Foundations of Materials Science and Engineering
Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 14.12, Problem 83AAP

(a)

To determine

The intrinsic electrical conductivity of GaAs at 75°C.

(a)

Expert Solution
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Answer to Problem 83AAP

The intrinsic electrical conductivity of GaAs at 75°C is 8.305×106Ω1m1.

Explanation of Solution

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

    σ300K=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)K=273K

    (75°C+273)K=348K

Write the expression for the conductivity of GaAs at 348K.

    σ348K=σ300Ke(Eg2kT300K)e(Eg2kT348K)                                                 (II)

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

Conclusion:

Refer to table 14-6 “ electrical properties of intrinsic semiconducting compounds at room temperature 300K” to obtain the mobility of electron and hole for GaAs as 0.720m2/Vs and 0.020m2/Vs respectively.

Refer to table 14-6 “ electrical properties of intrinsic semiconducting compounds at room temperature 300K” to obtain the intrinsic carrier and energy band gap as 1.4×1012m3 and 1.47eV respectively.

Here, the charge is 1.6×1019C and the Boltzmann constant is 8.62×105eV/K.

Substitute 1.6×1019C for q, 1.4×1012m3 for ni, 0.720m2/Vs for μn and 0.020m2/Vs for μp in Equation (II).

    σ300K=(1.4×1012m3)(1.6×1019C)(0.720m2/Vs+0.020m2/Vs)=(2.24×107Cm3)(0.74m2/Vs)(1As1C)(1V/A1Ω)=1.65×107Ω1m1

Substitute 1.65×107Ω1m1 for σ300K, 1.47eV for Eg, 8.62×105eV/K for k, 348K for T348K and 300K for T300K in Equation (II).

    σ348K=(1.65×107Ω1m1)e(1.47eV2(8.62×105eV/K)300K)e(1.47eV2(8.62×105eV/K)348K)=(1.65×107Ω1m1)e(28.42)e(24.50)=(1.65×107Ω1m1)4.54×10132.285×1011=8.305×106Ω1m1

Thus, the intrinsic electrical conductivity of GaAs at 75°C is 8.305×106Ω1m1.

(b)

To determine

The intrinsic electrical conductivity of InSb at 75°C.

(b)

Expert Solution
Check Mark

Answer to Problem 83AAP

The intrinsic electrical conductivity of InSb at 75°C is 2.7386×104Ω1m1.

Explanation of Solution

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

    σ300K=niq(μn+μp)                                                  (III)

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=273K75°C+273=348K

Write the expression for the conductivity of InSb at 348K.

    σ348K=σ300Ke(Eg2kT300K)e(Eg2kT348K)                                               (IV)

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

Conclusion:

Here, the charge is 1.6×1019C and the Boltzmann constant is 8.62×105eV/K.

Refer to table 14-6 “ electrical properties of intrinsic semiconducting compounds at room temperature 300K” to obtain the mobility of electron and hole for InSb as 8.00m2/Vs and 0.045m2/Vs respectively.

Refer to table 14-6 “ electrical properties of intrinsic semiconducting compounds at room temperature 300K” to obtain the intrinsic carrier and energy band gap as 1.35×1022m3 and 0.17eV respectively.

Substitute 1.6×1019C for q, 1.35×1022m3 for ni, 8.00m2/Vs for μn and 0.045m2/Vs for μp in Equation (II).

    σ300K=(1.35×1022m3)(1.6×1019C)(8.00m2/Vs+0.045m2/Vs)=(2160Cm3)(8.045m2/Vs)(1As1C)(1V/A1Ω)=1.7377×104Ω1m11.74×104Ω1m1

Substitute 1.74×104Ω1m1 for σ300K, 0.17eV for Eg, 8.62×105eV/K for k, 348K for T348K and 300K for T300K in Equation (II).

    σ348K=(1.74×104Ω1m1)e(0.17eV2(8.62×105eV/K)300K)e(0.17eV2(8.62×105eV/K)348K)=(1.74×104Ω1m1)e(3.2869)e(2.8335)=(1.74×104Ω1m1)0.037360.05880=2.7386×104Ω1m1

Thus, the intrinsic electrical conductivity of InSb at 75°C is 2.7386×104Ω1m1.

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Foundations of Materials Science and Engineering

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