Appendix: 

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Appendix 1a: Extended List of Symbols print file in PDF format

Symbol

Description

MKS Units

a

Acceleration

m/s2

a0

Bohr radius

m

A

Area

m2

A*

Richardson constant

m/s

AC

Collector area

m2

AE

Emitter area

m2

b

Bimolecular recombination constant

m3/s

c

Speed of light in vacuum

m/s

C

Capacitance per unit area

F/m2

CD

Diffusion capacitance per unit area

F/m2

CDS

Drain-source capacitance

F

CFB

Flatband capacitance per unit area of a MOS structure

F/m2

CG

Gate capacitance

F

CGS

Gate-source capacitance

F

CGD

Gate-drain capacitance

F

CHF

High-frequency capacitance per unit area of a MOS structure

F/m2

Cj

Junction capacitance per unit area

F/m2

CLF

Low-frequency (quasi-static) capacitance per unit area of a MOS structure

F/m2

CM

Miller capacitance

F

Cox

Oxide capacitance per unit area

F/m2

Cs

Semiconductor capacitance per unit area

F/m2

Dn

Electron diffusion constant

m2/s

Dp

Hole diffusion constant

m2/s

E

Energy

Joule

E

Electric field

V/m

E0

Lowest energy in a one-dimensional quantum well

Joule

Ea

Acceptor energy

Joule

Ebr

Breakdown field

V/m

Ec

Conduction band energy of a semiconductor

Joule

Ed

Donor energy

Joule

EF

Fermi energy (thermal equilibrium)

Joule

EF,n

Fermi energy in an n-type semiconductor

Joule

EF,p

Fermi energy in a p-type semiconductor

Joule

Eg

Energy bandgap of a semiconductor

Joule

Ei

Intrinsic Fermi energy

Joule

En

nth quantized energy

Joule

Eph

Photon energy

Joule

Et

Trap energy

Joule

Ev

Valence band energy of a semiconductor

Joule

Evacuum

Electron energy in vacumm

Joule

F(E)

Distribution function (probability density function)

 

fBE(E)

Bose-Einstein distribution function

 

fFD(E)

Fermi-Dirac distribution function

 

fMB(E)

Maxwell-Boltzmann distribution function

 

F

Force

Newton

Fn

Quasi-Fermi energy of electrons

Joule

Fp

Quasi-Fermi energy of holes

Joule

gE)

Density of states per unit energy and per unit volume

m-3J-1

g(E)

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

m-3J-1

g(E)

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

m-3J-1

gd

Output conductance of a MOSFET

S

gm

Transconductance of a MOSFET

S

G

Carrier generation rate

m-3s-1

Gn

Electron generation rate

m-3s-1

Gp

Hole generation rate

m-3s-1

h

Plank's constant

Js

Reduced Plank's (= h /2p)

Js

I

Current

A

IB

Base current of a bipolar transistor

A

IC

Collector current of a bipolar transistor

A

ID

Drain current of a MOSFET

A

IE

Emitter current of a bipolar transistor

A

IF

Forward active current of a bipolar transistor

A

ID,sat

Drain current of a MOSFET in saturation

A

Iph

Photo current

A

Ir

Recombination current

A

IR

Reverse active current of a bipolar transistor

A

Is

Saturation current

A

Isc

Short circuit current of a solar cell

A

J

Current density

A/m2

Jn

Electron current density

A/m2

Jp

Hole current density

A/m2

k

Boltzmann's constant
wavenumber

J/K
m-1

l

Mean free path

m

L

Length

m

LD

Debye length

m

Ln

Electron diffusion length

m

Lp

Hole diffusion length

m

Lx

Hole diffusion length

m

m

Mass

kg

m*

Effective mass

kg

mA

Atomic mass

kg

m0

Free electron mass

kg

me*

Effective mass of electrons

kg

mh*

Effective mass of holes

kg

M

Proton mass
Multiplication factor

kg

n

Electron density
Integer
Refractive index
Ideality factor

m-3
 
 
 

ni

Intrinsic carrier density

m-3

n(E)

Electron density per unit energy and per unit volume

m-3

n0

Electron density in thermal equilibrium

m-3

ni

Intrinsic carrier density

m-3

nn

Electron density in an n-type semiconductor

m-3

nn0

Thermal equilibrium electron density in an n-type semiconductor

m-3

np

Electron density in a p-type semiconductor

m-3

np0

Thermal equilibrium electron density in a p-type semiconductor

m-3

N

Number of particles
Doping density

 

Na

Acceptor doping density

m-3

Na-

Ionized acceptor density

m-3

NA

Avogadro's number

 

