Appendix A Universal Physical Constants978-1-4939-2751...Appendix A Universal Physical Constants Constant Symbol Value Avogadro’s constant A0,NA,L 6.0225 × 10 23/mol Boltzmann constant

Appendix AUniversal Physical Constants

Constant Symbol Value

Avogadro’s constant A0, NA, L 6.0225 × 1023/mol

Boltzmann constant k, kB 1.3807 × 10−23 J/K8.6174 × 10−5 eV/K

Electron rest mass m0 9.1094 × 10−31 kg

Electron-Volt eV 1.6022 × 10−19 J

Elementary charge q, e 1.6022 × 10−19 C

Energy equivalent of rest mass 0.5110 MeV

Gravitational acceleration g 9.9067 m/s2

Natural logarithm e 2.7183

Permittivity in vacuum ε0 8.8542 × 10−14 F/cm

Pi π 3.1416

Planck’s constant h 6.6261 × 10−34 Js4.1456 × 10−15 eV·s

Planck’s constant/2π �h 1.0546 × 10−34 Js

Speed of light c 2.9980 × 108 m/s

Thermal energy kT 0.02586 eV at 300 K

Thermal voltage kT/q 0.02586 V at 300 K

© Springer Science+Business Media New York 2015B. El-Kareh and L.N. Hutter, Silicon Analog Components,DOI 10.1007/978-1-4939-2751-7

583

Appendix BProperties of Silicon and GermaniumCrystals (300 K)

Property Symbol Unit Si Ge

Atomic number 14 32

Atomic weight g/mol 28.08 72.59

Atomic density cm−3 5.0 × 1022 4.42 × 1022

Crystal structure Diamond Diamond

Density g/cm3 2.328 5.327

Density of surface atoms

(100) cm−2 6.78 × 1014 6.27 × 1014

(110) cm−2 9.59 × 1014 8.87 × 1014

(111) cm−2 7.83 × 1014 7.24 × 1014

Dielectric constant εSi 11.7 16.0

Effective conduction band densityof states

NC cm−3 2.80 × 1019 1.04 × 1019

Effective valence band density ofstates

NV cm−3 1.04 × 1019 6.00 × 1018

Effective electron mass1 m*

Longitudinal (4.2 K) kg 10.9163m0 1.58m0

Transverse (4.2 K) kg 0.1905m0 0.082m0

Density of states (4.2 K) kg 1.062m0

Density of states (300 K) kg 1.090 m0

Effective hole mass1 m*

Longitudinal (4.2 K) kg 0.537m0 0.28m0

Transverse (4.2 K) kg 0.153m0 0.044m0

Density of states (4.2 K) kg 0.059m0

Density of states (300 K) kg 1.15 m0

Elastic constants c11 Pa 1.656 × 1011 1.26 × 1011

c12 0.639 × 1011 0.44 × 1011

c44 0.796 × 1011 0.68 × 1011

(continued)


585

1. mo: Free electron mass = 9.1091 × 10−31 kg2. Temperature dependence of Si and Ge energy gap:

Si: Eg ¼ 1:17� 4:73�10�4T2

Tþ651 eV; Ge: Eg ¼ 0:7437� 4:774�10�4T2

Tþ235 eV3. Temperature dependence of Si and Ge intrinsic carrier concentration

Si: ni ¼ 3:87� 1016 T3=2e�7014=T cm−3; Ge: ni ¼ 1:76� 1016 T3=2e�4553=T cm−3

4. This is the average energy loss per phonon scattering5. Velocity saturation is defined as

vs ¼ffiffiffiffiffiffiffiffi

8Ep

3pm0

q

� 107 cm/s

Property Symbol Unit Si Ge

Electron affinity χ V 4.15 4.00

Electron diffusivity in pure crystal Dn cm2/s 36.2 101

Electron mobility in pure crystal μn cm2/Vs 1450 3900

Energy gap2 Eg eV 1.12 0.664

Hardness H Mhos 7.0

Hole diffusivity in pure crystal Dp cm2/s 12.2 49

Hole mobility in pure silicon μp cm2/Vs 470 1900

Index or refraction N 3.44 3.97

Interatomic distance nm 0.234 0.244

Intrinsic carrier concentration3 ni cm−3 1.4 × 1010 2.4 × 1013

Intrinsic Debye length LD μm 24 0.68

Lattice constant a0 nm 0.543095 0.564613

Melting point tmoC 1412 937

Optical phonon energy4 Ep meV 63 37

Optical phonon mean-free path λ0Electrons nm 7.6 10.5

Holes nm 5.5

Poisson ratio 0.28 0.26

Pressure coefficient of Eg ΔEg/Δp eV/Pa ≈−1.5 × 10−11

Specific heat J/g·K 0.70 0.31

Temperature coefficient of latticemobility

Δμn/ΔT cm2/(V·s·K)

Electrons −11.6

Holes –4.3

Thermal conductivity κ W/cm·K 1.5 0.606

Thermal expansion coefficient,linear

ΔL/L·ΔT

K−1 2.5 × 10−6 5.7 × 10−6

Velocity saturation5 vs cm/s 107 107

Young’s modulus <100> Pa 1.30 × 1011 1.03 × 1011

586 Appendix B: Properties of Silicon and Germanium Crystals (300 K)

Sources

W. E. Beade, J. C. C. Tsai, and R. D. Plummer, Quick Reference Manual for Silicon IntegratedCircuit Technology, Wiley-Interscience, New York, 1985.

