In order to evaluate your information related to absorbance vs. wavelength, you must first convert your data. I suggest using a good mathematical/plotting program (I use PSI PLOT). MAKE SURE ALL OF YOUR UNITS ARE CORRECT! (meters to meters, etc)

Step 1: Convert your wavelength to electron volts; hv = (1.24*10-6 m*eV)/wavelength

Step 2: Calculate the absorption coefficient; a = (absorbance/thickness of glass)

Step 3: Calculate (ahv)

Step 4: Calculate Ln(ahv)

Step 5: Calculate the derivative; d[Ln(ahv)]

Step 6: If needed, smooth out those results using RMS smoothing (sometimes you need to do this twice.)

Step 7: Plot the absorption edge (only!) of d[Ln(ahv)] vs. hv

Step 8: Find the maximum and minimum value (of the y-axis measurement), and calculate the average. Find that average (still using y-axis measurements) on your plot. Where you find that average is your Eopt ( the value on the x-axis).

Hope this helps. It's as detailed as I can get without actually doing an example for you.

The formula for the absorption coefficient α(ν) as a function of photon energy as suggested by Mott and Davis is

 a(v) = B(hv - Eopt )n/ (hv)

For direct transitions, we have n=1/2 or 3/2 for allowed and forbidden transitions and for indirect transitions, n=2 or 3 for allowed and forbidden transitions, respectively. In this formula, B is constant and Eopt is the optical band gap.  The type of transition can be obtained from the value of n. To determine the value of n, the differential method is applied. 

 d[Ln(ahv)]/d[hv] = n/(hv - Eopt)

The differential curve has a discontinuity at the particular energy value (  which gives the optical band gap Eopt. To find the type of transition, the Eopt values are calculated by extrapolation of the linear parts of (αhν)1/n vs. hν curves to (αhν)1/n = 0  for different values of n. By comparing the values from the differential curve and the optical band gap using different values of n, we are able to find the type of transition.

I think Stewart covered everything and mentioned all details.

Stewart, do you have a source, possibly with an example for this process. I am still not following 100%.

How is d(hv) not just = 1?

What is the point of writing d{ln(αhν)}/d(hν) instead of just d{ln(ahv)} like you did in your first reply?

In this reference DOI: 10.1016/j.physe.2004.06.036 the authors say that the discontinuity IS the transition separation energy, instead of the average between the max and min for the given absorption edge. Using the discontinuity center always yields slightly higher energy then the average point from max to min. However, you also mention both and I am not sure which is right.

Also, when I plot (ahv)1/n vs hv I see that for all values of n, all plots cross (ahv)1/n=0 at the exact same point but the linear fits having very different slopes. What did i do wrong?

In the paper I cite above the authors dont use (ahv)1/n vs hv. Instead they use (ahv)1/n vs ln(hv-E), where E is the transition energy of interest determined from the d{ln(αhν)}/d(hν) vs hv plot. They then fit the slope of the linear portion of the edge in the range of the transition of interest, they say the slope of this line is equal to n (the transition character, i.e. 1/2, 2, 3/2, 3).

however I tried this for a FeCr2O4 spinel film on the and get 1/n>5 so its "super direct" or i messed something up. likely the latter.

Does anyone have any idea how this method compares to Tauc analysis?

Marc, if you read through my thesis, specifically section 2.5 Optical Band Gap (p. 21), section 3.7 PSI Plot Analysis (p. 35) for background on my work and an example of my data (Figure 3.4). Then, chapter 5 (p. 58) shows how to use the plots to visually determine the correct answer. I hope this helps. If not, I will try and clarify. You should be able to locate my thesis under my profile. If not, please let me know and I will share it with you.

Hi Stewart, Thank you for the quick reply!

I fixed a compounding error in my spread sheet which fixed a lot of my issues!

BUT,

I'm still a little fuzzy on the process outlined in figure 5.3 of your thesis. It seems like you encompass all of the transitions in the derivative spectrum rather than just focusing around a transition of interest. What is the basis for doing this? Do you have a reference justifying or outlining this process?

According to the "differential method" cited in the paper I mentioned earlier, there should be a discontinuity in the first derivative of ln(ahv) vs hv plot and the band gap (and presumably other transitions) are said to occur at these discontinuities. Is your way a method to use when your differential plot has no discontinuities?

Aren't amorphous materials considered "nondirect" absorbers and should follow n=2 in the a(v) = B(hv - Eopt )n/ (hv) relationship, but have much stronger absorption than indirect transitions? Is this related to a mixture of crystalline and amorphous regions being present? I did see somewhere where the authors fit the absorption of glass similar to the one in your thesis with an indirect forbidden model based on the same differential method used in the paper I mentioned in my previous post. Also, please see references DOI: 10.1143/JJAP.39.4820 and 10.1016/S0038-1098(97)00268-8

and this popular book chapter J. Tauc: Amorphous and Liquid Semiconductors (Plenum, London, New York, 1974) p. 159