Index. 1-π model, 370 1/f noise, 57, π model, 373 β-ratio, 425

Transcription

1 Index 1-π model, 370 1/f noise, 57, π model, 373 β-ratio, 425 A Ac symmetry test, 93 Acoustic phonons, 18 Admittance parameters, 209 All-around gate, 397, 410 Analytic potential model, 432, 447 Analytical approximations, 7 Asymmetric 2-π model, 375 Available bandwidth, 212 Avalanche, 214, 308 breakdown, 300 current, 238 current noise, 241 B Back-end of line (BEOL), 360 Back-gate induced bulk charge, 54 Balun, 380 Band-to-band tunneling, 46, 300, 307 Bandgap, 219 Bandgap circuit, 482 Base, 46 Base current components, 238 Base width, 169 Base-collector capacitance, 194 Base-collector junction, 168 Base-emitter junction, 168 Benchmark tests, 75 Bessel and Neumann functions, 444 Binning, 421 Bipolar gain, 47 Bipolar junction transistors, 167 BJTs, 167 Body contact, 53 Body doping, 421 Body factor, 5 Body potentials, 43 Body resistance, 42, 53 Body sheet resistance, 54 Body-contacted, 53 Body-contacted SOI nmosfet, 47 Boltzmann relation, 5 Boolean function, 50 Boundary condition, 5 Boundary conditions, 61 Backward propagation of variance (BPV), 491, 492 Brews model, 9 BSIM, 397 BSIM-CMG, 399, 409 BSIM-IMG, 399 BSIM-MG, 397 BSIM3, 397 BSIM4, 397, 425 BSIMSOI, 397 Built-in potential, 170 Built-in voltage, 318 Bulk charge, 122 Bulk charge effects, 144 Bulk FinFET, 397, 421 G. Gildenblat (ed.), Compact Modeling, DOI / , Springer Science+Business Media B.V

2 522 Index Bulk MOSFET, 64 Buried oxide, 43 C Capacitance, 52, 207 Capacitive coupling, 44 Channel induced gate noise, 57 Channel length modulation, 120, 124 Channel thermal noise, 139 Channel voltage, 5 Charge conservation, 407 Charge Control Relation, 216, 218 Charge density, 4 Charge neutrality, 10 Charge sheet approximation, 9, 83, 123, 432 Charge sheet model, 63, 83, 446 Charges, 206 Chemical mechanical polishing, 398 Cold S parameters measurements, 247 Collector, 46 Common centroid structures, 465 Common multi-gate (CMG), 409 Common-centroid structure, 466 Compact modeling, 3 Compressive stress, 461 Computational efficiency, 421 Computationally efficient, 415 Condition number, 505 Corner frequency, 58 Corner models, 514 Correlation coefficient between gate and drain thermal noise, 101 Coulomb scattering, 14 Covariance, 503 Critical current, 236 Cross-correlation, 142 Cross-coupled devices, 466 Current factor mismatch, 472 Current sheet, 362 Current sheet model, 362 Cut-off frequency, 214, 226 CV method, 247 D DC emitter current crowding, 239 Depletion charges, 225, 234 Derivation of spatial behavior, 485 Device invariant, 214 DIBL, 120 Dielectric permittivity, 4 Diffused resistor, 279 Diffusion capacitances, 47 Diffusion charges, 225 Direct gate tunneling, 43 Distortion, 260 Distribution effects, 56, 208, 240 Double-gate, 440, 447, 448 Double-gate FinFET, 397, 410 Double-gate MOSFET, 64, 431, 445 Drain charge, 122 Drain induced barrier lowering, 417 Drift region, 110 Drift-diffusion theory, 123 Dynamic depletion, 42, 60 Dynamic depletion effects, 41 Dynamic feedback, 425 Dynamically depleted SOI MOSFETs, 60, 61 E Early effect, 173, 218, 237 Early voltage, 47 Ebers-Moll model, 182 Eddy current, 371, 372 Effective channel mobility, 14 Effective electron mass, 30, 49 Effective lateral field, 15 Effective mass, 416 Effective width, 419 Electrical performances, 502 Electron and hole concentrations, 4 Electron conduction band tunneling (ECB), 31, 48 Electron current density, 177 Electron generation and recombination rates, 177 Electron quasi-fermi potential, 177 Electron valence band tunneling (EVB), 31, 42, 48 Electron-phonon interaction, 14 Emitter, 46 Emitter resistance, 239 Emitter-base junction, 46 Epilayer, 217 Equilibrium noise, 143 Equivalent circuit, 28 Equivalent oxide thickness, 417 Excess noise spectral density, 58