Properties of Crystalline Silicon, R. Hull, Editor, EMIS Datareviews Series, No 20, INSPEC,London, 1999.

M. Shur, Physics of Semiconductor Devices, Prentice-Hall, Englewood Cliffs, NJ, 1990.S. M. Sze, Physics of Semiconductor Devices, John Wiley and Sons, 1969.H. Wolf, Semiconductors, John Wiley and Sons, 1971./Para>

Appendix B: Properties of Silicon and Germanium Crystals (300 K) 587

Appendix CProperties of SiO2 and Si3N4 (300 K)

Sources

W. E. Beade, J. C. C. Tsai, and R. D. Plummer, Quick Reference Manual for Silicon IntegratedCircuit Technology, Wiley-Interscience, New York, 1985.

S. M. Sze, Physics of Semiconductor Devices, John Wiley and Sons, 1969.H. Wolf, Semiconductors, John Wiley and Sons, 1971.

Property Symbol Unit SiO2 Si3N4

Density g/cm3 2.27/2.18 2.9–3.2

Dielectric constant εSi 3.9 7.5

Dielectric strength V/cm 107 107

Energy gap Eg eV 9 5

Index or refraction n 1.46 2.05

Infrared absorption band μm 9.3 11.5–12.0

Melting point tm °C 1700 –

Molecular density cm−3 2.3 × 1022 –

Molecular weight g/mole 60.1 140.28

Poisson ratio 0.17

Stress in film on Si Pa 2–4 × 1010 9–10 × 1010

Thermal conductivity κ W/cm·K 0.014 –

Thermal expansion coefficient K−1 5.6 × 10−7 –

Young’s modulus <100> Pa 6.6 × 1010 –


589

Appendix DInternational System of Units

Property Unit name Symbol Dimension

Capacitance Farad F C/V

Conductance Siemens S A/V

Energy Joule J N·m

Electric charge Coulomb C A·s

Force Newton N kg·m/s2

Frequency Hertz Hz s−1

Inductance Henry H Wb/A

Length Meter m m

Magnetic flux Weber Wb V·s

Magnetic flux density Tesla T Wb/m2

Mass Kilogram kg kg

Power Watt W J/s

Potential Volt V J/C

Pressure Pascal Pa N/m2

Resistance Ohm Ω V/A

Temperature Kelvin K K

Time Second s s


591

Appendix EThe Greek Alphabet

Letter Upper case Lower case Letter Upper case Lower case

alpha Α α nu Ν ν

beta Β β xi Ξ ξ

gamma Γ γ omicron Ο ο

delta Δ δ pi Π π

epsilon Ε ε rho Ρ ρ

zêta Ζ ζ sigma Σ σ

êta Η η tau Τ τ

theta Θ θ upsilon Υ υ

iota Ι ι phi Φ ϕ

kappa Κ κ chi Χ χ

lambda Λ λ psi Ψ ψ

mu Μ μ omega Ω ω


593

Appendix FConversion Factors

Change of baseloge (N) = ln (N) = loge (10) × log10 (N)

Length

Area

m cm μm Å nm in.

1 meter (m) 1 102 106 1010 109 3.94 × 101

1 cm (cm) 10−2 1 104 108 107 3.94 × 10−1

1 micrometer (μm) 10–6 10−4 1 104 103 3.94 × 10–5

1 Angstrom (Å) 10−10 10–8 10−4 1 10−1 3.94 × 10−9

1 nm (nm) 10−9 10–7 10−3 10 1 3.94 × 10–8

1 inch (in.) 2.54 × 10−2 2.54 2.54 × 104 2.54 × 108 2.54 × 107 1

m2 cm2 μm2 Å2 nm2 in.2

1 square meter (m2) 1 104 1012 1020 1018 1.55 × 103

1 square centimeter(cm2)

10−4 1 108 1016 1014 1.55 × 10−1

1 square micrometer(μm2)

10−12 10–8 1 108 106 1.55 × 10−9

1 square Angstrom(Å2)

10−20 10−16 10–8 1 10−2 1.55 × 10−17

1 square nanometer(nm2)

