I am trying to calculate band gap energies of my heavy metal oxide glass samples but I am confused to choose among direct or indirect band gap energies. My samples have amorphous matrix and also contains small amount of (%1) quantum dots. I am performing heat-treatment to precipitate quantum dots. So, there are as-cast (which I am thinking completely amorphous) and heat-treated (contains crystalline quantum dots) samples. So which band gap value should I take into account for proper results? Finally I am going to calculate particle diameters according to effective mass approximation.
Thank you in advance.
Dear Orhan, please let me share my thoughts about your question.
You write, you are "trying to calculate band gap energies". I suspect you are trying to determine band gap energies experimentally instead as you refer to "Tauc Plot" as subject, is this correct? This would mean you probably do an optical experiment like transmission?
In the first step, your material is amorphous, so a classical semiconductor band gap (either direct or indirect) makes no sense at all, because no periodicity of lattice atoms is present which is the reason for a band structure. I am aware of amorphous materials where something like a band gap is discussed, however I am not sure if a distinction between direct and indirect is meaningful there.
After annealing you expect quantum dot formation. Well, this means you have strong localization of electronic states (in real space) and consequently some quantum confinement (in energy). There, the common wisdom is that you cannot distinguish optically by indirect and direct band gaps any more because in indirect case the optical transition matrix elements are enhanced a lot and it will look like a direct gap (while phonons are still needed for momentum conservation).
My final remark: A direct transmission experiment (like suggested by your use of "Tauc Plot" as a subject) is no tool to distinguish between direct and indirect band gaps even in bulk materials. The "Tauc Plot" idea is based on densities of states only which do not represent the physics happenening in optical experiments: In metal oxides Coulomb forces will be very strong.
Furthermore, usually an absolute scale is absent therefore you cannot distinguish between tails due to defects or size distribution and real absorption onset. Please do not use direct transmission and especially not a Tauc plot for determining band gaps.
All the best,
Martin.
First of all thank you for your detailed answer.
Yes, I am performing absorbance measurements via UV-Vis spectroscopy and then I am plotting Tauc curves to calculate band gap energies. Well, you say Tauc plot is not a good approximation so what should I do? I have seen something about calculating band gap energy through Urbach energy. What do you think about that?
Just to share some idea about the most common semiconductor materials and might be helpful:
Crystallite size is changed significantly under heat treatment and that gives rise to change in the optical-absorption peak. Growth of mixed crystallites of nano-metal clusters in glass may introduce blue shift band gap energy of direct-gap semiconductors that results from reduced crystal sizes saturates at very small sizes due to the mixing of amorphous matrix and small amount of quantum dots. Optical band gap can be estimated from the optical absorption spectra. The coefficient of absorption, α(υ) of the glasses is expressed. By drawing the Tauc’s plots between (αℏω)1/n and the photon energy (ℏω) and extrapolating the linear part of the plots, optical band gap values where obtained at (αℏω)1/2= 0 and (αℏω)2= 0 respectively for the indirect and direct transitions. The decrease in the values of both band gaps (indirect and direct) may be attributed to the electron localization degree due to the glass network’s structural changes. Since the major component of the sample is amorphous matrices so might have both direct and indirect band gap energies.
Well, the Tauc plot is based on the density of states and might indeed work well for the amorphous material itself, like Jiban Podder pointed out. Tauc developed this model for amorphous silicon if I am not mistaken.
However, it is for sure no good idea to use it analyzing the metal oxide quantum dots. Electron-hole pairs are formed during the absorption process and they form excitons which alter the shape of the absorption profile considerably from the oversimplyfied shape of the density of states.
The question remains, how to measure the band gap of the quantum dots. Personally, I think relying on the Urbach tails if a even worse idea than extrapolating arbitrary fractions of absorption onsets. I would propose either trying luminescence or maybe photoreflectance, depends a little on the specific system, the spectral range you are looking at, and the spectral width of the signals.
In your article Article The effect of UV exposure and heat treatment on crystallizat...
you are working on a ZnO-SiO2-Na2O and Al2O3 system. Which one is forming the quantum dots and where is the onset of strong absorption from the surrounding matrix? If the glass is transparent into the UV and the ZnO forms particles, you should be able to do luminescence.
All the best,
Martin.
That paper is about something else. Now I am working on rare-earth and QD doped tellurite glasses. Since there is rare-earth elements in my samples it is hard to distinguish emission peaks. Also, absorption edge of my glass system is almost coincident with the SPR band of the QD. This makes the things harder. By the way, yes samples are transparent. You can find the absorbance measurements attached.
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