Insulated Gate Bipolar Transistor (IGBT) Modeling Using IG-Spice Chang SU Mitter, Member, IEEE, Allen R

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24 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 30, NO. 1, JANUARYIEBRUARY 1993 Insulated Gate Bipolar Transistor (IGBT) Modeling Using IG-Spice Chang SU Mitter, Member, IEEE, Allen R. Hefner, Senior Member, IEEE, Dan Y. Chen, Senior Member, IEEE, and Fred C. Lee, Fellow, IEEE

Abstract-A physics-based model for the Insulated Gate Bipo- p+ body region (see Fig. 1). Thus the IGBT behaves as a lar Transistor (IGBT) is implemented into the widely avail- bipolar transistor that is supplied base current by a MOSFET able circuit simulation package IG-SPICE. Based on analytical as indicated by the simplified equivalent circuit in ~i~.2. equations describing the semiconductor-physics, the model accurately describes the nonlinear junction capacitances, moving A physics-based IGBT for genera' circuit boundaries, recombination, and carrier scattering, and effectively sh-"ation has been PreViOUSlY introduced l1-61 and verified predicts the device conductivity modulation. In this paper, the for representative circuit operating conditions. This model is procedure used to incorporate the model into IG-SPICE and var- based on the analytical equations describing the semiconductor ious methods necessary to ensure convergence are described. The physics. The model accurately describes the nonlinear junction effectiveness of the SPICE-based IGBT model is demonstrated by investigating the static and dynamic current sharing of paralleled capacitances, moving boundaries, recombination, and carrier IGBTs with different device model parameters. The simulation scattering, and effectively predicts the device conductivity results are verified by comparison with experimental results. modulation. Although many types of power devices exist, the semiconductor device models presently provided within most circuit simulation programs are based upon microelectronic I. INTRODUCTION devices and cannot readily be used to describe the inter- HE Insulated Gate Bipolar Transistor (IGBT) was intro- nal MOSFETs and internal bipolar transistors of the power T duced into the family of power devices to overcome the devices. high on-state loss of power MOSFETs while maintaining the The Simulation Program with Integrated Circuit Emphasis simple gate drive requirements of MOSFETs. The IGBT com- (SPICE circuit simulator) is used worldwide. It is appropriate bines both the bipolar and MOSFET structures and posseses to implement Hefner's model in a SPICE-based simulator to the best features of both device types. Because the IGBT has make the model available to many circuit designers. However, a low power gate drive requirement, a high current density the physicsbased Hefner's model [3] consists of many nonlin- capability, and a high switching speed, it is preferred over ear equations that must be implemented into the simulator due other devices in many highpower applications. to the complex physical mechanisms that govern the behavior A schematic representation of a single cell of an n-channel of IGBTs. Although SPICE provides a limited capability for IGBT is shown in Fig. 1, where the arrows indicated by Ih implementing equations via the use of controlled dependent and I, show the direction of the hole current and the electron sources, this capability is not sufficient for implementing com- current, respectively. The IGBT structure is similar to that of plicated equations. Although the PSPICE simulator (Personal a Vertical Double diffused MOSFET (VDMOSFET) with the computer SPICE) allows more flexibility by providing the user exception that a p-type, heavily doped substrate replaces the with the capability to implement equations through the use of a wtype drain contact of the conventional VDMOSFET. The supplemental program called Behavioral Modeling [7], it does effect of this extra y-type layer is to act as an emitter to inject not allow for conditional commands (ie., IF, THEN, ELSE). minority carriers (holes) into the main conducting region of On the other hand, the IG-SPICE simulator (Interactive Graph- the device, reducing its resistance and decreasing the onstate ics SPICE) overcomes these limitations by allowing the user voltage drop of the device. These excess minority carriers to implement equations using controlled dependent sources drift and diffuse through the base and are collected by the and by providing the user with programming capability to Paper JF 20-94, approved by the Power Electronics Devices and Compo- describe these nonlinear controlled sources [8]. Therefore, the nents Committee of the IEEE Industry Applications Society for presentation IG-SPICE circuit simulator is used in this work to implement at the 1991 Industry Applications Society Annual Meeting, Dearbom, MI, Hefner's model. September 28-October 4. This work was partially supported by Defense Advance Research Project Agency and U. S. David Taylor, Naval Ship R&D The purpose of this paper is to describe the implementation Center. Manuscript released for publication May I I, 1993. of the physics-based IGBT model into the commercially avail- C. S. Mitter, D. Y. Chen, and F. C. Lee are with the Virginia Power able circuit simulator IG-SPICE. The techniques used to ensure Electronics Center, Bradly Department of Electrical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 2406 I. convergence of the IG-SPICE model, and the applicability of A. R. Hefner is with the Semiconductor Electronics Division, National these techniques to other power semiconductor devices are Institute of Standards and Tech., Gaithersburg, MD 20899. also reviewed. Furthermore, the techniques used to ensure Contribution of the National Institute of Standards and Technology not subject to copyright. convergence in IG-SPICE are also applicable to other SPICE- IEEE Log Number 92 13428. based simulators, because all SPICE-based programs use the

0093-9994/94$04.00 0 1994 IEEE ~ ,.

