As it needs some back ground and this makes the answer a bit lengthy.Pls. bear with it. Of course, I, humbly, try to give all the values ashed by your self.
[A]ZnS is highly suitable as a window layer in hetero junction photovoltaic solar cells because the wide band gap decreases the window absorption losses and improves the short-circuit current of the cell . Thin films of ZnS doped with transition metal elements/ rare earth elements have also been used as effective phosphor materials . In optics, ZnS can be used as a reflector due its high refractive index , as a dielectric filter because of high transmittance in the visible region , and as a light emitting diode in the blue to ultraviolet spectral region due to its wide band.
[B]Optical and transition spectra were recorded in the wavelength range 300 - 900 nm using a double beamUV/Vis Spectrophotometer.A computer program was used to calculate the absorption coefficients and the electronic transitions.
Transmission spectra for ZnS samples as afunction of annealing temperature(200 C;2hrs ) show that the transmission peaks are shifted toward lower wavelengths after annealing compared to the transmission peaks of deposited films. The absorption coefficient (α ) WAS calculated with the help of the following relation :
T = (1-R)^- α .d----------------------------- (1)
where (d) is the thickness of the film. (T) and (R)
are the transmittance and reflectance, respectively. The calculated absorption coefficient α (hυ) ,is a function of photon energy. It is clearly seen thatα is greater than 10^4cm^-1 when (hυ ) is greater than 3.2 eV before annealing and 3.45 eV after annealing.
[C]The band gap energies of these films calculated with the help of an absorption spectrum, the absorption coefficient(α) and photon energy(hv) are related by the Tauc plot (Tauc and Meneth) as:
α -------A/ hv[hv-Eg]^n ----------------------(2)
where A is a constant while n can have values ½,2,3/2 and 3 for allowed
direct, allowed indirect and forbidden direct and indirect transitions respectively.
Experimentally, the curve has a straight line fit over a higher energy range above the absorption edge which indicates the presence of DIRECT OPTICAL TRANSITION near the absorption edge(n=1/2). This direct Energy Gap IS calculated to be 3.6 eV which increases to 3.65 eV after annealing. This increase is attributed to the INCREASE IN CRYSTALLITE SIZE which INDUCES A DECREASE IN THE DISLOCATION DENSITY.
[D]Now about URBACH TAIL AND URBACH ENERGY[EU or ∆E]
If we plot a graph between[ ln(α )] and [hv] both for BEFORE and AFTER ANNEALING, their slopes give Eo,the energies (Before) and (After) annealing and the value of α becomes α0. The following relation holds good:
α --------- α0 [exp(E/E0)] ------------(3)
where E is the photon enegy.
After having calculated Eo, we apply the relation
α=αo exp [(hv - Eo)/∆E] -------------(4)
or
α=αo exp [(hv - Eo)/EU]
where ∆E or EU is called the Urbach Energy or Urbach tail or Urbach width.
which can be calculated as all other parameters in the above relation are known.
The Urbach Enery values decrease after annealing. This decrease is slightly more as the annealing temperature increases which indicates an improvement in the quality of ZnS film on annealing. Its EU value BEFORE annealing is 1.38eV and AFTER annealing is1.10eV.
[Pls. find attached a five page paper for your kind perusal and authentication [ Look in TABLE- I on the top of PAGE -41 ]
The procedure mentioned by Manohar to calculate Urbach tail parameter in ZnS films is essentially correct, although the original question was about SnS. The values of Urbach tail parameter are dependent on the origin of the tail, for example, dislocation density, presence of active electrical/optical impurities including self doping for example by S vacancies, lack or increase of crystallinity and so on. You can do the calculations for Urbach parameter for your SnS samples by the suggested procedure and try to relate the values you get with the structure, the electrical behavior, composition and so on. Find a detailed treatment on the origin of Urbach tails in semiconductors in the following papers. We also have a couple of papers where the aforementioned correlations of Urbach parameter with impurities, microstructure, carrier density were made.
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