Callister - An introduction - 8th edition

734 • Chapter 18 / Electrical Properties
Table 18.3
Band Gap Energies, Electron and Hole Mobilities, and
Intrinsic Electrical Conductivities at Room Temperature
for Semiconducting Materials
Electrical
Band Gap Conductivity Electron Mobility Hole Mobility
Material (eV) [(#
m) 1 ] (m 2 /V#
s) (m 2 /V#
s)
Elemental
Si 1.11 4 10 4 0.14 0.05
Ge 0.67 2.2 0.38 0.18
III–V Compounds
GaP 2.25 — 0.03 0.015
GaAs 1.42 10 6 0.85 0.04
InSb 0.17 2 10 4 7.7 0.07
II–VI Compounds
CdS 2.40 — 0.03 —
ZnTe 2.26 — 0.03 0.01
the influence of an electric field, the position of this missing electron within the
crystalline lattice may be thought of as moving by the motion of other valence electrons
that repeatedly fill in the incomplete bond (Figure 18.11). This process is expedited
by treating a missing electron from the valence band as a positively charged
particle called a hole. A hole is considered to have a charge that is of the same magnitude
as that for an electron, but of opposite sign (1.6 10 19 C). Thus, in the
presence of an electric field, excited electrons and holes move in opposite directions.
Furthermore, in semiconductors both electrons and holes are scattered by lattice
imperfections.
Electrical
conductivity for an
intrinsic
semiconductor—
dependence on
electron/hole
concentrations and
electron/hole
mobilities
For an intrinsic
semiconductor,
conductivity in terms
of intrinsic carrier
concentration
Intrinsic Conductivity
Because there are two types of charge carrier (free electrons and holes) in an intrinsic
semiconductor, the expression for electrical conduction, Equation 18.8, must
be modified to include a term to account for the contribution of the hole current.
Therefore, we write
s nem e pem h
(18.13)
where p is the number of holes per cubic meter and h is the hole mobility. The
magnitude of h is always less than e for semiconductors. For intrinsic semiconductors,
every electron promoted across the band gap leaves behind a hole in the
valence band; thus,
n p n i (18.14)
where n i is known as the intrinsic carrier concentration. Furthermore,
s ne1m e m h 2 pe1m e m h 2
n i e1m e m h 2
(18.15)
The room-temperature intrinsic conductivities and electron and hole mobilities for
several semiconducting materials are also presented in Table 18.3.