MI'ITER et ai.: INSULATED GATE BIPOLAR TRANSISTOR (IGBT) MODELING USING IG-SPICE 25

p+ anode contact for the IGBT. Thus the MOSFET portion of the model behaves similarly to a VDMOSFET with the exception that the lightly doped epitaxial layer of the IGBT is considered as the conductivity-modulated base resistance, Rb, of the bipolar transistor. In addition, the drain-source and the gate-drain depletion capacitances overlap with the base- n- Epitnxbl luys "9ipolar" base\'h collector depletion capacitance of the bipolar transistor, and hence this capacitance is only included in the MOSFET. The "Bipolar" emin details of the equivalent circuit are discussed below. r-1 p+ Sub*nte I n+ Substrate lceThod( for MMOYET A. VDMOSFET Fig. 1. A single 71-channel IGBT cell. The MOSFET components of the equivalent circuit are defined as follows: C,, = gatesource capacitance. CO,, = gate oxide capacitance of the source overlap, C, = source metallization capacitance. L -.7;5j;plcgd = gatedrain feedback capacitance (Miller Capacitance).

1 n (W) 'T Cozd = gatedrain overlap oxide capacitance. Anode cgdJ = gatedrain overlap depletion capacitance, and Fig. 2. Simplified IGBT equivalent circuit Cdsj = drain-source depletion Capacitance.

9 Cathode QGate where the MOSFET symbol represents the MOSFET channel current, Imos.The VDMOSFET gate-source capacitance C,, consists of the parallel combination of the gate oxide capacitance of the source overlap CO,,, and the source metallization capacitance C, . The VDMOSFET gate-drain feedback capacitance (or Miller capacitance) consists of the series combination of the gatedrain overlap oxide capacitance Cozd, and the gate-drain overlap depletion capacitance cqdj. The VDMOSFET drain-source capacitance Cdsj consists of the depletion capacitance of the drain-source junction. To describe IGBTs made with other MOSFET structures, only the components of Fig. 2 associated with the MOSFET portion of the device, need to be changed.

B. Bipolar Transistor

Fig. 3. Detailed IGBT equivalent circuit components superimposed on a The bipolar transistor components of the equivalent circuit schematic of one cell of an n-channel IGBT. are defined as follows: C,,, = collector-emitter redistribution capacitance. same numerical algorithms. The effectiveness of the IG-SPICE Rb = conductivity-modulated base resistance, IGBT model developed in this paper is demonstrated by examining the static and dynamic current sharing of paralleled C&d = emitter-base diffusion capacitance, and IGBTs. C,,, = emitter-base depletion capacitance, where the BJT symbol represents the charge-controlled com- 11. IGBT PHYSICALMODEL ponents of collector and base current. The collector-emitter Figure 3 shows the detailed IGBT equivalent circuit super- redistribution capacitance C,,, is a result of the nonqua- imposed on one cell of an n-channel IGBT. In Fig. 3, the sistatic behavior of the bipolar transistor base charge for the components connected between the emitter (e),base (b), and changing base-collector depletion width. This capacitance is collector (c) nodes are associated with the bipolar transistor, orders of magnitude larger than the depletion capacitances and the components connected between the drain (d), gate, and dominates the effective output capacitance of the IGBT and source (s) nodes are associated with the VDMOSFET. As during turn-off [ 11. The bipolar transistor also contributes a mentioned earlier, the structure of the IGBT is similar to that conductivity-modulated base resistance Rb, an emitter-base of the power VDMOSFET, with the exception that the nf diffusion capacitance Cebd, and an emitter-base depletion drain contact of the conventional MOSFET is replaced by the capacitance C&l. 26 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 30, NO. 1, IANUARYIFEBRUAUY 1993

