Appendix 1: List of Symbols

Transcription

1 Appendix 1: List of Symbols Symbol Description A Area m 2 MKS Units c Speed of light in vacuum m/s C Capacitance F/m 2 C d Diffusion capacitance per unit area F/m 2 C FB Flatband capacitance per unit area of an MOS structure F/m 2 C j Junction capacitance per unit area F/m 2 C ox Oxide 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 E Electric field V/m E a Acceptor energy Joule E c Conduction band energy of a semiconductor Joule E d Donor energy Joule E F Fermi energy (thermal equilibrium) Joule E g Energy bandgap of a semiconductor Joule E i Intrinsic Fermi energy Joule E v Valence band energy of a semiconductor Joule E vacuum Electron energy in vacuum Joule f(e) Distribution function (probability density function) F n Quasi-Fermi energy of electrons Joule F p Quasi-Fermi energy of holes Joule A-1

2 g c (E) Density of states in the conduction band per unit energy and per unit volume m -3 J -1 g v (E) Density of states in the valence band per unit energy and per unit volume m -3 J -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 constant (= h /2π) Js I Current 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 J/K l Mean free path m L Length m L n Electron diffusion length m L p Hole diffusion length m m Mass kg m 0 Free electron mass kg m e * m h * Effective mass of electrons Effective mass of holes kg kg n Electron density m -3 n(e) Electron density per unit energy and per unit volume m -3 n i Intrinsic carrier density m -3 n n Electron density in an n-type semiconductor m -3 n n0 Electron density in an n-type semiconductor in thermal equilibrium m -3 A-2

3 n p Electron density in a p-type semiconductor m -3 n p0 Electron density in a p-type semiconductor in thermal equilibrium m -3 n 0 Electron density in thermal equilibrium m -3 N Doping density m -3 N a Acceptor doping density m -3 N a - Ionized acceptor density m -3 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 v Effective density of states in the valence band m -3 p Hole density m -3 p(e) Hole density per unit energy m -3 p n Hole density in an n-type semiconductor m -3 p n0 Hole density in an n-type semiconductor in thermal equilibrium m -3 p p Hole density in a p-type semiconductor m -3 p p0 Hole density in a p-type semiconductor in thermal equilibrium m -3 p 0 Hole density in thermal equilibrium m -3 q electronic charge C Q Charge C Q p,b Hole charge 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 A-3

4 structure Q i Interface charge density per unit area C/m 2 R Resistance Ohm R n Electron recombination rate m -3 s -1 R p Hole recombination rate m -3 s -1 t Thickness m t ox Oxide thickness m T Temperature Kelvin U n Net recombination rate of electrons m -3 s -1 U p Net recombination rate of holes m -3 s -1 v Velocity m/s v th Thermal velocity m/s V a Applied voltage V V B Base voltage V V C Collector voltage V V D Drain voltage V V E Emitter voltage V V FB Flatband voltage V V G Gate voltage V V t Thermal voltage V V T Threshold voltage of an MOS structure V w B Base width m w C Collector width m w E Emitter width m A-4

5 w n Width of an n-type region m w p Width of a p-type region m x Position m x d Depletion layer width 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 n-type semiconductor m x p Depletion layer width in a p-type semiconductor m α β Transport factor Current gain γ Body effect parameter V 1/2 γ E Emitter efficiency δ n Excess electron density m -3 δ p Excess hole density m -3 Q n,b Excess electron charge in the base C/m 2 Q p,e Excess electron charge in the emitter C/m 2 ε ox Dielectric constant of the oxide F/m ε s Dielectric constant of the semiconductor F/m ε 0 Permittivity of vacuum F/m µ n Electron mobility m 2 /V-s µ p Hole mobility m 2 /V-s ρ Charge density per unit volume Resistivity C/m 3 Ωm A-5

6 ρ ox Charge density per unit volume in the oxide C/m 3 σ Conductivity Ω 1 m -1 τ c Collision 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 Built-in potential of a p-n diode or Schottky diode V φ s Potential at a semiconductor surface V Φ M Workfunction of a metal V Φ MS Workfunction difference between a metal and a semiconductor V Φ S Workfunction of a semiconductor V χ Electron affinity of a semiconductor V A-6