Here's the issue I'm trying to wade through: 1. If you excite electrons from valence band to conduction band (with a laser say), you are out of thermodynamic equilibrium. In some recombination time, the system will go back to equilibrium. All well in good. 2. Now let us consider a very long recombination time. What are the non-equilibrium electrons in the conduction band doing? Do they relax to the band minima? Are they distributed according to the Fermi function? What is the chemical potential doing? Is it possible to even define a chemical potential here? Any help with these questions would be appreciated. Thanks.