The intrinsic electrical conductivity of InSb at 60 ° C . The intrinsic electrical conductivity of InSb at 70 ° C .

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Answer 1

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Chapter 14.12, Problem 82AAP

To determine

The intrinsic electrical conductivity of InSb at 60°C.

The intrinsic electrical conductivity of InSb at 70°C.

Expert Solution & Answer

Answer to Problem 82AAP

The intrinsic electrical conductivity of InSb at 60°C is 2.41×104 Ω−1⋅m−1.

The intrinsic electrical conductivity of InSb at 70°C is 2.62×104 Ω−1⋅m−1.

Explanation of Solution

Write the expression for the conductivity of InSb at 300 K.

σ300 K=niq(μn+μp) (I)

Here, the intrinsic carrier is ni, the charge is q, the mobility of the electron is μn and the mobility of the hole is μp.

Convert the temperature from degree Celsius to Kelvin.

0°C+273=273 K60°C+273=333 K

Convert the temperature from degree Celsius to Kelvin.

(0°C+273) K=273 K

(70°C+273) K=343 K

Write the expression for the conductivity of InSb at 333 K.

σ333 K=σ300 Ke(−Eg2kT300 K)e(−Eg2kT333 K) (II)

Here, the Boltzmann constant is k and the band energy gap is −Eg.

Write the expression for the conductivity of InSb at 343 K.

σ343 K=σ300 Ke(−Eg2kT300 K)e(−Eg2kT343 K) (III)

Conclusion:

Here, the charge is 1.6×10−19 C and the Boltzmann constant is 8.62×10−5 eV/K.

Substitute 1.6×10−19 C for q, 1.35×1022 m−3 for ni, 8.00 m2/V⋅s for μn and 0.045 m2/V⋅s for μp in Equation (II).

σ300 K=(1.35×1022 m−3)(1.6×10−19 C)(8.00 m2/V⋅s+0.045 m2/V⋅s)=(2160 C⋅m−3)(8.045 m2/V⋅s)(1 A⋅s1 C)(1 V/A1 Ω)=1.7377×104 Ω−1⋅m−1≈1.74×104 Ω−1⋅m−1

Substitute 1.74×104 Ω−1⋅m−1 for σ300 K, 0.17 eV for Eg, 8.62×10−5 eV/K for k, 333 K for T333 K and 300 K for T300 K in Equation (II).

σ343 K=(1.74×104 Ω−1⋅m−1)e(−0.17 eV2(8.62×10−5 eV/K)300 K)e(−0.17 eV2(8.62×10−5 eV/K)333 K)=(1.74×104 Ω−1⋅m−1)e(−3.2869)e(−2.9611)=(1.74×104 Ω−1⋅m−1)0.037360.05175=2.41×104 Ω−1⋅m−1

Substitute 1.74×104 Ω−1⋅m−1 for σ300 K, 0.17 eV for Eg, 8.62×10−5 eV/K for k, 343 K for T343 K and 300 K for T300 K in Equation (III).

σ343 K=(1.74×104 Ω−1⋅m−1)e(−0.17 eV2(8.62×10−5 eV/K)300 K)e(−0.17 eV2(8.62×10−5 eV/K)343 K)=(1.74×104 Ω−1⋅m−1)e(−3.2869)e(−2.87)=(1.74×104 Ω−1⋅m−1)0.037360.05642=2.62×104 Ω−1⋅m−1

Thus, the intrinsic electrical conductivity of InSb at 60°C is 2.41×104 Ω−1⋅m−1.

Thus, the intrinsic electrical conductivity of InSb at 70°C is 2.62×104 Ω−1⋅m−1.

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