TABLE I IGBT CURRENTSOURCES

f0 for V,, < VT

111. IG-SPICE IGBT MODELIMPLEMENTATION Law) are satisfied for the entire circuit using the controlled In this section, the requirements for implementing model current and voltage source functions of the IGBT. Thus each equations into IG-SPICE, and the procedures used to im- of the model equations necessary to describe the behavior of plement the IGBT model into IG-SPICE are described. The the IGBT [3] must be implemented as IG-SPICE controlled expressions describing the components of the IGBT equivalent sources as described below [SI. circuit are given in Tables I and 11. For detailed discussions of these equations, refer to [6]. These equations are separated A. Implementing General Device Models Into IG-SPICE into two categories which describe the anode voltage and SPICE users are constantly faced with the inability to the anode current of the IGBT. These equations are then analyze circuits that contain devices that are not well described implemented as an interconnection of controlled-current and by the SPICE semiconductor models. This can be overcome voltage sources that depend upon node voltages or branch by the use of the programming capabilities of IG-SPICE. The currents. When the IGBT model is included in a circuit, the IG-SPICE simulation program is an extended version of the simulator iterates the node voltages and branch currents until SPICE-2 computer-aided design and analysis program. IG- KVL (Kirchoff's Voltage Law) and KCL (Kirchoff's Current SPICE is designed to be more graphics-oriented and provides MITTER et nl.: INSULATED GATE BIWLAR TRANSISTOR (IGBT)MODELING USING IG-SPICE

0 13 cl(rr) 14 17 K U--A Flnw he lthl 1r +

Fig. 4. IG-SPICE IGBT equivalent circuit. the user with programming capability. This programming and a list of constant model parameters) and the user-defined capability of IG-SPICE enables the user to implement general model subroutine (which computes the actual output voltage or device models without having to add additional components current values based on the input lists). IG-SPICE requires that such as diodes or transistors to emulate the device model the inputs of the controlling variables be of only one source equations. The ability to directly implement model equations type: either all voltage or all current. Therefore, in the cases as IG-SPICE controlled sources results in more computation- where the output is dependent upon both current and voltage ally efficient simulations without the problems associated with type variables, the controlling variables of one of the types convergence. must be transformed into the other type. 1) IG-SPICE user defined device models: When implement- 2) ZG-SPICE controlled sources: The IG-SPICE controlled ing model equations into the IG-SPICE user-defined model sources are realized using the polynomial controlled sources of subroutine, the following formalities need to be considered in SPICE, which depend upon controlling variables. For example, detail: the general input format for a voltage-controlled current source 1. The model must be formulated as an interconnection in all SPICE programs is as follows: of controlled current and voltage sources which depend upon controlling currents or voltages, but not both GXXX(NS+)(NS-), Poly((ND))((NCl+), currents and voltages. (NCl-))((NC2+), (NCZ-)). . . (PO,Pl,.. .), 2. The variables must be normalized so that each variable that is solved for by the simulator has a comparable, where (NS+) and (NS-) are the output connection nodes of absolute error tolerance. the controlled source, Poly((ND)) specifies the dimension of 3. The independent variables must be converted into the the polynomial as ND, and PO, P1 ... are the polynomial current and voltage types. coefficients. For the voltage-controlled sources, the nodes 4. In general, the partial derivatives of the expressions for (NCZ+) and (NCZ-) specify the positive and negative con- the controlled sources with respect to the controlling nections of the controlling voltage. For the current-controlled variables must be evaluated. sources, the controlling voltage pair is replaced by the name The programming capability of IG-SPICE is made possible of the null voltage source (VSx) which is specified as a by the use of dependent controlled sources where the equa- current probe. The current probe statements have the form: tions describing the controlled sources are implemented using VSx (NS+),(NS-) OProbe, where the nodes (NS+), and the user-defined model subroutine. There are four types of (NS-) are introduced in the controlling current branch and controlled sources in the IG-SPICE simulation program: have zero voltage between them. However, when the programming capability of IG-SPICE Voltage-Controlled Current Source (VCCS), is utilized to implement a general model expression, the Voltage-Controlled Voltage Sources (VCVS), polynomial coefficient values are not used in the input field. Current-Controlled Current Sources (CCCS), and Instead, the program function name followed by the sequence Current-Controlled Voltage Sources (CCVS). of data are specified. This data is passed to the user-defined model subroutine to determine the values of the polynomial In implementing these controlled sources into the user-defined coefficients. An example of the input field when utilizing the model subroutine, the user must follow a particular format programming capability of IG-SPICE is: in order for the data to be passed properly between the IG- SPICE input file (which provides a list of voltages or currents Glmos 7, 60 POLY(2) (30, 60) (2, 60) lmos(Vt = 5.0). 28 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 30, NO. 1, JANUARYIFEBRUARY 1993

TABLE I1 the partial derivatives into the model subroutines, let the IGBT ANODEVOLTAGE variable Y be an output (dependent source function), and let X1, X2,.. . Xn be the input variables (controlling sources). 1lpC= [ xi 1n(1+ a2 (33-291 laI The source functions then take the form:

