Phonon driven transport in amorphous semiconductors: Transition probabilities

TL;DR

This paper derives transition probabilities for various state changes in amorphous semiconductors, explaining hopping and drift mobilities through phonon interactions and identifying a short-lifetime belt of extended states.

Contribution

It provides a theoretical framework for phonon-driven transition probabilities among localized and extended states in amorphous semiconductors, extending Holstein's polaron hopping model.

Findings

Mobility of localized states matches observed hopping mobility.

Drift mobility likely originates from localized to extended state transitions.

Existence of a short-lifetime belt of extended states inside conduction/valence bands.

Abstract

Inspired by Holstein's work on small polaron hopping, the evolution equations of localized states and extended states in presence of atomic vibrations are derived for an amorphous semiconductor. The transition probabilities are obtained for four types of transitions: from one localized state to another localized state, from a localized state to an extended state, from an extended state to a localized state, and from one extended state to another extended state. At a temperature not too low, any process involving localized state is activated. The computed mobility of the transitions between localized states agrees with the observed `hopping mobility'. We suggest that the observed `drift mobility' originates from the transitions from localized states to extended states. Analysis of the transition probability from an extended state to a localized state suggests that there exists a short-lifetime belt of extended states inside conduction band or valence band. It agrees with the fact that photoluminescence lifetime decreases with frequency in a-Si/SiO$_{2}$ quantum well while photoluminescence lifetime is not sensitive to frequency in c-Si/SiO$_{2}$ structure.