ECE305 Reference Sheet
Yangorang
Constants
q=1.6 ×10
−19
C(charge electron)
m0=9.11×10−31 Kg(mass electron)
ε
0
=8.85 ×10
−14
F
cm
(permittivity free space)
k=8.617 ×10
−5
eV
K
(Boltzmann)
h=6.63 ×10−34 J ∙ s
(Planck)
h=h
2π=1.0552×10
34
kT =0.0259 eV
(
Thermal energy at T =300 K
)
kT
q=0.0259V(Thermal voltage at T =300 K)
ni=1010/cm3
(for silicon at 300K)
Miller Indices
1. Note intercepts of desired plane with coordinate
axes
2. Divide each intercept by unit cell length
3. Take reciprocals of values
4. Use appropriate multiplier to convert to smallest
possible set of whole numbers
5. Enclose in ( … )
Bohr Model
E
H
=−m
0
q
4
2
(
4π ε
0
h n
)
2
=−13.6
n
2
eV
; n = 1, 2, 3…
EH
is electron binding energy within hydrogen atom
E=h ω
;
ω=2πf
;
c=fλ
;
p=h
λ
n = number electrons / cm3
p = number holes / cm3
n=p=ni
in intrinsic semiconductor under equilibrium
(assuming room temperature)
n
i
=2×10
6
/cm
3
(in GaAs)
ni=1×1010 /cm3
(in Si)
n
i
=2×10
13
/cm
3
(in Ge)
Donors (electron-increasing): P, As, Sb
Acceptors (hole-increasing): B, Ga, In, Al
Density of States (at energy level E)
gc
(
E
)
=mn
¿
√
2mn
¿(E−Ec)
π2h3
,
E ≥ E
C
g
v
(
E
)
=m
p
¿
√
2m
p
¿
(E
v
−E)
π
2
h
3
,
E ≤ E v
Fermi Function
f
(
E
)
=1
1+e(E−EF)/kT
where
EF
is the Fermi energy or level
Probably that state is not filled at given energy E is
1−f
(
E
)
Intrinsic Fermi level is slightly above the middle of the
bandgap if effective hole mass is greater than the effective
electron mass.
Equilibrium Carrier Concentrations
NC=2
[
mn
¿kT
2π h2
]
3/2
N
V
=2
[
m
p
¿
kT
2π h
2
]
3/2
