Why is the chemical potential halfway into the band gap for an intrinsic semiconductor?
I thought the chemical potential was the energy required to move another particle into the system. Shouldn't that energy equal either the valence band energy or the conduction band energy? Or is it kind of 50% chance that the new particle will go to the valence band or the conduction band?
Or is it kind of 50% chance that the new particle will go to the valence band or the conduction band?
Yes, while to omit some details, it can be interpreted so. The electron at the top of valence band excites to conduction band and relaxes back, being 50/50 here and there. So, the averaged energy of conduction electron is Eg/2. From the other hand, as the electron is excited into conduction band, we can tell about adding A COUPLE of carriers into system: electron+hole. It costs energy Eg. So, the increase of the energy of the system PER ONE carrier added into system is Eg/2.
Note, the attempt simply to add the excess electron into neutral system would violate its charge neutrality , probably making it to be unstable, so its thermodynamic equilibrium would be questionable.
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Materials Science
- Materials
- Semiconductor