Well we can keep with the diode theme here. The diode has no drift current until there is a certain voltage (electric field) that causes the charge carriers to move. Before then, there is just diffusion to equalize the holes and electrons. This movement causes the depletion region to form. Your bias comes in for how the depletion region interacts. A reverse bias causes the region to widen and causes the drift to increase and the diffusion to decrease, this results in a very small current density. A forward bias causes the region to narrow and decrease the drift and increase the diffusion, this results in a very high current density. This holds true until either the current demanded is too much and the electrons collide and heat the part until failure or the reverse bias is too high in which the depletion region is shorted and the device flows when it isn't supposed to. If the forward voltage is too right, the current density is too much and causes heating and failure. That's why you have a forward rating, a reverse breakdown, and a current rating.