Seems like most people don't know what's Kubelka-Munk function (F(R∞)). The derivation is a little complicated, but can be easily found in literature if you are interested. The main point is that a Kubelka-Munk function (F(R∞)) can be simplified as absorption coefficient (a) divided by scattering coefficient (s):
F(R∞) = a/s
Therefore the correlation, ^1/n vs. hν ,that everyone is struggling with can be rewritten as ^1/n vs. hν. Once you know this, follow the following steps, you should be able to get the bandgap energy. I hope it's clear by now. I personally don't think you can find any more detailed information than this anymore
1. Normally, the collected DR-UV-vis spectra could be converted into Kubelka-Munk function (F(R∞)) spectra using software such as Cary Win UV (pretty much all UV-vis instruments have a similar software installed initially)
2. The bandgap energy of a semiconductor material can be obtained from the correlation: aћω vs. (ћω-Eg)^n
Where: a= absorption coefficient (m-1);
ћ= Dirac’s constant, 1.054 × 10-34 J s;
ω= angular frequency of the incident radiation (s-1);
n= an exponent which have values of 1/2, 3/2, 2, and 3 for direct allowed, direct forbidden, indirect allowed, and indirect forbidden transitions.
Equation (1) can also be written as: ^(1/n) vs. (hv-Eg)
Where: F(R∞)= Kubelka-Munk function;
h= Plank’s constant, 6.626 × 10-34 J s;
v= frequncey of the light (s-1);
Eg= bandgap energy (eV).
The value of n for the exponent in the term n is usually determined by examining the shape of plots of 1/n vs. hν-Eg or 1/n vs. hν using n = 1/2, 3/2, 2, and 3 . When 1/n vs. hν was plotted for ETS-10 samples, whichever n gives the best linear fit in the lower energy absorption region should be used. For instance, for a direct allowed transition, n=1/2 would give the best linear fit.
3. Once the linear fit is obtained, the bandgap energy of the can be then determined from the intercept of the linear fit in the lower energy absorption region of the plot of ^(1/n) vs. hν.
This is a short version of what I have included in my Ph.D. thesis. Hopefully it's pretyy straightforward.
