Constant-density-of-states intrinsic semiconductor
= Constant-density-of-states intrinsic semiconductor
{title2=$n=p=Dk_BT\ln(1+e^{-E_g/(2k_BT)})$}
In a symmetric model with constant <density of states> $D$ per volume and energy in two broad bands, <charge neutrality> gives $\mu=(E_c+E_v)/2$ and $n=p=Dk_BT\ln[1+e^{-E_g/(2k_BT)}]$. In the nondegenerate limit, $n\simeq Dk_BT e^{-E_g/(2k_BT)}$. Thus the leading exponential activation law can coexist with an algebraic temperature prefactor.