D.C. CHARACTERISTICS OF SiC POWER SCHOTTKY DIODES MODELLING IN SPICE Janusz Zar^bski, Jacek D^browski Gdynia Maritime University, Department of Marine Electronics Key words: Silicon Carbide (SiC), Schottky Barrier Diodes (SBDs), modelling, self-heating, electrothermal macromodel, SPICE Abstract: In this paper the problem of SPICE modelling of the class of silicon-carbide (SIC) Schottky diodes with thermal effects (self-heating) taken into account is considered. Since April 2001 the SiC Schottky diodes made by Infineon Technologies have been commercially attainable. In the paper the SPICE electrothermal (including self-heating) macromodel of Infineon Technologies SIC Schottky diode is presented and in detail investigated. The considered macromodel has been verified experimentally. The silicon-carbide SDP04S60 rectifier has been tested. The nonisothermal characteristics obtained from measurements and SPICE calculations of SDP04S60 diode are compared. Due to the unacceptably large differences between measurements and calculations, some modifications of the macromodel have been proposed. DC karakteristike močnostnih SiC Schottky diod -modeliranje s programom SPICE Kjučne besede: Silicijev karbid ( SiC ), Schottky diode, modeliranje, pregrevanje, elektrotermični model, SPICE Izvleček: V prispevku obravnavamo probleme pri modeliranju SIC Sohottkyjevih diod s programom SPICE z upoštevanjem termičnih efektov. Od aprila leta 2001 so SIC Schottky diode izdelane pri podjetju Infineon Technologies tudi komercialno dosegljive. Tako v prispevku predstavimo in natančno obravnavamo SPICE elektrotermični model prav teh diod. Predastavljeni model smo preverili tudi eksperimentalno in sicer smo testirali SIC diodo z oznako SDP04S60. Primerjali smo izmerjene in izračunane neizotermične karakteristike. Zaradi velikih razlik med meritvami in napovedmi, predlagamo določene spremembe pri parametrih makromodela. 1. Introduction The silicon carbide (SiC) is a great promising semiconductor material for manufacturing of power devices. It occurs in over 170 polytypes, tlie most common of winicli are cubic 3C, iiexagonal 4H and 6H structures. A number of most important physical aspects of SiC compared to other semiconductors one can find in the literature, e.g. /1,2,3/. As results from the cited papers, silicon carbide has an order of magnitude higher breakdow/n electric field and an electron mobility only about 20% lower (for 4H-SiC) than silicon. A high breakdown electric field allows to design the SiC power devices with 10-times thinner and about 100-times higher dopend voltage blocking layers. Smaller dimensions of SiC material result in higher device switching frequency. Nowadays, a lot of SiC devices, as transistors, diodes, thy-ristors, LED's, thermistors etc. are manufactured and investigated in laboratories /4,5/. In the case of the power SiC devices a high breakdown voltage is needed. So far, the SIC power diodes, have been the class of semiconductor devices having the greatest values of the breakdown voltage equal to 10 kV for Schottky diodes /6/ and 19 kV for PIN diodes /7/. Since 2001 SIC Schottky diodes made by Infineon Technologies have been available in the market /8/. A very important feature of all semiconductor devices, including SiC SBDs, is a strong influence of the temperature on their characteristics. Due to the self-heating resulting from the change of the device dissipated power into the heat in the case of nonideai cooling conditions, the junction temperature (often much greater than the ambient one) affects the device characteristics, called the nonisothermal ones. In order to take into account the self-heating, the models of the special kind, called the electrothermal models (ETM) have to be used for the device simulations. Infineon Technologies, on their web-side /9/, offers the SIC Schottky's electrothermal macromodel for SPICE, indicated as Level 3. In the paper the Level 3 Infineon's SPICE macromodel is presented, in detail discussed and experimentally verified. The SDP04S60 diode: 4A/600V, has been chosen for investigations, instead of 6A/600V SIC Schottky diode (SDP06S60) considered in /10/. Due to the fact, that obtained results between measurements and calculations differ from each other significantly, therefore some modifications of the macromodel were introduced. 