3 Index 523 External base resistance, 239 External collector resistance, 239 F Fermi potential, 45 Filling factor, 363 FinFET, 397 FinFET SRAM, 425 Fingers, 29 Finlay, 368 Flat-band voltage, 52 Flicker noise, 32 Floating body effect, 41, 43, 58, 68 Forward and reverse Early voltages, 173 Forward Gummel plot, 192 Forward propagation of variation, 492 FPV, 492 Frlan, 368 Full depletion, 42 Fully depleted, 68 G g m /I d,79 Gain factors, 500 Gate contacts, 29 Gate oxide, 43, 48 Gate tunneling, 29 Gate tunneling current, 396 Gate-induced drain leakage current, 32, 51, 421 GIDL, 27 Gate-induced drain/source leakage, 44 Gate-induced source leakage current, 32 GISL, 32 Gate-to-body tunneling current, 48 Gate-tunneling current, 58 Generalized ICCR (GICCR), 237 Geometrical scaling, 204, 214 Geometry dependence, 242 Gradients, 460 Grading coefficient, 301 Gradual channel approximation, 4, 123, 434, 446 Green s function based solution, 242 Gummel integral charge control relation, 177 Gummel number, 216, 218 Gummel plot, 47, 48 Gummel symmetry test, 80, 85 Gummel-Poon (GP) model, 47, 130, 179 H Harmonic balance simulation, 87 Harmonic distortion, 87 Heterojunction bipolar transistors, 167, 217, 231 HBTs, 167 HiCuM, 231 High frequency noise, 241 High voltage MOS transistors, 105 High-frequency capacitance, 335, 342 High-frequency substrate coupling, 240 High-K gate dielectric, 396 High-level injection, 47, 180 Higher order derivatives, 86, 87 Hole valence band tunneling, 31 Hot carrier current, 222 Householder s cubic iteration method, 413 HVB, 48 Hysteresis behavior, 51 I ICCR, 177 Ideal current, 302 Ideal junction current, 300 Ideality factor, 302, 311 Impact ionization, 27, 29, 42, 43, 45, 58 Impact ionization current, 421 Impact ionization exponent, 45 Imref splitting, 5 Independent double-gate FinFET, 398 Independent double-gate MOSFET, 399 Induced bulk current noise, 101 Induced gate noise, 34, 96, 101, 141 Induced substrate noise, 143 Injection region, 224 Integral charge-control relation, 237 Interlayer dielectrics (ILD), 360 Internal base resistance, 239 Internal transistor model, 239 Intrinsic fluctuations, 139 Inversion charge density, 63 J JFETs, 112 Joule heat, 51 JUNCAP2, 299 JUNCAP2 express, 313 Junction capacitance(s), 129, 300 Junction leakage, 46

