taken by the conductivity modulation process in the bulk of the diode. The fixed internal resistance used in the standard model is inadequate for pred...

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Using Power Diode Models for Circuit Simulations—A Comprehensive Review Cher Ming Tan, Member, IEEE, and King-Jet Tseng, Senior Member, IEEE Abstract— In recent years, a number of new models for the power diode have been proposed. The objectives of this paper are to provide the power electronics community with a comprehensive review and summary of recent power diode models. The models have been categorized systematically according to their modeling concepts with objective comparison of their status pertaining to the various modeling issues. A summary table has been created to aid power circuit design engineers and power rectifier device engineers in selecting appropriate models for their applications. Index Terms—Circuit simulation, power semiconductor diodes, semiconductor device modeling.

I. INTRODUCTION

I

F THE standard SPICE diode model is used to simulate a high-voltage high-current diode, the forward and reverse recovery characteristics are not satisfactorily predicted. Fig. 1 shows a typical experimental trace of the current through a high-power diode when it is being turned off. The SPICE simulated response is also shown. The soft recovery of the power diode cannot be simulated by the SPICE diode model, leading to erroneous predictions of switching power dissipation. Another drawback of the SPICE diode model is its inability to simulate the forward recovery, as illustrated in Fig. 2. When a diode turns on abruptly under the influence of the external circuit, a sharp voltage overshoot occurs across the diode. This due to a number of factors, the chief of which is the finite time taken by the conductivity modulation process in the bulk of the diode. The fixed internal resistance used in the standard model is inadequate for predicting such characteristics. In recent years, a number of new models for the power diode have been proposed. Most of them were shown in their respective papers to be able to overcome the drawbacks of the standard SPICE model to a certain extent. However, for practicing engineers in the power electronics community, the most pressing issue is which of these models to adopt for their computer-aided design and analysis. The number of modeling concepts and techniques used in the reported models can be bewildering to these engineers, who just want reliable models to simulate their power electronic circuits. In addition, other side issues, such as accuracy of simulated results, validity range of the models, compatibility with existing simulators, implementation know-how, convergence performance, availability of model parameters and parameter Manuscript received January 11, 1998; revised August 20, 1998. Abstract published on the Internet March 1, 1999. The authors are with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 (email: [email protected]). Publisher Item Identifier S 0278-0046(99)04146-5.

Fig. 1. Inability of standard diode model to simulate soft reverse recovery in power diode current.

Fig. 2. Inability of SPICE diode model to simulate forward recovery in power diode voltage.

extraction techniques, arise when considering which of the models to adopt. The objectives of this paper are to provide the power electronics community with a comprehensive review and summary of recent power diode models. The models are categorized systematically according to their modeling concepts with objective comparison of their status pertaining to the various

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modeling issues. It is the hope of the authors that the review, categorization, and discussion will help to provide engineers with selection guidelines for models for their end applications. II. ISSUES

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POWER DIODE MODELING

The more important issues that should be addressed when selecting power diode models for power electronics CAD are discussed here. This discussion will help to elicit a more focused review of recent models. A. Model Formulation Techniques The most fundamental aspects that distinguish among different power diode models is the model formulation technique and concept employed. Classifying these concepts is not straightforward, as different literature attached somewhat different interpretations to the terminology involved. Very broadly, all models may be classified either as micromodels, or as macromodels. Micromodels are closely based on the internal device physics and, if properly formulated, should yield good accuracy over a wide range of operating conditions. Because device physics unavoidably require mathematical equations, micromodels are also known as mathematical models. Macromodels reproduce the external behavior of the device largely by using empirical techniques without considering its geometrical nature and its internal physical processes. This external behavior is usually modeled by means of simple data-fitting empirical equations, lookup tables, or an electrical subcircuit of common components to emulate known experimental data. Because of the latter reason, macromodels have been mistakenly labeled as subcircuit models. Many socalled subcircuit models are actually micromodels because they used subcircuits to simulate fairly complex physics-based mathematical equations. In our review here, the term subcircuit refers to the mode of model implementation rather than the model formulation technique. Macromodels were frequently reported in the earlier literature, before the 1990’s. However, because of their limitations in terms of accuracy and flexibility, they are rarely utilized nowadays. Micromodels are generally more computationally efficient, more accurate, and more related to the device structure and fabrication process. Most models proposed in the 1990’s are micromodels, which can be further classified as numerical models, analytical models, and hybrid models. Numerical modeling uses the partial differential equation set of the semiconductor physics and solves them using finiteelement or finite-difference methods. These equations describe the physical phenomena within the semiconductor, consisting of carrier drift and diffusion components, carrier generation and recombination effects, and the relationship between space charge and electric field. These models are sometimes further classified either as exact or as simplified. The term “fully” or “exact” refers to the solutions of the complete system of basic equations without simplifications. From the engineering point of view, the degree of accuracy that is achieved by an exact numerical model is not always necessary or even justified, in particular, if the input data, such as the doping profile, is only known with a limited accuracy. In such cases, simplified nu-

