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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 for metals and intrinsic semiconductors lies in the behavior of charge carriers. For metals, conductivity decreases with an increase in temperature due to the decreasing mobility of electrons caused by increased lattice vibrations and electron-lattice collisions. Conversely, in intrinsic semiconductors, conductivity increases with an increase in temperature primarily due to the increasing number of charge carriers generated by the thermal energy causing valence electrons to be excited into the conduction band.

Step by step solution

01

Understanding the conductivity of metals

In metals, conductivity mainly depends on the mobility of electrons, which act as the charge carriers. At low temperatures, the conductivity is high because of the fewer lattice vibrations, which means fewer collisions between the electrons and the lattice. As the temperature increases, the lattice vibrations increase, causing more collisions between the electrons and the lattice. This results in a decrease in electron mobility, and thus the conductivity of metals decreases with an increase in temperature.
02

Understanding the conductivity of intrinsic semiconductors

Intrinsic semiconductors are materials with a completely filled valence band and an empty conduction band at absolute zero temperature. As the temperature increases, the thermal energy causes valence electrons to be excited into the conduction band, creating more charge carriers (electron-hole pairs). The increase in charge carriers leads to an increase in conductivity. In addition to charge carrier concentration, the mobility of the charge carriers also plays a crucial role. However, for intrinsic semiconductors, the overall effect of temperature on conductivity is dominated by the increase in the number of charge carriers.
03

Comparing the temperature dependence of conductivity for metals and intrinsic semiconductors

For metals, conductivity decreases with an increase in temperature due to the decreasing mobility of electrons caused by increased lattice vibrations and electron-lattice collisions. On the other hand, for intrinsic semiconductors, conductivity increases with an increase in temperature primarily due to the increasing number of charge carriers generated by the thermal energy causing valence electrons to be excited into the conduction band.
04

Briefly explaining the difference in behavior

The difference in behavior between metals and intrinsic semiconductors in terms of the temperature dependence of conductivity can be attributed to the different mechanisms at play. In metals, the number of charge carriers is not significantly affected by temperature, and the dominant factor is the electron mobility. In contrast, for intrinsic semiconductors, the dominant factor is the increase in the number of charge carriers due to thermal excitation of valence electrons into the conduction band.

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Most popular questions from this chapter

Predict whether each of the following elements will act as a donor or an acceptor when added to the indicated semiconducting material. Assume that the impurity elements are substitutional. $$ \begin{array}{lc} \hline \text { Impurity } & \text { Semiconductor } \\ \hline \text { N } & \text { Si } \\ \hline \text { B } & \text { Ge } \\ \hline \text { S } & \text { InSb } \\ \hline \text { In } & \text { CdS } \\ \hline \text { As } & \text { ZnTe } \\ \hline \end{array} $$

(a) Calculate the number of free electrons per cubic meter for silver, assuming that there are \(1.3\) free electrons per silver atom. The electrical conductivity and density for \(\mathrm{Ag}\) are \(6.8 \times 10^{7}(\Omega \cdot \mathrm{m})^{-1}\) and \(10.5 \mathrm{~g} / \mathrm{cm}^{3}\), respectively. (b) Now, compute the electron mobility for \(\mathrm{Ag}\).

Consider a parallel-plate capacitor having an area of \(3225 \mathrm{~mm}^{2}\left(5\right.\) in. \(^{2}\) ), a plate separation of \(1 \mathrm{~mm}(0.04\) in.), and a material having a dielectric constant of \(3.5\) positioned between the plates. (a) What is the capacitance of this capacitor? (b) Compute the electric field that must be applied for \(2 \times 10^{-8} \mathrm{C}\) to be stored on each plate.

Briefly explain why the ferroelectric behavior of \(\mathrm{BaTiO}_{3}\) ceases above its ferroelectric Curie temperature.

How does the electron structure of an isolated atom differ from that of a solid material?
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