10−18 10−14 10–6 102 1 1.55 × 10−15

1 square inch (in.2) 6.45 × 10−4 6.45 6.45 × 108 6.45 × 1016 6.45 × 1014 1


595

Energy

Pressure

J eV kg cal

1 Joule (J) 1 6.24 × 1018 1.11 × 10−17 0.24

1 electron-Volt (eV) 1.6 × 10−19 1 1.76 × 10−36 3.83 × 10−20

1 Kilogram (kg) 8.99 × 1016 5.61 × 1035 1 2.15 × 1016

1 calorie (cal) 4.19 2.61 × 1019 4.66 × 10−17 1

Dyne/cm2 Pa atm bar PSI

1 Dyne/cm2 1 0.1 9.862 × 10–7 10–6 1.4504 × 10–5

1 Newton/m2

(Pa)10 1 9.862 × 10–6 10–5 1.4504 × 10−4

1 Atmosphere(atm)

1.01325 × 106 1.01325 × 105 1 1.0133 14.696

1 Bar 1.0 × 106 1.0 × 105 0.98692 1 14.5041 Pound/square in.(PSI)

6.8946 × 104 1.01325 × 103 6.8946 × 10−2 6.8948 × 10−2 1

596 Appendix F: Conversion Factors

Index

AAccelerated life test, 509Accelerated testing, 509Acceleration factor, 509Accumulation, 211, 212AC-DC converter-flyback, 344, 345Acoustical phonons, 49Activation energy, 527Active base, 158Amorphous, 25Analog CMOS, 17, 205Analog CMOS process, 412, 437Analog mindset, 11Analog product diversity, 9Analog-to-digital converter (ADC), 6, 13,

400Annealing, 416

RTA, 416Applications, 399Auger recombination, 57, 160Avalanche breakdown, 93

BBack-end of the line (BEOL), 421, 529

aluminum, 421, 423borophosphosilicate glass (BPSG), 423copper, 423dual damascene, 424–426fluorinated silicate glass (FSG), 424high-density plasma (HDP), 424inter-metal dielectric (IMD), 423low-K IMD, 425phosphosilicate glass (PSG), 423

Band diagram, 209, 211Band diagram, SBD, 113, 127Bandgap reference, 185Band model, 28Band-to-band tunneling, 227Barrier, 112

Barrier height extraction, SBD, 122, 128Barrier lowering, SBD, 119Base, 147

conductivity modulation, 167emitter recombination current, 159extrinsic, 164intrinsic, 164push-out effect, 169resistance, 164transport factor, 151width, 148, 150, 155, 168, 169, 171, 180,

182width modulation, 171

Bathtub curve, 510BCD, 276, 303, 304, 445Bias temperature instability (BTI), 549

acceleration, 549NBTI, 549, 550PBTI, 551

Bipolar CMOS (BiCMOS), 16, 18, 22Bipolar-CMOS-DMOS (BCD), 19Bipolar junction transistor (BJT), 12, 16, 147,

149, 185BJT process, 431Body-bias effect, 234, 240Boltzmann approximation, 32Boltzmann distribution, 30Breakdown voltage, 94

effect of curvature, 94effect of temperature, 95, 96

Buck switching converter, 341Built-in field, 52Built-in voltage, 73, 74Bulk charge per unit area, 214Buried-channel PMOS (BC-PMOS), 18, 247,

268Buried-channel PMOS process, 437Buried Zener diode process, 445Burn-in, 507


597

CCapacitor, 378

dielectric absorption (DA), 382lateral capacitance, 380lateral flux capacitor (LFC), 388leakage, 380metal-insulator-metal (MIM), 386–388metal to silicided poly, 387MOS, 384–385poly-insulator-poly (PIP), 386quality factor, Q, 383strength, 380temperature coefficient of capacitance

(TCC), 381voltage coefficient of capacitance (VCC),

381Capacitor dielectrics, 528

dispersion, 529high-K, 530inter-level dielectric (ILD), 531inter-metal dielectric (IMD), 531low-K, 531LPCVD oxide, 529MIM, 528PECVD nitride, PEN, 529PETEOS, 531nitride oxide, PNO, 529

Capacitor processes, 433–435lateral flux, LFC, 433, 434MIM vertical, aluminum, 434, 435MIM vertical, copper, 435, 436

Carrier lifetime, 54Central processing unit (CPU), 1Centroid, 459Channel, 147, 187Channel resistance, 279Charge neutrality, 116Charge pump, 401Charge storage, 120Charge to breakdown, 525CMOS, 3CMP, 416, 426Collector, 148

resistance, 165reverse-bias effect, 171

Common centroid, 459Component set comparison, 413Computed tomography, 5Conductance, 248, 264Conductance and drain, 262Conduction band, 29Conductivity, 43Contact chain, 142Copper, 539

bamboo structure, 540BEOL, 539corrosion, 540electroplating, 565electromigration MTF, 538, 540low-K ILD, 539

Copper BEOL, 423–426Covalent bond, 26Critical field (Ec), 277, 285, 286, 287, 288,

308, 332Cross-coupled configuration, 459Cumulative distribution function (CDF), 505,

