Appendix 1: List of symbols


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1 Appendix 1: List of symbols Symbol Description MKS Units a Acceleration m/s 2 a 0 Bohr radius m A Area m 2 A* Richardson constant m/s A C Collector area m 2 A E Emitter area m 2 b Bimolecular recombination constant m 3 /s c Speed of light in vacuum m/s C Capacitance per unit area F/m 2 C D Diffusion capacitance per unit area F/m 2 C DS Drainsource capacitance F C FB Flatband capacitance per unit area of a MOS structure F/m 2 C G Gate capacitance F C GS Gatesource capacitance F C GD Gatedrain capacitance F C HF Highfrequency capacitance per unit area of a MOS structure F/m 2 C j Junction capacitance per unit area F/m 2 C LF Lowfrequency (quasistatic) capacitance per unit area of a MOS structure F/m 2 C M Miller capacitance F C ox Oxide capacitance per unit area F/m 2 C s Semiconductor capacitance per unit area F/m 2 D n Electron diffusion constant m 2 /s D p Hole diffusion constant m 2 /s E Energy Joule
2 E Electric field V/m E 0 Lowest energy in a onedimensional quantum well Joule E a Acceptor energy Joule E br Breakdown field V/m E c Conduction band energy of a semiconductor Joule E d Donor energy Joule E F Fermi energy (thermal equilibrium) Joule E F,n Fermi energy in an ntype semiconductor Joule E F,p Fermi energy in a ptype semiconductor Joule E g Energy bandgap of a semiconductor Joule E i Intrinsic Fermi energy Joule E n n th quantized energy Joule E ph Photon energy Joule E t Trap energy Joule E v Valence band energy of a semiconductor Joule E vacuum Electron energy in vacumm Joule F(E) Distribution function (probability density function) f BE (E) BoseEinstein distribution function f FD (E) FermiDirac distribution function f MB (E) MaxwellBoltzmann distribution function F Force Newton F n QuasiFermi energy of electrons Joule F p QuasiFermi energy of holes Joule ge) Density of states per unit energy and per unit volume m 3 J 1 g(e) Density of states in the conduction band per unit energy and per unit volume m 3 J 1 g(e) Density of states in the valence band per unit energy and per unit volume m 3 J 1 g d Output conductance of a MOSFET S
3 g m Transconductance of a MOSFET S G Carrier generation rate m 3 s 1 G n Electron generation rate m 3 s 1 G p Hole generation rate m 3 s 1 h Plank's constant Js h Reduced Plank's (= h /2π) Js I Current A I B Base current of a bipolar transistor A I C Collector current of a bipolar transistor A I D Drain current of a MOSFET A I E Emitter current of a bipolar transistor A I F Forward active current of a bipolar transistor A I D,sat Drain current of a MOSFET in saturation A I ph Photo current A I r Recombination current A I R Reverse active current of a bipolar transistor A I s Saturation current A I sc Short circuit current of a solar cell A J Current density A/m 2 J n Electron current density A/m 2 J p Hole current density A/m 2 k Boltzmann's constant wavenumber J/K m 1 l Mean free path m L Length m L D Debye length m L n Electron diffusion length m
4 L p Hole diffusion length m L x Hole diffusion length m m Mass kg m * Effective mass kg m A Atomic mass kg m 0 Free electron mass kg * m e * m h M n Effective mass of electrons Effective mass of holes Proton mass Multiplication factor Electron density Integer Refractive index Ideality factor kg kg kg m 3 n i Intrinsic carrier density m 3 n(e) Electron density per unit energy and per unit volume m 3 n 0 Electron density in thermal equilibrium m 3 n i Intrinsic carrier density m 3 n n Electron density in an ntype semiconductor m 3 n n0 Thermal equilibrium electron density in an ntype semiconductor m 3 n p Electron density in a ptype semiconductor m 3 n p0 Thermal equilibrium electron density in a ptype semiconductor m 3 N Number of particles Doping density N a Acceptor doping density m 3 N a  N A Ionized acceptor density m 3 Avogadro's number
