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 • 485

contents are shown for both carrier types; furthermore, both sets of axes are scaled

logarithmically. From these plots, note that, for dopant concentrations of 10^24 m−^3

and below, both electron and hole mobilities decrease in magnitude with rising tem-

perature; again, this effect is due to enhanced thermal scattering of the carriers. For

both electrons and holes, and dopant levels less than 10^20 m−^3 , the dependence of

mobility on temperature is independent of acceptor/donor concentration (i.e., is rep-

resented by a single curve). Also, for concentrations greater than 10^20 m−^3 , curves in

both plots are shifted to progressively lower mobility values with increasing dopant

level. These latter two effects are consistent with the data presented in Figure 12.18.

These previous treatments have discussed the influence of temperature and

dopant content on both carrier concentration and carrier mobility. Once values ofn,

p,μe, andμhhave been determined for a specific donor/acceptor concentration and

at a specified temperature (using Figures 12.16, 12.17, 12.18, and 12.19), computation

ofσis possible using Equation 12.15, 12.16, or 12.17.

Concept Check 12.7

On the basis of the electron concentration-versus-temperature curve forn-type sili-

con shown in Figure 12.17 and the dependence of the logarithm of electron mobility

on temperature (Figure 12.19a), make a schematic plot of logarithm electrical con-

ductivity versus temperature for silicon that has been doped with 10^21 m−^3 of a donor

impurity. Now briefly explain the shape of this curve. Recall that Equation 12.16

expresses the dependence of conductivity on electron concentration and electron

mobility.

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

EXAMPLE PROBLEM 12.2

Electrical Conductivity Determination for Intrinsic

Silicon at 150◦C

Calculate the electrical conductivity of intrinsic silicon at 150◦C (423 K).

Solution

This problem may be solved using Equation 12.15, which requires specification

of values forni,μe, andμh. From Figure 12.16,nifor Si at 423 K is 4× 1019

m−^3. Furthermore, intrinsic electron and hole mobilities are taken from the

“< 1020 m−^3 ” curves of Figures 12.19aand 12.19b, respectively; at 423 K,μe=

0.06 m^2 /V-s andμh=0.022 m^2 /V-s (realizing that both mobility and temperature

axes are scaled logarithmically). Finally, from Equation 12.15 the conductivity

is equal to

σ=ni|e|(μe+μh)

=(4× 1019 m−^3 )(1. 6 × 10 −^19 C)(0.06 m^2 /V-s+ 0 .022 m^2 /V-s)

= 0 .52 (-m)−^1