A representation of the energy gap in diamond-structure semiconductors

It is shown that the experimental energy gap E-g , in the four semi-conductors C, Si, Ge and alpha-Sn with the diamond lattice structure is well represented by the relation E-g = A(a(c)(1/2) - a(1/2))(5/3), where a is the lattice parameter and a(c) the 'critical' lattice parameter corresponding to E-g = 0. It is suggested that (a(c)(1/2) - a(1/2)) is an order parameter of the transition from zero to non-zero band gap. It is also shown that the dielectric constant can be related to this order parameter. The band gap relation is also found to hold for the III-V semiconductors once the contribution to the band gap from their electronegativity has been subtracted.