Y = F(X1,X2,. . . Xn) (1) where F is the model equation that must be implemented to describe the controlled source. In general, IG-SPICE controlled source functions must be expressed in the form of a polynomial expression: Y = CO+ c1.xl+ c2 .x2 + . . . (2) The advantage of the IG-SPICE user-defined controlled sources is that the coefficients need not be constants, so that general expressions for the source functions containing conditional commands can be implemented. In IG-SPICE user- defined controlled sources, the coefficients of the polynomial expression represent the partial derivatives of the output source function with respect to the input controlling variables:

c1= -,dY C2 = -,...dY Cn = -ay (3) ax1 ax2 aXn The variable CO is then calculated as follows:

CO= Y - C1 .X1- C2.X2- . . .Cn.Xn (4) so that the sum of the terms of the polynomial eq. (2) will be equal to the source function Y. The values of the bias-dependent coefficients calculated in the user-defined controlled source function are returned to the IG-SPICE controlled source, which is then interpreted just as the generic SPICE polynomial controlled source function. 4) Implementing time derivatives of controlling variables: Another very important feature of the IG-SPICE program is the ability to save the state of the system variables between time steps during the transient analysis. The values of the previous state can be retrieved within the user-defined model subroutine to implement complicated state equations which require the time rate-of-change of the controlling variable. Basically, the time rate-of-change of a controlling current or voltage is calculated in a differential manner, using the variable at the previous time step: dV V-V‘ Glmos is the name of the voltage-controlled current source --- (5) (VCCS) in which the current enters through the positive node 7 dt at ’ and exits through the negative node 60. POLY(2) specifies that where V’ is the value of the variable V at the previous time the dimension of the number of controlling voltages is 2, where step, and At is the time-step size. The detailed explanation the node pairs (30, 60) and (2, 60) specify the controlling of the procedure for accessing the value of variables at the voltages. Imos is the name of the output function within the previous time steps are discussed in the IG-SPICE users user-defined model subroutine, and Vt is an example of a data manual [8]. value which is passed to the function Imos. 3) Implementing partial derivatives of model functions: In B. Implementing IGBT Model Equations addition to evaluating the source function, the user-defined The analytical IGBT model given in Tables I and I1 is suit- model subroutine must also evaluate the partial derivative of able for incorporation into general purpose circuit simulators the source functions with respect to each of the controlling [3-51. These equations are simplified expressions representing variables. These partial derivatives are required by the nu- the functions of the equivalent circuit as shown in Fig. 3. merical algorithms of the SPICE-based simulators to facilitate The circuit in Fig. 4 is an IG-SPICE IGBT equivalent circuit convergence. To describe the procedure for implementing representation of Hefner’s analytical model which shows the MI'ITER er al.: INSULATED GATE BIPOLAR TRANSISTOR (IGBT) MODELING USING IG-SPICE 29 interconnection of the various controlled sources required to implement the equations in Tables I and 11. The model is implemented using various controlled sources that are dependent on node voltages or branch currents (but not both the currents and voltages) as required by IG-SPICE. In the remainder of this section the procedures used to convert the Fig. 5. Collector hole current circuit equations which describe the IGBT into equivalent IG-SPICE current and voltage sources are discussed. The methods used to moving boundary condition [ 11. This third term is represented ensure convergence of the IG-SPICE model are also discussed. as the collector-emitter redistribution capacitance C,,, in Fig. 1) MOSFET: As stated above, the MOSFET current supplies 3, which is proportional to the instantaneous change in the the electron current to the base of the bipolar transistor. base, because this term depends on the time rate-of-change of This electron current, In(W),consists of both the static and the base-collector voltage. dynamic currents that flow through the MOSFET. Thus the Equation (8) depends upon current type, voltage type, expression describing the electron current