Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

GTBL042-12 GTBL042-Callister-v2 August 13, 2007 18:22

12.10 Intrinsic Semiconduction • 475

Concept Check 12.3

Which of ZnS and CdSe will have the larger band gap energyEg. Cite reason(s) for

your choice.

[The answer may be found at http://www.wiley.com/college/callister (Student Companion Site).]

Concept of a Hole

In intrinsic semiconductors, for every electron excited into the conduction band there

is left behind a missing electron in one of the covalent bonds, or in the band scheme,

a vacant electron state in the valence band, as shown in Figure 12.6b.^5 Under the in-

fluence 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 12.11). This process is expedited by

treating a missing electron from the valence band as a positively charged particle

called ahole. 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. Further-

more, in semiconductors both electrons and holes are scattered by lattice imper-

fections.

Intrinsic Conductivity

Since there are two types of charge carrier (free electrons and holes) in an intrinsic

semiconductor, the expression for electrical conduction, Equation 12.8, must be mod-

ified to include a term to account for the contribution of the hole current. Therefore,

we write

σ=n|e|μe+p|e|μh (12.13)

Electrical

conductivity for an

intrinsic

semiconductor—

dependence on

electron/hole

concentrations and

electron/hole

mobilities

wherepis the number of holes per cubic meter andμhis the hole mobility. The mag-

nitude ofμhis always less thanμefor semiconductors. For intrinsic semiconductors,

every electron promoted across the band gap leaves behind a hole in the valence

band; thus,

n=p=ni (12.14)

whereniis known as theintrinsic carrier concentration. Furthermore,

σ=n|e|(μe+μh)=p|e|(μe+μh)

=ni|e|(μe+μh)

(12.15)

For an intrinsic

semiconductor,

conductivity in terms

of intrinsic carrier

concentration The room-temperature intrinsic conductivities and electron and hole mobilities for

several semiconducting materials are also presented in Table 12.3.

(^5) Holes (in addition to free electrons) are created in semiconductors and insulators when
electron transitions occur from filled states in the valence band to empty states in the
conduction band (Figure 12.6). In metals, electron transitions normally occur from empty to
filled stateswithin the same band(Figure 12.5), without the creation of holes.