As I think, UV-Vis spectroscopy is the most easiest way to calculate the optical band gap.
Unfortunately for my research, the band gap of PbS is in the IR spectra. Wavelength of about 2500-3000nm.
Well then, the same goes for infraread. Diffuse reflectance spectroscopy might do. In the infrared, this might necessitate a gold coated integrating sphere for best performance [along with appropriate light source and detector etc.] (Many years back I used a spectralon integrating sphere but have forgotten the wavelength range).
You still need a tool to evaluate the data, though. The simplest of these would be Kubelka-Munk theory, but there are more elaborate methods on the market.
Thank you Kai for your answer. I am indeed familiar with the Kubelka-Munk theory and have already used it for band-gap estimations before. Do you by chance know where can I find a gold integrating sphere? Which companies produce them?
Labsphere is one such company, see
http://www.labsphere.com/
On their pages, you will see that the spectralon material loses its favorable diffuse reflectance properties above, say, 2 microns. They do offer "infragold" type integrating spheres for the longer wavelength regime. I have no specific opinion on these, though - haven't ever used them.
If you consider buying equipment, I'd suggest you thoroughly discuss the internal setup of the sphere. Integrating sphere measurements may go very wrong. You need to avoid direct ("first order") reflected light hitting the detector. Also you may have seen that the infragold response is not really Lambertian. It might be good then to have appropriate baffles installed in the sphere.
I remember a (1988 I think) paper in an optical journal discussing the issue for textured samples but cannot recall the author (it was a Scandinavian name, I think).
Google helps:
A. Roos: http://dx.doi.org/10.1364/AO.27.003828
Mabe the link below is also useful.
http://www.oceanoptics.com/applications/Integrating%20Spheres%20for%20Reflectance.pdf
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