merical models may suffice. The simplifications may be in the form of assumptions made to semiconductor physics, or in the finite-element algorithms. Numerical models are suitable for device manufacturers who want to evaluate the performance of their devices in power electronic circuit applications. Analytical micromodels rely on a set of mathematical functions to describe the devices’ terminal characteristics without resorting to finite-element methods. Examples are the standard diode and transistor models packaged in SPICE. There has been a school of thought that analytical models can never fully predict the characteristics of power devices. However, this is not necessarily true, as the mathematical equations can always be formulated to predict the characteristics as accurately as possible, at the expense of computational overheads. These equations could also be device physics related to provide realistic simulations over a wide range of operating conditions. Like numerical modeling, the limits to simulation accuracy are more due to the accuracy of the input parameters rather than due to the models themselves. The computational overheads of analytical models are far lower than those of numerical models. In addition, there is a large pool of popular commercial simulators, such as SPICE and Saber, the solver algorithms of which have been evolved to solve these types of models most efficiently. Having power device models in the libraries of these simulators allows the latter to function as general purpose power electronics circuits CAD tools. Analytical models are, thus, very appropriate for simulation of power electronic circuits over a large number of switching cycles. A third type of micromodel formulation technique is to use a combination of numerical and analytical models. The motivation behind such hybrid model arises from the fact that certain physical phenomena in power devices are very difficult to simulate realistically using only analytical equations, particularly the charge storage effects in the lightly doped drift regions. The basic idea of this method is to use a fast numerical algorithm that solves the semiconductor equations in the drift region only. Analytical equations are applied to the rest of the device structure. This procedure has the advantage that a high accuracy of the charge carrier behavior may be simulated without the long execution time associated with fully numerical models. This type of models is suitable for very detailed study of device interactions with the rest of the circuit over a few switching cycles, e.g., snubber design. B. Circuit Simulator and Model Implementation Any model formulated would require a circuit simulator as a vehicle for simulation. In some early reported work on power device models, entire circuit simulators were created together with the models to demonstrate the application of power electronics simulation. This is no longer necessary nor practical nowadays, as there are numerous commercial circuit simulation software packages that come complete with professional graphics user interface and vast libraries of electronic component models. The research focus has, therefore, currently shifted to power device model formulation, instead of creating new power electronic simulator from scratch.

