Question

An intrinsic semiconductor has a resistivity of 0.50 Ω m at room temperature. Find the intrinsic carrier concentration if the mobilities of electrons and holes are 0.39 m²V^-1S^-1 and O.11 m² v^-1S^-1 respectively:

Options

• 1.2 × 10¹⁸ m^-3

• 2.5 × 10¹⁹ m^-3

• 1.9 × 10²⁰ m^-3

• 30 × 10^-19 m^-3

Answer 1

2.5 × 10¹⁹ m^-3 

Explanation:

ρ = 0.50 Ωm

μ_e = 0.39 m²V^-1s^-1

μ_h = 0.11 m²V^-1s^-1

Resistivity of intrinsic semiconductor is

`1/rho = "e" (mu_"e" "n"_"i" + "n"_"i"mu_"h")`

Where, `"n"_"i" = 1/(rho"e" (mu_"e" + mu_"h"))`

`"n"_"i" = 1/((0.5)(1.6 xx 10^-19)(0.39 + 0.11))`

`= 2.5 xx 10^19 "m"^-3`