Abstract. The temperature dependence of electrical conductivity for many materials is shown to follow a function G(E, T) that is the derivative of the Fermi function with respect to temperature. It is noted that the Fermi function is a cumulative probability function. It then follows that the probability density function that is used in the calculation of the electron density in the conduction band is the derivative of the Fermi function. Use of the G(E, T) function in the appropriate equation for electrical conductivity predicts this property for materials for which the conductivities span a range of about 20 orders of magnitude. Examples of materials cited include single crystals of (SN)_x, (TMTSF)₂PF₆ and germanium, and vitreous Type 7740 borosilicate (Pyrex) glass. The G(E, T) function for values of E-E_F<or approximately=0.001 eV at temperatures approximately 1K predicts values of conduction band electron density that can be expected to lead to superconductivity. For the same values of E-E_F and temperature the Fermi function predicts electron densities in the conduction band that are vanishingly small.

Print publication: Issue 31 (10 November 1983)