512, 513, 515, 516Current hogging, 167Current mirror, 264Current-voltage characteristics, 117Cut-off frequency, fT, 182CV profiling, 128CV technique, 216, 217, 219–221Cylindrical edge approximation, 69, 80

breakdown voltage, 94, 95

DDamascene, dual damascene, 424DC-DC converter, 297, 305, 336, 341

buck converter, 341conduction loss, 340, 342efficiency, 343power loss, 297, 298, 338, 342switching loss, 342, 343

DECMOS process, 430, 431, 452Decoupling capacitor, 400Deep depletion, 214, 217, 226Deep trench isolation (DTI), 521DENMOS, 430Density of states, 31, 32Depletion

boundary, 79, 97region, 66, 70, 71, 76, 78, 86, 90width, 66, 71, 75, 81, 88, 90, 94, 212

Depletion approximation, 67, 70, 72Depletion-mode NMOS–process, 438Depletion width, 115DEPMOS, 430Dielectric absorption (DA), 8Dielectric reliability, 520Differential amplifier, 263Diffusion, 34, 40Diffusion current, 51Diffusion leakage current, 91Diffusion length, 58, 149, 150, 152, 161, 162Diffusivity, 51, 67, 161Digital, 3Digital CMOS process–BEOL, 422–427

598 Index

Digital signal processing (DSP), 6Dispersion, 529Doping, 34

acceptors, 35, 36compensation, 38donors, 34

Drain-extended CMOS (DE-CMOS), 16Drain-extended MOS (DEMOS)

asymmetric, 300complementary, 298DEPMOS, 299dielectric RESURF, 301field-gap, 277, 299key dimensions, 302laterally graded, 306, 307planar, 299RSP versus BVDSS data, 293, 303symmetric style, 300

Drain-induced barrier lowering (DIBL), 8, 253Drain, JFET, 149Drain-to-source resistance, RDS(on), 277,

278–282, 290, 293, 295, 297, 301, 309,331

components, 280effect of VGS, 282measurement technique, 279

DRAM half-pitch, 246Drawn dimensions, 359Drift, 40, 41Drift current, 52, 59Drift region, 277

on-resistance, 278, 279on-state analysis, 277

Drift velocity, 42, 43Dual-gate oxide, 428Dummy components, 460Duty cycle, 345, 528Dynamic element matching, 13

EEarly failure rate (EFR), 507Early voltage, 171, 172, 195Effective density of states, 32Effective mass, 31, 42Effective oxide charge, 210Einstein relation, 53Electromigration (EM), 532

acceleration factors, 534aluminum, 533bamboo effect, 533black’s equation, 533, 534blech effect, 538

blech length, Lc, 538contacts and vias, 537, 538copper effect, 534current acceleration factor, 534, 535current density specifications, 535effect of Cu, 534electron wind, 532grain boundary, 533MTF, 533redundant metal films, 536temperature acceleration factor, 534test, 515triple point, 533

Electron affinity, 113, 206Electrostatic discharge (ESD), 566

charged device model (CDM), 568grounded-gate NMOS (GGNMOS), 566,

567human body model (HBM), 568machine model (MM), 568models, 568protective devices, 566system-level test, 568TLP test, 568

Electrostatic potential, 52Emitter, 148

resistance, 164, 165Energy gap, 28, 36Energy-gap lowering, 160Energy harvesting, 133Epitaxy process, 446Equivalent oxide thickness, teq, 219Etching, 415

plasma, 415Exponential distribution, 510Extraction of barrier height, 122, 128Extraction of contact resistance, 138Extraction of teq, 219Extrinsic resistance, SBD, 119

FFailure, 503Failure in time (FIT), 508, 509Failure mechanisms, 520Failure probability function, 504, 509Failure rate, 505, 510, 516Fermi-Dirac distribution, 31Fermi level, 31Fermi-level pinning, 116Fermi potential, 39, 207Flatband, 206Flatband capacitance, voltage, 218

Index 599

Fluorinated silicate glass (FSG), 521Forward active mode, 150, 151, 153, 168Forward biased junction, 81, 82

bias voltage, 81, 83current, 81, 83saturation current, 83series resistance effects, 85

Forward-biased, SBD, 118Foundries, 14Frequency response, 182

GGate charge, 295, 297

charging waveform, 259figure of merit, RDS(on) x QG, 297gate capacitances, 296measurement technique, 295Miller Plateau, 296

Gate dielectric reliability, 5211/E model, 526accelerated stress-test, 523body current, 564carrier transport through oxide, 521charge to breakdown, QBD, 525DEMOS, 563direct tunneling, 522, 523E-model, 526extrinsic failure mechanism, 526Fowler Nordheim tunneling, 522

