# Question regarding FD distribution and doped SC

1. Sep 28, 2006

### niehls

Consider an n-doped semiconductor. I am trying to figure out at which temperature half of all the donors will be ionized, given energies of donor level and band gap.

I was thinking that, because the chance is 50% that the donors be populated, the Fermi level must lie exactly on the donor level energy, $$E_d$$. I was thinking that if we integrate the FD from the conduction band edge to infinity and set this integral equal to one half:

$$\int_{E_c}^{\infty} \frac{1}{e^{(\epsilon - \mu)/kT} + 1} d\epsilon = \frac{1}{2}$$

Obviously, this is the wrong way about to solve this problem, since i get the temperature 8570K(Using $$E_d = E_C - 0.025, E_g = 1.12$$ as example values (in eV). I am not very used to working with the FD distribution as you see, and i would need some input.

Another way to go about this problem i guess, is multiplying the FD distribution with the density of states and integrate, setting the integral equal to N_d/2, where N_d is the number of donor atoms.

Thanks

Last edited: Sep 28, 2006