Silicon at 300 K: nᵢ = 1.5×10¹⁰ cm⁻³. A sample is doped with phosphorus to N_D = 10¹⁶ cm⁻³ donors. (a) Find electron and hole concentrations. (b) Which type is it, and who are the majority carriers? Solution: (a) n ≈ N_D = 10¹⁶ cm⁻³ (donors dominate). p = nᵢ²/n = (1.5×10¹⁰)²/10¹⁶ = 2.25×10⁴ cm⁻³ — utterly negligible. (b) N-type; majority carriers are electrons (10¹⁶ vs 10⁴ holes). Doping raised conductivity by a factor ~10¹⁶/10¹⁰ = 10⁶ over intrinsic.