If the resistivity of pure silicon is 3000 Ω m and the mobilities of electrons and holes are 0 . 12 m 2 V - 1 s - 1 and 0 . 045 m 2 V - 1 s - 1 respectively, then what will be the resistivity of a specimen of silicon when 10 19 atoms of phosphorous are added per cubic metre?

Step-by-step solution

The resistivity of pure S is given by ρ = 1 σ = 1 e n e μ e + n h μ h = 1 en 1 μ e + μ h or n 1 = 1 eρ μ e + μ n = 1 1 . 6 × 10 - 19 × 3000 ( 0 . 12 + 0 . 045 ) = 1 . 26 × 10 16 m - 3 When 10 19 atoms of phosphorous (donor atoms of valence five) are added per m 3 , the semiconductor becomes n - type semiconductor. ∴ n e - n h ≈ n e = N d = 10 19 ∵ n n = 1 . 26 × 10 16 Resitivity ρ = 1 n e μ e e = 1 1 . 6 × 10 - 19 × 10 19 × 0 . 12 = 5 . 21 Ωm