I have fabricated PBI/n-Si hybird diode with study on different light illumination and different light intensity. When diode exposed with different light intensity increses the current.
Incoming photons of sufficient energy can excite electrons to the conduction band, and certainly do so. Now, if you increase the intensity of the light, you essentially increase the number of photons per unit time. As long as no nonlinearities are introduced, the relative charge yield of #electrons/photon remains constant and therefore the current increases with light intensity.
It's essentially an application of the photoelectric effect for which Einstein got his nobel prize in 1921...
Increase in light intensity and increase in current are directly proportional.
The increase in light intensity is increase of light photons per unit time. As explained by @Florian above, if a light photon has more energy than the bandgap of the diode material, each photon contributes to generation of charge carriers. Therefore increase in light intensity increases current in the photodiode.