POLITECNICO DI TORINO Facolt`adi Ingegneria Corso di Dottorato in Dispositivi Elettronici Tesi di Dottorato Modeling and Simulation of Power PiN Diodes within SPICE Gustavo Buiatti Direttore del corso di dottorato Prof. Carlo Naldi Tutore: Prof. Giovanni Ghione Febbraio 2006 Acknowledgements I wish to thank my Ph.D. thesis advisor, Professor Giovanni Ghione for his ad- vises and comments throughout the whole research activity, and also for his human support. I also wish to thank Federica Cappelluti for supporting my work with con- tinuous helpful suggestions and discussions, and in the preparation of this Thesis. Their scienti¯c methodology have been a reference for me and their contributions improve the quality of the results. I wish to kindly thank Professor Jos¶eRoberto Camacho, from Federal University of Uberl^andia,Brazil, for his support, ideas and fruitful discussions during my research period in that institution and even in Italy. Professor Jo~aoBatista Vieira J¶unioris also acknowledged, especially for the support on his Power Electronics Laboratory in the Federal University of Uberl^andia,Brazil. A ¯nal and very special thought goes to my wife, Natalia, and my daughter, Gabriela. Thank you for your encouragement, patience and constant support during the time we have been in Italy. Without you I would never ¯nish this work. I'll be always grateful for your love. To you, I dedicate this thesis. 1 Table of contents 1 Physics and Basic Equations of Power PiN Diode 3 1.1 The Ambipolar Di®usion Equation (ADE) . 5 1.2 Forward conduction . 8 1.2.1 The stationary forward behavior of the PiN diode . 9 1.2.2 End region recombination e®ect . 13 1.2.3 Carrier-carrier scattering . 18 1.2.4 Auger recombination . 19 1.2.5 Lifetime control . 21 1.3 Forward recovery . 23 1.4 Reverse recovery . 25 2 Power PiN Diode Models for Circuit Simulations 30 2.1 An overview of PiN diode modeling . 31 2.2 Circuit simulator and model implementation . 35 2.3 PiN diode models: di®erent approaches to solve the ADE . 35 2.3.1 Analytical model: Laplace transform for solving the ADE . 36 2.3.2 Analytical model: Asymptotic Waveform Evaluation for solv- ing the ADE . 38 2.3.3 Analytical model: Fourier based-solution to the ADE . 40 2.3.4 Hybrid model: Finite Element Method for solving the ADE . 44 2.3.5 Hybrid model: Finite Di®erence Method for solving the ADE . 48 3 Finite Di®erence Based Power PiN Diodes Modeling and Valida- tion 50 3.1 Nomenclature . 51 3.2 Introduction . 52 3.3 Model description . 53 3.3.1 Fundamental Equations . 53 3.3.2 Finite Di®erence Modeling of the Base Region . 54 3.4 The complete diode model . 57 3.4.1 Voltage drop on the junctions . 58 3.4.2 Voltage drop on the epilayer . 59 I TABLE OF CONTENTS 3.4.3 Voltage drop on the space-charge regions . 60 3.5 Model implementation within SPICE . 61 3.6 Model results and Validation . 65 3.6.1 Comparison with the FEM based diode model . 65 3.6.2 Simulation of Commercial Fast Recovery Diodes . 71 3.7 Simulation of Switched Mode Power Supplies . 80 4 Conclusions 86 A Pspice subcircuit listing - feedback scheme 87 B Pspice subcircuit listing - standard diode 90 Bibliography 93 II Introduction Power devices are very important for power electronics systems since the latter are closely related to these discrete devices performance. Their study, comprehension and performance improvement is of major importance for the development of e±cient power electronics equipments. The e®ort needed for assembling and experimenting a power electronics con- verter, even taking into account the simplest topology existent, takes to a strong motivation in the search for tools that in a simple and reliable way can simulate the operation of the semiconductors involved in the circuit, dependent on the vari- ous parameters of the load and control circuit, and that, in such a way, allows the comparison for di®erent options of control and topology of conversion. Time to market is an important target for modern, highly competitive industry. A widely used method to reduce time to market is the use of computer aided design (CAD) tools which reduce the number of prototypes needed for the implementation of the ¯nal design. The limited use of prototypes results in a reduction of the time needed to obtain the ¯nal product with a consequent saving of design cost. In the the power electronics ¯eld, circuit simulation is the favorite CAD tool. The simulation of converters, with the inclusion of detailed characteristics of the bipolar power semiconductors devices, by means of using a personal computer, allows an accurate understanding of the design and increases the possibility of a working ¯rst prototype close to the ¯nal product. We usually have two di®erent solutions for dealing with this simulation problem. The ¯rst one simulates a very simple circuit where the whole