Consider a PN junction. Say that the P and the N sides are just brought into contact and the diffusion process has started. We say that as the diffusion occurs, the charge carriers leave behind ionized dopant atoms which act in such a way so as to oppose the diffusion ( and we call the counter acting current as the drift ). After a while the two currents balance each so as to give zero net current under equilibrium in the device.
1) On a fundamental level, why does diffusion occur? The general answer is that it is due to concentration gradient. But in the PN diode, there is a concentration gradient even after the equilibrium is established. If concentration gradient is solely responsible for the diffusion, then why isn't diffusion happening under equilibrium too? ( To counter this, one might say that the diffusion is being opposed by the electric field. But my question is, if the carriers under equilibrium are unable to overcome this electric field even when there is a concentration gradient while the same charges are able to diffuse easily when there is no electric field, shouldn't that mean the carriers under equilibrium do not have enough energy to overcome this electric field? If so is that energy the thermal energy of the particles? And doesn't it all mean that on a fundamental level thermal energy is responsible for diffusion and not the entropy?
2) To formulate a simple thought experiment, consider a PN junction at absolute zero. The P and N sides are just brought into contact. Will there be diffusion of charge carries as the two sides are brought into contact? If not, shouldn't it be reasonable to say that thermal energy is responsible for diffusion and not entropy?
3) If we accept that thermal energy is responsible for diffusion, is it possible to excite the electrons on the N side thermally so that they can cross the energy barrier into the P side under equilibrium to produce current?
Thanking you all in advance for taking time to respond.