Band tail states

Band tail states are localized electronic states existing near conduction and valence band edges. Although present in a crystalline semiconductor, band tail states are much more important in determining the electronic properties of an amorphous semiconductor (or insulator). This is not surprising since band tail states arise as a consequence of disorder. Band tail states are invariably found to exhibit an exponential distribution defined by a characteristic (Urbach) energy. The first objective of this contribution is to derive an expression for the total band tail state density. Assuming a continuous density of states and its derivative with respect to energy across the mobility edge, this total band tail state density is found to depend on only two parameters – the Urbach energy and an effective mass characterizing the extended state density above the mobility edge. A second task undertaken herein is 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. A brief tutorial on amorphous semiconductors will precede this presentation.