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

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

12.11 Extrinsic Semiconduction • 477

EXAMPLE PROBLEM 12.1

Computation of the Room-Temperature Intrinsic Carrier

Concentration for Gallium Arsenide

For intrinsic gallium arsenide, the room-temperature electrical conductivity

is 10−^6 (-m)−^1 ; the electron and hole mobilities are, respectively, 0.85 and

0.04 m^2 /V-s. Compute the intrinsic carrier concentrationniat room temperature.

Solution

Since the material is intrinsic, carrier concentration may be computed using

Equation 12.15 as

ni=

σ

|e|(μe+μh)

=

10 −^6 (-m)−^1

(1. 6 × 10 −^19 C)[(0. 85 + 0 .04)m^2 /V-s]

= 7. 0 × 1012 m−^3

12.11 EXTRINSIC SEMICONDUCTION

Virtually all commercial semiconductors are extrinsic; that is, the electrical behavior

is determined by impurities, which, when present in even minute concentrations,

introduce excess electrons or holes. For example, an impurity concentration of one

atom in 10^12 is sufficient to render silicon extrinsic at room temperature.

n-Type Extrinsic Semiconduction

To illustrate how extrinsic semiconduction is accomplished, consider again the ele-

mental semiconductor silicon. An Si atom has four electrons, each of which is cova-

lently bonded with one of four adjacent Si atoms. Now, suppose that an impurity atom

with a valence of 5 is added as a substitutional impurity; possibilities would include

atoms from the Group VA column of the periodic table (e.g., P, As, and Sb). Only

four of five valence electrons of these impurity atoms can participate in the bonding

because there are only four possible bonds with neighboring atoms. The extra non-

bonding electron is loosely bound to the region around the impurity atom by a weak

electrostatic attraction, as illustrated in Figure 12.12a. The binding energy of this

electron is relatively small (on the order of 0.01 eV); thus, it is easily removed from

the impurity atom, in which case it becomes a free or conducting electron (Figures

12.12band 12.12c).

The energy state of such an electron may be viewed from the perspective of the

electron band model scheme. For each of the loosely bound electrons, there exists a

single energy level, or energy state, which is located within the forbidden band gap

just below the bottom of the conduction band (Figure 12.13a). The electron binding

energy corresponds to the energy required to excite the electron from one of these

impurity states to a state within the conduction band. Each excitation event (Figure

12.13b) supplies or donates a single electron to the conduction band; an impurity

of this type is aptly termed adonor. Since each donor electron is excited from an

impurity level, no corresponding hole is created within the valence band.

At room temperature, the thermal energy available is sufficient to ex-

donor state cite large numbers of electrons fromdonor states;in addition, some intrinsic