Can all the valence electrons in an atom jump to conduction band?

Question

I know that when sufficient energy is given, electrons jump from valence band to conduction band and the atom itself gets in its excited state. Nevertheless, can all the valence electrons in the atom jump to conduction band?

Answer 1

First, energy levels in crystals (such as semiconductors that have a gap between the valence band and the conduction band) are not associated with specific atoms. Second, there are many valence electrons per atom in most solids, so lets focus on one electron per atom in the valence band here.

Assume a classic semiconductor with a band gap of 1 eV. This is in between Ge and Si, so not too bad. Taking one electron per atom in the crystal from the valence band into the conduction band then takes 1eV/atom (actually more, given real band structures, but we are doing a back-of-the-envelope calculation here). In units more directly tied to thermodynamics of materials, that is 96.5 kJ/mol.

OK, how much energy is that? Well, depends - it is either a lot or not so much. What do I mean? Well, what will happen when those electrons start dropping into the valence band and releasing energy back into the material? Assume all energy goes into heat in the solid as a worst case.

OK, lets use thermodynamic parameters for Si (ignoring that the energy gap is a bit more than 1eV for now).

The heat capacity is 19.88 J/mol/K.

Starting at room temperature and going up to the melt temperature then takes 27.57 kJ/mol.

The heat of melting is 50.55 kJ/mol, so getting the mole of silicon to melt (starting at room temperature) you are now up to using 78.12 kJ/mol.

Assuming the heat capacity of the liquid is similar to the crystal, the remaining (96.5-78.12) = 18.7 kJ of energy raises the temperature of the liquid by about 940K, leaving the liquid just at the boiling point.

The enthalpy of vaporization is quite steep, about 384kJ/mol, so we can't possibly vaporize the whole mole of silicon. Slight changes to parameters (total energy cost to get 1 electron per atom into the conduction band, the actual heat capacity across temperatures, the heat capacity of the liquid, ...) mean either we don't make it all the way to boiling, or we might even boil a bit of silicon.