Bent-band theory of conductivity in heavily doped semiconductors at low temperatures

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Abstract
A theory is presented of the conductivity in heavily doped semiconductors at low temperatures on the basis of the bent-band model. With the use of the Green’s-function formalism, the vertex part as well as the the free part of the two-particle Green’s function is calculated, taking into account all the diagrams representing the electron-impurity interaction. An analytical expression convoluting the free part and the vertex part is obtained in a compact form represented by multiple integrations. The computation of the conductivity is carried out on n- and p-type Si and Ge and n-type GaAs at 0 K. Agreement between the theory and experiments is very good for Ge:As but is worse for Ge:Sb, Ge:Ga, Si:P, and Si:As. The cause of the good agreement for Ge:As is ascribed to the suitability of the impurity potential assumed for the calculation. However, the considerable agreement, which is found also for the other materials at doping levels down to that for the metal-insulator transition, suggests that the present theory may be more useful under another suitable choice of the impurity potential. The role of the vertex part is shown to be important especially at doping levels around that of the metal-insulator transition.