in Fig. 4 are taken from the maximum and minimum values of the measured JF of 19 nickel/nGaN (ND = 7.6×1016 cm-3) SBDs, excluding one SBD with large leakage, reported in Suda et al., 2010. Using these data and assuming TE theory, Suda et al. determined qΦB as qΦB, TE of 0.93 eV. They also used capacitance/voltage measurement and determined qΦB as qΦB, C-V of 0.99 eV. Note here that qΦB, TE is 0.06 eV lower than qΦB, C-V. The three JF-VF curves in Fig. 4 were simulated under the assumption that μ is 1000 cm2/Vs (Suda, 2011). As is clear from the figure, the measured results (Suda et al., 2010) are precisely reproduced by a qΦB of 0.98 eV. Although this qΦB is consistent with the reported qΦB, C-V, it is 0.05 eV higher than the reported qΦB, TE (Suda et al., 2010).

E = [2 q ND (Vbi + VR) / ε]1/2.

(4)

On the basis of the results in Fig. 4, however, the numerically determined ΦB (0.98 V) should be used instead of ΦB, TE (0.93 V) in Eq. (3). This approach will reduce calculated JR and make its deviation from measured JR larger, leading to a different interpretation of the reported JR/VR characteristics in Suda et al., 2010.

Equations (1) and (2) suggest that λ is an order of magnitude lower than W when μ is much less than 1000 cm2/Vs, which is considered to be an ordinary case, including hetero-epitaxially formed GaN SBDs. Numerical determination of qΦB by fitting the JF/VF characteristics is therefore considered to be indispensible for analyzing the JR/VR characteristics of GaN SBDs. It has to be noted here that although the use of a single parameter (qΦB) is enough for fitting the JF/VF characteristics of GaN SBDs having large μ (Fig. 4), fine tuning of μ may also be needed for fitting those of GaN SBDs having small μ.

Conclusion

FIG. 4 MEASURED (AS REPORTED in Suda et al., 2010) AND CALCULATED FORWARD-CURRENT-DENSITY/FORWARDVOLTAGE CHARACTERISTICS OF A NICKEL/n-GaN SCHOTTKY-BARRIER DIODE ON GaN SUBSTRATES UNDER ASSUMED ELECTRON MOBILITY OF 1000 cm2/Vs The error bars show the maximum and minimum forward current density of the 19 diodes reported in Suda et al., 2010.

Schottky barrier height of reported nickel/n-GaN SBDs having a large electron mobility of 1000 cm2/Vs was numerically determined. The determined barrier height was 0.05 eV higher than the value based on thermionic-emission theory when the depletion-layer width was about eight times as large as the electron mean free path. Since electron mobility in n-GaN is usually lower than 1000 cm2/Vs, qΦB of GaN SBDs needs to be determined not by analytically but by numerically fitting the measured current/voltage characteristics.

Discussion

ACKNOWLEDGMENT

To analyze the reverse-current-density (JR)/reversevoltage (VR) characteristics of GaN SBDs on GaN substrates, Suda et al. used the following equation for

The authors gratefully acknowledge Prof. Tohru Nakamura of Hosei University for his fruitful discussions.

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Kazuhiro Mochizuki was born in Tokyo, Japan, in 1963. He received B.E., M.E., and Ph.D. degrees in electronic engineering from the University of Tokyo, in 1986, 1988, and 1995, respectively. Since 1988, he has been with the Central Research Laboratory, Hitachi, Ltd., Tokyo. He has contributed significantly to advances in growth, device, and modeling technologies for compound semiconductors, including

Journal of Modern Mathematics Frontier Volume 3 Issue 2, June 2014

InAlGaAsP, ZnMgSSe, AlGaN, and SiC. He is the author or coauthor of 93 research papers in international journals and conference proceedings. He is the holder of 20 U.S. patents.

From 1999 to 2000, he was a Visiting Researcher at the University of California, San Diego, where he worked on tunneling-collector heterojunction bipolar transistors. He has served as a part-time lecturer at the University of ElectroCommunications, Tokyo (2003–present) and at Hosei University, Tokyo (2010–present). Dr. Mochizuki is a Senior Member of the IEEE Electron Devices Society.

