Optical Bandgap Definition via a Modified Form of Urbach's Rule

We are reporting an esoteric method to determine the optical bandgap of direct gap materials by employing Urbach's rule. The latter, which describes the slope of the band tail absorption in semiconductors, in its original version, cannot be employed to pinpoint the optical bandgap. Herein, however, we show that a modified form of Urbach's rule defines the optical bandgap, and therefore, enables the accurate determination of the optical bandgap energy, which turns out to be identical with the threshold energy for the band tail absorption. The model further produces an explicit expression for the absorption coefficient at the optical bandgap energy.