TAN AND TSENG: USING POWER DIODE MODELS FOR CIRCUIT SIMULATIONS

For numerical models, finite-element semiconductor simulators such as MEDICI are available. These simulators are usually equipped with rudimentary SPICE-type time-stepping solvers. The drawbacks are extremely slow simulation times, and not all power semiconductor devices physics are included, as these simulators were originally created for microelectronics applications. Analytical micromodels can be implemented in commercial simulators by the insertion of mathematical equations. The method of insertion varies from one simulator to another. In PSpice, the technique is known as analog behavioral modeling (ABM) and is based on subcircuits of user-defined controlled E-type voltage sources and G-type current sources. These sources allow transfer functions for nonlinear devices to be specified by mathematical expressions, lookup tables, Laplace transforms, or frequency-response tables. Saber offers its own proprietary analog hardware description language called MAST to facilitate the incorporation of new device models in the form of templates. The templates can also call up foreign subroutines written in C or Fortran languages. Hybrid micromodels involved many mathematical equations to solve the finite-difference portion of the model. Subcircuit form of implementation becomes very unwieldy and is, therefore, not practical for simulators such as PSpice. Simulators that provide powerful simulation languages such as Saber are required for this type of models. C. Convergence Performance Another important issue is how fast and convenient the simulation results can be obtained. It can be expected that numerical, hybrid, and analytical models generally have increasing simulation speed in this order. This is provided that convergence problems are not encountered. Many models proposed in the past have been discarded, because power electronics designers find that they frequently give rise to stalled and incomplete simulations. As a result, the standard SPICE diode model is still one of the most popular choices for modeling the power diode in power electronics simulations, despite its obvious shortcomings in terms of accuracy. In industry, there is little point in using a model that promises much but runs the risk of delivering little or even nothing when convergence difficulties surface. This is also the main reason why most commercial versions of SPICE do not incorporate any of the many micromodels reported in the literature so far. D. Accuracy and Validity Range Before a power diode model can be generally accepted and adopted by the power electronics community, its accuracy and validity should be thoroughly verified. Proposed models are usually reported in technical journals, where the limited paper length does not permit detailed presentation on the accuracy and validity range. Therefore, it may be necessary to write to the authors for more details before deciding on the adoption of the model. There is also the need to standardize test circuits for the power diode, e.g., the adoption of an “RG1” type of test circuit. Fig. 3 shows a typical current waveform obtained from such test circuit.

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Fig. 3. Current waveform in RG1 reverse recovery test circuit.

E. Model Parameters Extraction In numerical and hybrid models, it is necessary to have information on geometrical dimensions and the fabrication processes in order to obtain the necessary parameters for the models. Unless device manufacturers actively support the models by providing the parameters, it can be difficult for these models to be adopted by the circuit design community. Hence, the applications of numerical and hybrid models have so far been confined to the device manufacturers for the investigation of their own products. For analytical models, it is usually possible for the user to figure out the parameters by comparing trial simulation results with sample experimental results. However, if a model requires a large number of parameters, the task of parameter extraction becomes tedious. Thus, the number of input parameters, as well as the availability of the parameter extraction procedure, should be important considerations.

III. REVIEW OF RECENT POWER DIODE MODELS Research in modeling of the power diode has been ongoing, ever since the p-n junction was invented, but it was in the last ten years that interest has picked up considerably, with the surge in power electronics applications. In this paper, only the models developed in this period are reviewed, as any significant contributions from earlier models would also have been included in the more recent models. Once again, the original SPICE diode model is used as a benchmark by which other models may be compared. For easy referencing, the name of each model to be reviewed is given as the name of the first author of the particular published paper, followed by the corresponding reference number as listed at the end of the paper, and the year of the publication. For each review, the principle used in the model formulation, the assumptions (including any inherent assumptions in the derivation) made in the model development, the applicability of the model as a result of the assumptions, and the derivations of the model equations are discussed. A summary table of the various models discussed is provided at the end of the section to aid engineers in the power

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TABLE I MODELS BASED ON LUMPED CHARGE CONCEPT

electronics community in selecting an appropriate model for their applications. A. Analytical Models Several principles have been based in the development of analytical models. They can be classified as follows: 1) lumped charge concept by Linvill [1]; 2) charge control model; 3) dynamic charge model; 4) asymptotic waveform evaluation method. The lumped charge concept has been adopted by Lauritzen and Ma et. al. [2]–[5] from the University of Washington. The advantages of the models are easy to implement, easy parameter extraction and high computation efficiency. Table I lists the development of the models developed by them, and their applicability. One can see the progression of the model

development from only the reverse recovery of p-i-n diode to forward and reverse recovery of p-v-n, including the voltagedependent reverse recovery and emitter recombination effects. The charge control model uses the charge control equation as in PSpice, so that the models can be implemented in PSpice. At the same time, the physical processes in the power diode can also be taken into account in the modeling. Table II lists the models developed based on the principle. The dynamic charge model recognizes the dynamic nature of the charge distribution in the base region. This nature arises from the fact that the charge distribution in the base region depends not only on the instantaneous values of diode voltage and current, but also on the previous state of the diode. Table III lists the models in this category. The asymptotic waveform evaluation method makes use of the continued fraction expression of the carrier distribution in the base region to convert the solution of the ambipolar

