CIE A Level Physics (9702) 2019-2021

Revision Notes

27.3.4 Band Theory

Band Theory: Basics

  • In solid-state physics, the band structure of a solid describes the ranges of energy, called energy bands, that an electron within the solid may have
    • Allowed bands represent the range of energies an electron may have
    • Forbidden bands represent the range of energies an electron cannot have
  • The band structure determines a material’s electronic properties, optical properties, and a variety of other properties of solids

Band Theory: Key Terms

  • Electrons exist in orbitals around a nucleus
  • In size order, electron energy levels are organised by:
    • Electrons → orbitals → sub-shells → shells
  • Orbitals and the energy needed to remove each of these electrons from the atom are set by quantum mechanics
  • Electrons that are closer to the nucleus are in filled orbitals and are called core electrons
  • The electrons further out from the nucleus are called valence electrons
  • Valence electrons are defined as:

Electrons which orbit the nucleus in the outermost atomic shell of an atom

  • Valence electrons are positioned the farthest from the positive charge, therefore, they tend to be easier to remove than core electrons
    • This means that it takes them less energy to move them far away from the atom
    • This difference arises from the inverse square law of electric force

 

  • In band theory, conductors, insulators and semiconductors can be defined by the relative positions of their valence, conduction and forbidden bands
  • A valence band is defined as:

The outermost electron orbital of an atom

  • A conduction band is defined as:

The band of electron orbitals that electrons can jump up into when excited

 

  • The electrons in this band are responsible for electrical conductivity
  • A forbidden band, or bandgap, is defined as:

The energy difference between the highest occupied energy state of the valence band and the lowest unoccupied state of the conduction band

  • Electrons cannot exist in this energy gap between bands
  • In the band gap lies the Fermi level, which is defined as:

The highest energy level that an electron can occupy at absolute zero

  • The position of the Fermi level with the relation to the conduction band is a crucial factor in determining electrical properties of different solids

Conductors

  • A conductor is a material which contains movable electric charges
    • In metallic conductors, such as copper or aluminium, the movable charged particles are electrons
  • According to band theory, a conductor is simply a material that has its valence band and conduction band overlapping
    • This overlap allows electrons to flow through the material with minimal applied voltage

Insulators

  • An insulator is a material which contains very few movable electric charges
  • According to band theory, insulators have very large band gaps
  • Therefore, an impossibly large amount of energy is required to move electrons out of the valence band into the conduction band to form a current

Semiconductors

  • A semiconductor is a material which has the electrical conductivity between an insulator and a conductor, which can be altered depending on environmental conditions
  • According to band theory, semiconductors have a small band gap that allows for a reasonable fraction of the valence electrons to move into the conduction band if given a certain amount of energy
  • This is why semiconductors act like a conductor at higher temperatures and as an insulator at low temperatures
  • Because of this, their conductivity is somewhere between conductors and insulators
    • This property makes them ideal for electric circuits as they will not cause a short circuit like a conductor

Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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