Gennady Gildenblat. Editor. Compact Modeling. Principles, Techniques and Applications. Springer

Transcription

1 Gennady Gildenblat Editor Compact Modeling Principles, Techniques and Applications Springer

2 Contents Part I Compact Models of MOS Transistors 1 Surface-Potential-Based Compact Model of Bulk MOSFET 3 Gennady Gildenblat, Weimin Wu, Xin Li, Ronald van Langevelde, Andries J. Schölten, Geert D.J. Smit, and Dirk B.M. Klaassen 1.1 Introduction Surface Potential Equation Symmetric Linearization Method The Effective Channel Mobility Velocity Saturation Lateral Doping Non-uniformity Punch-Through Effect and Vertical Doping Non-uniformity The Extrinsic Model Overlap Region Charges Parasitic Resistances Impact Ionization Current Gate Tunneling Current Gate-Induced Drain Leakage Current Surface-Potential-Based Noise Model Flicker Noise Thermal Noise Other Noise Sources Conclusions 35 References 36 2 PSP-SOI: A Surface-Potential-Based Compact Model of SOI MOSFETs 41 Weimin Wu, Wei Yao, and Gennady Gildenblat 2.1 Introduction PD-SOI Floating Body Effect Modeling Impact Ionization 45 ix

3 x Contents Junction Diode Parasitic Bipolar Current Gate-to-Body Tunneling Current Gate-Induced Drain Leakage Current Self-Heating Effect Body Contact Model Noise Modeling PD-SOIMOSFET Model Verification Modeling of Dynamically Depleted SOI MOSFETs Surface Potential and Coupling Equations Symmetrically Linearized Charge-Sheet Model for DD-SOI DD-SOI Model Verification and Discussion Conclusions 70 References 70 3 Benchmark Tests for MOSFET Compact Models 75 Xin Li, Weimin Wu, Gennady Gildenblat, Colin С McAndrew, and Andries J. Schölten 3.1 Introduction Benchmark Tests Weak and Moderate Inversion Regions Capacitances Symmetry and Non-Singularity at Zero Drain-Source Bias Non-Quasi-Static (NQS) and Noise Model Tests Self-Heating Effect Test (SHE) Conclusion 98 Appendix 1 Derivation of (3.49) and (3.50) 98 Appendix 2 Correlation Coefficient Between Gate and Drain Thermal Noise at V ds =0 101 References High-Voltage MOSFET Modeling 105 E. Seebacher, К. Molnar, W. Posch, В. Senapati, A. Steinmair, and W. Pflanzl 4.1 Introduction HV LDMOS Modeling with Sub-Circuits HV MOSFET Sub-Circuit Using a Drain Resistor HV MOSFET Sub-Circuit Using a JFET HV MOSFET Sub-Circuit Using Three JFETs HV MOSFET Sub-Circuit Using JFETs, Resistors and Controlled Sources Symmetrical HV MOSFET Sub-Circuit with Bulk Current Modeling EKV High-Voltage MOSFET Model EKV-HV DC Model EKV-HV Charge Model 118

4 Contents xi 4.4 MM20 High-Voltage MOSFET Model MM20 DC Model MM20 Charge Model HiSIM_HV High-Voltage MOSFET Model HiSIM_HV Model Features Resistance Modeling with HiSIM_HV Capacitance Modeling with HiSIM_HV Modeling of HV MOSFET Parasitics in HV CMOS Technology Substrate Based Devices Isolated Devices Measurement Requirements for HV MOS Modeling DC Measurements for HV MOS Modeling AC Measurements for HV MOS Modeling Pulsed Measurements for HV MOS Modeling 132 References Physics of Noise Performance of Nanoscale Bulk MOS Transistors 137 R.P. Jindal 5.1 Introduction Preliminary Considerations Intrinsic Fluctuations Channel Thermal Noise Induced Gate Noise Induced Substrate Noise Equilibrium Noise Bulk Charge Effects Extrinsic Fluctuations Gate Resistance Noise Substrate Resistance Noise Substrate Current Super-Shot Noise Gate Current Noise Short-Channel Effects Physical Origin Effect On Channel Noise No Excess Noise School of Thought Shot Noise School Of Thought Hot Carrier School of Thought //Noise Number versus Mobility Fluctuations Debate Current Status Noise Capabilities of Compact MOS Models Conclusions 158 References 159

5 xii Contents Part II Compact Models of Bipolar Junction Transistors 6 Introduction to Bipolar Transistor Modeling 167 Colin C. McAndrew and Marcel Tutt 6.1 Introduction Basic Bipolar Transistor Operation and Modeling Base Current Gummel Integral Charge Control Relation SPICE Gummel-Poon Model Small-Signal Model Kull-Nagel Model III-V HBTs: Device Physics and Modeling Challenges Conclusions 195 References Mextram 199 R. van der Toorn, J.C.J. Paasschens, W.J. Kloosterman, and H.C. de Graaff 7.1 Introduction History Lumped-Element Modeling Modeling Time-Dependence, Non-Linearity, Large Signals Temperature Dependence and Heating Noise Model Geometric Scaling and Statistical Modeling Model Structure and Components Outline Relevance of Model Structure to Modeling Results Mextram Philosophy Introduction Main Transistor Current Model Conclusion 226 References The HiCuM Bipolar Transistor Model 231 Michael Schröter and Bertrand Ardouin 8.1 Introduction Model Fundamentals Charges Transfer Current Base Current Components Series Resistances NQS Effects Substrate Effects Temperature Effects Noise 241

