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Chapter 18: Problem 36

Compare the temperature dependence of the conductivity for metals and intrinsic semiconductors. Briefly explain the difference in behavior.

Short Answer

Expert verified
Answer: The main difference in the temperature dependence of conductivity between metals and intrinsic semiconductors is that in metals, the conductivity decreases with increasing temperature, while in intrinsic semiconductors, the conductivity increases with increasing temperature. This difference is due to the fact that in metals, increasing temperature leads to more electron scattering due to lattice vibrations, whereas in intrinsic semiconductors, the increase in temperature results in a higher number of free charge carriers due to the creation of more electron-hole pairs.

Step by step solution

01

Conductivity in metals

In metals, the conductivity is mainly due to the movement of free electrons. When the temperature increases, the vibration amplitude of atoms in the metal lattice also increases. This causes more scattering of the free electrons, leading to a decrease in their average drift velocity, and ultimately a decrease in the conductivity. Therefore, the conductivity of metals generally decreases with increasing temperature.
02

Conductivity in intrinsic semiconductors

Intrinsic semiconductors are pure semiconductors with no impurities. Their conductivity is due to the presence of both free electrons and holes. At low temperatures, the number of free charge carriers (electrons and holes) is very small, resulting in low conductivity. However, as the temperature increases, the thermal energy helps to break more covalent bonds and creates more electron-hole pairs. This leads to an increase in the number of free charge carriers and, therefore, an increase in the conductivity. Hence, the conductivity of intrinsic semiconductors increases with increasing temperature.
03

Main difference in behavior

The main difference in the temperature dependence of the conductivity between metals and intrinsic semiconductors is that in metals, the conductivity decreases with increasing temperature, while in intrinsic semiconductors, the conductivity increases with increasing temperature. This difference can be attributed to the fact that in metals, increasing temperature leads to more electron scattering due to lattice vibrations, whereas in intrinsic semiconductors, the increase in temperature results in a higher number of free charge carriers due to the creation of more electron-hole pairs.

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Most popular questions from this chapter

Briefly tell what is meant by the drift velocity and mobility of a free electron.

A parallel-plate capacitor using a dielectric material having an \(\epsilon_{r}\) of \(2.5\) has a plate spacing of \(1 \mathrm{~mm}(0.04 \mathrm{in} .)\). If another material having a dielectric constant of \(4.0\) is used and the capacitance is to be unchanged, what must be the new spacing between the plates?

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