Gate overdrive, 214Gate oxide integrity (GOI), 525

guard rings, 562Gate stack, 419Gate-Induced Drain Leakage (GIDL), 223, 224Gauss’s law, 72Generation, 27, 28, 54, 56Generation leakage current, 90Gradual channel approximation, 237Grain, 25Grain boundaries, 25Grounded-base current gain α, 151Grounded-emitter current gain β, 152Guard ring, 128Gummel number, 150, 155, 162, 172Gummel plot, 159

HHalf H-bridge, 336Halo, 255H-bridge, 306, 336, 337High doping effects, 160High field effects, 48High voltage MOSFET reliability, 563

high-temperature gate bias, HTGS, test, 565

high-temperature reverse-bias, HTRB, test,565

hot carrier effects, 564intrinsic failure, 526Kirk effect, 564latch-up, 563LDMOS, 561, 564on-resistance, 564percolation model, 526ramped voltage test, 524, 525specific on-resistance stability, 564stress-induced leakage, SILC, 523, 524TDDB model, 526, 527temperature coefficient of expansion (TCE),

565temperature cycling, 565time-dependent dielectric breakdown

(TDDB), 516, 525, 526High-frequency NLDMOS process, 448High-level injection effects, 163, 167High-voltage CMOS (HVCMOS), 14High-voltage CMOS process, 428Hole, 27Hot-carrier distribution, 243Hot-carrier injection, 243Hot carrier reliability, 541

band diagram, 544bipolar junction transistor (BJT), 542buried-channel PMOS, 547channel, 543CMOS, 541–545electron temperature, 545gate current, 543inverter switching, 546lifetime prediction, 545lightly-doped drain (LDD), 543, 548lucky electron model, 545Maxwell distribution of electrons, 541pn junction, 541process and design solutions, 547pulsed stress lifetime, 545substrate current, 543substrate hot electrons, 547walkout effect, 541

Hot carrier, 50

IIdeality factor, 119Idealized NPN transistor, 153Image-force lowering, 119Impact ionization, 93, 94, 225, 315, 325Inductive switching, 335Inductor, 16Inductor-process, 437

600 Index

Inductor, spiral, 397eddy current, 399inductance, 397proximity effects, 399self-resonance, 398skin effect, 398

Injection efficiency, 151Injection ratio, 120Integrated device manufacturer (IDM), 14Interface states, 115, 116Intermediate states, 56International Electrotechnical Commission

(IEC), 568International Technology Roadmap (ITRS), 21Internet of things, 2Intrinsic carrier concentration, 30, 39, 207Intrinsic energy level, ni, 32, 33Intrinsic failure rate (IFR), 507Intrinsic MOSFET, 279, 316–319, 325, 331,

334Intrinsic silicon, 30, 32, 33, 39Intrinsic voltage gain, 8Inverse area law, 461–466, 470, 472, 483Inversion charge, 214Inverter, 4Ion implantation, 415Ionization energy, 36Ionized-impurity limited mobility, 45Isolated-drain NLDMOS process, 451Isolated NMOS, 15Isolated NMOS process, 429, 430Isolation module, 417

LOCOS, 417STI, 417

JJFET effect, 280, 281, 320, 322JFET-process, 440Joule heating, 551Junction capacitance, 77–79, 88

junction edge, 69, 79reverse-biased, 88, 90

Junction curvature effect, 80, 94Junction depth, 69Junction field-effect transistor (JFET), 147, 187

application, 198early voltage, 195channel-length modulation, 195gate-leakage sources, 197in CMOS technology, 196linear mode, 189modulation factor, 195pinch-off, 191saturation mode, 192

saturation conductance, 194saturation transconductance, 195thermal equilibrium, 188

Junction radius of curvature, 80Junction series resistance, 84, 85

KKelvin test structure, 141Key point, 277Kirchhoff law, 151Kirk effect, 167, 170, 317, 319, 325, 326

LLatch-up, 557, 558, 559

bipolar model, 557CMOS, 559, 560forward-biased junction, 560guard rings, 562, 563holding current, voltage, 558inverter, 560layout solutions, 562LDMOS, 561mechanism, 557parasitic NPN, 561prevention, 561reduction of bipolar gain, 561reduction of well resistances, 561Shockley diode, 557silicon-controlled rectifier (SCR), 557, 559substrate resistance, 562transient triggering, 560trigger current, voltage, 557well resistance, 561

Lateral double-diffused MOS (LDMOS), 19,275, 299, 303, 413, 445

graded channel doping, 306high side NLDMOS, 305impact ionization, 315, 325integrated body contact, 310isolated drain NLDMOS, 305key dimensions, 310low side NLDMOS, 304on-state breakdown voltage, 327parasitic NPN, 325, 334, 340PLDMOS, 306RSP vs. BVDSS data, 313reverse recovery, 338–340self-heating, 315, 318, 328, 340snapback, 325snappy recovery, 340superjunction, 308, 310temperature effects, 328–333

