On some electron properties of tellurium and Wilson's mechanism of semi-conductivity

Abstract

In a previous investigation it was found that the unusually high value for the Wiedemann-Franz ratio of tellurium could be explained as being only a formal anomally. The amount of heat transferred by the bound atoms is the same in tellurium as in conducting metals; but, in tellurium, in contrast to good conductors, it is responsible for almost the entire heat conductivity because the heat transferred by the free electrons is especially small. This indicates that tellurium differs from true metals in that the density of free electrons is very small. Classical statistics is therefore applicable and the electrical conductivity is given by x = 4/3 e 2 ln (2 πmk T) -5/9 , (1) where n is the density of free (conduction) electrons and l is their mean free path. Taking the specific resistance of tellurium at room temperature as 0.3 ohm-cm and l as 5.2 X 10 -6 cm (Sommerfeld's value for silver, found by applying Fermi-Dirac statistics), n is 2.9 X 10 16 , or about one free electron per million tellurium atoms in contrast to good conductors in which there is approximately one free electron per atom. Even in the limiting case with l = 3.2 X 10 -3 cm (the distance between the tellurium atoms), n is 4.7 X 10 18 which is about one free electron for every 6000 tellurium atoms.