Real- and reciprocal-space attributes of band tail states

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Band tail states are localized electronic states existing near conduction and valence band edges. Band tail states are invariably found to exhibit an exponential distribution defined by a characteristic (Urbach) energy. To a large extent, the band tail state density of states determines the electronic performance of an amorphous semiconductor (or insulator) in terms of its mobility. Real-space assessment of a suitable density of states model for extended (delocalized) conduction or valence band states and nearby localized band tail states leads to an expression for the peak density of band tail states at the mobility edge and for the total band tail state density. Assuming a continuous density of states and its derivative with respect to energy across the mobility edge, these densities are found to depend on only two parameters – the Urbach energy and an effective mass characterizing the extended state density above the mobility edge. Reciprocal-space assessment is then employed to deduce a probability density function associated with band tail states. The full width at half maximum of the resulting Gaussian probability density function is found to be equal to the average real-space distance of separation between band tail states, as estimated from the total band tail state density. This real- and reciprocal-space insight may be useful for developing new high-performance amorphous semiconductors and for modeling their electronic properties.