I Introduction to Theory of Phase Transition 9 1 Demystifying Phase Transition 13 1.1 Introduction: The mystery of phase transition 13 1.2 Buckling of a slender beam captures the essence of phase transition 14 1.3 Snap transition of an pre-buckled stick 19 1.4 A few observations about phase transition 25 1.5 Minimum Energy, Maximum Flow, and Maximum Entropy Principles 27 1.6 Conclusions 28 2 Phase Transition in NEMS 31 2.1 Introduction: MEMS/NEMS phase transition 31 2.

2 Equilibrium Phase transition of MEMS/NEMS 32 2.3 Negative capacitance and spring softening 39 2.4 Phase transition and hysteretic response 42 2.5 Dynamics of electro-mechanical switches: Unsteady phase transition 46 2.6 Conclusions 50 3 Electronic Phase Transition in Ferroelectrics 53 3.1 Introduction: What is a ferroelectric material 53 3.2 A simple model for ferroelectric capacitors 54 3.3 Landau Theory of Phase Transition 58 3.

4 Conclusions 63 4 Material Phase Transition by van der Waals Theory 65 4.1 Phase transition in Homogeneous systems 65 4.2 vdW equation in terms of critical vc, pc, Tc 68 4.3 Implications of scaled vdW equation 71 4.4 Energy functions of vdW equation 73 4.5 Conclusions 75 5 Phase-Field Theory Describes Semiconductor Memories 77 5.1 The need for a phase-field theory 78 5.2 Phase-Field model generalizes Landau Theory 78 5.

3 Approximate solution of the phase field model 80 5.4 Conclusions 84 II Phase Transition in Transistors 87 6 Voltage-Driven Phase Transition in Logic Transistors 93 6.1 Phenomenological theory of NCFETs 94 6.2 NCFET Design by FE negative capacitance 96 6.3 Hysteresis as a by-product of AV maximization 101 6.4 ZSubFET for Hysteresis-free abrupt switching 103 6.5 Physics-based Circuit Model for NCFET 107 6.6 Features of NCFET I-V Characteristics 108 6.

7 Conclusions 112 7 Channel Phase Transition 117 7.1 Introduction to MottFET and PhaseFET 117 7.2 Theory of electronic phase transition 118 7.3 Theory of MottFET 123 7.4 Theory of PhaseFET 127 7.5 Conclusions 130 8 Current Driven Phase Transition 135 8.1 Steep switching in RTD, TFET, and NEMFET 136 8.2 RTD: Device structure and band diagram 136 8.

3 Single Electron Transistors 141 8.4 Principles of Tunnel FET 144 8.5 NEMS-relay as a logic transistor, NEMFET 149 8.6 Conclusions 153 9 SuperFET 157 9.1 Negative Capacitance Tunnel FET (NC-TFET) 158 9.2 Phase-Change Tunnel FET (PC-TFET) 159 9.3 Conclusions 161 III Phase Transition in Memories 163 10 Two-terminal non-volatile memories 167 10.1 Introduction 168 10.

2 Physics of FeRAM Memory 168 10.3 Physics of RRAM memory 175 10.4 Physics of Phase change memory 182 10.5 Memories based on Tunnel Junction 186 10.6 Conclusions 188 11 FeFET 193 11.1 Introduction 193 11.2 Device structure and I − V characteristics 194 11.3 Design of FeFET gate stack 195 11.

4 Threshold voltage and Memory Window 196 11.5 Conclusions 205 IV Phase Transition in Biosensors 209 12 Frequency and Amplitude Phase Transition in BioMEMS 213 12.1 Introduction 213 12.2 The classical cantilever BioMEMS 214 12.3 Bifurcation biosensing and amplitude phase transition 219 12.4 Conclusions 222 13 Phase-Transition in Electro-mechanical Biosensors 225 13.1 Introduction 225 13.2 Principle of Operation of FlexureFET 226 13.

