# Optical absorption edge

## Main Question or Discussion Point

Hello, I am trying to determine the band gap of an amorphous material (a glass sample) and I read that you can do this from the determination of the optical absorption edge.
From this kind of measurements you fitt an equation of the type (αhν) = B (hv-Eo) 2.
my question are:
1 - is it possible to determine the optical band gap from transmittance or absorbance measure ? I am using a basic spetcrophotometer (which only measure transmittance or absorbance) without having any kind of accesory to measure reflectance?
2 - what kind of equation I need to use to interpret this experiments

thanks very much

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Hello, I am trying to determine the band gap of an amorphous material (a glass sample) and I read that you can do this from the determination of the optical absorption edge.
From this kind of measurements you fitt an equation of the type (αhν) = B (hv-Eo) 2.
my question are:
1 - is it possible to determine the optical band gap from transmittance or absorbance measure ? I am using a basic spetcrophotometer (which only measure transmittance or absorbance) without having any kind of accesory to measure reflectance?
2 - what kind of equation I need to use to interpret this experiments

thanks very much
Method 1) Plot different powers of the absorbance against photon energy. The powers correspond to different models of the band edge transition. The one that provides the most linear tail gives the correct mechanism.
This may be better for thin films.
Method 2) Plot the absorbance on a semilog scale. The log axis should be absorption, while the linear axis should be photon energy.
For heavily doped insulators, which describe most glasses, the impurities form an exponential tail just below the band gap. The absorbance versus photon energy will thus be a straight line on semilog paper. You use plotting software to plot on semilog scales, too. The straight line will break at the larger photon energies, leveling out at the band gap energy.
Method 3) Plot on a log-log scale. Wherever the straight line breaks, there is the band edge. Furthermore, the slope can be estimated by the mechanism.
With solid state studies, especially glasses and semiconductors, the sample to sample variation is very important. Even the band gap may change. Getting the right model isn't as important as establishing the degree of sample variation. So try to get as many samples of this glass as possible.
You may even try looking at the absorption in different section of the same glass sample. Glasses are not alway homogeneous.
Some suggestions.
A) Try to obtain samples with largely different thicknesses. You have to find a thickness small enough so that the absorbance at the band edge doesn’t saturate your spectrometer, yet large enough so diffraction between the two surfaces doesn’t bias your results. You may not have a large choice of thicknesses, but vary the thickness as much as you can.
You may also find different phenomena with different thicknesses. You may not even get an optical band edge with very thick samples. However, there may be absorption peaks due to deep impurity states.
B) Try to get lots of different samples of “the same” glass, preferably with the same thickness. The impurity tails will vary with the sample. However, the optical band gap tends to vary less.

If you use the same method with different samples, getting the same band gap each time, then you can be more certain of your measurement. Determinations of band gap using only one sample may not be entirely reliable.
Here are links to an article showing how the band edge was determined in other type of glass.
This study, they plotted several powers of absorbance versus photon energy.
“Study the Optical properties of Amorphous Structure (Glassy) of
B2O3-CdO Binary System. After determination of absorption coefficient α (ω,) then we traced out (αћω) 1/n against (ћω) diagrams for obtaining the value of n. In this research, by considering n=2, we have obtained a linear diagram with exponential tail. Therefore, according to Mott and Davis’s statement, it was established that, the type of transition is indirect allowed. By extrapolating the linear part of (αћω) 1/2 against (ћω) diagram, we determined the optical gap energy (Eopt) at (αћω) 1/2 = 0.”

Here, the link only used a square dependence.
http://joam.inoe.ro/arhiva/pdf1_1/Iovu.pdf
“Tin Doped Arsenic Selenide glasses.”

This link shows how the optical band gap may vary with thickness.
http://www.chalcogen.infim.ro/433_Chijoke-CdS-PVA-aug4.pdf [Broken]
“VARIATION OF OPTICAL BAND GAP WITH POST DEPOSITION ANNEALING IN CdS/PVA THIN FILMS”

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Claude Bile
Excellent post Darwin123.

