Constant-density-of-states intrinsic semiconductor ($n=p=D{k}_{B}T\ln (1+e^{-E_g/(2k_{B}T)})$)

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 $n=p=D{k}_{B}T\ln [1+e^{-E_g/(2k_{B}T)}]$. In the nondegenerate limit, $n\simeq D{k}_{B}T{e}^{-E_g/(2k_{B}T)}$. Thus the leading exponential activation law can coexist with an algebraic temperature prefactor.