33
Review of Basic Device Physics
impurity scattering. The detailed temperature dependence of mobility can
be found in Arora and Arora et al. [17,21].
The carrier mobility discussed earlier is the bulk mobility applicable to conduction in the silicon substrate far away from the surface. In the channel
region of MOSFET (metal-oxide-semiconductor field-effect transistor) devices,
the current flow is governed by the surface mobility. The surface mobility is
much lower than the bulk mobility due to additional scattering mechanism
between the carriers and Si/SiO 2 interface in the presence of the high electric
field normal to the channel as discussed in Section 5.3.1 of Chapter 5.
2.2.5.2 Electrical Resistivity
The drift of charge carriers under an applied electric field E results in a current, called the drift current. For a homogeneous n-type silicon, if there are n
number of electrons per unit volume each carrying a charge q flow with a
drift velocity v d , then the electron drift current density is given by
J
qnv
qn E
n drift
d
n
,
=
= µ
(2.30)
where we have used Equation 2.28 for v d ; in Equation 2.30, q = 1.6 × 10 –19  C
is the electronic charge and μ n is the electron mobility. From Ohm’s law,
the resistivity ρ of a conducting material is defined by E/J n ; therefore, from
Equation 2.30, the resistivity ρ n to electron current flow is given by
ρ
µ
n
n
qn
=
1
(2.31)
Similarly, for a p-type silicon, the hole drift current density, J p,drift , and resistivity, ρ p are given by
J
qpv
qp E
p drift
d
p
,
=
= µ
(2.32)
ρ
µ
p
p
qp
=
1
(2.33)
where:
μ p is the hole mobility
If the silicon is doped with both donors and acceptors, then the total resistivity can be expressed as
ρ
µ
µ
=
+
1
qn
qp
n
p
(2.34)
Thus, the resistivity of a semiconductor depends on the electron and hole
concentrations and their mobilities. Empirical resistivity versus impurity