# How strict is the "to excite electrons the energy must equal the energy state difference" fact?

We are always told that to excite an electron from one state to a higher energy states, for example from the valance band to the conduction band, the energy must equal the energy difference between the two energy states.

The conduction band consists of many allowed energy states, separated from the valance band by an energy gap. For the element Si, this energy gap is (at room temperature) about 1,1 eV. The range of energies for visible light is 1.8 eV to 3.1 eV. Since Si indeed conducts electricity at room temperature, is it then assumed that there is an allowed energy states with exactly the same energy as the energy difference between the two states? The conduction band, or the valance band for that matter, is not continuous, but discrete. Or is it sufficient that the photon energy "roughly equals", or is "close enough"? If so, how close is close enough?

I hope my question is clearly stated.

• There are two things here mixed: 1) there is a conservation of energy, which requires the states to have a given energy (with the error allowed by Heisenberg uncertanity principle) and 2) the fact that semiconductors and such have bands instead of separate electronic states, i.e. there is a broad, continuous margin whet the allowed transition energies are. Maybe you want to focus some part (1st?) in the question, instead of mixing them up.
– Greg
Nov 9 '15 at 2:27