physics of the semi- conductor is taken into account, and we focus our attention on the semiconductors behavior considering this particular simpli¯ed situation. In the second option the whole converter is simulated, but making use of simpli¯ed models for the semicon- ductors involved in the design. Both solutions are usually incompatible in terms of integration. Therefore, the development of designs in the ¯eld of power electronics can be bene¯ciated if somehow we can simulate both the macroscopic aspect of the converter, and the microscopic aspect of the commutations of the semiconductors involved in the circuit. Unfortunately, the models available in commercial circuit simulators are not suited to model the actual behavior of bipolar power semiconductors, which are not suited either for a study that intends to be physics-based. 1 So, the main goals of this work were to create a mathematical model applicable for bipolar power semiconductors, that must be physics-based, capable to be imple- mented in any commercial circuit simulator and to reproduce reliable and accurate results. Many power devices have been proposed in the past years but the need of bet- ter models is always present since circuit models need to adapt to the demand of advanced CAD tools and to the increased computation power available. Another reason for the development of new device models is that they are the result of the trade-o® between contradicting requirements such as low computation complexity and accuracy. A better trade-o® between these requirements is always desirable and pushes the development of more e±cient device models. In this thesis the results obtained during the study and research period at he Politecnico di Torino are reported. The attention is focused on the power PiN diode, a power device as simple as essential in power systems, with emphasis to the development of compact circuit models of this device, ideally suited for circuit simulation. Main characteristic of the model presented in this work are the low computational power needed and the accurate modeling of static characteristic and of forward and reverse recovery e®ects. The model is implemented for simulation and comparison with experimental data in Pspice simulator. However, the model can be handled by any other SPICE-based simulator. The thesis is structured as follows. Chapter 1 is devoted to a general introduc- tion to the physics of power PiN diodes, aimed to highlight the main static and dynamic e®ects of the same, and to provide the background underlying the design and optimization of such devices. In chapter 2 the main topics on power diode modeling are introduced, and dif- ferent techniques and models are presented in order to compare the same and clarify this issue. Chapter 3 focuses on a novel approach for modeling power PiN diodes. The complete diode model is described and introduced, followed by its implementation within the Pspice circuit simulator. Circuit simulations of practical power circuits are reported, and the model is validated against experimental and simulations using di®erent diode models. Finally, in chapter 4 the ¯nal conclusions are presented. 2 Chapter 1 Physics and Basic Equations of Power PiN Diode The PiN diode was one of the ¯rst semiconductor devices developed for power cir- cuit applications. It is the simplest semiconductor device present in every power electronics converter, as can be seen by the structure presented in Fig. 1.1. The PiN diode is basically composed of three regions: the cathode, the epilayer and the anode. The cathode is a wide highly N doped region; the epilayer is a lightly N doped region, epitaxially grown over the cathode; the anode is a highly P doped region placed at the top of the epilayer. The main di®erence between signal diodes (low power PN diodes) and power PiN diodes is this additional sandwiched region, the epilayer, which allows the PiN diode to block large negative voltages depending on its width and low doping. The presence of this region also has important e®ects on the diode's direct characteristic and dynamic behavior. Regarding the direct characteristic, the presence of the epilayer (which behaves as a series resistance) increases on-state voltage drop with respect to signal diodes. With respect to the dynamic behavior, two important drawbacks are worth point- ing out. During forward conduction the epilayer is flooded with charge carriers, holes and electrons injected from diode end regions (anode and cathode), and the resis- tance of the epilayer becomes very small, allowing the diode to carry a high current density with limited voltage drop. If not flooded by the carriers, the epilayer is highly resistive. So, the resistance of the epilayer depends on the carriers distribu- tion in the same, which in turn depends on the current density through the diode.