Lateral-flux capacitor (LFC), 15Lateral flux capacitor-process, 433

Index 601

Lateral PNP, 180Lattice constant, 26Layout configurations, 459

common-centroid, 459, 460cross-coupled, 459interleaved, 460parallel, 459

Leakage current, 223Lifetime, 503Light-emitting diode (LED), 20Linearization, 5Linear mode, 5Line-edge roughness (LER), 465LOCOS, 417Lognormal distribution, 510, 513–515Lognormal plotting, 515Low-complexity NPN, 158Low-cost NLDMOS process, 449, 450Low-level injection, 55, 162Low-noise amplifier, 185Low-voltage analog CMOS process, 429

MMaximum frequency of oscillation, fmax, 184Mean, 511Meander resistor, 359Mean time to fail (MTTF), 505, 510, 514Median, 511Median rank, 515Median time to fail (MTF), 505, 510, 517Metal-induced gap states (MIGS), 115Metallurgical junction, 66Metal to silicon contact, 114, 118MESFET, 112MIM capacitor in aluminum BEOL, 434MIM capacitor in copper BEOL, 435Minority-carrier injection, 55, 82, 120Minority-carrier lifetime, 55Minority carriers, 36, 55–57Mismatch, 458

bipolar transistor, 469, 470capacitor, 472, 473centroid, 459common centroid, 459constant, 462cross-coupled, 460current mirror, 490floating gate measurement, 473, 474global, 458halo implant, 465implant scatter effect, 467inverse-area law, 465

limitations of Pelgrom’s law, 465line edge roughness (LER), 465, 466local, 458metal coverage effect, 468MOSFET, 462–468parallel, 459proximity effects, 458, 466random, 457, 458, 459–461, 467resistor, 461, 471, 472standard deviation, 458, 462, 463, 470, 471,

493STI proximity effect, 466systematic, 458threshold voltage, 462–464well proximity effect, 466

Mixed-signal CMOS (MS-CMOS), 12Mobility, 43–46, 317

bulk, 39drift, 42ionized-impurity scattering, 44lattice scattering, 44Matthiesson’s rule, 45, 46plots, 46–48temperature dependence, 47

Mobility, surface, effective, 233, 235, 236degradation, 232effective, 233, 235, 236electron, 236empirical relationships, 236hole, 236inversion, temperature dependence, 235inversion universal, 235surface, 233, 235, 236surface field, 238

Modular CMOS process, 412MOSFET, 3, 205

band-to-band tunneling, 227body bias effect, 234, 240buried-channel, 247capacitances, 261cutoff frequency, 260depletion-mode, 247, 266drain-induced barrier lowering (DIBL), 253enhancement-mode, 222extrinsic capacitances, 262extrinsic resistances, 240GIDL, 223, 225halo implant, 255ID-VG characteristic, 223impact ionization, 225isolated NMOS, 245leakage, 223

602 Index

linear mode, 233linear transconductance, 234maximum oscillation frequency, 261moderate inversion, 233multiple threshold, 246narrow-channel effect, 223, 251, 259native, 246, 265NMOS, 221normally-off, 222normally-on, 247, 266, 267off-current, 229output resistance, 239, 251PMOS, 221punch-through voltage, 254reverse narrow-channel effect, 260reverse short-channel effect, 258saturation region, 237saturation transconductance, 239short-channel effect, 251–258snapback, 257, 258strong inversion, 212substrate current, 242–244subthreshold region, 229–232subthreshold transconductance, 232surface-channel, 222threshold voltage, 213transit time, 260velocity overshoot, 256velocity saturation, 257weak inversion, 212

MOS structure, 205C-V technique, 217energy band diagram, 206flatband, 206

MS CMOS process, 412, 427Multiplication factor, 176

NNarrow-channel effects (NCE), 259Native NMOS, 246, 265Native NMOS process, 438N-buried layer (NBL), 305, 446–448, 451Neutrality level, 116NJFET, 148, 187NLDMOS, 446

epitaxy process, 446high-frequency, 448high frequency process, 448high-side, HS, 446isolated, 451isolated drain process, 451low complexity process, 449

low-side, LS, 448non-epi process, 448

NMOS, 3Noise, 475

1/f in BJT, 4881/f in CMOS, 4811/f in JFET, 4891/f in resistors, 472, 486base current, 488collector current, 488corner frequency, 479current, 475drain current, 482, 483effect of fluorine, 484, 485effect of hydrogen, 484effect of metal coverage, 468effect of nitrogen, 484, 485effect of STI, 485flicker 1/f, 476, 480fluctuation, 476generation-recombination, 478Hooge’s constant, 486in two stage transconductance amplifier,

491input referred, 482, 493Lorentzian, 478mobility fluctuation, 457, 464, 476normalized drain current, 483number fluctuation, 476, 482power spectral density (PSD), 476, 479,

484random telegraph signal (RTS), 478, 479,

485resistance equivalent, 477shot, 476temperature equivalent, 477thermal, 476, 477tunneling attenuation length, 482voltage, 475white, 477