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TABLE II MODELS BASED ON CHARGE CONTROL CONCEPT

diffusion equation into subcircuit. This principle is adopted by Strollo [13]. Only one assumption is known, and other assumptions made in the derivations cannot be known as its reference list is not provided. The one assumption is that at a constant where , and is the base width. The model includes the effects of emitter recombination, depletion boundary movement, and conductivity modulation in the base region. Thus, the model seems to apply to the p-v-n diode at all conditions. B. Numerical and Hybrid Models There have been several numerical and hybrid models developed in the 1990’s. One is for the p-v-n diodes developed by Vogler et al. [14], and another focused on the reverse recovery of abrupt p-n junction, which is developed by Winternheimer et al. [15], [16]. For the model developed by Vogler et al. [14], finitedifference method is employed to solve the ambipolar diffusion equation with only one assumption, that is, temperature >77 K. In the development of the model, the ambipolar diffusion equation includes the spatial dependence of carrier–carrier scattering, auger recombination, avalanche effects, doping and carrier lifetime profiles, and effect of buffer layers. Thus, the uses of the unphysical effective parameters, such as mean carrier concentration, average mobility, etc., are avoided. However, the self-heating effect is not included. This model has also been implemented in Saber as a hybrid model and used to simulate a hard-driven gate-turn-off (GTO) inverter [25]. For the model developed by Winternheimer et al. [15], [16], the physical processes in the semiconductor devices are carefully included, so that the model can predict the performance of diodes without any fitting parameters. The assumptions made in the derivation are as follows: n and n n junctions; 1) abrupt p 2) carrier lifetime is constant over time; 3) steady-state forward conduction; 4) emitter recombination is neglected;

5) excess charge in the swamped zone is approximated by straight line; 6) current in the space-charge zone is caused by holes only; 7) current in the resistance zone is caused by electrons only; 8) ratio is assumed to be equal to in the resistance zone; 9) diffusion current of holes in the space-charge zone is neglected. As this model considered only the turn-off behavior, and selfheating is not included, it is applicable to the study of the reverse behavior of the abrupt p-n junction. In view of the long computation time required by the numerical models, Goebel et al. [17], [18] developed a hybrid model. This model solves the differential equations describing the semiconductor device partly analytically and partly numerically with the following assumptions: is known, where is temperature, and is carrier 1) lifetime in the base region; 2) mobilities are affected by phonon scattering only; 3) conduction modulation only affects the resistivity of the lightly doped region. Its effect on the ambipolar diffusion length is neglected. In this model, both static and dynamic self-heating are included. The derivation also allows nonsteady-state turn-on and turn-off conditions to be considered. The effects of mobile charge carriers in the space-charge region and velocity saturation of the carriers are included in the model. The trap density can also be included in the model, if desired. Therefore, this model can be applied to all p-v-n power diodes under is determined various switching conditions, provided that experimentally. Table IV gives a list of models based on numerical and hybrid numerical concepts. C. Empirical Model There is only one empirical model developed since the 1990’s, by Bertha et al. [19]. This model modifies an existing power diode PSpice model so as to reduce the number of ideal

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TABLE III MODELS BASED ON DYNAMIC CHARGE CONCEPT

components in the model. In the derivation of the model, the following assumptions are made: 1) dependency of voltage across diode on diode current can be expressed as third-order polynomial;

2) base contraction due to the moving of the depletion region boundary is omitted, which resulted in single fixed time constant in the reverse recovery;

