Phonon driven transport in amorphous semiconductors: transition probabilities

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.

The microscopic response method: Theory of transport for systems with both topological and thermal disorder

“…Figure 1 is a schematic energy spectrum of AS; (ii) a carrier in a localized state f A polarizes the nearby atoms: the static displacements d p A of the atoms ( p A is the index of atoms participating in localized state f A ) induced by the e-ph interaction is comparable to or even larger than a v , the larger of the amplitudes of thermal and zero point vibrations. In contrast, the static displacements of atoms caused by the carriers in extended states j B are negligible [12]. The imaginary time integral in the Kubo formula can be avoided in the microscopic response method (MRM) [3,4,13].…”

“…One has to adopt different Hamiltonian partitions for the two situations. For a well-localized state A (we use A with or without subscript to label a localized state), we take h [12]. The zero order Hamiltonian is h 0 ¼ h…”

“…In this partition, LL and LE transitions are caused by the transfer integrals [12], cf. Section 6 of Ref.…”

“…To find c 0 (t), we expand it using the approximate eigenstates of the single-particle Hamiltonian [12]: where the arguments of c 0 are ðr; x 1 ; x 2 ; . .…”

“…To find c 0 (t), it is convenient to transform the vibrational displacements {x} of the atoms into normal coordinates {Q} [12]. We expand probability amplitude a A 1 ðÁ Á Á Q a Á Á Á ; tÞ with the eigenfunctions of h A 1 :…”