Practice question

**Doping** is adding impurity to pure semiconductor to increase carriers, pentavalent (P, As, Sb) donates extra electron, 1 ppm doping in Ge with 4×10²⁸ atoms/m³ gives donor density N_d = 4×10²⁸×10⁻⁶ =4×10²² m⁻³ for 1 ppm, acceptor atoms p-type trivalent B, Al, Ga. Overall charge neutrality maintained because donor ion core positive but electron negative, net neutral. The fifth electron of a pentavalent dopant (e.g., As) in Si or Ge is weakly bound, requiring very small energy (~0.01 eV for Ge, ~0.05 eV for Si) to become free, much less than the intrinsic energy gap. Substituting values gives Very small, which matches expected behaviour for