Band Gaps
The size of the band gap varies with the type of compound involved.
The Band Gap in Ionic Solids
The dominant term in determining the band gap is the Madelung energy.
Band gap in Sodium Chloride | |
Na^{+}Cl^{–} is unstable with respect to Na-Cl at infinite r, but is stabilised by the Madelung potential at small r (or large 1/r). | At the separation when the ions are touching, the band gap is 7 eV, and the width of the lower energy (Cl 3p) band is 2 eV, and the higher energy (Na 3s) band is 6 eV. |
The band gap, E_{gap}, follows the trend in 1/r, where r is the separation of the ions, so E_{gap}(CsI) < E_{gap}(LiF), as the sum of the ionic radii in LiF is smaller than the sum of the radii in CsI. Hence, ionic solids with large lattice enthalpies, reflecting large madelung energies, have large band gaps, and so are white (ie. they do not have any absorption transitions in the visible region) and insulators.
The Band Gap in Covalent solids
The band gap increases with the electronegativity difference between the elements.
Band Gap in M-M | Band Gap in M-X |
This accounts for the trend in band gaps:
CuBr (5.6 eV) > ZnSe (3.8 eV) > GaAs (1.9 eV) > Ge (0.7 eV)
The band gap also decreases down a group: the bond strength decreases, and this reflects the decreasing amount of orbital overlap. Large band gaps are the result of a high degree of orbital overlap.
Materials with large band gaps are insulators, and materials with no band gaps are metals. There is a class of materials with small band gaps, and their conductivity increases with temperature. These are known as semiconductors.