Is my calculation of carrier density sufficient for all electrons in bulk?

[dhirendra2212]

Hello,

I am solving Schrödinger and poisson's equation in a self consistent way. I solved Schrödinger equation and obtained eigen values which are allowed energy states. now I am calculating electron density with
n=sum(psi*psi*f(E))

where f(E)=1/(1+exp((E-Ef)/kT)) fermi function.

Now I am calculating charge density with carrier densities and putting that in poisson's equation for modified potential.

I am strongly doubtful of calculation of this carrier density n.
My question is, is that single equation is sufficient to account for all electrons in bulk.
though all electrons are identical and indistinguishable, so solution for every electron will be same, but then I think I have to multiply n (above mentioned) with Nn0 which is electron density at equilibrium = ni*ni/Na (for p-type bulk)

 

[Kholdstare]

Did you integrate your results over reciprocal space?
In that case you should find out the DOS and use n = integration of D(E) x f(E)

Schrödinger's equation in its basic form is not applicable to many electron problems. Apply exchange-correlation for that.

The n you calculated is total number of electrons, not all of which are carriers. Identify the conduction band and use that energy as limits to get carrier electrons.