= Effective density of states
{title2=$N_c,N_v$}
The <effective density of states> of a parabolic semiconductor band is its <density of states> integrated against a thermal Boltzmann factor measured from its edge. For one spin-degenerate valley,
$$
N_c=2\left(\frac{m_e^*k_BT}{2\pi\hbar^2}\right)^{3/2},\qquad
N_v=2\left(\frac{m_h^*k_BT}{2\pi\hbar^2}\right)^{3/2}.
$$
These quantities have units of number per volume, unlike the energy-resolved <density of states>. In a nondegenerate <semiconductor>, $n=N_c e^{-(E_c-\mu)/(k_BT)}$ and $p=N_v e^{-(\mu-E_v)/(k_BT)}$; multiple equivalent valleys add their contributions.
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