NB

Base doping density

m-3

Nc

Effective density of states in the conduction band

m-3

NC

Collector doping density

m-3

Nd

Donor doping density

m-3

Nd+

Ionized donor density

m-3

NE

Emitter doping density

m-3

Nss

Surface state density

m-2

Nt

Recombination trap density

m-2

Nv

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

p0

Hole density in thermal equilibrium

m-3

pn

Hole density in an n-type semiconductor

m-3

pn0

Thermal equilibrium hole density in an n-type semiconductor

m-3

pp

Hole density in a p-type semiconductor

m-3

pp0

Thermal equilibrium hole density in a p-type semiconductor

m-3

q

electronic charge

C

Q

Heat
Charge

Joule
C

QB

Majority carrier charge density in the base

C/m2

Qd

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

C/m2

Qd,T

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

C/m2

Qi

Interface charge density per unit area

C/m2

Qinv

Inversion layer charge density per unit area

C/m2

QM

Charge density per unit area in a metal

C/m2

Qn

Charge density per unit area in the depletion layer of an n-type region

C/m2

Qp

Charge density per unit area in the depletion layer of a p-type region

C/m2

Qss

Surface state charge density per unit area

C/m2

re

Emitter resistance

Ohm

rp

Base resistance

Ohm

R

The Rydberg constant
Resistance

J
Ohm

Rn

Electron recombination rate

m-3s-1

Rp

Hole recombination rate

m-3s-1

Rs

Sheet resistance

Ohm

s

Spin

 

S

Entropy

J/K

t

Thickness

m

tox

Oxide thickness

m

T

Temperature
Kinetic energy

Kelvin
Joule

uw

Spectral density

Jm-3s-1

U

Total energy

Joule

UA

Auger recombination rate

m-3s-1

Ub-b

Band-to-band recombination rate

m-3s-1

Un

Net recombination rate of electrons

m-3s-1

Up

Net recombination rate of holes

m-3s-1

USHR

Shockley-Read-Hall recombination rate

m-3s-1

v

Velocity

m/s

vR

Richardson velocity

m/s

vsat

Saturation velocity

m/s

vth

Thermal velocity

m/s

V

Potential energy
Volume

Joule
m3

Va

Applied voltage

V

VA

Early voltage

V

Vbr

Breakdown voltage

V

VB

Base voltage

V

VBE

Base-emitter voltage

V

VBC

Base-collector voltage

V

VC

Collector voltage

V

VCE

Collector-emitter voltage

V

VD

Drain voltage

V

VDS

Drain-source voltage

V

VDS,sat

Drain-source saturation voltage

V

VE

Emitter voltage

V

VFB

Flatband voltage

V

VG

Gate voltage

V

VGS

Gate-source voltage

V

Voc

Open circuit voltage of a solar cell

V

Vt

Thermal voltage

V

VT

Threshold voltage of an MOS structure

V

w

Depletion layer width

m

wB

Base width

m

wC

Collector width

m

wE

Emitter width

m

wn

Width of an n-type region

m

wp

Width of a p-type region

m

W

Work

Joule

x

Position

m

xd

Depletion layer width in an MOS structure

m

xd,T

Depletion layer width in an MOS structure at threshold

m

xj

Junction depth

m

xn

Depletion layer width in an n-type semiconductor

m

xp

Depletion layer width in a p-type semiconductor

m

a

Absorption coefficient
Transport factor

m-1

 

aF

Forward active transport factor

   

an

Ionization rate coefficient for electrons

m-1

 

aR

Reverse active transport factor

   

aT

Base transport factor

   

b

Current gain

   

g

Body effect parameter

V1/2

 

gE

Emitter efficiency

   

Gn

Auger coefficient for electrons

m6s-1

 

Gp

Auger coefficient for holes

m6s-1

 

d n

Excess electron density

m-3

 

d p

Excess hole density

m-3

 

d R

Depletion layer recombination factor

   

DQn,B

Excess electron charge density in the base

C/m2

 

e

Dielectric constant

F/m

 

e0

Permittivity of vacuum

F/m

 

eox

Dielectric constant of the oxide

F/m

 

es

Dielectric constant of the semiconductor

F/m

m0

Permeability of vacuum

H/m

 

Q

Tunnel probability

   

l

Wavelength

m

 

m

Electro-chemical potential

Joule

 

mn

Electron mobility

m2/V-s

 

mp

Hole mobility

m2/V-s

 

n

Frequency

Hz

 

r

Charge density per unit volume
Resistivity

C/m3
Wm

 

rox

Charge density per unit volume in the oxide

C/m3

 

s

Conductivity

W-1m-1

 

t

Scattering time

s

 

tn

Electron lifetime

s

 

tp

Hole lifetime

s

 

f

Potential

V

 

fB

Barrier height

V

 

fF

Bulk potential

V

 

fi

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

V

 

fs

Potential at the semiconductor surface

V

 

F

Flux

m-2s-1

 

FM

Workfunction of the metal

V

 

FMS

Workfunction difference between the metal and the semiconductor

V

 

FS

Workfunction of the semiconductor

V

 

c

Electron affinity of the semiconductor

V

 

Y

Wavefunction

   

w

Radial frequency

rad/s