I would add only that the Mott & Davis method assumes a parabolic density-of-states, which may not be a good approximation if there are absorption bands in your glass near the band edge.

Claude.

Excellent post Darwin123.

I would add only that the Mott & Davis method assumes a parabolic density-of-states, which may not be a good approximation if there are absorption bands in your glass near the band edge.

Claude.
I had performed a similar experimental study on a crystal of cadmium selenide back in 1984. Although it is not "online", maybe I could provide it as a reference. There are some useful details in this study for anyone studying the absorption edge of a material.
D. Rosen, Q. X. Li & R. R. Alfano, "Native Defects in Undoped Semi-Insulating CdSe Studied by Photoluminescence and Absorption," Phys. Rev. B31, 2396(1985).
One important lesson in this article is that not all "absorption thresholds" come from intrinsic band edge. In my experimental study with thick crystals (1 mm thick), the absorption edge came from a transition of an electron from a shallow acceptor to the first conduction band. The crystals band gap was about 104 meV above the absorption edge.
Other people had studied the "intrinsic absorption edge" of cadmium selenide using thinner crystals. However, one couldn't get near that intrinsic absorption edge using the thick crystals.
Some very important data in my study came from the sample to sample variations of similar crystals with the same thickness. I also did a lot of luminescence measurements to correlate with the absorption measurements. The samples varied great deal. Other people in my laboratory discarded similar data because sample variation isn't "real". However, there were certain invariants in my measurements. These invariants told me something important concerning the impurities.
Part of the problem was establishing that this absorption edge was a shallow acceptor. Cadmium selenide is "an intrinsically n-type" semiconductor. There was no such thing as "p-type cadmium selenide" at the time.
"Intrinsic n-type" means that when you dope the crystal with shallow acceptors, and equal or greater amount of donors are formed. The result is that if you try to p-dope cadmium selenide, the resistivity of the crystal increases instead of decreases.Thus, there is no electrical way to determine the presence of shallow acceptors. So a lot of my study was characterizing that "shallow acceptor".
I actually found two absorption thresholds due to defects. One was a threshold associated with the shallow acceptor, and one was an absorption threshold from a deep level. Both of them were far different from the absorption threshold of the "intrinsic crystal".
I also found shallow donors and a deep level in my crystals. Some of my measurements were at 77 degrees Kelvin (liquid nitrogen). I don't know if the OP could measure absorbance at cryogenic temperatures. However, more data would come out by measuring both at room temperature and cryogenic temperatures. The more variation in measurements, the better he could characterize his sample. I don't know if a one "optical absorption edge" would tell him anything important.
Other people in my laboratory called referred to the crystals as "intrinsic cadmium selenide." They tried to determine some "intrinsic" properties of these crystals. I made my project into optically characterizing the important impurities in the "intrinsic crystal". I used all sorts of optical methods to study how the defects and impurities affected the optical and electronic properties of this material. Part o
This is why I recommended that he try to obtain more than one sample of the material. I wouldn't even be sure that I was studying defects if the measurements didn't vary with sample. Unless you work with a lot of samples of the same material, you can't even be sure that the absorption threshold is "intrinsic". Sample variation is a lot more important than deciding whether the transition is "direct" or "indirect".
I didn't mention this because the OP is working with glasses. I don't think that glasses even have an "intrinsic absorption edge". Impurity states are inhomogeneously broadened that they overlap the conduction and valence bands of the glass. So the band gap is somewhat arbitrary. One can make a fairly approximate model for absorption and essentially get a "plausible" answer. However, there are some absorption edges more important than others.
I can't stress enough. The more samples that you study, the more reliable your results. This is probably more important with glasses than with crystals. There is no such thing as a "pure crystal"! A "pure glass" is an oxymoron!

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