3 Biomolecule adsorption changes spring constant 229 13.4 Signal-to-Noise Ratio 232 13.5 Conclusions 236 14 Phase-Transition in Potentiometric Nano-Biosensors 239 14.1 Introduction 239 14.2 Charging of the oxide/electrolyte surface 241 14.3 Qsurf is balanced by Qdl and Qs 243 14.4 Sensor I-V Characteristics 245 14.5 Figures of merit: Sensitivity and buffer capacity 246 14.

6 NCFET improves ISFET sensitivity 248 14.7 Signal-to-noise ratio of ISFET and NC-ISFET 250 14.8 Conclusions 252 V Phase transition in Circuits 255 15 Circuit Applications of Phase-Transition Transistors 259 15.1 Introduction 259 15.2 CMOS Inverter with NCFET 260 15.3 Performance of an SRAM Cell with NCFET 261 15.4 Ring Oscillator with NCFET 264 15.5 A PhaseFET inverter 266 15.

6 RO and PTM-based Relaxation Oscillator 268 15.7 Conclusions 270 16 NEMFET Logic Circuits 273 16.1 Introduction 273 16.2 4-T and 6-T relays for complementary logic 274 16.3 An inverter created by 4-T NEMFETs 275 16.4 4-T NEM-relay can implement Complex Logic 277 16.5 6-T see-saw logic 278 16.6 Conclusions 279 17 Neuromorphic Circuits 283 17.

1 The need for a new computing model 283 17.2 Introduction to Neural Networks 284 17.3 Operation of "non-spiking" NNs 287 17.4 Challenges of NN based on phase-transition memories 290 17.5 Cross-bar architecture with FeFET 294 17.6 Conclusions 296 18 Oscillator-based Phase Logic 301 8.1 Phase-based logic vs other logic models 301 18.2 Sub-Harmonic Injection Locking (SHIL) creates oscillators with discrete phases 303 18.

3 Boolean logic with Coupled Oscillators 309 18.4 Coupled oscillators solve optimization problems 310 18.5 Conclusions 317 19 Conclusions and Outlook 321 VI Appendices 325 Appendix A Fundamentals of Semiconductor Physics 327 A.1 Introduction 327 A.2 Conclusions 331 Appendix B Theory of Classical MOSFET 333 B.1 Device structure and Operating principle 333 B.2 Drain Current Analytical Model 334 B.3 Conclusions 348 Appendix C MOSFET as charge, pH, and image sensors 349 C.

1 Introduction: MOSFET is a versatile device 349 C.2 Conclusions 353 Appendix D Basic Digital Circuit Elements 355 D.1 Introduction 355 D.2 CMOS Inverter 356 D.3 SRAM 359 D.4 DRAM 360 D.5 Ring Oscillator 361 D.6 Conclusions 363 Appendix E Minimum Energy, Maximum Flow, and Maximum Entropy 365 E.

1 Background and Introduction 365 E.2 Lagrange Principle unifies Conservative and Dissipative Systems. 369 Appendix F Energy-Power Landscape of Semiconductor Memories 375 F.1 Introduction 375 F.2 DRAM and Flash Memory store information by minimizing electrostatic energy 375 F.3 SRAM state defined by power minimization 380 F.4 Frustrated Stability of a Ring Oscillator 383 F.5 Conclusions 384 Appendix G Low power Boltzmann Electronics 385 G.

1 Introduction 385 G.2 Cryogenic electronics reduces S, but increase ION/IOFF ratio 386 G.3 Near Threshold Computing reduces VDD → VT 388 G.4 Approximate Computing trades off precision for power 388 G.5 Conclusions 390 Appendix H Model Parameters 393 H.1 Part II - NCFET 393 H.2 Part II - PhaseFET Phenomenological Model 394 H.3 Part III 395 H.

4 Part III - FeFET Simulation 397 H.5 Part IV 398 H.6 Appendix - CMOS Inverter 398 Appendix I List of Symbols 401 Appendix J Physical constants.