On the basis of the band theory of solids, how do conductors, insulators, and semiconductors differ?

Short Answer

Expert verified
Conductors have overlapping valence and conduction bands, enabling free electron flow. Insulators have a full valence band and a wide energy gap to an empty conduction band, preventing electron flow. Semiconductors have a filled valence band and a small energy gap to the conduction band, allowing thermal energy to excite electrons for limited conductivity.

Step by step solution

01

Overview of Band Theory

Band theory explains the behavior of electrons in solids by considering the allowed energy levels. In solid materials, the individual energy levels of atoms blend to form bands, specifically, the valence band and the conduction band.
02

Description of Conductors

In conductors, the valence band and conduction band overlap, or the conduction band is partially filled, allowing electrons to move freely. This results in a high electrical conductivity.
03

Description of Insulators

Insulators have a full valence band and an empty conduction band with a wide energy gap between them. This large gap prevents electrons in the valence band from moving to the conduction band, making electrical conduction very difficult.
04

Description of Semiconductors

Semiconductors have a filled valence band and an empty conduction band like insulators, but the energy gap between these bands is smaller. At room temperature, sufficient thermal energy can excite electrons to cross the gap, allowing for controlled electrical conductivity.

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Key Concepts

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

Conductors
In the study of the band theory of solids, conductors stand out for their exceptional ability to allow electrons to move through them with ease. This movement is what facilitates the flow of electric current. Conductors like copper and silver have a unique arrangement where their valence band, which contains the outermost electrons that can participate in bonding, either overlaps with the conduction band, or the conduction band itself has readily accessible spaces. This means that electrons can easily flow from one atom to the next with minimal resistance, which is why these materials make excellent wires and components in electronics and electrical systems.

Insulators
At the opposite end of the spectrum, we find insulators, such as glass or rubber. These materials have a full valence band, meaning all the available electron states are occupied. It's the large energy gap to the conduction band that sets insulators apart. In insulators, this gap is so vast that under normal conditions, electrons in the valence band cannot gain enough energy to leap into the conduction band. Because of this, insulators do not conduct electricity under typical circumstances; instead, they are used to protect us from the dangers of electrical currents.

Semiconductors
Semiconductors, such as silicon and germanium, are the goldilocks of materials in terms of electrical conductivity. They have similar band structures to insulators, with the valence band being full and the conduction band being empty, but the energy gap between them is much narrower. This unique positioning means that when energy, such as heat, is applied, some electrons gain enough energy to make the jump to the conduction band. This semi-conductive behavior is key in modern electronics, allowing for the fine control of electrical current and the creation of diodes, transistors, and integrated circuits.

Electrical Conductivity
Electrical conductivity is the measure of a material's ability to conduct an electric current. It is directly related to the availability of free electrons that can move through the material. High electrical conductivity implies that a material allows electrical charges to flow freely across it due to a high concentration of free and mobile electrons, typically found in conductors. In contrast, materials with low electrical conductivity, such as insulators, have a negligible number of free electrons, preventing the flow of electric current. Semiconductors fall in between, with their conductivity varying significantly with temperature, impurities, or the presence of an external electric field.

Valence Band
The valence band in band theory refers to the energy band that is composed of the valence electrons. These are the electrons in the outer shell of an atom that are involved in forming chemical bonds. In a solid, the valence band is generally filled with electrons. The capacity of electrons within this band to jump to the conduction band determines if the material will behave as a conductor, an insulator, or a semiconductor. For the valence band to effectively give up electrons to the conduction band, energy must be supplied to elevate the electrons across the band gap, if one exists.

Conduction Band
In contrast, the conduction band is the higher energy band in solids above the valence band. When electrons have enough energy to move into the conduction band, they are free to move about within the solid, contributing to electrical conductivity. In conductors, the conduction band contains free spaces even at very low energy levels, enabling electrons to move freely and conduct electricity efficiently. For insulators, this band is empty and lies significantly higher in energy than the filled valence band, rendering the material non-conductive under ordinary conditions.

Energy Levels
The concept of energy levels is fundamental to the band theory of solids. In isolated atoms, electrons occupy fixed energy levels. However, when atoms are packed together to form a solid, these discrete energy levels blend to form bands due to the interaction between neighbouring atoms' electrons. The arrangement and spacing of these energy bands define whether a material is a conductor, an insulator, or a semiconductor. The presence of available energy levels within reach of the valence electrons, without a prohibitive gap, determines how freely electrons can transition and, hence, how well the material can conduct electricity.

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