Diffusion coefficient of charge carriers in disordered semiconductors retaining a combination of exponential and Gaussian mobility-gap states: application to amorphous selenium

Charge carrier transport in disordered semiconductors is highly influenced by the defect states near the mobility edges. The ratio of the diffusion coefficient and drift mobility in crystalline semiconductor under a wide range of carrier concentration can conveniently be calculated by the Einstein relation. The density of states (DOS) in the mobility gap in amorphous/disordered semiconductors can change the generalized Einstein relation. It has been found that the ratio of the diffusion coefficient and drift mobility is larger than the conventional Einstein relation even at the presence of lower carrier concentration than the degenerate limit. A theoretical model for the generalized Einstein relation (GER), namely, the diffusivity-mobility ratio, for disordered semiconductors retaining a combination of exponential and Gaussian mobility-gap states with square-root distribution of extended states, is presented in this thesis work. The conditions for determining the diffusion coefficient of charge carriers from Einstein relation are described in the thesis work. The effects of various parameters constituting the density of states (DOS) distribution on the Einstein relation are examined. The results show that the diffusivity-mobility ratio for such DOS distribution substantially deviates from traditional constant value for carrier concentration larger than 1010 cm-3. The value of diffusivity-mobility ratio strongly depends on the amount, energy position and the shape of the Gaussian peaks. The diffusion coefficient determined from Einstein relation in amorphous semiconductors is valid at equilibrium transport when the electric field is very low. Under applied field, charge carriers undergo many trapping-detrapping events in the energy distributed mobility gap states during their travel. The statistical variations of the trapping and release times create a considerable spreading of signal. Thus, the actual diffusion coefficient appears to be much larger than it should be from the known Einstein relation. The additional diffusion coefficient due to multiple trapping in disordered semiconductors (namely field diffusion) under quasi-equilibrium transport is also examined as a function of electric field and carrier concentration