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 fermi-level 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 d-dimensional semiconductor?