APPENDIXES. A. List of Symbols. G Properties of Si and GaAs H. Properties of SiO, and Si,N,
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1 Physics of emiconductor Devices, 3rd Edition by. M. ze and Kwok K. Ng Copyright 0 John Wiley & ons, Inc. PPENDIXE. List of ymbols B. International ystem of Units C. Unit Prefixes D. Greek lphabet E. Physical Constants F. Properties of Important emiconductors G Properties of i and Gas H. Properties of io, and i,n,
2 ppendix Physics of emiconductor Devices, 3rd Edition by. M. ze and Kwok K. Ng Copyright 0 John Wiley & ons, Inc. List of ymbols ymbol Description Unit Lattice constant rea Effective Richardson constant for free electron Effective Richardson constant 2 /2K2 /2K2 Bandwidth Magnetic induction peed of light in vacuum peed of sound Diffusion capacitance per area Depletionlayer capacitance per area Capacitance per area at flatband Insulator capacitance per area Interfacetrap capacitance per area Oxide capacitance per area pecific heat Capacitance Oxide thickness Insulator thickness Diffusion coefficient mbipolar diffusion coefficient Interfacetrap density Diffusion coefficient for electrons Diffusion coefficient for holes Electric displacement Energy ctivation energy Ionization energy for acceptors Bottom edge of conduction band Ionization energy for donors Fermi level Hz WbI2, d2 cds cds F/2 F/2 F/2 F/2 F/2 F/2 J/gK F s 2/s 2e' s 2/s C/2 e e e e e e 775
3 776 LIT OF YMBOL ymbol Description Unit Metal Fermi level QuasiFermi (imref) level for electrons QuasiFermi (imref) level for holes Energy gap Intrinsic Fermi level Opticalphonon energy Trap energy level Top edge of valence band Electric field Critical electric field Maximum electric field Frequency Maximum frequency of oscillation (unilateral gain is unity) Cutoff frequency FermiDirac distribution function FermiDirac integral FermiDirac distribution function for electrons Fill factor FermiDirac distribution function for holes Transconductance Transconductance, intrinsic Transconductance, extrinsic Conductance Gain Generation rate Electron generation rate Hole generation rate Power gain Thermal generation rate Planck constant mallsignal commonbase current gain, = a Commonbase current gain, = a,, mallsignal commonemitter current gain, = p Commonemitter current gain, = Po Reduced Planck constant, h12z Magnetic field Intrinsic (undoped) material
4 LIT OF YMBOL 777 ymbol Description Unit Current aturation current Forward current Holding current Electron current Hole current Photocurrent Recombination current Reverse current hortcircuit current in response to light Current density aturationcurrent density Forwardcurrent density Generationcurrent density Electroncurrent density Holecurrent density Photocurrent density Recombinationcurrent density Reversecurrent density hortcircuitcurrent density Tunnelingcurrent density Thresholdcurrent density Boltzmann constant Wave vector Extinction coefficient, imaginary part of index of refraction Phonon wave number vector Dielectric constant, E/q, Dielectric constant of insulator Dielectric constant of oxide Dielectric constant of semiconductor Length Inductance mbipolar diffusion length Diffusion length Debye length Diffusion length of electrons Diffusion length of holes /2 M2 N2 /2 M2 N2 M2 /2 M2 N2 /2 M2 J/K I ' H
5 778 LIT OF YMBOL ymbol Description Unit Electron rest mass Effective mass Conductivity effective mass Conductivity effective mass for electrons Conductivity effective mass for holes Densityofstate effective mass for electrons Densityofstate effective mass for holes Electron effective mass Hole effective mass Effective mass for heavy hole Longitudinal effective mass for electron Effective mass for light hole Transverse effective mass for electron Multiplication factor Number of equivalent minima in the conduction band Multiplication factor of electrons Multiplication factor of holes Concentration of free electron Of ntype semiconductor (with donor impurity) Intrinsic carrier concentration Electron concentration in ntype semiconductor (majority carriers) nn in thermal equilibrium Electron concentration in ptype semiconductor (minority carriers) np in thermal equilibrium Real part of refractive index Complex refractive index, = n, + ik, ~ m ~ ~ m ~ p3 Doping concentration Density of states cceptor impurity concentration Ionized acceptor impurity concentration Gummel number Effective density of states in conduction band Donor impurity concentration Ionized donor impurity concentration Bulktrap concentration Effective density of states in valence band Density per area Interfacetrap density per area urfacetrap density per area evl? ~ m ~ ~ m ~ 2 3 P3 3 ~ m ~ ~ m ~ * 2 2
