What insures the charge neutrality condition in the self-consistent solution of Poisson and Schrodinger equations?
Let's say we wish to have a self-consistent Poisson-Schrodinger calculation for a nanowire in equilibrium.
The electron concentration obtained from the Schrodinger equation (which is supposed to handle the confinement problem) is calculated using the following formula:
with being the valley degeneracy, and the states are obtained from the 2D Schrodinger equation in the transverse direction.
I was wondering what guarantees that this equation for electron concentration results in charge neutrality (i.e. for the whole device)?
Does the self-consistent solution result in charge neutrality by construction? If not, how should we take care of this problem (the problem of not having charge neutrality in our answers)?