Krane, Chapter 11, Question 5

(a) Why does the electrical conductivity of a metal decrease as the temperature is increased?

(b) How would you expect the conductivity of a semiconductor to change with temperature?

Answer: part (a) see page 354, middle of page

“Recall that the Fermi energy in a conductor lies near the middle of the conduction band (see Fig. 11.17), and that electrons near the middle of an allowed band are not scattered at all by the lattice (Fig. 11.27). In a perfect lattice, the conductivity would be infinite – the electrons would not scatter at all!”

“In a real metallic lattice …. The atoms are in thermal motion and therefore do not occupy exactly the positions of a perfectly aligned lattice.”

This thermal motion is of course temperature dependent, and the greater the temperature the greater the deviation from a perfectly aligned lattice and the greater the scattering, hence the greater the resistance.

Answer to part (b)

In a semiconductor, the greater the temperature the more electrons there are that exceed the Fermi energy and are able to jump the gap and enter the conduction banc, hence the lower the resistance.

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Krane, Chapter 11, Question 13

If a semiconductor is doped at a level of one impurity atom per 10⁹ host atoms, what is the average spacing per host atom?

If there is one impurity atom within a cubical volume containing 10⁹ host atoms, each side of that cube will have a length

L = (10⁹)^1/3 = 1000 host atoms