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Recently I read about band theory of solids. The energy difference between valence band and conduction band determines the conductive property of solids.
Suppose I take an insulator and shine it with light whose energy is greater than the energy difference between valence and conduction band. In this case, will the electrons enter conduction band and start conducting electricity?
Yes. Whether the result is a good conductor depends on how localized electrons and holes in the respective bands are (or, saying the opposite phenomenologically: on their mobility). Their recombination time limits for how long you will have even just two charge carriers available for conduction. This tends to make such conduction very energy-inefficient because you have to use one or even many electronvolts of photon energy to create just one pair of short-lived charge carriers. In metals, you get on the order of Avogadro's number of conducting charge carriers for free!
As pointed out in comments, the result is a photoconductor. In a semiconductor, it is feasible to combine this with a diode, in which case you have a photodiode, also known as solar cell. It can be used to convert your photons into useable electric energy by separating the charges (but you can also use it with a reverse bias voltage applied to turn it into a better photon detector).
I think selenium was such a thing that was used for old fashioned photocopiers. The cylinder was charged electrostatically, then exposed to the image of the paper being copied. The areas exposed to light became conductive and lost their charge. The toner had the opposite charge and would the stick to the black areas. This would then be put onto a new piece of paper to make a copy. Ingenious!