Non-equilibrium condition, 54Non-ohmic behavior, 369Non-uniform doping concentration, 52Non-volatile memory (NVM), 20, 524Normal (Gaussian) distribution, 510NPN transistor, 148, 152, 153NPN transistor in CMOS, 157, 158

OOff-current, 4, 229, 253Off-state, 278, 282, 283, 297Ohmic contact, 134

Index 603

On-current, 4On-state, 277, 278, 297, 298, 309, 318, 322Operating voltage, Vop, 9Operational amplifier (Op-amp), 7Optical phonons, 49Output resistance, 171Oxidation, 414

PParasitic PNP transistor, 167P-buried layer (PBL), 305, 412, 446, 451Peak field, 73, 93, 115, 120Pelgrom-Law, 462, 465Photolithography, 414Pinch-off, 191Pinch-off voltage, 237, 242PIN diode, 103–105

conductivity modulation, 104forward biased, 103

PIP capacitor process, 443PJFET, 148, 187Planarization, 416

CMP, 416Plasma, 551

antenna effect, 554, 555charge, 553, 554damage, 553MIM capacitor, 556MOSFET, 554protection, 555protective diode, 556reactor, 554sheath, 554

Plating, 416, 426PLDMOS process, 448, 451PMOS, 4PN junction, 66PN product, 33PNP transistor, 148, 152, 154PNP transistor in CMOS, 180Poisson relation, 75Poly resistor, 364

band diagram, 367effective carrier concentration, 366, 367effective carrier mobility, 366electrical trimming, 372end resistance, 369energy-band diagram, 367free carrier concentration, 366non-ohmic behavior, 370parasitic capacitance, 373resistivity, 367sheet resistance, 368

temperature coefficient of resistance, TCR,370

transport mechanism, 365voltage coefficient of resistance, 370

Polysilicon depletion, 220Polysilicon-insulator-polysilicon capacitor, 8Polysilicon, silicon resistors, 432

high sheet resistor process, 440Population, 504Power law model, 510, 519, 545, 550Power spectral density, 476Process delivery kit (PDK), 11Probability density function (PDF), 504, 514,

516Process integration flow, 411Pulse-width modulation (PWM), 338Punch-through, 175, 253

QQuality factor, (Q), 16Quasi-Fermi level, 118Quasi-saturation, 315, 316, 326

JFET effect, 318Kirk effect, 315velocity saturation, 315

RRadio-frequency CMOS (RF-CMOS), 12Ramped voltage test, 525Recombination, 28, 54–57, 57

Auger, 57, 58Rate, U, 58

Rectifying contact, 111Reliability function, 504Reliability models, 509

exponential, 510lognormal, 510, 513, 514normal, 510, 510power law, 511, 518Weibull, 516

Resistance, intrinsic, 240Resistance, extrinsic, 240Resistance, spreading, 241Resistivity, 44Resistor, 357

body, 359effective dimensions, 359electrical dimensions, 368end resistance, 357, 358, 360head resistance, 357, 360Joule heating, 361linearity, 363parasitic capacitances, 363

604 Index

resistance linearity, 363self heating, 361, 363sheet resistance, 359temperature coefficient of resistance (TCR),

361thermal conductivity, 361thermal resistance, 362voltage coefficient of resistance, 361

Resistor reliability, 551high, low, medium sheet resistances, 551poly resistor, 551thermal resistance, 552thin-film TFR, 551, 553

Resonant circuit, 343RESURF, 286, 288, 290, 291, 301, 309, 312,

313, 333charge balance, 287, 292, 301double, 290dielectric, 301, 302sensitivity to drift layer thickness, 288sensitivity to substrate doping, 289single, 287SOI, 312–314triple, 291

Reverse active mode, 155Reverse biased junction, 88

capacitance, 88depletion region, 88leakage current, 90–93

Reverse-biased SBD, 127Reverse narrower-channel effects (RNCE), 260Reverse recovery, 338, 339Reverse recovery time, 96–98, 167Reverse short-channel effects (RSCE), 255,

258, 259RF CMOS, 205RF CMOS process, 412, 427RF mixer, 132Richardson constant, 117Roadmap, 21

SSafe operating area (SOA), 327, 329, 333–335,

340commutating, 340electrical, 334electro-thermal, 335–336forward bias, 340reverse bias, 340snappy, 340temperature compensation point, 336

