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Chapter 18: Problem 8

In terms of electron energy band structure, discuss reasons for the difference in electrical conductivity among metals, semiconductors, and insulators.

Short Answer

Expert verified
Answer: The primary factor causing the difference in electrical conductivity among metals, semiconductors, and insulators is the arrangement of their electron energy bands. Metals have overlapping valence and conduction bands that enable high conductivity, semiconductors have a small band gap between the bands that allow moderate conductivity when energy is provided, and insulators have a large band gap that results in low conductivity due to minimal electron movement.

Step by step solution

01

Introduction to Electron Energy Bands

In solids, the energy levels of electrons are quantized and form energy bands. The two most crucial energy bands to consider when discussing electrical conductivity are the valence band and the conduction band. The valence band contains the highest occupied energy levels, and the conduction band contains the lowest unoccupied energy levels. The energy difference between these two bands is called the band gap.
02

Metals, Semiconductors, and Insulators: Band Structures

In metals, the valence and conduction bands overlap, which means that electrons can easily move from the valence band to the conduction band with no energy input, enabling high electrical conductivity. In semiconductors, there is a small band gap between valence and conduction bands. When energy is provided, electrons can transition from the valence band to the conduction band, allowing electrical conductivity. In insulators, the band gap is significant, making it difficult for electrons to transition from the valence band to the conduction band, which results in low electrical conductivity.
03

Metals - High Electrical Conductivity

Metals have high electrical conductivity because their valence and conduction bands overlap. Due to this overlap, electrons can easily move from the valence band to the conduction band without any additional energy input. The free movement of these electrons allows metals to act as excellent conductors of electricity.
04

Semiconductors - Moderate Electrical Conductivity

Semiconductors have a small band gap between their valence and conduction bands. When external energy (such as heat or light) is provided, electrons can overcome this small energy gap and transition from the valence band to the conduction band. The movement of these electrons allows for moderate electrical conductivity in semiconductors. The amount of conductivity can be altered by adding impurities called dopants, which can either increase the number of electrons (n-type) or create holes for electrons to move into (p-type).
05

Insulators - Low Electrical Conductivity

Insulators have a significant band gap between their valence and conduction bands. Due to this large energy gap, it is challenging for electrons to gain enough energy to transition from the valence band to the conduction band. As a result, insulators have very low electrical conductivity. In summary, the difference in electrical conductivity among metals, semiconductors, and insulators arises from the arrangement of their electron energy bands. Metals' overlapping bands allow for easy electron movement and high conductivity, semiconductors' small band gap enables moderate conductivity when energy is provided, and insulators' large band gap results in minimal electron movement and low conductivity.

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Most popular questions from this chapter

Define the following terms as they pertain to semiconducting materials: intrinsic, extrinsic, compound, elemental. Provide an example of each.

The polarization \(P\) of a dielectric material positioned within a parallel- plate capacitor is to be \(4.0 \times 10^{-6} \mathrm{C} / \mathrm{m}^{2}\) (a) What must be the dielectric constant if an electric field of \(10^{5} \mathrm{~V} / \mathrm{m}\) is applied? (b) What will be the dielectric displacement \(D\) ?

Is it possible for compound semiconductors to exhibit intrinsic behavior? Explain your answer.

For each of the following pairs of semiconductors, decide which has the smaller band gap energy, \(E_{g}\), and then cite the reason for your choice. (a) C (diamond) and Ge (b) AlP and InAs (c) GaAs and \(\mathrm{ZnSe}\) (d) \(\mathrm{ZnSe}\) and \(\mathrm{CdTe}\) (e) \(\mathrm{CdS}\) and \(\mathrm{NaCl}\)

(a) In your own words, explain how donor impurities in semiconductors give rise to free electrons in numbers in excess of those generated by valence band-conduction band excitations. (b) Also, explain how acceptor impurities give rise to holes in numbers in excess of those generated by valence band-conduction band excitations.
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