SEMICONDUCTOR DEVICE SIMULATION OF LOW-FREQUENCY NOISE UNDER PERIODIC LARGE-SIGNAL CONDITIONS By JUAN EUSEBIO SANCHEZ 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 2002 Copyright 2002 by Juan Eusebio Sanchez To those from the unincorporated area surrounding New Port Richey, Florida. ACKNOWLEDGMENTS I would like to thank my parents Drs. Juan and Ruby Sanchez, and Theresa and Larry Speer for their encouragement and support. I would also like to thank my brothers John Sanchez and William Rockwell for their encouragement. I have been fortunate to stay in contact with many of the friends I grew up with in New Port Richey, Florida. The most “tenured” have been Christopher Tidroski and Christopher Gotwalt. Christopher Gotwalt’s enthusiasm for the PhD process reminds me why I chose graduate school in the first place. While at the University of Florida, I have had the pleasure of meeting some incredibly unique people. Beth Chmelik, Jaime Chmelik, Jim and Sharon Chmelik, Jerome Chu, Susan Earles, Jennifer Fritz, Jennifer Laine, Aaron Lilak, Dave Maring, Carl and Aimee Miester, Heather Smith, Chad and Jodi Uhrick, Racquel White, and Chip Workman have made Gainesville a more enjoyable place to live. I would like to thank my colleagues in the Noise Research Laboratory, Fan- Chi (Frank) Hou, Lisa Kore, Jonghwan Lee, Derek Martin, and Matthew Perkins for their informative discussions. I would also like to thank my advisor, Professor Gijs Bosman, for his direction, encouragement, and careful review of this dissertation. This work was funded in part by the Semiconductor Research Corporation (SRC). Part of this work was completed at Motorola during a summer internship at Motorola in Tempe, Arizona. The methods discussed in this dissertation were implemented in the Florida Object-Oriented Device Simulator (FLOODS), which was written by Professor Mark Law. I would like to thank Professor Law for his assistance, for helpful discussions, and for serving on my committee. iv I would like to thank Professors Jerry Fossum, Ken O, and Loc Vu-Quoc for their suggestions and for serving as my committee members. I would also like to thank Linda Kahila for her assistance in the administrative process. v TABLE OF CONTENTS page ACKNOWLEDGMENTS ............................... iv LIST OF TABLES .................................. ix LIST OF FIGURES .................................. x ABSTRACT ...................................... xiv CHAPTER 1 INTRODUCTION ............................... 1 2 PRINCIPLES OF NOISE AND SEMICONDUCTOR DEVICE SIMULATION 5 2.1 Overview ................................ 5 2.2 Fluctuation Phenomena in Semiconductor Devices ........... 6 2.2.1 Frequency Domain and Spectral Densities ........... 6 2.2.2 Types of Noise .......................... 7 2.3 Newton Iteration Method ........................ 9 2.4 DC Steady-State Device Simulation .................. 10 2.5 Noise Simulation of Semiconductor Devices .............. 12 2.5.1 Small-Signal AC Simulation .................. 12 2.5.2 Noise Simulation ........................ 12 2.5.3 Efficient Simulation of the Scalar Green’s Functions ...... 15 2.5.4 Noise Simulation Examples ................... 16 2.6 Device Simulation in Terms of Circuit Simulation Concepts ...... 17 3 HARMONIC BALANCE ............................ 26 3.1 Example ................................. 26 3.2 Frequency-Domain Jacobian for the Steady-State Solution ...... 28 3.3 Selection of the Number of Harmonics ................. 33 3.4 Device Simulation ............................ 34 3.5 Harmonic Balance Simulation Using Iterative Methods ........ 35 3.5.1 Matrix-Vector Products ..................... 35 3.5.2 Single-Tone Preconditioner ................... 37 3.6 Simulation Results ........................... 38 vi 4 FREQUENCY CONVERSION OF SMALL SIGNALS ............ 49 4.1 Small-Signal Diode Example ...................... 49 4.1.1 Frequency Conversion of an Applied Small-Signal Voltage .. 49 4.1.2 Frequency Conversion of Small-Signal Current Generators .. 50 4.2 Large-Signal Small-Signal Analysis .................. 51 4.3 Cyclostationary Noise Analysis ..................... 55 4.4 Semiconductor Noise Analysis ..................... 59 4.4.1 Frequency Conversion Matrix .................. 59 4.4.2 Noise Analysis for the Semiconductor ............. 59 4.4.3 Iterative methods for Frequency Conversion and Noise Analysis 60 4.5 Simulation Results ........................... 62 5 GENERATION-RECOMBINATION NOISE IN SEMICONDUCTOR DEVICES .................................... 71 5.1 Introduction ............................... 71 5.2 GR Noise for the DC Steady State ................... 72 5.3 Periodic Steady-State GR Noise .................... 