Callister - An introduction - 8th edition

18.12 The Temperature Dependence of Carrier Concentration • 741
Electron concentration (m –3 )
Temperature (°C)
3 × 10 21 –200 –100 0 100 200 300
2 × 10 21
1 × 10 21
Freeze-out
region
Extrinsic region
Intrinsic
region
n i
Figure 18.17 Electron
concentration versus
temperature for silicon
(n-type) that has been doped
with 10 21 m 3 of a donor
impurity, and for intrinsic
silicon (dashed line). Freezeout,
extrinsic, and intrinsic
temperature regimes are
noted on this plot. (From
S. M. Sze, Semiconductor
Devices, Physics and
Technology. Copyright © 1985
by Bell Telephone Laboratories,
Inc. Reprinted by permission of
John Wiley & Sons, Inc.)
0
0 100 200 300 400 500 600
Temperature (K)
intermediate temperatures (between approximately 150 K and 475 K) the material
is n-type (inasmuch as P is a donor impurity), and electron concentration is constant;
this is termed the “extrinsic-temperature region”. 7 Electrons in the conduction band
are excited from the phosphorus donor state (per Figure 18.13b), and because the
electron concentration is approximately equal to the P content (10 21 m 3 ), virtually
all of the phosphorus atoms have been ionized (i.e., have donated electrons). Also,
intrinsic excitations across the band gap are insignificant in relation to these extrinsic
donor excitations. The range of temperatures over which this extrinsic region
exists will depend on impurity concentration; furthermore, most solid-state devices
are designed to operate within this temperature range.
At low temperatures, below about 100 K (Figure 18.17), electron concentration
drops dramatically with decreasing temperature and approaches zero at 0 K. Over
these temperatures, the thermal energy is insufficient to excite electrons from the
P donor level into the conduction band. This is termed the “freeze-out temperature
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 18.17, electron concentration
increases above the P content and asymptotically approaches the intrinsic
curve as temperature increases. This is termed the intrinsic temperature region because
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 18.6
On the basis of Figure 18.17, as dopant level is increased would you expect the temperature
at which a semiconductor becomes intrinsic to increase, to remain essentially
the same, or to decrease? Why?
[The answer may be found at www.wiley.com/college/callister (Student Companion Site).]
7 For donor-doped semiconductors, this region is sometimes called the saturation region;
for acceptor-doped materials, it is often termed the exhaustion region.