Compensated semiconductor ($n-p=N_D-N_A,np=n_i^2$)

A compensated semiconductor contains both donor impurities and acceptor impurities. In a nondegenerate equilibrium model with both species fully ionized, charge neutrality gives $n-p=\Delta =N_D-N_A$, while the semiconductor semiconductor mass-action law gives $np=n_i^2$. Solving yieldsFor $\Delta >0$ and $n_i\ll \Delta$, $n\simeq \Delta$ and $p\simeq n_i^2/\Delta$. Numerically the minority concentration is better obtained as $n_i^2/n$ than by subtracting nearly equal numbers. If dopants are only partly ionized, replace $N_D,N_A$ in charge neutrality by their ionized concentrations and determine the chemical potential self-consistently.