Draw the bands of MO energy levels and the electron population for: (a) A semiconductor (b) An e

Draw the bands of MO energy levels and the electron...

Key Concepts

Electrical Conductivity

Electrical conductivity is the measure of how easily electrons can move through a material. In semiconductors, the small band gap allows a significant number of electrons to be thermally excited from the valence band to the conduction band, resulting in higher conductivity compared to insulators. The presence of these mobile charge carriers (electrons in the conduction band) is the key to the semiconductor's ability to conduct electricity.

Electron Population Distribution

Electron population distribution in a solid refers to how electrons occupy the available energy bands. At absolute zero, electrons fill the valence band up to a certain energy level, leaving the conduction band empty. The distribution changes with temperature or doping, where electrons may gain sufficient energy to jump across the band gap into the conduction band, thereby influencing the material’s electronic properties.

Band Gap

The band gap is the energy difference between the top of the valence band and the bottom of the conduction band. Its size is a critical parameter that determines a material’s electrical conductivity. Semiconductors have a relatively small band gap, allowing electrons to be thermally excited into the conduction band more easily compared to insulators, which have a much larger band gap.

Conduction Band

The conduction band is the range of electron energies higher than the valence band where electrons are free to move throughout the material, contributing to electrical conduction. In both semiconductors and insulators, the conduction band is typically empty at zero temperature, but the ease with which electrons can be excited into this band defines the conductivity of the material.

Valence Band

The valence band is the highest range of electron energies in a material where electrons are normally present at absolute zero temperature. In the context of semiconductors and insulators, the valence band is fully or nearly fully occupied by electrons. The occupancy of the valence band and the availability of electrons for excitation play a key role in determining the material’s electrical properties.

Band Theory of Solids

Band theory explains how atomic orbitals in individual atoms combine to form continuous bands of energy levels in solids. These energy bands arise due to the overlapping of atomic orbitals when atoms are brought together in a crystal lattice. Understanding band theory is essential for analyzing the electronic properties of materials, such as semiconductors and insulators, as it introduces the idea of allowed and forbidden energy levels.

Transcript

00:03 Today, we are going to look at how to draw illustrations to represent the bands of molecular orbital energy levels and differentiate between insulators and semiconductors.

00:17 Also, we are going to explain why a semiconductor has a high electrical conductivity.

00:26 To begin, we want to look at these bands of molecular orbitals, which are represented, using squares or rectangles and are divided by a space.

00:43 There are three main regions or areas of these molecular orbital bands.

00:51 The top one is called the anti -bonding or conducting band.

01:00 This is where you would find the electrons that are involved in creating the electric current, and also this represents the high -energy electrons.

01:19 The bottom band is called the valence or bonding band.

01:26 This is where you will find the electrons that are in the outer energy level of the molecule and are bound together in pairs.

01:42 So this is the valence band or the bonding band.

01:47 And if you notice, it's separated by a gap.

01:50 This gap is called the band gap.

01:58 The band gap represents a quantity of energy that is necessary for an electron to move or migrate from the valence band to the anti -binding band.

02:11 So we're going to represent this energy difference as delta e.

02:23 So this is the general setup of these bands molecular orbitals.

02:28 Now to apply this to an insulator and conductor.

02:33 To begin, we want to look at an insulator, and we'll look at carbon.

02:41 If you recall, carbon is in group 14 of the periodic table, and it has four valence electrons, and we're going to look at carbon in the form of diamond...

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