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TABLE IV NUMERICAL

ON

3) charge at the end of phase 1 of the reverse recovery ) is zero, implying a slow , as (i.e., at mentioned by Tseng [12]. The accuracy of the simulation depends on the accuracy of the polynomial approximation, which depends on the measurement data. Thus, the model applies to a specific diode under a specific circuit condition. D. Summary of Review From the review of the diode models, a summary table is constructed (Table V) to assist power circuit designers and device designers in the selection of the models. Through

AND

HYBRID CONCEPT

the model development, one find the importance of endregion recombination and carrier–carrier scattering in highcurrent device modeling. The significance of the end-region recombination on the forward characteristics of the power diode has been studied by Choo [20]. For high blocking voltage devices, the voltage-dependent reverse recovery is important. For p-v-n diodes, the nonquasi-static nature of the charge distribution should be considered. From Table V, one can also see that model development for the p-v-n power diode began in 1991. After 1993, the focus on model development shifted to the analytical model, in order to include the physical effect of the power rectifiers.

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TABLE V VARIOUS POWER DIODE MODELS

However, after 1994, the number of published works on the power rectifier dropped to one per year. However, this reduction in the number of published works does not indicate the maturity of the diode model, as many outstanding issues remain unresolved, as will be discussed below. IV. DISCUSSION All the power diode models developed so far are only for one-dimensional (1-D) structure. However, as power diodes are mostly of mesa type, the shape, the bevel angle, and passivation type of the junctions may be important in determining the characteristics of the diode. Three shapes of mesa-type power diodes are generally employed. They are circular, square, and hexagonal. The current and electric field of the noncircular die shape will be nonuniform along the edge of the die. Current crowding might occur at the corners of the die, thus resulting in local heating and local breakdown. The local heating and nonuniform current distribution can affect the forward and reverse recovery. The depletion region width will be nonuniform as the electric field distribution is nonuniform. Hence, the forward and reverse recovery might also be affected. The effect of shape on the transient characteristics has not been studied to the knowledge of the authors. The effect of bevel angle on the reverse breakdown voltage has been studied by several individuals, such as Baliga [21]. The effect is due mainly to the change in depletion region width at the edge of the die. The local heating and nonuniform current distribution as a result of the nonuniform depletion width can also affect the forward and reverse recovery. The effect of bevel angle on the transient characteristic of power diodes has also not been studied. Passivation of mesa-type power diodes could be silicon–resin, glass, silicon oxide, or semi-insulating polycrystalline silicon (SIPOS). The silicon–resin, glass, and silicon oxide passivation could trap charges from the p-n junction, thus resulting in the walkout phenomena observed in [22]. Although SIPOS passivation does not have the problem, , a transient-voltage-induced leakage current under high

will appear due to the time lag between the application of the voltage and the change in resistivity of SIPOS [23]. How different types of passivation will affect the transient characteristic of the power diode remain unknown. As the switching frequency for the power diode in most applications is increasing, the switching loss becomes important. Because of the presence of and , as well as and , the switching loss can be very high, resulting in the rise of junction temperature during operation. This rise in junction temperature causes the change in diode characteristics in a dynamic nature. More and more cases reported from the field were due to self-heating from the experience of one of the authors. However, very little work has been done in investigating the self-heating effect. The surge capability is also important in the selection of the power diode. Diode breakdown occurs, even when a surge voltage across the diode was lower than its static breakdown voltage [24]. The surge capability is closely related to the self-heating effect of a power diode. The inclusion of surge capability in the diode model has not been found, although some investigations have been made in this area. For a high-switching-speed power diode, lifetime killers are added to the base region of the p-v-n diode. The distribution of the killers might not be uniform, as it is depends on the nature of the killers and the method of introduction of the killers. The nonuniform distribution of the killers causes a local variation of the carrier lifetimes and the related parameters. The allowance for the inclusion of spatial variation of lifetime in the model can be found in one model only. This model was developed by Vogler et al. [14]. From the above discussion, one can see that modeling of the power diode can no longer be limited to 1-D modeling. Several multidimensional effects and self-heating effect should be considered in order to produce an accurate model. For the existing models, the implication of the application of the p-i-n model to the p-v-n diode or vice versa is not known. This is important, since most power circuit design engineers do not know the inside of a power diode. The implication of a wrong model should be assessed.

