“…The width of band tails related to bands (VB and CB) is considered to have emerged from the transition of electrons between the localized states, where the density of localized states exponentially varies with photon energy. Urbach et al first introduced the spectral dependency of the optical absorption coefficient ( α ) on incident energy below the energy gap; the correlation between the optical absorption coefficient ( α ) and incident photon energy ( hυ ) is expressed as
, 57,58 where α 0 is a constant and E U is the Urbach band energy, often signifying the band tail width. As discussed earlier, the absorption coefficient is analogous to the K–M coefficient, and so the equation can be modified as 47
, and the plot of ln F ( R ) vs. photon energy ( hυ ) below the energy gap is shown in Fig.…”