• Tags: doping, n-type, p-type, donors, acceptors
• Difficulty: Moderate

Doping introduces controlled impurities to dramatically increase conductivity. n-type: pentavalent dopant (P, As, Sb) in Si. Each dopant atom has 5 valence electrons; 4 form covalent bonds, 1 is loosely bound (ionization energy ~0.05 eV << 1.1 eV gap). At room temperature, nearly all donor electrons are free: $n_e$ ≈ $N_D$ >> $n_i$. Minority carriers (holes): $n_h$ = $n_i^2$/$N_D$ << $n_i$. The Fermi level shifts toward the conduction band. p-type: trivalent dopant (B, Al, Ga, In) creates an "acceptor" level just above the valence band. Each dopant creates a hole: $n_h$ ≈ $N_A$ >> $n_i$, $n_e$ = $n_i^2$/$N_A$. Fermi level shifts toward the valence band. Critical: both n-type and p-type are electrically neutral — the dopant ions provide balancing charges. The mass action law $n_e$*$n_h$ = $n_i^2$ holds for all temperatures and doping levels.