Both the values and the intrinsic conductivity expression

12.12 The Temperature Variation of Conductivity and Carrier Concentration	●	383

termed p-type because positively charged particles are primarily responsible for electrical conduction. Of course, holes are the majority carriers, and electrons are present in minority concentrations. This gives rise to a predominance of the second term on the right-hand side of Equation 12.13, or

� � p�e��h	(12.17)

(a) Phosphorus is a Group VA element (Figure 2.6) and, therefore, will act as a donor in silicon. Thus, the 1023m�3charge carriers will be virtually all electrons. This electron concentration is greater than that for the intrinsic case (1.33 �1016m�3, Example Problem 12.1); hence, this material is extrinsically n-type.

(b) In this case the conductivity may be determined using Equation 12.16, as follows:

S O L U T I O N

12.12 THE TEMPERATURE VARIATION OF CONDUCTIVITY AND CARRIER CONCENTRATION

Chapter 12 / Electrical Properties					FIGURE 12.15 temperature
10,000		–100	0		FIGURE 12.15 temperature
10,000		–100	0
1,000		0.0052 at% B		Intrinsic	electrical conductivity
					(log–log scales) for


	10 1
					[Adapted from G. L.

		Intrinsic			Bardeen, Phys. Rev.,
		Intrinsic

0.1

0.01 50	100	200	400	600	1000

ln � � C �Eg 2kT	(12.18)

where C represents a temperature-independent constant and Eg and k are the band gap energy and Boltzmann’s constant, respectively. Since the increase of n and p with rising temperature is so much greater than the decrease in �e and �h, the dependence of carrier concentration on temperature for intrinsic behavior is virtu-ally the same as for the conductivity, or

ln n � ln p � C� �Eg 2kT	(12.19)