2. The Macromodel Form of The SIC Schottky Diode To derive the electrothermal macromodel of the considered device, the following dependencies have to be used /11/: the current-voltage-temperature dependence (isothermal model). the dependence of the inside (junction) temperature Tj on the electrical power dissipated in the device, along with the dependence of this electrical power on the device terminal currents and voltages (thermal model). The structure of such a macromodel is shown in Fig. 1. Fig. 1. The structure of the electrothermal macromodel of the SIC Schottky diode Next, the detailed form of the isothermal model and the thermal model, forming the considered electrothermal macromodel are presented and discussed. The network form of the isothermal model of the SiC Schottky diodes is presented in Fig. 2. /9/. ANODE o CATHODE o GSCHOTTKY ERSCHOTTKY VIA Fig. 2. The network form of the isothermal model of the SiC Schottky diode As seen, the model is composed of three elements: the controlled current GSCHOTTKY source, the controlled voltage ERSCHOTTKY source and the independent source VIA of the efficiency equal to zero. Due to the d.c. dependencies considered here, the wire inductance and junction capacitance are not taken into account in further considerations. The control current source GSCHOTTKY is of the efficiency exp V-q k-in+T) -1 (11 where T - the analysis temperature (7 TEMP) in Celsius degrees, V - voltage between ANODE and MID nodes, Ibw - reverse (saturation) current, q - electron charge, k -Boltzmann's constant. To - the reference temperature. The saturation current is expressed by the formula ^ -9-<\>sic ^ k\T,+T) K (2) where AREA - relative device area, Ao - Richardson's constant, (psic - metal-semiconductor barrier height. In Eq.(2) the factor K models the lowering effect existing in the reverse range of the Schottky diode operation which is given by the following expression 1 + exp k-iT„ + T) , s , a, ■ EFLD.u^ AA + AB-(j--ni)+ AC-{r-nij + —-^ EFLD / ,,dt\ (3) where b, AA, AB, AC, a-i and VPTare the model parameters. The description of the electric field {EFLD) dependent on the junction reverse voltage is divided into three ranges according to the value of the anode-cathode voltage, up to the pattern (4), where V denotes the voltage on the diode, EPT denotes the critical electrical field, whereas x and g are the model parameters. /./M/Tdenotesthe SPICE standard function. EFLD = EPT-Y V VPT - + 1 if V>0 if -V VPT (4) In turn, the voltage source ERSCHOTTKY controlled by the current of VIA source models the influence of the diode series resistance on the i(u) characteristics. Thus ^ERS ~ ^(VJA) ' ^S(r) _ ^(yiA) ' ^OSQ ~ AREA-V]- To+T Tr, (5) where Rsm is the series resistance dependent on the temperature, Rosa is the specific series resistance at the reference temperature To, whereas I(via) is the zero voltage source current and x are the model parameters. The isothermal model parameter values of the diode are collected in Table 1 /9/. The thermal model of the considered diode has been presented in the network form (Cauer leader) consisting of four resistors (RTHD) and capacitances (CTHD), representing the junction-to-case thermal impedance of the diode (Fig. 3.) /9/. The values of those elements are given in Table 2. The nodes TJ and TCASE represent the junction and the case temperatures respectively, whereas the potential value of the node TREF representing the ambient temperature, can be fixed by the efficiency of the voltage source VREF. This form of the thermal model is not acceptable by SPICE due to the fact, that the TREF node has not d.c. connection with the other one. Therefore, in the case of the ideal conditions of the case cooling, the nodes TREF and TCASE have to be shorted. Otherwise, between the nodes TCASE and TREF, the RC network of the Cauer leader, representing the phenomena of heat removing from the case to the ambient (e.g. by means of a heat-sink), has to be added. Table 1 The parameters values of the isothermal model of the SDP04S60 diode Parameter Value q[C] 1.602 • 10"'^ k [J/K] 1.38 • nm 273 Ao [A • cm"^ • K'^] 110 1.3 AA, AB, AC -1.5, -12.95 •10"\ 91-10"® «1 3.8 Roso [mQ • cm^] 