• 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.