Physics-Based Thermal Impedance Models for the Simulation of Self-Heating in Semiconductor Devices and Circuits

PHYSICS-BASED THERMAL IMPEDANCE MODELS FOR THE SIMULATION OF SELF-HEATING IN SEMICONDUCTOR DEVICES AND CIRCUITS By JONATHAN SCOTT BRODSKY A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1997 This work is dedicated to my parents, Lawrence and Jeraldine, my brother Matthew and sister Alexandra. ACKNOWLEDGEMENTS First, I wish to express my deepest gratitude to my advisor Dr. Robert M. Fox. His constant support and patient guidance provided a clear path for my research. I thank Drs. Mark It is both a pleasure and a privilege to have worked with Dr. Fox. E. Law and Jerry G. Fossum for extending their expertise and help to my unending questions. I would also like to thank Drs. William R. Eisenstadt, John G. Harris and Chen-Chi Hsu for their willingness to serve on my supervisory committee. I am also very grateful to Mary Turner for all of her help throughout my graduate career. I would like to acknowledge and thank the Semiconductor Research Corporation (SRC) for the financial support that made this research possible. I am also grateful to Dr. Surya Veeraraghavan for his guidance and friendship during my internship at Motorola. I would like to thank the "TCAD elders", and now my friends, Keith Green, Dongwook Suh, Ping-Chin Yeh, Haeseok Cho, Chih-Chuan Lin, Ming-Chang Liang and Scott Miller, for helping me get comfortable in my new surroundings and setting the standard of excellence. I am also grateful to my good friends/workmates/"happy hour buddies" Srinath Krishnan, Samir Chaudhry, David Zweidinger, Omer Dokumaci, Ming-Yeh Chuang, Dukhyun Chang, Susan Earles, Hernan Rueda, Glenn Workman and Meng- 111 Hsueh Chiang, for all of the enlightening discussions, the Friday lunch tradition and the weekend adventures. There is a very special group of individuals who have my admiration and love for the friendships they have given me. I would like to thank my best friends Douglas Weiser, Martin Weiss, Stephen Cea, Edward Cometz and Peter Lynch. I can not completely express the role my family has played in my life and in the completion of this dissertation. For simple words seem to diminish their unconditional and unending love and support. I owe everything I have, everything I have done and everything I am, to my family. I give my deepest love to my parents, Jeraldine and Lawrence Brodsky, my brother Matthew and my sister Alexandra. Finally, I am grateful to all of the wonderful friends that I met in Gainesville for making this period of my life truly enjoyable. IV 1 1 TABLE OF CONTENTS ACKNOWLEDGEMENTS iii ABSTRACT viii 1 INTRODUCTION 1 1 1 . Self-Heating Effects in Semiconductor Devices 1.1.1 Bipolar Transistors 3 1.1.2 Field-Effect Transistors 6 1.2 Self-Heating Effects in Semiconductor Circuits 8 1.2.1 Small-Signal Circuit Performance 8 1 .2.2 Large-Signal Circuit Performance 11 1 .3 Self-Heating Effects in Parameter Extraction 12 1.4 The Simulation of Self-Heating Effects 13 1.5 Thermal Equivalent Circuits 16 1.6 The Need for Physics-Based Thermal Impedance Models 20 1 .7 Organization 25 2 A THREE-DIMENSIONAL THERMAL IMPEDANCE MODEL FOR JUNCTION-ISOLATED BIPOLAR TRANSISTORS 27 2. Introduction 27 2.2 Derivation of the Single-Emitter BJT/HBT Thermal Impedance Model. 28 2.2. Modification for Finite Wafer Thickness 39 2.2.2 Effects of Interconnect Metallization on the Thermal Impedance ... 43 2.2.3 A Model for the Thermal Impedance of the Emitter Interconnect ... 49 2.2.4 Effects of Isolation Structures on the Thermal Impedance 52 2.3 Verification of the Single-Emitter Thermal Impedance Model 61 2.4 Derivation of the Multiple-Emitter BJT/HBT Thermal Impedance Model . 66 2.5 Verification of the Multiple-Emitter Thermal Impedance Model 72 2.6 Summary 76 3 A CIRCUIT MODEL FOR THERMAL COUPLING AND A LUMPED ELECTROTHERMAL MODEL FOR BULK MULTIPLE-EMITTER BIPOLAR TRANSISTORS 77 3.1 Introduction 77 3.2 A Circuit Model for Thermal Coupling 80 1 3.3 A Lumped Electrothermal Model for Multiple-Emitter BJT/HBT's 86 3.3.1 A Review of Base-Current Thermometry 90 3.3.2 Generation of the Lumped Electrothermal Model 91 3.4 Verification of the Lumped Electrothermal Model 96 3.5 Summary 101 A THREE-DIMENSIONAL THERMAL IMPEDANCE MODEL FOR VERTICAL BIPOLAR TRANSISTORS FABRICATED WITH FULL DIELECTRIC ISOLATION 103 4. Introduction 103 4.2 Derivation of the DIBJT Thermal Impedance Model 106 4.2.1 Derivation of the Buried-Oxide Heat-Transfer Coefficient 1 16 4.2.2 Derivation of the Trench Heat-Transfer Coefficient 120 4.2.3 Effects of Interconnect Metallization on the Thermal Impedance . 126 4.2.4 A Model for the Thermal Impedance of the Emitter Interconnect . 