TAN AND TSENG: USING POWER DIODE MODELS FOR CIRCUIT SIMULATIONS

In fact, the lack of information on the structure of the power diode from the point of view of power circuit design engineers suggests a necessity for the collaboration of three parties in power diode modeling in industry. These three parties are the device manufacturers, the device users, and the company that produces the simulator. The absence of any one of these parties will render a model impractical in usage due to either too many unknown parameters needing to be input, or inaccurate results due to the use of a wrong model, or the model is difficult to simulate with the commonly used simulator.

V. CONCLUSIONS About 20 published power diode models were reviewed in this paper. The recent focus on model development has shifted to analytical micromodels, in order to include effects arising from internal device physics. These models can achieve better accuracy over a wide range of operating conditions. Although the rate of publication of papers containing power diode models has been tapering off in the last few years, this does not indicate all outstanding issues have been resolved. These include multidimensional effects, self-heating, and surge characteristics. For the existing models, a summary table has been created to aid power electronic engineers in selecting appropriate models for their applications. REFERENCES [1] J. G. Linvill and J. F. Gibbons, Transistors and Active Circuits. New York: McGraw-Hill, 1962, p. 92. [2] P. O. Lauritzen and C. L. Ma, “A simple power diode model with reverse recovery,” IEEE Trans. Power Electron., vol. 6, pp. 188–191, Mar. 1991. [3] C. L. Ma and P. O. Lauritzen, “A simple power diode model with forward and reverse recovery,” IEEE Trans. Power Electron., vol. 8, pp. 342–346, July 1993. [4] C. L. Ma, P. O. Lauritzen, and P. Y. Lin, “A physically based lumpedcharge P-v-N diode model,” in Proc. European Power Electronics Conf., 1993, pp. 23–28. [5] C. L. Ma, P. O. Lauritzen, and J. Sigg, “Modeling of power diodes with the lumped-charge modeling technique,” IEEE Trans. Power Electron., vol. 12, pp. 398–405, May 1997. [6] A. T. Yang, Y. Liu, and J. T. Yao, “An efficient nonquasistatic diode model for circuit simulation,” IEEE Trans. Computer-Aided Design, vol. 13, pp. 231–239, Feb. 1994. [7] R. Kraus, K. Hoffmann, and H. J. Mattausch, “A precise model for the transient characteristics of power diodes,” in Conf. Rec. IEEE PESC’92, 1992, pp. 863–869. [8] Y. Liang, and V. J. Gosbell, “Diode forward and reverse recovery model for power electronic SPICE simulations,” IEEE Trans. Power Electron., vol. 5, pp. 346–356, May 1990. [9] H. A. Mantooth, R. G. Perry, and J. L. Duliere, “A unified diode model for circuit simulation,” in Conf. Rec. IEEE PESC’95, 1995, pp. 851–857. [10] Y. Jin, K. Hoffmann, and W. Kiffe, “A forward recovery model of power diodes,” in Proc. European Power Electronics Conf., 1991, pp. 339–342. [11] K. J. Tseng, C. F. Foo, and P. R. Palmer, “Implementing power diode models in SPICE and Saber,” in Conf. Rec. IEEE PESC’94, 1994, pp. 59–63. [12] K. J. Tseng, “Modeling of diode forward recovery characteristics using a modified charge-control equation,” Int. J. Electron., vol. 84, no. 5, pp. 437–444, 1998. [13] A. G. M. Strollo, “SPICE modeling of power PiN diode using asymptotic waveform evaluation,” in Conf. Rec. IEEE PESC’96, 1996, vol. 1, pp. 44–49. [14] T. Vogler and D. Schroder, “A new and accurate circuit modeling approach for the power diode,” in Conf. Rec. IEEE PESC’92, 1992, pp. 870–876.