4 524 Index Junction noise, 300 Junction shot noise, 309 K Kirk effect, 107, 214, 221 Knee current, 47, 218 Knee frequency, 34 Kull model, 220 Kull-Nagel model, 186 L Ladder circuit, 370, 371 Lateral electric field, 124 Lateral flux, 361 Lateral substrate RC coupling, 375 Lay-out common centroid, 466 LDMOS, 105 Leakage inductance, 381 LER, 493 Line edge roughness (LER), 426, 493 Linear charge partition, 445 Litho-proximity effect, 459 Lithography errors, 456 LNA, 367 Local optimization, 245 Lorentzian noise spectrum, 33 Low frequency noise, 57, 241 Low-field mobility, 273 Low-noise amplifiers, 32 M Magnetic coupling coefficient, 381 Majority carriers, 44 Matthiessen s rule, 14 Maximum velocity saturation, 124 McAndrew symmetry, 32 Measuring offset and mismatch, 477 Metal gate electrodes, 396 Mextram, 199 MIM, 360 Minority carrier diffusion length, 47 Mismatch, 453 Mismatch for various processes, 474 Mismatch in strong and weak inversion, 472 Mixer, 367 Mobile charges, 235 MOCVD, 189 Modified symmetry test (MST), 91, 92 Monte Carlo simulation, 426 MOS threshold mismatch, 469 MOS varactor, , 333, 336, , 346, 347, 350, 351 MOSVAR, , 333, , 341, 342, 346, 347, Multi-gate devices, 396 Multiple V th flavors, 410 Multiple-gate device(s), 43, 448 Mutual heating, 203 Mutual inductance, 380 N Nanowire, 448 Nanowire MOSFET(s), 397, 431, 437, 438, 440, 444, 445, 447 Narrow-width effects, 56 Newton Raphson iteration, 417 Newton-Raphson procedure, 7 Nodal charge, 122 Nodal voltage, 52 Noise, 204 Noise margins, 46 Noise spectra, 33 Non-ideality factors, 183 Non-quasi-static (NQS), 28, 93, 240 Non-uniformity, 13 Normalized base charge, 47, 179 Normalized body factor, 10 Nyquist relation, 139 O OD-spacing effect, 462 Offset voltage, 194 Offsets, 453 Ohmic carrier transport, 221 On-resistance, 107 ON/OFF ratio, 41 OPC, 492 Optical proximity correction, 492 Orthogonality relationship, 442, 444 Overlap, 27 Overlap capacitances, 27 Overview of matching models, 476 Oxide capacitance, 5 Oxide permittivity, 5 Oxide thickness, 5

5 Index 525 P Pao-Sah model, 83 Pao-Sah s integral, 432, 435, 437 Parameter extraction, 42, 244, 386 Parameter fluctuation model, 467 Parasitic BE capacitance, 240 Parasitic bipolar current, 47 Parasitic bipolar effect, 46 Parasitic bipolar transistor, 42, 46 Parasitic BJT effect, 108 Parasitic PNP-transistor, 207 Parasitic substrate transistor, 241 Partial depletion, 42, 414 Partially depleted, 41, 68 Partially-depleted SOI devices, 42 Pass-gate logic, 47 Passitivity, 369 PCA, 492 PD-SOI MOSFETs, 43, 46 Perturbation, 402, 411 Phase shift, 240 Phase-shift masking, 492 Pinch-off, 109 Planar double-gate SOI, 398 Pocket implants, 21 Poisson s equation, 400, 411 Poly-silicon gate depletion, 396 Poly-space effect, 463 Polysilicon, 29 Possion s equation, 61 Power amplifiers, 367 Primary and secondary windings, 388 Principle component analysis, 492 Process control monitor, 243 Process tolerances, 243 Process variation, 498 Process-voltage-temperature PVT analysis, 455 Proximity effect, 374, 458 PSM, 492 Pulsed measurements, 132 Punch-through effect, 23 Q Q, 328, 330, 347, 349, 350 Q for a transformer, 385 Quadruple-gate, 410 Quality-factor Q, 363 Quantum mechanical effects, 415, 419 Quasi-Fermi level, 434 Quasi-neutral body, 47 Quasi-neutral body region, 54 Quasi-saturation, 220, 222 Quasi-saturation effect, 108 Quasi-static, 28 Quasi-static approximation, 141 R Random dopant fluctuation (RDF) effect, 396 Random fluctuations, 466 RDF, 400, 426 Reciprocity, 82 Recombination current, 47 Recombination-generation current, 47 Resistivity, 273 RESURF, 107 Reverse Gummel plot, 193 RF CMOS, 327, 328, 348 RF LDMOS, 109 S Saturation, 206, 220 Saturation current, 47, 173 Saturation velocity, 17 Scale length, 418, 444 Scale length model, 432 Scharfetter-Gummel model, 18 Self inductances, 388 Self-heating, 42, 203, 287 Self-heating effect, 51, 96, 108 Self-resonant frequency, 366, 370, 386 Series resistance, 47, 239 Shallow trench isolation (STI), 124, 462 Sheet resistance, 29, 273, 359 Shockley-Read-Hall (SRH) process, 175, 300, 302 Short channel effect, 417 Shot noise, 34, 95 SiGe HBT, 231 Silicide, 29 Silicon trench isolation, 462 Skew, 495 Skin and proximity effects, 366 Skin/proximity effects, 370 SLCSM, 12 Slope of the harmonic, 88

