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8 Transport
Table 8.1 Conductivity at room temperature for various metals, semiconductors, insulators and liquids
Material
σ ( −1 cm −1 )
Ag
6.25 × 10 5
Al
3.6 × 10 5
Au
4.35 × 10 5
Cu
5.62 × 10 5
Fe
1.1 × 10 5
Pt
1.02 × 10 5
Ge pure (N D ∼ 10 13 cm −3 )
10 −2
Ge (N D ∼ 10 15 cm −3 )
1
Ge (N D ∼ 10 17 cm −3 )
2 × 10 1
Ge (N D ∼ 10 18 cm −3 )
2 × 10 2
Si pure
4.5 × 10 −6
Si:As (N D ∼ 3 × 10 19 cm −3 )
4 × 10 2
Si:B (N A ∼ 1.5 × 10 19 cm −3 )
1.2 × 10 2
GaAs pure
1.4 × 10 −7
ZnO:Al (highly doped)
≈1 × 10 4
Pentacene
10 −8 – 10 −4
SiO 2
≈10 −15
Al 2 O 3
≈10 −16
H 2 O pure
4 × 10 −8
Hexane
≈10 −18
8.3.1 Mobility
The mobility is defined (scalar terms) as
μ =
v
E
.
(8.8)
By definition, it is a negative number for electrons and positive for holes. However, the numerical value
is usually given as a positive number for both carrier types. In an intrinsic semiconductor the mobility
is determined by scattering with phonons. Further scattering is introduced by impurities, defects or
alloy disorder. The conductivity is (8.4)
σ = q n μ
(8.9)
for each carrier type. Using (8.5) the mobility in the relaxation time approximation is
μ =
q τ
m ∗ .
(8.10)
In the presence of both electrons and holes,
σ = σ e + σ h = −e n μ n + e p μ p ,
(8.11)
where μ n and μ p are the mobilities for electrons and holes, respectively. These are given by μ n =
−e τ n /m
∗
e and μ p = e τ p /m
∗
h .
As the unit for mobility, usually cm
2 /Vs is used. While Cu at room temperature has a mobility
of 35 cm
2 /Vs, semiconductors can have much higher values. In two-dimensional electron gases (cf.