at the collector edge and charge type controlling variables (i.e., IT,Q, Vbc). As of neutral base is expressed as the sum of the MOSFET previously mentioned, the controlling variables of the source channel current and the displacement currents through the functions need to be of one type: either current or voltage. drain-source and gate-drain capacitances [3]: To accomplish this, eq. (8) is separated into three different dependent sources: FIpa, GIpb, and GIpc, which are paralleled to obtain the total bipolar transistor hole current Ip(W).This paralleling method, which reduces the number of controlling where lmos is given in terms of the system variables of the source type conversions, ensures better convergence. The IGBT as shown in Table I. collector hole current portion of Fig. 4 is shown in Fig. 5. In the IG-SPICE IGBT equivalent circuit model, this elec- The first term in eq. (8) is represented as the current- tron current is decomposed into three user-defined functions: controlled current source FIpa, where IT is the total current of Imos, Icds, and Icgd.The current sources corresponding to the device which is defined as a current source probe (see Fig. these functions are indicated in Fig. 4 as: GImos, GIcgd, and 4). The second and third terms are implemented as voltage- Glcds, respectively. The MOSFET channel current of the IG- controlled current sources GIpb and GIpc, respectively, where SPICE IGBT model is described by the current source GImos, the base charge Q is represented as a node voltage. while the currents through the nonlinear capacitances (C,, 3) Bipolar transistor base charge control: The equation and Cds) are represented by the controlled sources GIcgd and describing the conservation of excess majority carrier base Glcds. These nonlinear voltage-dependent depletion capaci- charge is [6]: tances (Cgd and Cds)are indicated on Fig. 4 by the capacitor symbols with diagonal lines through them. When implementing the capacitor currents, the value of the capacitor voltage at the previous time step needs to be used where the charge Q is supplied by the electron current at (see eq. 5) to calculate the derivative of the capacitor voltage the collector edge of the base ITL(W),and is depleted by the Then the current through the capacitances can be expressed as: recombination in the base (the second term on the right-hand- dV side of the equation) and by the injection of electrons into the ic = (7) c.-dt emitter (third term on the righthandside of the equation). The The gate-source capacitance C,, of the IG-SPICE IGBT model same problem encountered with the hole current is encountered is assigned a fixed value. The feedback capacitance Cgd is in eq. (9). That is, the expression consists of several controlling voltage dependent and has a two-phase dependency: (one sources, and it would be impractical to implement the whole phase for Vd, < V,, - VT~and another for Vd, > V,, - VT~equation within a single controlled source. Therefore, this as described in Table I), where the capacitor Cozd is a fixed equation is also separated into different parts. In addition, value. The drain-source depletion capacitance is also voltage because Q is neither current nor voltage type, it must be dependent, but there is only one phase associated with this represented as a voltage or current type. capacitance. To do this, the expression describing the relationship be- 2) Bipolar transistor collector current: The hole current at tween the charge, capacitance, and voltage: Q = CV, is the collector edge of the neutral base for the moving boundary substituted into eq. (9). By using C = 1 F, the voltage on condition is expressed as 131: the 1 F capacitance (VQ)represents the base charge Q, and the carrier lifetime Thl can now be identified as a resistance. 1 b 40, C~cj Q dVbc Ip(W)= -. IT+-.- Q+-.--.- (8) As a result, the following equivalent expressions are derived: l+b (l+b) W2 3 QB dt The first term on the right-hand side of this equation results -dQ E net current through capicitance C; and (IO) dt from the coupling between the transports of electrons and Th[ = R E 1.0~- 6 : where Q/R z Ithl. (1 1) holes for ambipolar transport, the second term is the high-level injection charge control term, and the third term is a non-quasi- In addition, because the value of the resistance associated with static term which describes the redistribution of carriers for the thl is on the order of magnitude of 10V6 ohms, the values of 30 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 30, NO. 1, JANUARYEBRUARY 1993

