If you have prepared it by an electrochemical method I would take the working elektrode and apply a positive potential on it (a few hundred mV). Then I would add to a base electrolyte (e.g. sodium sulfate) an alcohol (e.g. methanol). Now I would illuminate the n-type semiconductor surface with light of different wavelengths (scan from around 200 nm to around 700 nm with the aid of a continuum light source and a monochromator). If the energy of the light is sufficient to create an electron – hole pair (electron in the conduction band, hole in the valence band) then you might see some flowing current increase. By the positive charge at the metallic working electrode the electrons move in this direction and the holes in the opposite (towards the surface and the electrolyte. Since holes are every strong oxidizing they probably will oxidize the alcohol. Therefore the increase in the current beginning with the light energy sufficient for that. This can be regarded as the band gap if calculated in eV.