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(jj II < fill i Jfl "TH -1 ©HT 1 - t_W JT |T1 I r^g) FORWARD I-V CHARACRERISTICS SIMULATION OF SILICON CARBIDE SCHOTTKY DIODE Potapov Leonid Alexeevich, Krayushkina Elena Yurevna, Rybalka Sergey Borisovich, Demidov Andrey Alexandrovich, Shishkina Olga Anatolevich, Khvostov Vacheslav Alekseevich, Malakhanov Alexey Alexeevich, Bryansk state technical university, Bryansk, Russia E-mail: kineticx@bk.ru
Abstract. Current-voltage (I-V) characteristics of 4H-SiC Schottky diode based on thermionic emission theory and simulation in the physical analytical models based on Poisson's equation, drift-diffusion and continuity equations has been calculated and simulated. It is established that forward current-voltage characteristics by proposed the simulation model of Schottky diode corresponds to the "non-ideal" diode in terms of the thermionic emission theory with Schottky barrier height ^=1.4 eV with ideality factor of Schottky diode «=1.37.
Keywords: diode, Schottky, silicon carbide, thermionic emission.
Introduction
Studying of silicon carbide (SiC) as material for semiconductor electronics has been made at first in Leningrad (St. Petersburg) by the O.V. Losev's at the A.F. Ioffe Institute at the beginning of the 1930s. Now silicon carbide represents an excellent candidate for high-temperature electronic device applications because of its high breakdown voltage, low series resistance, and stability under harsh chemical and high temperature conditions. SiC Schottky diodes are of special interest since these unipolar devices avoid reverse recovery effects of bipolar devices, thereby offering higher frequency operation.
It is very perspective silicon carbide type material for manufacturing of Schottky diodes is 4H-SiC-type which is more preferable to power semiconductors electronics before high mobility of electrons in this silicon carbide type. In particular, similar 4 H-SiC Schottky diodes for power electronics were made in A.F. Ioffe Institute and in future may be produced by the «GROUP KREMNY L» company (Bryansk). It is
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obviously that for development of component base on the base of SiC studying and optimisation of such important device as Schottky diode it is necessary and therefore in the present work simulation of current-voltage (I-V) characteristics in 4^-SiC Schottky diode with Ni Schottky contact has been made.
Materials and methods
For calculation current-voltage (I-V) characteristics in 4^-SiC Schottky diode was applied of the thermionic emission theory which taking into account of the electron-phonon interaction, quantum-mechanical tunneling through barrier and reduction of barrier height under influence of image force effect [1]. For simulation were used the physical analytical models to solve transport equations and numerical models based on Poisson's equation together with drift-diffusion and continuity equations.
Results and discussion
According to the thermionic emission classical theory [1] current-voltage (I-V) characteristics dependence of forward current I from the voltage V for semiconductors can be described by the following equation:
qV qV
I = Ioe"kBT (1 - ek*T ) (1)
where Io - the saturation current [A]; T - the absolute temperature, [K]; V - the voltage, [V]; q - the elementary charge, [C]; kB -Boltzmann constant, [J/K]; n - the Schottky diode ideality factor:
Vb
Io = SA*T2e kBT (2)
where S - the area of Schottky contact, [cm ]; A* - the Richardson's effective constant, [A/(K xcm )]; T - the absolute temperature, [K]; yB - the effective Schottky barrier height, [eV]; kB - the Boltzmann constant, [J/K].
For simulation model of current-voltage (I-V) characteristics has been solved electrostatic Poisson's equation together with drift-diffusion and continuity equations. In particular, we assumed that in within the framework of Fermi-Dirac statistics can be approximated by the Maxwell-Boltzmann distribution and mobility and diffusion coefficients can be described by Einstein's equations. Finally the system of the equations for simulation model of Schottky diode must be given by expressions of the form [1]:
v(sr vV )= q(n - p - ND) (3)
1 v- j =-v
Jn n
q
1 v-j =-V
"j p p
q
Jn = nMnVEc + VnkBTlVn J'p = PMpVEV - VpkBTlVP Ec =-q(V + z) Ev =-q(V + Z + Eg )
(4)
(5)
(6)
(7)
(8) (9)
where sr = 9.7 - the dielectric relative permeability, n, p - the concentration of electron's and holes, N+D= 1016 cm-3 - the donor impurity concentration, * N = 1.7 -1019 cm-3 - the density of state in conduction band, NF = 2.5 -1019 cm-3 - the • density of state in valence band, Eg = 3.23 eV - the band-gap energy of 4^-SiC, jn and jp - the electron's and holes electric current density, % = 3.7 V - the electron affinity, nn= 800 cm2/(V - s) - the electron mobility, = 115 cm2/(V - s) -the
mobility of holes according to the data [2, 3]. Boundary conditions between Ni metal contact and 4^-SiC layer and on a lateral surface of the cylinder were used as standard for Schottky diode [1].
Fig. 1 Forward I-V characteristics of the Ni/4H-SiC Schottky diode
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For forward I-V characteristics calculation in the framework of the thermionic emission theory by equations (1) and (2) were used the data: A *=34.8 A/(K xcm ) -the effective Richardson's constant, T=298 K - the absolute temperature, yB=1.4 eV -the effective height of Schottky barrier in accordance with data from [3-5].
Model Schottky diode was presented as cylinder with radius R=2.54 mm consisting of the 4^-SiC layer of n-type with height h=254 mm, the Schottky metal contact from Ni (anode) and the metal ohmic contact (cathode). The results of calculations in terms of the thermionic emission theory base on equations (1)-(2) and numerical simulations of computer model base on the equations (3)-(9) in MathCAD are shown in Figure 1.
As can be seen from Fig. 1, results of numerical simulation of Schottky diode in accordance with computer's model well describe the forward I-V characteristics for Ni/4H-SiC Schottky diode which were calculated by thermionic emission theory. Because of this, comparison of the theoretical analysis and Schottky diode computer model it is established that the Schottky barrier height equals ~1.4 eV with ideality factor of Schottky diode n equals 1.37 that approximately corresponds to experimentally obtained value for the 4^-SiC-diode with Ni Schottky contact [2-5].
Conclusions
The current-voltage (I-V) characteristics in 4^-SiC Schottky diode with Ni Schottky contact has been calculated and simulated. It is established that forward current-voltage characteristics in terms of the Schottky diode simulation model corresponds to the "non-ideal" Schottky diode describes in framework of the thermionic emission theory with effective Schottky barrier height ^B=1.4 eV and with ideality factor of Schottky diode n=1.37.
This work was supported by the Russian Ministry of Education (Grant No. 02.G25.31.0201).
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3. Akira Itoh, Tsunenobu Kimoto, Hiroyuki Matsunami. High performance of highvoltage 4H-Sic Schottky barrier diodes // IEEE Electoron Device Lettters. - 1995. -Vol. 16. - No. 6. - P. 280-282.
4. Potapov A.S., Ivanov P.A., Samsonova T.P. Effect of annealing on the effective barrier height and ideality factor of nickel Schottky contacts to 4^-SiC // Semiconductors. - 2009. - Vol. 43. - No. 5. - P. 612-616.
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5. Zhao J.H., Sheng K. and Lebron-Velilla R.C. Silicon Carbide Schottky Barrier Diode // in "SiC materials and devises", ed. by M. Shur, S. Rumyantsev and M. Levinshtein, Singapore: World Scientific, 2006, Vol. 1. - P. 117-162.
