242
8 Transport
Fig. 8.19 Impact
ionization rates for
electrons and holes as a
function of the inverse
electric field for Si, Ge and
other compound
semiconductors at 300 K.
Adapted from [574]
Fig. 8.20 Averaged rates
for electron initiated impact
ionization in GaAs (circles)
and GaN (squares).
Adapted from [774]
For a harmonic field E ∝ exp(−iωt) the complex conductivity (j = σE = nqv) is
σ =
n e
2
τ
m ∗
1
1 − i ωτ
=
n e
2
m ∗
i
ω + iγ
,
(8.36)
with γ = 1/τ being the damping constant. Splitting into real and imaginary parts yields
σ =
n e
2
τ
m ∗
1
1 + ω 2 τ 2 + i
ωτ
1 + ω 2 τ 2
.
(8.37)
For small frequencies (ω → 0) the dc conductivity from (8.5) is recovered, i.e. σ = ne
2
τ /m
∗ . For
high frequencies (ωτ 1)
σ =
n e
2
τ
m ∗
1
ω 2 τ 2 + i
1
ωτ
.
(8.38)
8 Transport
Fig. 8.19 Impact
ionization rates for
electrons and holes as a
function of the inverse
electric field for Si, Ge and
other compound
semiconductors at 300 K.
Adapted from [574]
Fig. 8.20 Averaged rates
for electron initiated impact
ionization in GaAs (circles)
and GaN (squares).
Adapted from [774]
For a harmonic field E ∝ exp(−iωt) the complex conductivity (j = σE = nqv) is
σ =
n e
2
τ
m ∗
1
1 − i ωτ
=
n e
2
m ∗
i
ω + iγ
,
(8.36)
with γ = 1/τ being the damping constant. Splitting into real and imaginary parts yields
σ =
n e
2
τ
m ∗
1
1 + ω 2 τ 2 + i
ωτ
1 + ω 2 τ 2
.
(8.37)
For small frequencies (ω → 0) the dc conductivity from (8.5) is recovered, i.e. σ = ne
2
τ /m
∗ . For
high frequencies (ωτ 1)
σ =
n e
2
τ
m ∗
1
ω 2 τ 2 + i
1
ωτ
.
(8.38)