If two materials having same value of energy band gap. One is showing sharp value of slope and other shows gradual slope. - both are giving same value on intercept on Eg axis.
Does that have any significance related to transition time?
Direct band gap materials will have a sharp rise in the absorption coefficient just above the band gap energy. Therefore, the slope will be large. Shallower slope probably indicates the level of defect states (Urbach tail) near the band edge that absorbs the photons. If the density of states are distributed widely over the energy levels then the slope of the Tauc plot will be shallower.
The slope could be correlated to the transition time indirectly - shallower the slope slower the transition...
Mathematically, such two materials can NOT have, at the same time, the same values of:
a- The exponent (r), in the term (αhν)1/r.
b- The absorption coefficient (α).
c- Low absorption region.
Now the possible cases are:
1- If they have the same low absorption region, then they can NOT have the same exponent (r) and, hence, their absorption coefficients must be different, hence, different transition time.
2- If they have different low absorption region, they may have the same exponent (r) and their absorption coefficients must be different, hence, different transition time.
3- If they have different low absorption region and different exponent (r), they may and may NOT have the same absorption coefficients and, hence, their transition time may and may NOT be equal.
the explanation which I found and seems logical is in the link,
https://www.youtube.com/watch?v=P6Ioh6OunoU&t=392s
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