Effective density of states ($N_c,N_v$)

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,These quantities have units of number per volume, unlike the energy-resolved density of states. In a nondegenerate semiconductor, $n=N_c{e}^{-(E_c-\mu )/(k_{B}T)}$ and $p=N_v{e}^{-(\mu -E_v)/(k_{B}T)}$; multiple equivalent valleys add their contributions.

A scalar effective mass chosen to reproduce carrier state counting near a band edge. For $g_v$ equivalent ellipsoidal conduction valleys, $m_{\mathrm{DOS}}^{3/2}=g_v(m_l{m}_t^2{)}^{1/2}$ when the displayed factor two accounts for spin degeneracy. The valley degeneracy is then already included and must not be multiplied in again. A conductivity mass weights inverse curvatures and is generally different; for an isotropically averaged set of ellipsoids, $3/m_{\mathrm{cond}}=1/m_l+2/m_t$.