Sampling, 504Saturation current, SBD, 119Saturation voltage, VCEsat, 156

SBD applications, 131SBD clamp, 131Scale parameter, 514, 516Scattering, 42Schottky-barrier diode (SBD), 111Schottky-barrier lowering, 119Self-heating, 361, 371Series resistance, 125Shallow trench isolation (STI), 68, 417Shape parameter, 516Sheet resistance, 359, 468Shockley’s relation, 83Shockley-Read-Hall (SRH), 57Short-channel effects (SCE), 251Signal chain, 2Silicidation, 416Silicide block, 15Silicon-germanium (SiGe), 16Silicon resistor, 375

source and drain, 375temperature-coefficient of resistance (TCR),

376, 377voltage coefficient of resistance (VCR), 376well, 377

Silicon resistor-process, 432Single crystal, 25Small signal model, 7Small-size effects, 251Snapback, 566Snubber diode, 102Snubber diode-AC-DC converter, 345Soft breakdown, 524SOI, 312

advantages, 312double RESURF, 313NLDMOS, 312PLDMOS, 313

Source, JFET, 149Source-drain module, 421Space charge, 67Specific contact resistivity, 135Specific on resistance (RSP), 279, 293, 294,

298, 301, 303, 304, 306, 308, 310, 313,333, 337, 342

DENMOS vs BVDSS, 303ideal, 293, 294NLDMOS vs BVDSS, 312PLDMOS, 306superjunction, 308

Spherical edge approximation, 69Standard deviation, 511, 512, 513, 514, 518Standard normal distribution, 511, 513Statistical process control (SPC), 511Step junction, 70

Index 605

Step junction (cont.)band diagram, 73built-in voltage, 73capacitance, 76–78depletion width, 75–76, 79effect of curvature, 80electric field, 71forward bias, 82junction capacitance, 77parallel-plate capacitance, 77peak field, 73

Storage delay time, 97Stress-induced leakage current (SILC), 524Stress-induced voiding, 533, 539Stress migration, 532, 538Strong inversion, 212Substrate, 414Substrate current, 242Substrate current and parasitic NPN, 243Substrate PNP, 180Subsurface Zener diode—process, 445Subthreshold current, 231Subthreshold leakage, 300Successive approximation register (SAR), 8Superjunction, 308–309

charge compensation, 309concept, 308LDMOS, 309

Surface charge density, 213Surface field, 214, 235, 238Surface generation, 90, 92Surface potential, 210, 213Surface recombination, 86Symbols, 153System on a chip (SoC), 10

TTechnology migration path, 413Temperature compensation point (TCP), 336Temperature dependence of β, VA, 174, 175Temperature dependence of forward voltage,

84–86Thermal conductivity, 552Thermal equilibrium, 30, 67, 69, 74Thermal resistance, 553Thermionic emission, 117, 118Thin-film deposition, 415

ALD, 415CVD, 415PECVD, 415PVD, 415

Thin film resistor-process, 442

Thin-film resistor (TFR), 18, 358, 359, 377advantages, 378conduction mechanisms, 377laser trimming, 378structure, 377temperature coefficient of resistance (TCR),

377Threshold voltage, 3, 213, 215, 223, 231, 232,

234, 235, 240, 241, 244adjustment, 245buried-channel PMOS, 247dependence on channel length, 252dependence on drain voltage, 252depletion-mode NMOS, 250DIBL, 253double hump, 260extraction, 122halo, 255off-current, 229roll-off, 252temperature-dependence, 231

Time-dependent dielectric breakdown (TDDB),525

TLM model, 139Transconductance, 7, 234, 235, 261, 263, 264

degradation, 234, 241linear, 234maximum, 234, 244saturation, 239subthreshold, 231

Transient voltage suppressor diode, 98, 102Transistor action, 149Transistor breakdown voltage, 178Transistor resistances, 163Tunneling, 95, 521

direct, 522, 523Fowler-Nordheim (FN), 522

UUnit processes, 414–416Useful life, 507

VVacuum level, 112Valence band, 29, 38Van der Pauw measurement, 368Varactor, 16, 389

junction varactor, 390hyperabrupt, 392layout, 393MOS varactor, accumulation-mode, 393,

395

606 Index

MOS varactor, inversion-mode, 393, 395sensitivity, 389Schottky-barrier, 389three terminal, 396tuning range, 389

Velocity saturation, 8, 49, 50, 315–318, 320,332

Vertical DMOS, 303Vertical MIM capacitor, 387Voltage coefficient of capacitance (VCC), 8Voltage controlled oscillator (VCO), 402Voltage reference circuit, 399Voltage regulator, 399Voltage snapback, 566Volt-second balance, 345

WWafer-level reliability, 520Weak inversion, 212Wearout, 507

Weibull distribution, 516Weibull plotting, 518, 525–527, 529, 530Well process, 417Work function, 112, 206Work function difference, 208Work function temperature dependence, 208

ZZener breakdown, 95, 96

temperature dependence, 101Zener diode, 99

breakdown voltage, 96quantum efficiency, 104reverse bias, 104subsurface, 100surface, 99temperature dependence of breakdown, 101transient voltage suppressor, 102voltage reference, 99

Index 607

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Appendix A Universal Physical Constants978-1-4939-2751...Appendix A Universal Physical Constants Constant Symbol Value Avogadro’s constant A0,NA,L 6.0225 × 10 23/mol Boltzmann constant