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

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

12.13 Factors That Affect Carrier Mobility • 483

region” inasmuch as charged carriers (i.e., electrons) are “frozen” to the dopant

atoms.

Finally, at the high end of the temperature scale of Figure 12.17, electron concen-

tration increases above the P content, and asymptotically approaches the intrinsic

curve as temperature increases. This is termed the “intrinsic temperature region”

since at these high temperatures the semiconductor becomes intrinsic; that is, charge

carrier concentrations resulting from electron excitations across the band gap first

become equal to and then completely overwhelm the donor carrier contribution with

rising temperature.

Concept Check 12.6

On the basis of Figure 12.17, as dopant level is increased would you expect the temper-

ature at which a semiconductor becomes intrinsic to increase, to remain essentially

the same, or to decrease? Why?

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

12.13 FACTORS THAT AFFECT CARRIER MOBILITY

The conductivity (or resistivity) of a semiconducting material, in addition to being

dependent on electron and/or hole concentrations, is also a function of the charge

carriers’ mobilities (Equation 12.13)—that is, the ease with which electrons and holes

are transported through the crystal. Furthermore, magnitudes of electron and hole

mobilities are influenced by the presence of those same crystalline defects that are

responsible for the scattering of electrons in metals—thermal vibrations (i.e., tem-

perature) and impurity atoms. We now explore the manner in which dopant impurity

content and temperature influence the mobilities of both electrons and holes.

Influence of Dopant Content

Figure 12.18 represents the electron and hole mobilities in silicon as a function of

the dopant (both acceptor and donor) content, at room temperature—note that both

axes on this plot are scaled logarithmically. At dopant concentrations less than about

Impurity concentration (m–3)

Mobility (m

2 / V – s)

1019 1020 1021

Holes

Electrons

1022 1023 1024 1025

0.001

0.01

0.1

Figure 12.18 For

silicon, dependence of

room-temperature

electron and hole

mobilities (logarithmic

scale) on dopant

concentration

(logarithmic scale).

(Adapted from W. W.

G ̈artner, “Temperature

Dependence of Junction

Transistor Parameters,”

Proc. of the IRE,45,

667, 1957. Copyright

©c1957 IRE now

IEEE.)