Temperature variation of the mobility gap in non-polar amorphous semiconductors

Abstract

Listen

Translate article

For a non-polar amorphous semiconductor such as a-Si, we derive an explixit formula for ( ϖE g/ ϖT) V , the derivative with temperature of the mobility gap E g at constant volume V. Within the framework of second-order perturbation theory for the electron-phonon (eφ) interaction, many of our physical assumptions are fundamentally different from those that apply to the crystal phase. The principal ingredients of our model are: (1) the random-phase-model ( RPM); (2) the principle of non-conservation of particle momentum in the eφ interaction; and (3) the deformation potential approximation. Narrowing of E g is found with increasing values of the temperature T. At very low T, we have (ϖE g /ϖT) V ≌ − ¢A · c V(T) , where c V ( T) is the average lattice specific heat per mode at constant volume and ¢A is a positive dimensionless quantity in the model. By contrast with low-temperature behavior of the crystal, this result implies that the mobility gap at constant volume dynamically responds to the phonomic “gas” of the disordered lattice. The high-T limit yields behavior quite similar to that of the crystal phase. We find (ϖE g /ϖT) V ≌ − x ¢A · k B , where k B is Boltzmann's constant and the parameter x, expected to be confined to the interval 1 2 ⪕ x ⪅ 1 , measures the admixture of the optical-phonon and acoustical-phonon coupling strengths.