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The physical law or better said physical effect behind the solar photovoltaic cells is the internal photoelectric effect.
The photoelectric effect was first discovered and explained by Einstein at the beginning of the last century (1905) and for this he was awarded his only Nobel Prize (contrary to what is believed that he won the Nobel for Theory of Relativity). The name of the effect was the external photoelectric effect, and it consists of expulsion of electrons in vacuum from the surface of a metal illuminated with light whose photons have energy above a certain threshold. The laws of the external photoelectric effect (one electron is liberated for one photon, the kinetic energy of electron is equal to the energy of the photon minus the work function of the metal) lead Einstein for the first time to postulate the existence of the photon. Thus the discovery of this effect opened the gates into the study of quantum mechanics.
The effect that is behind solar photovoltaic cells is a slightly modified version of the above effect. Its name is the internal photoelectric effect and consists of the generation of a pair electron-hole in a semiconductor by an external incoming photon that illuminates the semiconductor.
Imagine you have a diode (a p-n junction) which has one electrode transparent. Because of the barrier that exist at the contact between the p and n zones (difference of p and n work functions), a depletion layer will form in this region (the p-n contact zone is depleted of the electric charges). Because of this, an internal electric field is present in this region. When the depletion layer is illuminated, an incoming photon will generate a pair electron-hole. Instead of recombining, the pair will be fast separated is space by the internal electric field that is present in this region. Thus an external voltage will be generated and a current will flow in a closed external circuit connected at the p and n ends of the diode.
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