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

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

486 • Chapter 12 / Electrical Properties

EXAMPLE PROBLEM 12.3

Room-Temperature and Elevated-Temperature Electrical

Conductivity Calculations for Extrinsic Silicon

To high-purity silicon is added 10^23 m−^3 arsenic atoms.

(a)Is this materialn-type orp-type?

(b)Calculate the room-temperature electrical conductivity of this material.

(c)Compute the conductivity at 100◦C (373 K).

Solution

(a)Arsenic is a Group VA element (Figure 2.6) and, therefore, will act as a

donor in silicon, which means that this material isn-type.

(b)At room temperature (298 K) we are within the extrinsic temperature

region of Figure 12.17, which means that virtually all of the arsenic atoms

have donated electrons (i.e.,n= 1023 m−^3 ). Furthermore, inasmuch as this

material is extrinsicn-type, conductivity may be computed using Equation

12.16. Consequently, it is necessary for us to determine the electron mobility

for a donor concentration of 10^23 m−^3. We can do this using Figure 12.18:

at 10^23 m−^3 ,μe=0.07 m^2 /V-s (remember that both axes of Figure 12.18 are

scaled logarithmically). Thus, the conductivity is just

σ=n|e|μe

=(10^23 m−^3 )(1. 6 × 10 −^19 C)(0.07 m^2 /V-s)

=1120 (-m)−^1

(c)To solve for the conductivity of this material at 373 K, we again use Equation

12.16 with the electron mobility at this temperature. From the 10^23 m−^3

curve of Figure 12.19a, at 373 K,μe=0.04 m^2 /V-s, which leads to

σ=n|e|μe

=(10^23 m−^3 )(1. 6 × 10 −^19 C)(0.04 m^2 /V-s)

=640 (-m)−^1

DESIGN EXAMPLE 12.1

Acceptor Impurity Doping in Silicon

An extrinsicp-type silicon material is desired having a room-temperature con-

ductivity of 50 (-m)−^1. Specify an acceptor impurity type that may be used as

well as its concentration in atom percent to yield these electrical characteristics.

Solution

First, the elements that, when added to silicon, render itp-type, lie one group to

the left of silicon in the periodic table. These include the group IIIA elements

(Figure 2.6): boron, aluminum, gallium, and indium.