TABLE 111 ” Inw) “ do/& ” NOMINALDEVICE PARAMETERS

7.5 ps 2 x 1014 cm-3 0.1 cm2 93 pm Fig. 6. Base charge control circuit. 6.0 x 10-14 A 0.46 A/V2 (VQ) that are solved for by the simulator are many orders of 0.95 A/V2 magnitude smaller than the other voltages in the circuit. This 4.7 v would require that the error tolerance be made very small 0.05 cm2 1.6 nF for the SPICE-based algorithm, which would result in much 0.6 nF longer convergence times. This problem can be alleviated by -0v normalizing eq. (9) [4], in order to increase the resistance 1.45 x 10” cm-3 associated with ~hlto a value on the order of 1.00. In doing 1500 cm2/V-s this, a value of capacitance 1 pF is used to convert the 450 cm2/V-a chargetype variable Q to voltage (VQe6) type variable. The 1.05 x Flcm resulting normalized charge control expression is converted to 1.428 x 1OZ0(cmVs)-’ an auxiliary circuit which is shown in the IG-SPICE IGBT 4.54 x 10’1cm-2 equivalent circuit of Fig. 4 and is repeated in Fig. 6. 1.1 x 107cm/s In the base charge control circuit of Fig. 6, the current- 0.95 x 107cm/s controlled current sources, FInw and Flne, describe the base 1.0 4.0 current and the component of electron current injected into the 0.01 Y-1 emitter, respectively. The current through the resistance Rthl, which emulates the recombination in the base is represented by the current probe Ithl. The current through the normalizing Cebj and those associated with the diffusion capacitance Cebd. capacitance Cnorm, represents the time rate-of-change of In general, a discontinuity in the partial derivatives can cause stored base charge (VQe6). convergence problems. 4) Emitter-base voltage and conductivity modulated resistance: The emitter-base voltage consists of three components IV. SIMULATIONRESULTS as shown in Fig. 3: 1) the voltage drop across the conductivity- In order to examine the effectiveness of the IG-SPICE IGBT modulated base resistance, 2) the emitter-base diffusion capac- model, tests were performed for single and paralleled IGBTs itance potential, and 3) the emitter-base depletion capacitance with an inductive load circuit (see Figs. 7 and 8). The test potential. For forward conduction, the emitter-base voltage conditions were such that the anode supply voltage was 300 was shown in [3] to be given by: V, and the gate voltage pulse amplitude was 20 V. The external load resistance RL was set so that the maximum steady-state veb = vebd(vbc, Q)+ IT ’ Rb(Vbcr Q)-t IT ’ Rs (12) current was 10 A. Table I11 shows the nominal values for where the conductivity-modulated resistance Rb, and the po- the IGBT model parameters and the semiconductor device tential drop across the emitter-base diffusion capacitance Vebd constants. are obtained in terms of instantaneous values of both Q and Vbc. For dynamic operation, the total current IT can flow A. Single IGBT through the base before sufficient charge, Q, is present to modulate the base resistance Rb; thus IGBTs can exhibit The test circuit used to simulate the inductive load operation dynamic saturation [3, 91. The emitter-base junction depletion of a single IGBT is shown in Fig. 7. The simulated and measured anode voltage and anode current results are shown capacitance Cebj is important when the emitterbase junction is reverse biased or has a small forward biases, but for large in Fig. 9. Extensive testing of the device was also performed for all of the circuit conditions presented in reference [3]. The forward bias, Cebd is dominant. Table I1 shows the equations that are needed to describe simulated results of the IG-SPICE IGBT model are nearly the behavior of the emitter-base voltage junction. To describe identical to the results obtained in [3]. the emitter-base junction voltage Veb,and the conductivity- modulated base resistance Rb, a voltage-controlled voltage B. Paralleled IGBT Operation source (VCVS) is used. Therefore, all of the current-type Paralleled IGBTs are used extensively in power modules to controlling sources are transformed into voltage-type control- obtain higher current ratings [lo, 111. However, the typical ling sources by the use of the simple resistor networks shown process variation of device model parameters within a given in the lower right-hand corner of Fig. 4. Due to the complexity device type is significant enough to result in uneven static of the Veb function, the partial derivatives must be analyzed in and dynamic current sharing if the paralleled devices were detail in order to reduce the discontinuity between the partial chosen randomly from a given lot of IGBTs of the same type. derivatives associated with the junction depletion capacitance Simulations of paralleled IGBTs are given in Figs. 10 and I1 ~

MI'ITER et al.: INSULATED GATE BIPOLAR TRANSISTOR (IGBT) MODELING USING IG-SPICE 31

L1: BOuH w3a Rg: 1K WD: SOW

=1MD T AI Fig. 7. Inductive load operation for a single IGBT.

~ l,,aA-lyyi VOG 10 - - Rq2 . . > U I N - Fig. 8. Paralleled IGBTs used in inductive load. Q + I YI 5 a 8 0 Y 0 8 e TIME (5 ps /6N) (b) Fig. IO. Paralleled IGBTs with variation in lifetime: (a) simulated (b) measured.

TIME (5p/dN)

(a) thl, threshold voltage Vt, and transconductances Kp were - varied from the nominal values. These parameters were chosen U. s:> because the normal process variation of these parameters has 8 the most impact on current sharing for parallel operation. The 5 test results for these parameter variations are shown in Figs. 10 s and 11. Figure 10 compares the (a) simulated and (b) measured anode current and voltage waveforms for paralleled IGBTs !2 where the base lifetime of one of the devices is varied from TIME (5 ps / div) the nominal values in Table I11 (ie., ~hl= 2.45 ,us for one (b) of the devices). Figure 11 compares the (a) simulated and (b) Fig. 9. Anode current and voltage waveforms for a single IGBT switched with an inductive Load. (a) simulated (b) measured. measured anode current and voltage waveforms for parallel operation of IGBTs where one of the devices has a threshold voltage and transconductance that are varied from the nominal for variation in device parameters which are representative of a values (ie., V,=3.8 V and Kpsat= 0.64 AN2 for one of the situation which would occur if the devices were not screened devices). for similar parameters and were chosen randomly. The test The anode voltage and anode current waveforms of the circuit used to examine the paralleled operation of IGBTs is paralleled IGBTs with different device base lifetimes (Fig. shown in Fig. 8. 10) are similar to those for the single device (Fig. 9), with For the paralleled operation, the gate resistances (Rgl and the exception that the static current sharing of the paralleled Rg2), load resistance RL, and the load inductance L1, were devices are uneven, and the current tail is smaller for the chosen so that the devices operated similar to the single IGBT lower lifetime device. For the devices with different MOSFET circuit of Fig. 7 when the nominal parameter values were used threshold voltages and transconductances (Fig. 1l), a turn-on for both devices. In order to accomplish this task, the values delay exists for the device with the lower transconductance, of L1, and RL were reduced by a factor of 2, and the gate and a turnoff current spike exists for the device with the larger resistor values were fixed at 1 kS2 for each device. transconductance. The turn-on delay occurs for the lower In order to observe how the dissimilar parameters affected transconductance device because it has a higher resistance than current sharing of the paralleled IGBTs, the parameters lifetime the other device until its gate voltage becomes large enough 32 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 10. NO. I. JANUARY/FEHRUARY 1993