6 LIT OF YMBOL 779 ymbol Description Unit Concentration of free hole Of ptype semiconductor (with acceptor impurity) Momentum Hole concentration in ntype semiconductor (minority carriers) pn in thermal equilibrium Hole concentration in ptype semiconductor (majority carriers) pp in thermal equilibrium Pressure Power Optical power density or intensity Total optical power Unit electronic charge, = 1.6~ C, absolute value Quality factor of capacitor and inductor Charge density pacecharge density in depletion region Fixedoxidecharge density Interfacetrapcharge density Mobileioniccharge density Oxidetrappedcharge density Dynamic forward resistance Hall factor Dynamic reverse resistance Reflection of light Resistance pecific contact resistance Contact resistance Coupling ratio of floating gate Recombination rate Recombination coefficient Hall coefficient Load resistance Nonradiative recombination rate Radiative recombination rate heet resistance per square Responsivity 3 Jsl ~ m ~ ~ m ~ 3 ; N/2 W Wl2 W C Cl2 C/2 Cl2 C/2 CI2 C/2 Q R Q a2 Q 331 3/s 3/C Q 3s I 3s1 Rlo /W train ubthreshold swing ldecade of current
7 780 LIT OF YMBOL ymbol Description Unit, p urface recombination velocity for electrons urface recombination velocity for holes ls ls t Time tr Transit time T bsolute temperature T tress T Transmission of light T, Electron temperature Tf Tunneling probability K N/2 K U Net recombinatiodgeneration rate, U = R G. u Carrier velocity ud Drift velocity ug Group velocity n Electron velocity up Hole velocity up,, Phonon velocity us aturation velocity ufh Thermal velocity pplied voltage, Early voltage, Breakdown voltage Bcs0 Collectorbase openemitter breakdown voltage, Collectoremitter openbase breakdown voltage,, Backsubstrate voltage,,,upply voltage F Forward bias, Flatband voltage h Holding voltage, Hall voltage,,, Opencircuit voltage in response to light Pinchoff voltage PT Punchthrough voltage, Reverse bias, Threshold voltage W Thickness W, Base thickness W, Depletion width ls ls ls ls ls ls ls ls
8 LIT OF YMBOL 781 ymbol Description Unit Maximum depletion width Depletion width in ntype material Depletion width in ptype material Distance or thickness Young's modulus, modulus of elasticity Impedance N/2 R Optical absorption coefficient mallsignal commonbase current gain, = hfl Ionization coefficient Commonbase current gain, = h, Ionization coefficient for electrons Ionization Coefficient for holes Base transport factor ' ' 1 ' mallsignal commonemitter current gain, = hre Commonemitter current gain, = h, Reciprocal of thermal potential, = q/kt Emitter injection efficiency Excess electron concentration beyond equilibrium Excess hole concentration beyond equilibrium Permittivity Permittivity of vacuum Permittivity of insulator Permittivity of oxide Permittivity of semiconductor 3 F/, CN F/, CN F/, CN F/, CN F/, CN Quantum efficiency Ideality factor of rectifier under forward bias External quantum efficiency Internal quantum efficiency ngle rad, O
9 782 LIT OF YMBOL ymbol Description Unit Thermal conductivity Wavelength Mean free path Phonon mean free path Drift mobility (= u/g) Permeability Permeability in vacuum Differential mobility (= dv/d Z?) Hall mobility Electron mobility Hole mobility Frequency of light Poisson s ratio Lightly doped ntype material Lightly dopedptype material Resistivity Charge density Conductivity Capture crosssection Capture crosssection for electrons Capture crosssection for holes Carrier lifetime mbipolar carrier lifetime uger lifetime Energy relaxation time Carrier generation lifetime Mean free time in scattering Carrier lifetime for electrons Carrier lifetime due to nonradiative recombination Carrier lifetime for holes Carrier lifetime due to radiative recombination Dielectric relaxation time torage time Transit time W/K Ws H/ H/ 2Ns 2/s 2/s 2Ns Hz, ssl 0 C/3 I 2 2 2
10 LIT OF YMBOL 783 ymbol Description Unit Work function or barrier height Barrier height chottky barrier height on ntype semiconductor chottky barrier height on ptype semiconductor Metal work function Workfunction difference between metal and semiconductor, Fermi potential from conductionband edge in ntype semiconductor, (E, E,)/q. Negative for degenerate material (see figure) Fermi potential from valenceband edge inptype semiconductor, (EF E,)/q. Negative for degenerate material (see figure) emiconductor work function Thermal potential, kt/q Photon flux Electron affinity Electron affinity for semiconductor Wave function Builtin potential at equilibrium (always positive) Fermi level from intrinsic Fermi level, IEF Eil/q, in bulk tyb in ntype material (see figure) (vb inptype material (see figure) emiconductor potential, Ei /q urface or interface 4 IvBn f ;1 ntype., EF 1. ptype urface or interface Fig. 1 ymbols and definitions for semiconductor potentials. Note that surface potentials are with respect to the bulk, and are positive when the band bends downwards. IP~ and q5p are negative when EF are outside the bandgap (degenerate).
11 784 LIT OF YMBOL ymbol Description Unit yn Potential at ntype boundary with respect to ntype bulk y, (band bending in ntype material, positive when bending down in the energyband diagram) (see figure) Potential atptype boundary with respect toptype bulk ys (band bending in ptype material, positive when bending down in the energyband diagram) (see figure) urface potential with respect to bulk (band bending, positive when bending down in the energyband diagram) (see figure) w ngular frequency, = 2qfor 27rv Hz
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