Practice question

**Number of carriers** from doping: Ge crystal 4×10²⁸ atoms/m³ doped 2 ppm trivalent gives acceptor atoms 8×10²² m⁻³, holes ≈ that, for 1.5 ppm 6×10²² m⁻³, for 0.5 ppm pentavalent Si 5×10²⁸ atoms/m³ gives 2.5×10²² donors/m³. Acceptor atom effectively negative when accepts electron, donor positive when donates, but crystal neutral. Trivalent dopants (valency 3) like Boron (B), Aluminium (Al), and Indium (In) are used in p-type semiconductors to create holes. Phosphorus (P) is pentavalent. Substituting values gives Aluminium, which matches expected behaviour for this semiconductor device configuration, confirming doping, depletion and rectifier principles.