Band Theory
Physics: Cambridge International A Level, topic 14.1.8
Band Theory
Band theory was formulated by considering the quantum effects of the periodic arrangement of the nuclei of atoms in crystalline solids. Band theory explains the various properties of solids.
Band theory
- Band theory supposes that there are energy bands occupied by the electrons in solids, as opposed to the sea of freely moving electrons used to model metals.
- Bands can be thought of as electron energy levels for the whole solid rather than an individual atom.
- The existence of these bands can explain the differences in conductivity, insulation and semiconductivity of solids.
Band gaps
- Between each band, there is a range of energies that are forbidden for an electron bound within the solid to have.
- These ranges are called band gaps or forbidden bands.
Types of band
- There are two specific bands that are of interest in determining the properties of a solid, the valence band and the conduction band.
- The valence band of a solid is the highest energy band that is completely filled.
- A completely filled energy band is one that has each available state occupied by an electron.
- The next available energy band is called the conduction band.
Conductors and insulators
- Conductors have conduction bands and valence bands that overlap.
- Electrons in the partially filled conduction band gain kinetic energy from the electric field by filling higher energy states in the conduction band.
- This is the process of conduction of electricity.
Conductors and insulators
- Insulators have empty conduction bands due to their large band gaps.
- This means no electrons have enough energy to excite and occupy the conduction band.
Applications of Band Theory
Band theory can be used to explain the thermal and conductive properties of solids.
Metals
- Metals are conductors, which means they have an overlap between the valence and conduction bands.
- This means an increase in temperature does not decrease the resistance of the metal.
Metals
- However, the resistance of metals actually increases with an increase in temperature.
- As the temperature increases, the ions in the metallic lattice vibrate with increasing frequency, causing collisions with the electrons.
- These collisions absorb some of the kinetic energy of the electrons, and so the resistance of the metal is increased.
Intrinsic semiconductors
- An intrinsic semiconductor is a pure material with a band structure similar to that of insulators, except their band gaps are much smaller.
- This means electrons at room temperature have enough energy to excite into the conduction band.
Intrinsic semiconductors
- An increase in temperature increases the number of electrons with enough energy to excite, which decreases the resistance of the semiconductor.
Light-dependent resistors
- The absorption of light can cause electrons to excite into higher energy levels in atoms.
- The same is true for electrons in semiconductors, which can be excited into the conduction band by absorbing a photon.
Light-dependent resistors
- The higher the intensity of light shone upon the material, the more photons are absorbed, resulting in more electrons that are excited into the conduction band.
- This means the resistance of the material decreases as the light intensity increases.
- This is a light-dependent resistor or LDR.
Test yourself on Band Theory
Which of the following is NOT a type of energy band in solids?
Which of the following has no band gap?