0.9 VPT [V] 400 EPT[\lcm\ 1.05 • 10"^ ß 1.49 ■ 10'^ 2.811 -10^ Y 5.33-10^ X 1.5 AREA 0.0116 V: 0.75 TJQ tdi RTHDO CTHD1 RTHD1 CTHD2■ td2 td3 TCASE -<-1 RTHD2 CTHD3' RC GPOW/f TREF . (^VREF CRGPOW Fig. 3. The general form of the thermal model of the SIC SDP04S60 Schottky diode Table 2 The parameter values of the thermal model of the SDP04S60 diode Parameter Unit Value RTHDO [K/W] 1.756 RTHDI 1.717 RTHD2 0.545 RTHD3 0.094 CTHDO [J/K] 5.243 • 10"^ CTHDl 1.076 • 10"^ CTHD2 0.044 CTHD3 2.025 RGPOW ["] 100• 10® CRGPOW [F] 10 • 10"'' The controlled current source GPOW represents the real power dissipated in the diode. Its efficiency is described by ^GPOW ~ ^BS ■ Vf^^oDE,CATHODE) ) ^ > 25nS 0 if t < 25ns (6) where I(via) is the total current flowing through the diode, V(ANODE,CATHODE) is the voltage on the diode, whereas ABS is the standard SPICE function denoting the absolute value of any function. In the case of the analysis at the steady-state the simplified, shown in Fig. 4, thermal network is used. In this figure the resistance /?i denotes the junction-to-case thermal resistance represented by the sum of RTHDi (i = 0+3) and equal to 4.112 K/W, whereas the resistance R2 represents the case-to-ambient resistance of the value depending on the case cooling conditions. Note, that the thermal model can be used in d.c. analysis, if the time limitations in Eq.(6) are eliminated. ?TJ Ri^i'^THD, TCASE Ri + R2 - Rthi-i TREF 0 GPOW VPT/5 ^LS(VPT/5) = 10.87 ^LS(vpm) = 7.55 4. Conclusions In the paper the electrothermal macromodel of the SIC Schottky diode has been investigated and verified experimentally. As was proved, the original macromodel is of poor accuracy, whereas after the author's modifications the characteristics obtained from measurements and calculations fit very well. Note, thatto perform the simulations the value of the thermal resistance from the case to the sourround-ing had to be additionally measured. Acknowledgments This work is supported by the Polish State Committee for Scientific Research in 2005-2006, as a research project No. 3T11B08229. References /1 / J.B. Casady, and R.W. Johnson, "Status of Silicon Carbide (SiC) as a Wide-Bandgap Semiconductor for High-Temperature Applications: a Review", Solid-State Electronics, Vol. 39, No. 10, pp. 1409-1422, 1996. /2/ http://www.grc.nasa.gov/www.sic/sicreview.html: P.G. Neudeck, "Recent Progress in Silicon Carbide Semiconductor Electronics", 1995. /3/ A. Elasser, andT.P. Chow, "Silicon Carbide Benefits and Advantages for Power Electronics Circuits and Systems", Proceedings of the IEEE, Vol. 90, No 6, June 2002. /4/ C.M. Johnson, "Recent Progress and Current Issues in SiC Semiconductor Devices for Power Applications", lEE Proc.-Circ. Dev. Sysf.,Vol. 148, No 2, pp. 101-108, April 2001. /5/ J. A. Cooper, and A. Agarwai, "SIC Power-Switching Devices -the Second Electronics Revolution?", Proc. of the IEEE, Vol. 90, No 6, pp. 956-968, June 2002. /6/ www.ecn.purdue.edu/WBG/DataBank, "Best Reported WBG Power Device Performance", February 2003. /7/ Y. Sugawara, D. Takayama, K. Asano, R. Singh, J. Palmour, and T. Hayashi, "12-19kV 4H-SiC Pin Diodes with Low Power Loss", International Symposium on Power Semiconductor Devices &iCs, Osaka 2001. /8/ I. Zverev, M. Treu, H. Kapeis, O, Hellmund, and R. Rupp, "SiC Schottky Rectifiers: Performance, Reliability and Key Applications", EPE 2001 Conf. Proc., Graz, August 2001. /9/ http://www.infineon.com: Psice_SiC_L3_2.zip. /10/ J. Zar^bski, and J. D^browski, "Simulations of Nonisothermal D.C. Characteristics of the SiC Schottky Diode with the Use of SPICE", Ivlixed Design of Integrated Circuits and Systems MIXDES, Szczecin, June 2004, pp. 441-444. /11/ J.Zarijbski, "Modelling, Simulationsand Measurements of Electrothermal Course, in Semiconductor Devices and Electronic Circuits" (in Polish), Maritime Academy in Gdynia, 1996. /12/ J. Zar^bski, and J. D^browski, "Calculations and Measurements of the SIC Schottky Diode", IC-SPET0V4 (in Polish), Nidzica, May 2004, pp. 363-366. Prof Janusz ZarQbskI; fvl.Sc. Jacek D^browskl Gdynia Maritime University, Department of Marine Electronics Morska 83, 81-225 Gdynia, POLAND, Tel. ++48 58 6901599, ++48 58 6901609, fax ++48 58 6217353 E-mail: zarebskl@am.gdynla.pt, oakjack@am.gdynla.pl