 Extracting a semiconductor band gap from diode saturation current

In a diffusion-dominated p-n junction, $I_s=C(T)n_i^2$ with a transport prefactor determined by minority-carrier diffusion and dopant densities. Combining this with the intrinsic carrier concentration gives, for fixed gap and effective masses,The slope against $1/T$ is $-E_g/k_B$. A measured diode ideality factor helps identify the transport regime: generation or recombination current can have a different dependence on $n_i$, so its activation slope cannot automatically be interpreted with the diffusion formula.