5 N B Base doping density m 3 N c Effective density of states in the conduction band m 3 N C Collector doping density m 3 N d Donor doping density m 3 N d + Ionized donor density m 3 N E Emitter doping density m 3 N ss Surface state density m 2 N t Recombination trap density m 2 N v Effective density of states in the valence band m 3 p Hole density Particle momentum Pressure m 3 kgm/s Nm 2 p(e) Hole density per unit energy m 3 p 0 Hole density in thermal equilibrium m 3 p n Hole density in an ntype semiconductor m 3 p n0 Thermal equilibrium hole density in an ntype semiconductor m 3 p p Hole density in a ptype semiconductor m 3 p p0 Thermal equilibrium hole density in a ptype semiconductor m 3 q electronic charge C Q Heat Charge Joule C Q B Majority carrier charge density in the base C/m 2 Q d Charge density per unit area in the depletion layer of an MOS structure C/m 2 Q d,t Charge density per unit area at threshold in the depletion layer of an MOS structure C/m 2 Q i Interface charge density per unit area C/m 2 Q inv Inversion layer charge density per unit area C/m 2
6 Q M Charge density per unit area in a metal C/m 2 Q n Charge density per unit area in the depletion layer of an ntype region C/m 2 Q p Charge density per unit area in the depletion layer of a ptype region C/m 2 Q ss Surface state charge density per unit area C/m 2 r e Emitter resistance Ohm r π Base resistance Ohm R The Rydberg constant Resistance J Ohm R n Electron recombination rate m 3 s 1 R p Hole recombination rate m 3 s 1 R s Sheet resistance Ohm s Spin S Entropy J/K t Thickness m t ox Oxide thickness m T Temperature Kinetic energy Kelvin Joule u ω Spectral density Jm 3 s 1 U Total energy Joule U A Auger recombination rate m 3 s 1 U bb Bandtoband recombination rate m 3 s 1 U n Net recombination rate of electrons m 3 s 1 U p Net recombination rate of holes m 3 s 1 U SHR ShockleyReadHall recombination rate m 3 s 1 v Velocity m/s v R Richardson velocity m/s v sat Saturation velocity m/s
7 v th Thermal velocity m/s V Potential energy Volume Joule m 3 V a Applied voltage V V A Early voltage V V br Breakdown voltage V V B Base voltage V V BE Baseemitter voltage V V BC Basecollector voltage V V C Collector voltage V V CE Collectoremitter voltage V V D Drain voltage V V DS Drainsource voltage V V DS,sat Drainsource saturation voltage V V E Emitter voltage V V FB Flatband voltage V V G Gate voltage V V GS Gatesource voltage V V oc Open circuit voltage of a solar cell V V t Thermal voltage V V T Threshold voltage of an MOS structure V w Depletion layer width m w B Base width m w C Collector width m w E Emitter width m w n Width of an ntype region m w p Width of a ptype region m
8 W Work Joule x Position m x d Depletion layer width in an MOS structure m x d,t Depletion layer width in an MOS structure at threshold m x j Junction depth m x n Depletion layer width in an ntype semiconductor m x p Depletion layer width in a ptype semiconductor m α α F Absorption coefficient Transport factor Forward active transport factor m 1 α n Ionization rate coefficient for electrons m 1 α R α T β Reverse active transport factor Base transport factor Current gain γ Body effect parameter V 1/2 γ E Emitter efficiency Γ n Auger coefficient for electrons m 6 s 1 Γ p Auger coefficient for holes m 6 s 1 δ n Excess electron density m 3 δ p Excess hole density m 3 δ R Depletion layer recombination factor Q n,b Excess electron charge density in the base C/m 2 ε Dielectric constant F/m ε 0 Permittivity of vacuum F/m ε ox Dielectric constant of the oxide F/m
9 ε s Dielectric constant of the semiconductor F/m µ 0 Permeability of vacuum H/m Θ Tunnel probability λ Wavelength m µ Electrochemical potential Joule µ n Electron mobility m 2 /Vs µ p Hole mobility m 2 /Vs ν Frequency Hz ρ Charge density per unit volume Resistivity C/m 3 Ωm ρ ox Charge density per unit volume in the oxide C/m 3 σ Conductivity Ω 1 m 1 τ Scattering time s τ n Electron lifetime s τ p Hole lifetime s φ Potential V φ B Barrier height V φ F Bulk potential V φ i Builtin potential of a pn diode or Schottky diode V φ s Potential at the semiconductor surface V Φ Flux m 2 s 1 Φ M Workfunction of the metal V Φ MS Workfunction difference between the metal and the semiconductor V Φ S Workfunction of the semiconductor V χ Electron affinity of the semiconductor V Ψ Wavefunction
10 ω Radial frequency rad/s
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