Appendix
A.2 Physical constants

Appendix 1: Symbol Index by Name

Description

Symbol

MKS Units

- A -

Acceptor doping density

Na

m-3

Acceptor energy

Ea

Joule

Applied voltage

Va

V

Area

A

m2

- B -

Barrier height

φB

V

Base doping density

NB

m-3

Base voltage

VB

V

Base width

wB

m

Body effect parameter

γ

V1/2

Boltzmann's constant

k

J/K

Built-in potential of a p-n diode or Schottky diode

φi

V

Bulk potential

φF

V

- C -

Capacitance per unit area

C

F/m2

Charge

Q

C

Charge density per unit area at threshold in the depletion layer of an MOS structure

Qd,T

C/m2

Charge density per unit area in the depletion layer of an MOS structure

Qd

C/m2

Charge density per unit volume

ρ

C/m3

Charge density per unit volume in the oxide

ρox

C/m3

Collector doping density

NC

m-3

Collector voltage

VC

V

Collector width

wC

m

Conduction band energy of a semiconductor

Ec

Joule

Conductivity

σ

Ω-1m-1

Current

I

A

Current density

J

A/m2

Current gain

β

 

- D -

Density of states in the conduction band per unit energy and per unit volume

gc(E)

m-3J-1

Density of states in the valence band per unit energy and per unit volume

gv(E)

m-3J-1

Depletion layer width

w

m

Depletion layer width in a p-type semiconductor

xp

m

Depletion layer width in an MOS structure

xd

m

Depletion layer width in an MOS structure at threshold

xd,T

m

Depletion layer width in an n-type semiconductor

xn

m

Dielectric constant of the oxide

εox

F/m

Dielectric constant of the semiconductor

εs

F/m

Distribution function (probability density function)

f(E)

 

Donor doping density

Nd

m-3

Donor energy

Ed

Joule

Doping density

N

 

Drain voltage

VD

V

- E -

Effective density of states in the conduction band

Nc

m-3

Effective density of states in the valence band

Nv

m-3

Effective mass of electrons

me*

kg

Effective mass of holes

mh*

kg

Electric field

E

V/m

Electron affinity of the semiconductor

χ

V

Electron current density

Jn

A/m2

Electron density

n

m-3

Electron density in thermal equilibrium

n0

m-3

Electron density per unit energy and per unit volume

n(E)

m-3

Electron diffusion constant

Dn

m2/s

Electron diffusion length

Ln

m

Electron energy in vacumm

Evacuum

Joule

Electron generation rate

Gn

m-3s-1

Electron lifetime

τn

s

Electron mobility

μn

m2/V-s

Electron recombination rate

Rn

m-3s-1

electronic charge

q

C

Emitter doping density

NE

m-3

Emitter efficiency

γE

 

Emitter voltage

VE

V

Emitter width

wE

m

Energy

E

Joule

Energy bandgap of a semiconductor

Eg

Joule

Excess electron charge density in the base

ΔQn,B

C/m2

Excess electron density

δ n

m-3

Excess hole density

δ p

m-3

- F -

Fermi energy (thermal equilibrium)

EF

Joule

Flatband capacitance per unit area of a MOS structure

CFB

F/m2

Flatband voltage

VFB

V

Free electron mass

m0

kg

- G -

Gate voltage

VG

V

- H -

Hole current density

Jp

A/m2

Hole density

p

m-3

Hole density in an n-type semiconductor

pn

m-3

Hole density in thermal equilibrium

p0

m-3

Hole density per unit energy

p(E)

m-3

Hole diffusion constant

Dp

m2/s

Hole diffusion length

Lp

m

Hole generation rate

Gp

m-3s-1

Hole lifetime

τp

s

Hole mobility

μp

m2/V-s

Hole recombination rate

Rp

m-3s-1

- I -

Interface charge density per unit area

QI

C/m2

Intrinsic carrier density

nI

m-3

Intrinsic carrier density

nI

m-3

Intrinsic Fermi energy

EI

Joule

Ionized acceptor density

Na-

m-3

Ionized donor density

Nd+

m-3

- J -

Junction capacitance per unit area

Cj

F/m2

Junction depth

xj

m

- K -

- L -

Length

L

m

- M -

Mass

m

kg

Mean free path

l

m

- N -

Net recombination rate of electrons

Un

m-3s-1

Net recombination rate of holes

Up

m-3s-1

- O -

Oxide capacitance per unit area

Cox

F/m2

Oxide thickness

tox

m

- P -

Plank's constant

h

Js

Position

x

m

Potential

φ

V

Potential at the semiconductor surface

φs

V

- Q -

Quasi-Fermi energy of electrons

Fn

Joule

Quasi-Fermi energy of holes

Fp

Joule

- R -

Reduced Plank's constant (= h/2π)

Js

Resistance

R

Ω

Resistivity

ρ

Ωm

- S -

Speed of light in vacuum

c

m/s

- T -

Temperature

T

Kelvin

Thermal velocity

vth

m/s

Thermal voltage

Vt

V

Thickness

t

m

Threshold voltage of an MOS structure

VT

V

Transport factor

α

 

- U -

- V -

Valence band energy of a semiconductor

Ev

Joule

Velocity

v

m/s

- W -

Width of a p-type region

wp

m

Width of an n-type region

wn

m

Workfunction difference between the metal and the semiconductor

ΦMS

V

Workfunction of the metal

ΦM

V

Workfunction of the semiconductor

ΦS

V

- X -

- Y -

- Z -