6 Contents xiii Geometry Dependence Statistical and Predictive Modelling Parameter Extraction Parameter Extraction Methods Application Examples Conclusions 260 References 263 Part Ш Compact Models of Passive Devices 9 Integrated Resistor Modeling 271 Colin С McAndrew 9.1 Introduction Semiconductor Resistors Effective Resistor Geometry and Total Resistance Resistor Temperature Dependence Terminal Resistor Models Physical 3-Terminal Resistor Model Diffused Resistor (JFET) Depletion Effect Model Poly Resistor Depletion Effect Model Unified Depletion Effect Model Velocity Saturation Self-Heating Complete 3-Terminal Resistor and JFET Model Parasitics, Noise and Statistical Modeling Parameter Extraction Details of Model Implementation Conclusions 295 References The JUNCAP2 Model for Junction Diodes 299 A.J. Schölten, G.D.J. Smit, R. van Langevelde, and D.B.M. Klaassen 10.1 Introduction Model Derivation Capacitance Ideal Current Shockley-Read-Hall Current Trap-Assisted Tunneling Current Band-to-Band Tunneling Current Avalanche Breakdown Current Noise Geometrical Scaling Parameter Extraction Test Structures Extraction of CV Parameters Extraction of IV Parameters 311

7 xiv Contents 10.4 Model Verification Capacitances Currents JUNCAP2 Express Model Implementation and Availability Conclusion 318 Appendix 1 Built-in Voltage 318 Appendix 2 Evaluation of WSRH 320 Appendix 3 Evaluation of Wr 320 Appendix 4 Evaluation of Гщдх, 321 Appendix 5 Approximation of the erfc-function 322 Appendix 6 JUNCAP2 Express 323 References Surface-Potential-Based MOS Varactor Model 327 Zeqin Zhu, Gennady Gildenblat, James Victory, and Colin С McAndrew 11.1 Introduction Device Technology Intrinsic Device Model Inversion Layer Inertia Relaxation Time Approximation Analytical Solution for the Small-Signal Case The Effects of Finite Polysilicon Doping and Quantum Mechanical Corrections Gate Tunneling Current Parasitic Elements Parasitic Capacitance C/ r Gate Tunnel Current in the Overlap Region Parasitic Resistances Silicon Data Validation of RF Model Circuit Applications Examples Conclusions 352 References Modeling of On-chip RF Passive Components 357 Zhiping Yu 12.1 Introduction Circuit Requirement and Applications for On-chip RF Passive Components R and С Realization in RF CMOS С Resistors Capacitors in 1С Process Inductors and Transformers Non-planar Inductors: Solenoid Spiral Inductors from Current Sheet 362

8 XV CMOS Spiral Inductors Planar Transformers Monolithic Spiral Transformers: Structures Modeling of Spiral Inductors and Transformers Characterization of Spiral Inductors Г Model for Spiral Inductors jr Model for Spiral Inductors Improved l-тг Models for Spiral Inductors Models for Transformers and Baluns Parameter Extraction for Transformer Model Summary 388 References 390 IV Modeling of Multiple Gate MOSFETs Multi-Gate MOSFET Compact Model BSIM-MG 395 Darsen Lu, Chung-Hsun Lin, Ali Niknejad, and Chenming Hu 13.1 Introduction Various Flavors of Multi-gate MOSFET BSIM-MG and BSDVI-CMG Core Model for the Independent Double-gate MOSFET Basic Modeling Framework Surface Potential Calculation Drain Current Model Capacitance Model Core Model for the Common Multi-gate MOSFET Basic Modeling Framework Surface Potential Calculation Drain Current Model Capacitance Model Real Device Effects Quantum Mechanical Effects Short-Channel Effects Effective Width Model Bulk and SOI Substrate Models Other Real Device Effect Models Experimental Verification Computational Efficiency Simulation Examples V t h Tuning Simulation for Independent Double-gate MOSFETs FinFET SRAM Technology and Simulation Examples Statistical Simulation of FinFET SRAM Cells 425 References 426

9 xvi Contents 14 Compact Modeling of Double-Gate and Nanowire MOSFETs Yuan Taur 14.1 Introduction Analytic Potential Models for Double-Gate and Nanowire MOSFETs Analytic Solutions to Double-Gate MOSFETs Analytic Solutions to Nanowire MOSFETs Explicit, Continuous Solutions to the Implicit Equations Short-Channel Models Short-Channel Model for Double-Gate MOSFETs Short-Channel Model for Nanowire MOSFETs Charge and Capacitance Models Discussion of Surface-Potential Based Current Expression Conclusion 447 References 448 Part V Statistical Modeling 15 Modeling of MOS Matching 453 Marcel Pelgrom, Hans Tuinhout, and Maarten Veitregt 15.1 Introduction Variability: An Overview Deterministic Offsets Offset Caused by Electrical Differences Offset Caused by Lithography Proximity Effects Temperature Gradients Offset Caused by Stress Offset Mitigation Random Matching Random Fluctuations in Devices MOS Threshold Mismatch Current Factor Mismatch Current Mismatch in Strong and Weak Inversion Mismatch for Various Processes Application to Other Components Modeling Remarks Measuring Offset and Mismatch Matched Pair Test Structures Mismatch Measurement Precision Considerations Statistics for Mismatch Characterizations Consequences for Design Analog Design Digital Design 484

10 Contents xvii 15.7 Conclusion 485 Appendix: Derivation of Spatial Behavior 485 References Statistical Modeling Using Backward Propagation of Variance (BPV) 491 Colin С. МсAndrew 16.1 Introduction Sources of Statistical Variability Statistical Modeling Basis Statistical Modeling Requires Engineering Judgment Modeling Parameter Correlations Using Uncorrelated Parameters Theoretical Formulation of BPV BPV Requirements BPV Application Examples Corner Models Why Modeling Correlations is Important Conclusions 519 References 519 Index 521