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Chapter 37: Problem 11

Why does the size of the band gap determine whether a material is an insulator or a semiconductor?

Short Answer

Expert verified
The size of the band gap determines whether a material is an insulator or a semiconductor because it influences how easily electrons can transition from the valence band to the conduction band. A large band gap, typical for insulators, makes this transition difficult, impeding electrical conductivity. Conversely, a small band gap, typical for semiconductors, makes this transition easier, allowing for electrical conductivity.

Step by step solution

01

Discuss the concept of band gap

The band gap is a key concept in solid-state physics, especially in semiconductors. It refers to the energy difference between the top of the valence band and the bottom of the conduction band in insulators and semiconductors. In these materials, electrons are forbidden to possess energy in the band gap.
02

Explain electrical conductivity

Electrical conductivity in materials is determined by the ease with which electrons can move from the valence band (where they are normally located) to the conduction band (where they can move freely, and thus conduct electricity). The ability of an electron to do this is determined by the size of the band gap.
03

Discuss how band gap size determines if a material is an insulator or a semiconductor

In insulators, the band gap is large. Seeking to acquire enough energy to overcome this gap, and transition from the valence band to the conduction band, is difficult for electrons, making insulators poor conductors of electricity. Conversely, in semiconductors, the band gap is small enough such that thermal energy is often sufficient to cause the electrons to move from the valence band to the conduction band, making semiconductors good conductors of electricity.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Band Gap
The band gap in solid-state physics is a fundamental principle, particularly crucial for understanding the behavior of semiconductors and insulators. This concept represents the energy difference between the valence band and the conduction band of a material.
This gap is significant because it influences how electrons can move within a material. If electrons in the valence band gain enough energy, they can jump across the band gap into the conduction band.
It is in this conduction band that electrons are free to move and contribute to electrical conductivity.
  • Valence Band: The energy band where electrons are typically present.
  • Conduction Band: The higher energy band where electrons can move freely.
  • Band Gap: The energy region that electrons must overcome to break free and conduct electricity.
Understanding the size of the band gap helps differentiate between insulators, semiconductors, and conductors based on their electrical properties.
Semiconductors
Semiconductors are materials that have a unique capacity to conduct electricity, but not as freely as conductors. This property is due to their small band gap. Unlike insulators, which have large band gaps, semiconductors have band gaps that are small enough to allow some electrons to move across with relatively low energy input, such as thermal energy from ambient temperature.
This means that under certain conditions, semiconductor materials can allow electrons to jump from the valence band to the conduction band, facilitating electrical flow.
  • Intrinsic Semiconductors: Pure semiconductors without any significant impurities.
  • Extrinsic Semiconductors: Doped semiconductors where impurities are intentionally added to change their electrical properties.
  • Examples: Silicon and germanium are classic examples of semiconductors.
Semiconductors are the backbone of modern electronics, from computers to smartphones, due to their ability to switch between conductive and non-conductive states.
Electrical Conductivity
Electrical conductivity refers to a material's ability to conduct electric current. It depends directly on the presence of free or mobile electrons. In the context of band gaps and semiconductors, electrical conductivity is determined by how easily electrons can transition from the valence band to the conduction band. The smaller the band gap, the more readily electrons can gain energy and move across, enhancing the material's conductivity.
In insulators, the band gap is too large, restricting electron movement and therefore making these materials poor conductors. Semiconductors, with their narrower band gaps, allow easier electron transition, moderately conducting electricity.
  • Good Conductors: Typically metals with no band gap, allowing free electron flow.
  • Insulators: Large band gaps restricting electron flow.
  • Semiconductors: Small band gaps allowing conditional conductivity.
Understanding electrical conductivity is key to developing techniques in electronics, where the fine control of electrical supply is critical.

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Most popular questions from this chapter

The lower-energy states in a covalently bound diatomic molecule can be found approximately from the so-called Morse potential \(U(r)=U_{0}\left(e^{2\left(r-r_{0}\right) / a}-e^{-2\left(r-r_{0}\right) / a}\right),\) where \(r\) is the atomic separation and \(U_{0}, r_{0},\) and \(a\) are constants determined from experimental data. Calculate \(d U / d r\) and \(d^{2} U / d r^{2}\) to show that \(U\) has a minimum, and find expressions for (a) \(U_{\min }\) and (b) the separation \(r_{\min }\) at the minimum energy.

Carbon dioxide contributes to global warming because the triatomic CO, molecule exhibits many vibrational and rotational excited states, and transitions among them occur in the infrared region where Earth emits most of its radiation. Among the strongest IR-absorbing transitions is one that takes \(\mathrm{CO}_{2}\) from its ground state to the first excited state of a "bending" vibration and sets the molecule rotating in its first rotational excited state. The energy required for this transition is 82.96 meV. What IR wavelength does this transition absorb?

A molecule drops from the \(l=2\) to the \(l=1\) rotational level, emitting a 2.50 -meV photon. If the molecule then drops to the rotational ground state, what energy photon will it emit?

What are the approximate relative magnitudes of the energies associated with electronic excitation of a molecule, with molecular vibration, and with molecular rotation?

The transition from the ground state to the first rotational excited state in diatomic oxygen \(\left(\mathrm{O}_{2}\right)\) requires \(356 \mu \mathrm{eV}\). At what temperature would the thermal energy \(k T\) be sufficient to set diatomic oxygen into rotation? Would you ever find diatomic oxygen exhibiting the specific heat of a monatomic gas at normal pressure?
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