75 5.4 Simulation Results ........................... 76 5.4.1 Resistor Simulation ....................... 76 5.4.2 Resistor with 2 Trap Levels ................... 78 5.4.3 Diode Simulation with Majority Carrier Noise in Quasi-Neutral Region .............................. 78 5.4.4 Diode Simulation with GR Noise in the Space Charge Region .80 6 CROSS-SPECTRAL DENSITY SIMULATION ................ 99 6.1 Introduction ............................... 99 6.2 Noise Simulation Under Periodic Large-Signal Conditions ...... 99 6.2.1 The Periodic Steady State .................... 99 6.2.2 The Impedance Field Method .................. 100 6.2.3 Cyclostationary Noise Analysis ................. 102 6.3 Noise Correlation Matrix for Circuit Simulation ............ 105 6.3.1 Theory .............................. 105 6.3.2 Diffusion Noise ......................... 106 6.3.3 GR Noise ............................ 107 6.4 Simulation Results ........................... 109 6.4.1 Shot Noise ............................ 109 6.4.2 GR Noise ............................ 110 7 CONCLUSION ................................. 129 7.1 Summary and Contributions of this Work ................ 129 7.2 Future Work ............................... 129 vii APPENDIX A PERIODIC LARGE-SIGNAL STEADY STATE AND CYCLOSTATIONARY NOISE IMPLEMENTATION IN FLOODS ..... 131 B HARMONIC BALANCE AND CYCLOSTATIONARY NOISE SIMULATION MANUAL ........................... 134 B.1 Introduction ............................... 134 B.1.1 Harmonic Balance ........................ 134 B.1.2 Noise Analysis .......................... 135 B.2 Simulation Commands ......................... 144 B.2.1 circuit: Specifying Stimuli ................. 144 B.2.2 hbcircuit: Extract Response at the Device Terminals . 145 B.2.3 hbdevice: Starting the Simulation .............. 146 B.2.4 pdbSetString Specifying the Noise Sources ........ 148 B.2.5 Accessing the Device Profiles .................. 148 B.2.6 Known Simulation Issues .................... 149 B.3 Examples ................................ 150 B.3.1 Harmonic Balance MOSFET Simulation ............ 150 B.3.2 Diffusion Noise of a Diode ................... 151 B.3.3 Generation-Recombination Noise of a Resistor ......... 152 B.4 MOS Simulation Scripts ........................ 165 B.4.1 hbdevice.ckt: Circuit Elements .............. 165 B.4.2 hbdevice.cnt: Contact Specification ............ 165 B.4.3 hbdevice.phy: Device Physics ............... 165 B.4.4 hbdevice.test: Initial Solution .............. 166 B.4.5 hbdevice.swp-hb: Initial Solution ............. 166 B.4.6 pscripts: Prints Solution to screen ............. 167 B.4.7 sweeps.tcl: Initial Solution ................. 168 B.4.8 hbfuns.tcl: Harmonic Balance Simulaton ......... 169 B.5 GR Noise Example Script ........................ 169 REFERENCES .................................... 172 BIOGRAPHICAL SKETCH ............................. 178 viii LIST OF TABLES Table page 2.1 Comparison of device and circuit simulation ................ 17 5.1 Trap parameters for the 5 µm resistor example ............... 78 6.1 Device simulation variables ......................... 104 A.1 Components added to the simulator. ..................... 132 A.2 Components modified in the simulator. ................... 133 B.1 Description of MOS simulation files ..................... 151 ix LIST OF FIGURES Figure page 2.1 Overview of FLOODS ........................... 18 2.2 Types of noise ................................ 19 2.3 Discretized volume ............................. 20 2.4 Noise contribution per unit length to the output for a 1-D diode ...... 21 2.5 The 2-D diode structure ........................... 22 2.6 Comparison of simulated and theoretical results for the current noise of the 2-D diode structure ........................... 23 2.7 Electron diffusion noise contributions to the contact of the 2-D diode ... 24 2.8 Hole diffusion noise contributions to the contact of the 2-D diode ..... 25 3.1 Diode circuit ................................. 40 3.2 Doping profile for the 0.4 µm transistor .................. 41 µ 3.3 IDS versus VDS for the 0.4 m transistor .................. 42 µ 3.4 IDS versus VGS for the 0.4 m transistor .................. 43 3.5 The HB test circuit ............................. 44 ( ) 3.6 IDS versus periods of VGS t for the circuit of Figure 3.5 .......... 45 ( ) ( ) 3.7 IDS t versus VGS t ............................. 46 3.8 Fourier coefficients of the electron concentration .............. 47 3.9 Fourier coefficients of the potential ..................... 48 4.1 The diode as a small-signal conductance in the presence of a small-signal voltage source ................................ 63 4.2 Small-signal current response of the diode ................