= Spin and valley factors in the semiconductor mass-action constant
In a <nondegenerate semiconductor>, the <semiconductor mass-action law> is $np=N_cN_v e^{-E_g/(k_BT)}$. Its prefactors count states, so <spin degeneracy> and <valley degeneracy> must be included once each.
For equivalent parabolic conduction valleys with one-valley density-of-states <effective mass> $m_d$, $N_c=g_sg_v(m_dk_BT/(2\pi\hbar^2))^{3/2}$. The analogous valence expression must sum distinct relevant bands when one effective band is insufficient. If a tabulated <effective mass> or effective density of states already incorporates a degeneracy, multiplying by it again overcounts states. This changes the mass-action prefactor even though the exponential gap factor is unchanged.
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