Is it possible to locate the Fermi level (in a double doped semiconductor) without knowing the intrinsic Fermi level?

Question

Suppose phosphorus ($\require{mhchem}\ce{P}$) is introduced into $\require{mhchem}\ce{p-Si}$. At a given temperature (say at room temperature $300K$) is it possible to find the location of the Fermi level, if I don't know the intrinsic Fermi level position?

The information I have is:

• The ratio of acceptors and donors i.e. $N_A/N_D$

• The intrinsic concentration $n_i$

• The concentration of holes in $\require{mhchem}\ce{p-Si}$ i.e. $p_o$

The general equation used for locating Fermi level is:

$$E_F-F_{F_i}=kT\ln\left(\dfrac{n_o}{n_i}\right)$$ (for $n$ type)

$$E_{F_i}-F_{F}=kT\ln\left(\dfrac{p_o}{n_i}\right)$$ (for $p$ type)

But, here I don't know the intrinsic Fermi level ($E_{F_i}$). Any way to know the Fermi level just with the given information? (Also, without looking up values from other sources)

Answer 1

For, n-type

$$E_F=E_C-kT\ln \frac{N_C}{N_D}$$

For, p-type

$$E_F=E_V+kT\ln \frac{N_V}{N_A}$$

So, net Fermi level would be

$$E_F=\frac{E_C+E_V}{2}-0.5kT\ln \frac{N_CN_A}{N_DN_V}$$

You can approximate $$n_i=\sqrt {N_CN_V}$$

But of course, you need to know these other parameter values to determine the Fermi level.