UV-Vis spectroscopy can be used for this purpose. Tauc's relation can be used to calculate the energy band gap from the obtained values of absorbance and wavelength.
to calculate absorbance coefficient alpha = 2.303 A/t
where t is the width of the cuvette and A is the absorbance. I think the standard width of the cuvette is equal to 1 cm. Please. check out my recent published paper for more information.
If you plot absorbance, you don't need the thickness. If you do the Tauc plot then also it is not essential. You can plot (ahn)2 vs hn and there Y axis is in arbitrary units (a.u.) if you don't divide it by thickness. Still you can get the value of bandgap.