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Chapter 12: Problem 115

Unlike metals, semiconductors increase their conductivity as you heat them (up to a point). Suggest an explanation.

Short Answer

Expert verified
Semiconductors increase their conductivity as temperature rises (up to a point) because the increased temperature provides necessary energy to transition more electrons from the valence band to the conduction band. This increase in the number of charge carriers (electrons) enhances conductivity, unlike metals where lattice vibrations interfere with electron movement at higher temperatures. However, this behavior is observed only up to a certain temperature, where other factors may counteract this effect.

Step by step solution

01

Understand semiconductors properties

Semiconductors are materials that have electrical conductivity between that of insulators and conductors (e.g., metals). Their valence electrons are not as tightly bound as in insulators but are not freely moving like in metals. The most common example of semiconductor materials is silicon (Si) and germanium (Ge).
02

Band structure

The energy and position of electrons in materials are typically arranged in energy bands. There are two main energy bands in semiconductors - the valence band that contains the valence electrons responsible for bonding within the material and the conduction band, which is separated from the valence band by a bandgap. Electrons in the conduction band are free to move around the material, and hence, contribute to electrical conductivity. For good electrical conductivity, the electrons must be able to transition from the valence band to the conduction band.
03

Temperature effects

As the temperature increases, the energy of the electrons in the material also increases. This added energy can cause some electrons in the valence band to gain enough energy to overcome the bandgap and transition into the conduction band. When more electrons are in the conduction band, the conductivity of the semiconductor increases.
04

Explain the phenomenon

Semiconductors increase their conductivity as you heat them (up to a point) because the increased temperature provides the necessary energy to move more electrons from the valence band to the conduction band. Unlike metals, whose lattice vibrations increase with temperature, leading to a decrease in conductivity due to more frequent electron scattering, the dominant effect in semiconductors is the increase in the number of charge carriers (electrons). However, this effect is only observed up to a certain temperature, beyond which other factors can counteract this behavior.

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Most popular questions from this chapter

Potassium metal (atomic weight \(39.10 \mathrm{~g} / \mathrm{mol}\) ) adopts a body-centered cubic structure with a density of $0.856 \mathrm{~g} / \mathrm{cm}^{3}\(. (a) Use this information and Avogadro's number \)(6.022 \times\( \)10^{23}$ ) to estimate the atomic radius of potassium. (b) If potassium didn't react so vigorously, it could float on water. Use the answer from part (a) to estimate the density of \(\mathrm{K}\) if its structure were that of a cubic close-packed metal. Would it still float on water?

Rhodium crystallizes in a face-centered cubic unit cell that has an edge length of \(0.381 \mathrm{nm}\). (a) Calculate the atomic radius of a rhodium atom. (b) Calculate the density of rhodium metal.

Which of the three-dimensional primitive lattices has a unit cell where none of the internal angles is \(90^{\circ}\) ? (a) Orthorhombic, (b) hexagonal, (c) rhombohedral, (d) triclinic, (e) both rhombohedral and triclinic.

Calcium crystallizes in a face-centered cubic unit cell at room temperature that has an edge length of \(558.8 \mathrm{pm}\). (a) Calculate the atomic radius of a calcium atom. (b) Calculate the density of Ca metal at this temperature.

The first LEDs were made from GaAs, which has a band gap of $1.43 \mathrm{eV}$. What wavelength of light would be emitted from an LED made from GaAs? What region of the electromagnetic spectrum does this light correspond to: ultraviolet, visible, or infrared?
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