IC-SPICE IGBT model is demonstrated by examining the effects of the normal process variation of the model parameters tyrrnt: Wll” Uolta,.: WlIU upon the static and dynamic sharing of paralleled IGBTs. The results indicate that the threshold voltage and transconductance variations tend to result in dynamic current spikes, whereas lifetime variations tend to result in uneven current tails. Both lifetime and transconductance variations result in uneven static sharing. Certain commercial equipment, instruments. or materials - ‘I (ire identijed in this paper in order to adequately specifv 12.eer 2i.aeu a&.aeu .#.mar &#.emu the experimentul procedure. Such ident$cation does not imply (a) recotnmendution or endorsement by the National Institute of Statidurds and Technology, nor does it imply that the materials or equipment identified cire necessarily the best available for the purpose.

REFERENCES

- - I I I A. R. Hefner, “An Improved Understanding for the Transient Operation U U of the Power Insulated Gate Bipolar Transistor (IGBT),” in Con$ Rrc,. >. a. -D -N IEEE Poicer Electronics Specicilistr Cor$, 1989; also in IEEE Trcins. W I- Po+r.rr Electron., vol. 5, p. 459. 1990. 5 121 A. R. Hefner, “Device Models, Circuits Simulation, and Computer- 5 U 9 3 Controlled Measurements For the IGBT,” in Proc. cffheIEEE Workshop w ori Conipiifer.s in Power E/ec.tro,iic.c. p. 233. 1990. n n [3] A. R. Hefner, “An Investigation of the Drive Circuit Requirements for 9 P the Power Insulated Gate Bipolar Transistor (IGBT),” in Con$ RK. TIME (5 p t div) IEEE Pmw E/ectronic.c Specirrlisrs Cor$, 1990; also in IEEE Truns. Poit.c,r Electron., vol. 6, p. 208. 1991. (b) [4] A. R. Hefner, “INSTANT-IGBT Network Simulation and Transient Fig. 1 I. Paralleled IGBTs with threshold voltage and transconductance Analysis Tool,” Nutionul In.\fifute of Stnnrkurds and Technology Specinl variation: (a) simulated (b) measured. Piihliccitron SP 400-88. [SI A. R. Hefner, “An Experimentally Verified IGBT Model Implemented in the Saber Circuit Simulator,” in Con$ Rrc. of IEEE Power electronic.^ that the on-state resistances of both devices are primarily S/x&r/i.\ts Conf:, I99 1 . [6] A. R. Hefner, “An Analytical Model for the Steady-State And Tran- determined by the bipolar emitter-base voltages. The turn-off \istent Characteristics of the Power Insulated-Gate Bipolar Transistor,” current spike in the higher transconductance device occurs Solid-Srcrrr Elrcrronics, vol. 31. no. 10. p. 1513 1988. [7] PSPICE Users Munucrl. MicroSim Corp.: Fairbanks Irvine, CA, July because the resistance of the low transconductance device 1989. becomes larger sooner than for the high transconductance ]XI IC-SPICE Mmud, A. B. Associates, Inc.,: Tampa, FL, 1986. device, and the inductor current is transferred to the lower 191 U. Rangan, D. Y. Chen, J. Yany. and J. Lee, “Application of Insulated Gate Bipolar Transistor to Zero Current Swilching Converters,” in IEEE resistance, high transconductance device. Trcins. Po+cer Electron. vol. 4, p. 2, 1989. I IO] M. Hideshima, T. Kuramoto. and A. Nakagawa, “I000 V, 300 A Bipolar-Mode MOSFET (IGBT) Module.” in Proc. 1988 Internutiod V. CONCLUSION .Yyniposium on Power Semiconductor DeiYcrs, pp. 80-85, 1988. ] 1 I ] R. Idor. .‘Static and Dynamic Behavior of Paralleled IGBTs,” in Conf A previously developed physics-based IGBT model is im- Rec.. IEEE Iridu.stricil Appliccitiom Soc.irty Meefing. p. I604 1990. plemented into the IC-SPICE circuit simulator. The IC-SPICE circuit simulator was chosen for this study because it provides the user with programming capability. This programming capability is essential for implementing the complex model equations that are necessary to describe the behavior of the ICBT. When implementing physics-based models into IC- SPICE: 1) the model must be formulated as an interconnection of controlled sources, 2) the variables used to formulate the model must be normalized so that each variable has a comparable absolute error tolerance, and 3) the partial Chang Su Mitter (S’91-M’92) received teh B.S. derivatives of the controlled source functions with respect to degree in electrical technology from Purdue Uni- each controlling variable must be evaluated. versity, West Lafayette, IN, and the M.S. degree in The IG-SPICE IGBT model developed in this paper is ver- electrical engineering from Virginia Tech Univer- sity, Blacksburg, in 1989 and 1991, respectively. ified by comparing the results of the model with experimental From 1989 to I991 he worked as a Research results for various circuit operating conditions. The model Assistant under Dr. Dan Y. Chen. The research performs well and describes experimental results accurately consisted of testing and modeling of power devices. He is currently working as a design engineer at for the range of static and dynamic conditions in which the Fairchild Space & Defense Corporation, German- device is intended to be operated. The effectiveness of the town, MD. MITTER rf U/.: INSULATED GATE BIPOLAR TRANSISTOR tlGBT) MODELING USING IC-SPICE 33