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[15] S. Winternheimer and B. Laska, “Investigations on turn-off effects in fast recovery power diodes by modeling and simulation,” Proc. Inst. Elect. Eng., vol. 139, pt. B, no. 2, pp. 55–61, 1992. [16] B. Laska and S. Winternheimer, “Simulation of turn-off dynamics in fast recovery power diodes,” Proc. Inst. Elect. Eng., vol. 139, pt. B, no. 2, pp. 405–410, 1992. [17] H. Goebel and K. Hoffmann, “Full dynamic power diode model including temperature behavior for use in circuit simulators,” in Proc. ISPSD Conf., 1992, pp. 130–135. [18] H. Goebel and K. Hoffmann, “Power diode HYBRID model with forward and reverse recovery for use in circuit simulators,” in Proc. IEEE APEC’92, 1992, pp. 426–432. [19] F. Bertha, B. Velaerts, P. Mathys, E. Tatakis, A. Wyns, D. Bogaerts, and M. Miller, “An improved power diode model for PSpice, applied to converter simulation,” in Proc. European Power Electronics Conf., 1993, pp. 249–254. [20] S. C. Choo, “Effect of carrier lifetime on the forward characteristics of high power devices,” IEEE Trans. Electron Devices, vol. 17, pp. 647–652, Sept. 1970. [21] B. J. Baliga, Modern Power Devices. New York: Wiley, 1987. [22] E. P. Burte, “On the blocking behavior of mesa high voltage power devices passivated by semi-insulating polycrystalline silicon films,” Thin Solid Films, vol. 168, pp. 41–50, 1989. [23] A. Yahata and M. Atsuta, “Transient voltage induced leakage current in power diode with semi-insulating polycrystalline silicon resistive field plate,” Jpn. J. Appl. Phys, vol. 35, pp. 2595–2598, 1996. [24] Y. Tomomatsu et al., “An analysis and improvement of destruction immunity during reverse recovery for high voltage planar diodes under high dIrr/dt condition,” in Proc. IEEE Int. Symp. Power Semiconductor Devices and IC’s (ISPSD), 1996, pp. 353–356. [25] P. K. Steimer, H. Gurning, J. Werninger, and D. Schroder, “State-of-theart verification of the hard driven GTO inverter development for a 100 MVA Intertie,” in Proc. IEEE PESC’96, 1996, vol. 2, pp. 1401–1407.

Cher Ming Tan (S’83–M’84) was born in Singapore in 1959. He received the B.Eng. degree from the National University of Singapore, Singapore, in 1984 and the M.A.Sc. and Ph.D. degrees from the University of Toronto, Toronto, Ont., Canada, in 1988 and 1992, respectively, all in electrical engineering. He was a Quality and Reliability Manager and an Engineering Consultant with LiteOn Power Semiconductor Corporation, Taiwan, R.O.C., for five years. In 1996, he joined Chartered Semiconductor Manufacturing Ltd., Singapore, as a Quality and Reliability Section Manager. In April 1997, he joined the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, as a Lecturer. Dr. Tan is a member of the American Society for Quality Control.

King-Jet Tseng (S’85–M’88–SM’98) was born in Singapore. He received the B.Eng. (first-class honors) and M.Eng. degrees from the National University of Singapore, Singapore, and the Ph.D. degree from Cambridge University, Cambridge, U.K. He was a Lecturer with Ngee Ann Polytechnic, Singapore, in 1989. He is currently a University Lecturer in the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. He teaches power electronics and drives at the undergraduate level and supervises a number of research students. He is also the Supervisor of the Power Electronics and Drives Laboratory. He has been involved in research on power electronics, drives, and motion control since 1988. Dr. Tseng is a Fellow of the Cambridge Commonwealth Society and the Cambridge Philosophical Society and a member of the Institute of Engineers, Singapore. In 1996, he was awarded the Swan Premium by the Institution of Electrical Engineers, U.K., for his work on gate turn-off thyristors. Since 1996, he has been the Chairman of the Singapore Chapter of the IEEE Industry Applications Society. He has been listed in Marquis’ Who’s Who in the World for his contributions to engineering education and research.