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

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

482 • Chapter 12 / Electrical Properties

Temperature (°C)

Temperature (K)

Electron concentration (m

–3

)

0 100 200

Freeze-out

region

Intrinsic

region

ni

Extrinsic region

(^0300400500600)
1 × 1021
2 × 1021
3 × 1021
–200 –100 0 100 200 300
Figure 12.17 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).
Freeze-out, extrinsic, and
intrinsic temperature regimes
are noted on this plot. (From
S. M. Sze,Semiconductor
Devices, Physics and
Technology. Copyright©c 1985
by Bell Telephone
Laboratories, Inc. Reprinted
by permission of John Wiley &
Sons, Inc.)
electrons from the valence to the conduction band (per Figure 12.6b). In addition,
at all temperatures, carrier concentration in Ge is greater than for Si. This effect is
due to germanium’s smaller band gap (0.67 versus 1.11 eV, Table 12.3); thus, for Ge,
at any given temperature more electrons will be excited across its band gap.
On the other hand, the carrier concentration–temperature behavior for anex-
trinsicsemiconductor is much different. For example, electron concentration versus
temperature for silicon that has been doped with 10^21 m−^3 phosphorus atoms is plot-
ted in Figure 12.17. [For comparison, the dashed curve shown is for intrinsic Si (taken
from Figure 12.16)].^6 Noted on the extrinsic curve are three regions. At intermedi-
ate temperatures (between approximately 150 K and 450 K) the material isn-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 12.13b), and since 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 de-
pend on impurity concentration; furthermore, most solid-state devices are designed
to operate within this temperature range.
At low temperatures, below about 100 K (Figure 12.17), 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
(^6) Note that the shapes of the “Si” curve of Figure 12.16 and the “ni” curve of Figure 12.17 are
not the same even though identical parameters are plotted in both cases. This disparity is due
to the scaling of the plot axes: temperature (i.e., horizontal) axes for both plots are scaled
linearly; however, the carrier concentration axis of Figure 12.16 is logarithmic, whereas this
same axis of Figure 12.17 is linear.
(^7) For donor-doped semiconductors, this region is sometimes called thesaturationregion; for
acceptor-doped materials, it is often termed theexhaustionregion.