The_Cambridge_Handbook_of_Physics_Formulas

134 Solid state physics
Band theory and semiconductors
Bloch’s theorem Ψ(r +R)=exp(ik ·R)Ψ(r) (6.84)
Electron
velocity
Effective mass
tensor
Scalar effective
mass a
Mobility µ = |v d|
|E| = eD
k B T
Net current
density
Semiconductor
equation
p-n junction
v b (k)= 1¯h ∇ kE b (k) (6.85)
m ij =¯h 2 [ ∂ 2 E b (k)
∂k i ∂k j
] −1
(6.86)
m∗ =¯h 2 [ ∂ 2 E b (k)
∂k 2 ] −1
(6.87)
(6.88)
J =(n e µ e +n h µ h )eE (6.89)
n e n h = (k BT ) 3
2(π¯h 2 ) 3 (m∗ em ∗ h) 3/2 e −E g/(k B T )
( eV
I = I 0
[exp
k B T
) ]
−1
(6.90)
(6.91)
(
I 0 = en 2 De
i A +
D )
h
L e N a L h N d
(6.92)
L e =(D e τ e ) 1/2 (6.93)
L h =(D h τ h ) 1/2 (6.94)
Ψ
k
R
r
v b
¯h
b
E b (k)
m ij
k i
m ∗
k
electron eigenstate
Bloch wavevector
lattice vector
position vector
electron velocity (for wavevector
k)
(Planck constant)/2π
band index
energy band
effective mass tensor
components of k
scalar effective mass
= |k|
µ particle mobility
v d mean drift velocity
E applied electric field
−e electronic charge
D diffusion coefficient
T temperature
J current density
n e,h electron, hole, number densities
µ e,h electron, hole, mobilities
k B
E g
m ∗ e,h
I
I 0
V
n i
A
D e,h
L e,h
τ e,h
Boltzmann constant
band gap
electron, hole, effective masses
current
saturation current
bias voltage (+ for forward)
intrinsic carrier concentration
area of junction
electron, hole, diffusion
coefficients
electron, hole, diffusion lengths
electron, hole, recombination
times
N a,d acceptor, donor, concentrations
a Valid for regions of k-space in which E b (k) can be taken as independent of the direction of k.