6 526 Index Slope ratio, 77 Slope ratio test, 77 Small-geometry effects, 67 SOI FinFET, 397, 421 SOI MOSFETs, 43, 45 SOI multi-gate, 419 Solenoid, 361 Source/drain symmetry, 415 Specific contact resistance, 29 Spectral density, 58, 96 Spiral inductors, 358, 362 SRF, 366, 370 Static noise margin (SNM), 425 Statistical modelling, 243 Statistical variations, 454 Statistics for mismatch, 480 Strained silicon, 396 Stress, 461 Subcircuit, 52 Substrate current, 45 Substrate depletion capacitance, 240 Substrate effects, 240 Substrate inductance, 376 Substrate transconductance, 147 Substrate-eddy-π model, 376 Subthreshold region, 45 Super-shot noise, 148 Supply function, 30 Surface electric field, 5 Surface potential equation, 4, 61 Surface potential midpoint, 12 Surface potentials, 400 Surface recombination velocity, 176 Surface roughness scattering, 14, 397 Surface-potential-based approach, 3 Surface-roughness, 124 Surrounding-gate MOSFET, 431 Symmetric linearization method, 4, 9, 41, 43, 64, 447 Systematic offsets, 456 Systems-on-chip, 57 T T-model(s), 375, 377 Temperature coefficient, 359 Temperature dependence, 203, 421 Temperature effects, 241 Tensile stress, 461 Test structure approach, 479 Thermal capacitance, 241 Thermal channel noise, 95 Thermal conductance, 53 Thermal coupling, 241 Thermal noise, 34, 57, 96 Thermal resistance, 52, 241 Threshold voltage, 48 Topology, 205 Transcapacitance(s), 13, 68, 81, 407, 445 Transconductance efficiency g m /I ds, 405 Transfer current, 236 Transformers, 367 Transient switching, 46 Transit time, 47, 225, 236 Transmission coefficient, 30 Transmission line model, 98 Transmission-gate multiplexer, 50 Transport factor, 47 Trap-assisted tunneling, 46, 300, 305 Tree-top test, 79 Triple-gate FinFET(s), 397, 410 Tsu-Esaki equation, 30 Tsu-Esaki formulation, 49 Tunneling, 239 Tunneling barriers, 30 Tunneling current(s), 27, , 352 Tunneling current density, 30 Tunneling transmission coefficient, 49 U Unilateral gain, 214 V V th tuning, 424 Valence band, 49 Variability, 424, 425, 454, 492 Variational method, 416 VCO, 327, 347, 348, , 367 Vector network analyzer, 247 Velocity saturation, 17, 67, 120, 285 Velocity saturation effects, 57 Vertical doping non-uniformity, 23 Volume inversion, 436 W Ward-Dutton charge partition, 408 Ward-Dutton partition, 13, 66 Weak inversion, 77

7 Index 527 Webster effect, 218 Well-proximity effect, 460 Wheeler, 362 Wheeler formula, 365 White-noise gamma factor, 95 WKB approximation, 49 Worst-case, 495 Y Yield, 483