= 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,
$$
\log\frac{I_s}{C(T)T^3}=\text{constant}-\frac{E_g}{k_BT}.
$$
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.
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