Allen R. Hefner Jr. (S’84-M‘84-S’X5-S’86- Fred C. Lee (S’72-M’74-SM’87-F’90) received M”%M’87-SM’93) was born in Washington D.C. the B.S. degree in electrical engineering from the on June 29, 1959. He received the B.S., M.S., and National Cheng Kung University in Taiwan in 1968, Ph.D. degrees in electrical engineering from the and the M.S. and Ph.D. degrees from Duke Univer- University of Maryland in 1983. 1985, and 1987, sity in 1971 and 1974, respectively. respectively. After working with TRW from 1974 to 1977 as a He joined the Semiconductor Electronics member of the Technical Staff, he joined the faculty division of the National Institute of Standards at Virginia Tech. He is the endowed James S. Tucker and Technology (formerly the National Bureau Professor in the Bradley Department of Electrical of Standards) in 1983. where he has been working Engineering and the Director of the Virginia Power in the device technology area. Electronics Center (VPEC). Under his leadership, Dr. Hefner’s research interests include Characterization, modeling, and VPEC became a designated Technology Development Center of the Virginia’s circuit utilization of power semiconductor devices. He is the author of 20 Center for Innovative Technology in 1987. The Center’s Industry Partnership publications in IEEE TRANSACTIONSand conference proceedings and is the Program, founded by Dr. Lee over a decade ago, is one of the largest such recipient of an IEEE Industry Applications Society Prize Paper Award. Dr. consortiums in the country. To date, 63 companies from around the world Hefner was also an instructor for IEEE Power Electronic Specialist Conference have subscribed to the program. tutorial course (1991 and 1993). Dr. Hefner has served as a program committee Dr. Lee’s research interests include: high-frequency power conversion, member for the IEEE Power Electronics Specialist Conference (1991-1993) distributed power systems, space power systems, device characterization, and as the IEEE Industry Applications Society Transactions Review Chairman modeling and control of converters, and design optimization. During his for the Power Semiconductor Committee (1989-1993). career, he has published over 80 referred journal papers and over 150 technical papers. He was the recipient of nine best paper awards from various technical conferences, was awarded ten patents with five additional patents pending, and has served as an active consultant for over 20 power electronics companies. He has been a member of the AdCom Committee of the IEEE Power Electronics Dan Y. Chen (S‘72-M’75-SM’83) received the Society, and Associate Editor of IEEE TRANSACTIONSON POWER ELECTRONICS, B.S. degree from National Chaio-Tung University, the Chairman of the 1987 Power Electronics Specialists Conference, and Taiwan, and the Ph.D. degree from National Chiao- for the past four years, served as the Chairman of teh Society’s Meetings Tung University, Taiwan and the Ph.D. degree from Committees. He is currently President of the IEEE Power Electronics Society. Duke University, Durham, NC, in 1969 and 1975, Dr. Lee was a recipient of the Society of Automotive Engineering 1985 respectively, both in electrical engineering. Ralph R. Teeter Educational Award; the IEEE Power Electronics Society From 1975 to 1979 he was a Research Engineer at 1989 William E. Newell Power Electronics Award; the 1990 PCIM Award General Electric Research and Development Center, for Leadership in Power Electronics Education, and the 1990 Virginia Tech Schenectady, NY. Since 1970 he has been with Alumni Award for Research Excellence. the Department of Electrical Engineering, Virginia Polytechnic Institute and State University, Blacks- burg, where he is currently a Full Professor. His research activities include work in power semiconductor circuits, circuit-device interactions. device characterization, magnetic devices for power electronic applications, and product applications such as brushless motor robotics dri\ e, electronic ballast, appliance power supply, and electric car drive. He has coedited one IEEE Press book and more than SO papers, and holds six U.S. patent5 in the field of power electronics. Dr. Chen was Chair of the Power Semiconductor Committee of the IEEE Industry Applications Society from 1984 to 1986.