Let's consider a very simplified picture of some of the basic physics of a semiconductor. In an 'n-type' semiconductor, there are some 'trapped' states for electrons, which don't contribute to the electrical conductance. There is also a band of states at higher energy which do contribute to the conductance. At low temperature, T, the electrons settle into the traps, but at high T they are in the conduction band. Here we simplify by considering only ONE trapped state and by letting all the band states have the same energy as each other. The temperature is K. Assume that there is just ONE electron.

a) If the band energy were the same as the trap energy what would be the ratio of the probability that the electron is trapped, P_trap to the probability that it's in the band, P_band?
P_trap/P_band =

b) Now let's say that the band states have energy J greater than the trapped state. what would P_trap/P_band be?
P_trap/P_band =

c) So what's the probability that the electron is trapped?

P_trap=