A semiconductor having electron and hole mobilities μ_n and μ_p respectively. If its intrinsic carrier density is n_i then what will be the value of hole concentration P for which the conductivity will be minimum at a given temperature?

Correct option is A. n_i√(μ_n/μ_p)
Let the hole concentration be n_h. Then the electron concentration = n_e = n_i²/n_h
The total conductivity of the semiconductor material = σ = σ_e + σ_h = e n_e μ_n + e n_h μ_p = e n_i²/n_h μ_n + e n_h μ_p
Hence, the condition for minimum conductivity is found by dσ/dn_h = 0
→ e n_i² μ_n (-1/n_h²) + e μ_p = 0
→ n_h = n_i √(μ_n/μ_p)