Energy of band of ddimensional semiconductor when voltage V is applied across
Let's say we have a onedimensional semiconductor and I apply voltage V across it, I want to calculate the energy of a parabolic band, when a source and drain voltage is applied across it. I expect it to be $U = \Sigma_k \frac{\hbar^2 k^2}{2 m^*}f(k)$ where f(k) is the fermi function.
When no voltage is applied $U_0 = \Sigma_k \frac{\hbar^2 k^2}{2 m^*}f_0(k)$
(I am just confused what the fermilevel should be in the case when voltage is applied and I want to do a full integral including temperature dependence)
My question basically is, what is the expression for $f(k)$ and $f_0(k)$. Would it be different in the ballistic and diffusive regime? And how do I extend this for ddimensional semiconductor?