129 4.3 Verification of the DIBJT Thermal Impedance Model 132 4.4 Derivation of a Compact DIBJT Thermal Resistance Model 134 4.5 Verification of the DIBJT Thermal Resistance Model 146 4.6 Summary 149 A THREE-DIMENSIONAL THERMAL IMPEDANCE MODEL FOR BULK METAL-OXIDE-SEMICONDUCTOR FIELD-EFFECT TRANSISTORS ..150 5. Introduction 1 50 5.2 Derivation of the Bulk MOSFET Thermal Impedance Model 153 5.2.1 The Linear Source Thermal Impedance 161 5.2.2 The Saturated Source Thermal Impedance 164 5.2.3 Effects of the Device Interconnects on the Thermal Impedance ... 165 5.2.4 Effects of Isolation Structures on the Thermal Impedance 171 5.3 Verification of the Bulk MOSFET Thermal Impedance Model 176 5.4 Summary 182 A QUASI-THREE-DIMENSIONAL THERMAL IMPEDANCE MODEL FOR SILICON-ON-INSULATOR METAL-OXIDE-SEMICONDUCTOR FIELD- EFFECT TRANSISTORS 184 6. Introduction 1 84 6.2 Derivation of the SOI MOSFET Thermal Resistance Model 187 6.3 Verification of the SOI MOSFET Thermal Resistance Model 202 6.4 Derivation of the SOI MOSFET Thermal Impedance Model 204 6.5 Verification of the SOI MOSFET Thermal Impedance Model 212 6.6 Summary 216 THE THERMAL IMPEDANCE PRE-PROCESSOR: TIPP 219 VI 1 7. Introduction 219 7.2 A Description of TIPP 220 7.3 Generation of Thermal Equivalent Circuits 225 7.3.1 Approximation of the Thermal Equivalent Poles/Time Constants. 226 7.3.2 Calculation of the Thermal Equivalent Components 230 7.4 The Interface Between TIPP and Circuit Simulators 232 7.5 Summary 234 8 CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK ... 238 8. Conclusions 238 8.2 Recommendations for Future Work 240 8.2.1 The Temperature Dependence of the Thermal Conductivity 240 8.2.2 Models for Thermal Effects Due to Advanced Isolation 242 8.2.3 A Model for Thermal Coupling in SOI MOSFET Circuits 243 REFERENCES 247 BIOGRAPHICAL SKETCH 257 vn Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy PHYSICS-BASED THERMAL IMPEDANCE MODELS FOR THE SIMULATION OF SELF-HEATING IN SEMICONDUCTOR DEVICES AND CIRCUITS By Jonathan Scott Brodsky August 1997 Chairman: Robert M. Fox Major Department: Electrical and Computer Engineering Inherent in the operation of semiconductor devices is self-heating, an increase in operating temperature due to a device's own power dissipation. The magnitude of the self-heating effect can be quantified by the value of the thermal impedance, which describes the dynamic response of the device temperature to variations in device power. The thermal impedance is determined primarily by material properties and device structure. The implication of the self-heating effect is that the change in temperature can alter the operating characteristics of a device, which in turn, can affect circuit performance. The primary focus of this dissertation is the development of physics-based models for the thermal impedances of semiconductor devices. Models for the thermal impedances of bipolar and field-effect transistors, on both bulk and silicon-on- Vlll insulator (SOI) substrates, are presented. All of the thermal impedance models were derived from the time-dependent heat conduction equation, resulting in compact analytic expressions for the thermal impedances. The physical nature of the thermal impedance models allows them to scale with the device structure and material properties, and they successfully reproduce results from both measurements and three-dimensional finite-element simulations. A circuit model for thermal coupling between transistors in a common substrate is also presented. The coupling model was used in conjunction with the bulk bipolar thermal impedance model to extract a lumped electrothermal model for multiple-emitter bipolar transistors. The secondary objective of this work is the provision of an approach for incorporating these models into circuit simulators. It has been shown that the thermal impedance models can be represented by thermal equivalent circuits made up of resistors and capacitors, making them suitable for efficient circuit simulation. The computer program TIPP (Thermal Impedance Pre-Processor) is introduced. TIPP was developed to provide circuit simulators with convenient algorithms for generating thermal equivalent circuits. TIPP can calculate the component values for thermal equivalent circuits from either physical models or measured data, and is easily modified to interface with different circuit simulators. IX CHAPTER 1 INTRODUCTION 1.1 Self-Heating Effects in Semiconductor Devices The physical properties of the materials used to fabricate semiconductor transistors depend on temperature. Therefore, the operating characteristics of a transistor (e.g. electrical currents and potentials), which are determined by the material properties, are also temperature dependent. The temperature at which a transistor operates is determined by the temperature of the surrounding environment (referred to as the "local ambient temperature") and the power dissipated in the device (referred to as the "self-heating effect").

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