# Fermie levels and so on

A sample of silicon is doped with indium for which the electron acceptor level is 0.16eV above the top of the valence band. What impurity density would cause the fermi level to coincide with the impurity level at 300K? What fraction of the acceptor levels is then filled? What are the majority and minority carrier concentrations?

E_g = 1.1eV, m_e = 0.26m_0, m_h =0.39m_0, my_e = 0.15m^2/Vs, my_h = 0.05m^2/Vs

I suppose m_e and m_h is the effeicient mass of the electrones and holes
my is the mobility and E_g is the bandgap

I got that the electron concentration is given by
N_e = N_c * exp((-E_g-E_f)/kT) where N_c = 2*(2*pi*m_e*kT/h^2)^(3/2)
N_h = N_v * exp(-E_f/kT) where N_v = 2*(2*pi*m_h*kT/h^2)^(3/2)

I can get E_f = E_g/2 + 3/4 * kT*ln(m_h/m_e) my formula sheet says that this is true for an intrinic semiconductor. In my ears that sounds like an n-doped semiconductor. How do I know if this semoconductor is n-doped? The assignment only says that it's doped with indium.

My other problem is that I just stumble in the dark here. Sure I find some fornulas that I can use, but what for? I dont really understand what the fermielevel is and even less how I calculate "What impurity density would cause the fermi level to coincide with the impurity level"

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Since I couldnt get this right I did some backwards calculating. I have parts of a solution given, and there I could find the real value for N_e. And reverse engineering gave me that E_f = 0.16eV, whick is the given acceptor level for indium. This puzzles me since I tought the fermi energy should be the total energy from the lowest an electron can have up to the highest, and not the difference between the acceptors energy and the valence band.

This also tells me that E_f = E_g/2 + 3/4 * kT*ln(m_h/m_e) is not valid here (since it gives the wrong value), and this is probably since we dont have an intrinic semiconductor.

But I still stumble in the dark. What impurity density would cause the fermi level to coincide with the impurity level?

Seems like monologs teach me a lot, maby I can solve this by talking a bit more to my self :)