For a particular semiconductor material following parameters

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For a particular semiconductor material following parameters are observed—
µ_a = 1000 cm²/ V-s,
µ_p = 600 cm²/ V-s,
N_c = N_v = 10¹⁹ cm^–3
These parameters are independent of temperature. The measured conductivity of the intrinsic material is σ = 10^–6 (Ω - cm)^{– 1} at T = 300 K. The conductivity at T = 500 K is—

1. 2 × 10^{– 4} (Ω - cm)^{– 1}
2. 4 × 10^{– 5} (Ω - cm)^{– 1}
3. 2 × 10^{– 5} (Ω - cm)^{– 1}
4. 6 × 10^{– 3} (Ω - cm)^{– 1}

Correct Option: D

Given data, µ_n = 1000 cm²/ V-s
µ_P = 600 cm²/ V-s
N_c = N_V = 10¹⁹ cm^–3
Conductivity, σ = 10^–6 (Ω-cm)^–1 at temp, T = 300 K,
Let the conductivity at T = 500 K is σ′
Now, σ′ = 9 n′₁ (µ_n + µ_p), at T = 300 K
10^–6 = 1.6 × 10^–19. n_i (1000 + 600)
or n_i = 3.9 × 10⁹ cm^–3
Now calculate new n′₁
n_i ² = N_i. N_V. e^{– (Eg/ kT)}

where E_g = kT I_n		N_CN_V
		n_i ²

= 26 × 10^–3 I_n		10¹⁹ · 10¹⁹
		(3.91 × 10⁹) ²

= 1.122 eV

at T = 500 K ⇒ kT = 26 × 10^–3		500		= 0.432 eV
		300

Now, n′ ² _i = 10¹⁹.10¹⁹. e (1.122 / 0.432) = 2.29 × 10¹³ cm^–3
σ′ = q n′_i (µ_n + µ_p)
= 1.6 × 10^–19 × 2.29 × 10¹³ (1000 + 600)
= 5.86 × 10^–3 (Ω-cm)^–1
Hence alternative (D) is the correct choice.