Which value is closest to the resistivity of n-type silicon with a donor concentration of 1.0×10¹⁶ cm⁻³ (room temperature, all donors ionized)? Take the electron mobility as 1350 cm²/(V·s) and the elementary charge as 1.60×10⁻¹⁹ C, and neglect the hole contribution.

Answer: A. About 0.46 Ω·cm

The conductivity is σ = neμ = 1.0×10¹⁶ × 1.60×10⁻¹⁹ × 1350 ≈ 2.16 S/cm, and the resistivity is its reciprocal, ρ = 1/σ ≈ 0.46 Ω·cm. About 2.2 Ω·cm mistakes the conductivity value for the resistivity. About 4.6×10³ Ω·cm is an error from mixing units, combining the mobility converted to m²/(V·s), 0.135, directly with a concentration in cm⁻³. Metals have a large carrier concentration of about 10²² cm⁻³, so their resistivity is essentially fixed by the material, whereas in semiconductors doping can change n by many orders of magnitude, so the resistivity can be controlled over a wide range.