Akihisa Terano was born in Niigata, Japan, in 1967. He joined the Central Research Laboratory, Hitachi Ltd., Tokyo, in 1985, where he has been engaged in research and development of metal processes for III-V compound semiconductor devices. Mr. Terano is a member of the Japan Society of Applied Physics.

Takashi Ishigaki received B.E. and M.E. degrees in electrical and electronic engineering from Kobe University in 1999 and 2001, respectively. He also received a Ph.D. degree in electronic engineering from Tokyo Institute of Technology in 2012. He joined the Compound Semiconductor Division, NEC Corporation, Otsu, Japan, in 2001, where he was involved in research and development of GaAs heterojunction FETs and HBTs for microwave applications.

Since 2004, he has been with the Central Research Laboratory, Hitachi, Ltd., Tokyo, Japan, working on research and development of high-capacity flash memories, SOI CMOSFETs, spin-transferred magnetic memories, and widebandgap semiconductor-based power devices. Dr. Ishigaki is a Member of the IEEE Electron Devices Society.

Tomonobu Tsuchiya was born in Gunma, Japan, in 1963. He received B.S., M.S., and Ph. D degrees from Tsukuba University, Ibaraki, Japan, in 1986, 1988, and 2012, respectively. He joined the Central Research Laboratory, Hitachi Ltd., Tokyo, in 1988 and has been working on research and development of crystal growth of III-V-compound semiconductors by MOVPE. Dr. Tsuchiya is a member of the Japan Society of Applied Physics, the Japanese Association for Crystal Growth, and the Institute of Electronics, Information, and

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Communication Engineering of Japan.

Tomoyoshi Mishima was born in Tokyo, Japan, in 1955. He received B.M., M.S., and Ph.D. degrees in physical electronics from the Tokyo Institute of Technology in 1978, 1980, and 1983, respectively. In 1983, he joined the Central Research Laboratory, Hitachi Ltd., Tokyo. He has worked in the areas of compound semiconductors and their applications to highfrequency devices. His key emphasis was on the development of high-quality metamorphic InAlGaAs heterostructures by MBE and their applications to highfrequency devices. He moved to the Research and Development Laboratory, Hitachi Cable Ltd. in 2003 (which was merged into Hitachi Metals Ltd. in 2013.) He is currently engaged in research on GaN-based power devices. From 1989 to 1990, he was an exchange researcher at Philips Central Research Laboratory, Eindhoven, the Netherlands, where he worked in the areas of high-mobility twodimensional-hole gas in Si/SiGe modulation-doped structures. He has also been a concurrent lecturer at Waseda University (1992-1995 and 1998-1999), Tokyo Institute of Technology (1996-1998, 2010-2011), Nagoya Institute of Technology (2002), and Hosei University (2000-present ).

Since 2013, he has been a visiting professor at Hosei University. He has authored or co-authored more than 100 research papers in international journals and conference proceedings. Dr. Mishima is a fellow-grade member of the Japan Society of Applied Physics. He has served as an Organizer of SOTAPOCS (1994-1996) and a Subcommittee Member of the ISCS’98, ICCBE-7, and the Research Board of the IEE Japan (2003-2013).

Naoki Kaneda received an M.S. degree from Nagoya University, Japan, in 1996.

In 1996, he joined the Advanced Research Center, Hitachi Cable, Ltd., Ibaraki, Japan (which was merged into Hitachi Metals Ltd. in 2013.) He started his work on crystal growth of compound semiconductors. From 1998 to 2004, he was engaged in the development of AlGaInP epitaxial layers for high-brightness light-emitting diodes and high-power laser diodes. After that, he moved to development of MOVPE technology for GaN devices. Recently, his research has focused on development of high-quality GaN epitaxial layers for power-electronics applications. Mr. Kaneda is a member of the Japan Society of Applied Physics.

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