Calculate the intrinsic electrical conductivity of GaAs at 125°C. [ E g = 1.47 eV; μ n = 0.720 m 2 /(V · s); μ p = 0.020 m 2 /(V · s); n i = 1.4 × 10 12 m −3 .]

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Answer 1

Textbook Question

Chapter 14.12, Problem 81AAP

Calculate the intrinsic electrical conductivity of GaAs at 125°C. [E_g = 1.47 eV; μ_n = 0.720 m²/(V · s); μ_p = 0.020 m²/(V · s); n_i = 1.4 × 10¹² m⁻³.]

Expert Solution & Answer

To determine

The intrinsic electrical conductivity of GaAs at 125°C.

Answer to Problem 81AAP

The intrinsic electrical conductivity of GaAs at 125°C is 1.81×10−4 Ω−1⋅m−1.

Explanation of Solution

Write the expression for the conductivity of GaAs 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) K=273 K

(125°C+273) K=398 K

Write the expression for the conductivity of GaAs at 398 K.

σ398 K=σ300 Ke(−Eg2kT300 K)e(−Eg2kT398 K) (II)

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

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, 1.4×1012 m−3 for ni, 0.720 m2/V⋅s for μn and 0.020 m2/V⋅s for μp in Equation (II).

σ300 K=(1.4×1012 m−3)(1.6×10−19 C)(0.720 m2/V⋅s+0.020 m2/V⋅s)=(2.24×10−7 C⋅m−3)(1 A⋅s1 C)(0.74 m2/V⋅s)(1 V/A1 Ω)=1.65×10−7 Ω−1⋅m−1

Substitute 1.65×10−7 Ω−1⋅m−1 for σ300 K, 1.47 eV for Eg, 8.62×10−5 eV/K for k, 398 K for T398 K and 300 K for T300 K in Equation (II).

σ398 K=(1.65×10−7 Ω−1⋅m−1)e(−1.47 eV2(8.62×10−5 eV/K)300 K)e(−1.47 eV2(8.62×10−5 eV/K)398 K)=(1.65×10−7 Ω−1⋅m−1)e(−28.42)e(−21.42)=(1.65×10−7 Ω−1⋅m−1)4.54×10−134.982×10−10=1.81×10−4 Ω−1⋅m−1

Thus, the intrinsic electrical conductivity of GaAs at 125°C is 1.81×10−4 Ω−1⋅m−1.

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Answer 2

Textbook Question

Chapter 14.12, Problem 81AAP

Calculate the intrinsic electrical conductivity of GaAs at 125°C. [E_g = 1.47 eV; μ_n = 0.720 m²/(V · s); μ_p = 0.020 m²/(V · s); n_i = 1.4 × 10¹² m⁻³.]

Expert Solution & Answer

To determine

The intrinsic electrical conductivity of GaAs at 125°C.

Answer to Problem 81AAP

The intrinsic electrical conductivity of GaAs at 125°C is 1.81×10−4 Ω−1⋅m−1.

Explanation of Solution

Write the expression for the conductivity of GaAs 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) K=273 K

(125°C+273) K=398 K

Write the expression for the conductivity of GaAs at 398 K.

σ398 K=σ300 Ke(−Eg2kT300 K)e(−Eg2kT398 K) (II)

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

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, 1.4×1012 m−3 for ni, 0.720 m2/V⋅s for μn and 0.020 m2/V⋅s for μp in Equation (II).

σ300 K=(1.4×1012 m−3)(1.6×10−19 C)(0.720 m2/V⋅s+0.020 m2/V⋅s)=(2.24×10−7 C⋅m−3)(1 A⋅s1 C)(0.74 m2/V⋅s)(1 V/A1 Ω)=1.65×10−7 Ω−1⋅m−1

Substitute 1.65×10−7 Ω−1⋅m−1 for σ300 K, 1.47 eV for Eg, 8.62×10−5 eV/K for k, 398 K for T398 K and 300 K for T300 K in Equation (II).

σ398 K=(1.65×10−7 Ω−1⋅m−1)e(−1.47 eV2(8.62×10−5 eV/K)300 K)e(−1.47 eV2(8.62×10−5 eV/K)398 K)=(1.65×10−7 Ω−1⋅m−1)e(−28.42)e(−21.42)=(1.65×10−7 Ω−1⋅m−1)4.54×10−134.982×10−10=1.81×10−4 Ω−1⋅m−1

Thus, the intrinsic electrical conductivity of GaAs at 125°C is 1.81×10−4 Ω−1⋅m−1.

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Answer 3

Textbook Question

Chapter 14.12, Problem 81AAP

Calculate the intrinsic electrical conductivity of GaAs at 125°C. [E_g = 1.47 eV; μ_n = 0.720 m²/(V · s); μ_p = 0.020 m²/(V · s); n_i = 1.4 × 10¹² m⁻³.]

Expert Solution & Answer

To determine

The intrinsic electrical conductivity of GaAs at 125°C.

Answer to Problem 81AAP

The intrinsic electrical conductivity of GaAs at 125°C is 1.81×10−4 Ω−1⋅m−1.

Explanation of Solution

Write the expression for the conductivity of GaAs 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) K=273 K

(125°C+273) K=398 K

Write the expression for the conductivity of GaAs at 398 K.

σ398 K=σ300 Ke(−Eg2kT300 K)e(−Eg2kT398 K) (II)

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

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, 1.4×1012 m−3 for ni, 0.720 m2/V⋅s for μn and 0.020 m2/V⋅s for μp in Equation (II).

σ300 K=(1.4×1012 m−3)(1.6×10−19 C)(0.720 m2/V⋅s+0.020 m2/V⋅s)=(2.24×10−7 C⋅m−3)(1 A⋅s1 C)(0.74 m2/V⋅s)(1 V/A1 Ω)=1.65×10−7 Ω−1⋅m−1

Substitute 1.65×10−7 Ω−1⋅m−1 for σ300 K, 1.47 eV for Eg, 8.62×10−5 eV/K for k, 398 K for T398 K and 300 K for T300 K in Equation (II).

σ398 K=(1.65×10−7 Ω−1⋅m−1)e(−1.47 eV2(8.62×10−5 eV/K)300 K)e(−1.47 eV2(8.62×10−5 eV/K)398 K)=(1.65×10−7 Ω−1⋅m−1)e(−28.42)e(−21.42)=(1.65×10−7 Ω−1⋅m−1)4.54×10−134.982×10−10=1.81×10−4 Ω−1⋅m−1

Thus, the intrinsic electrical conductivity of GaAs at 125°C is 1.81×10−4 Ω−1⋅m−1.

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Answer 4

Textbook Question

Chapter 14.12, Problem 81AAP

Calculate the intrinsic electrical conductivity of GaAs at 125°C. [E_g = 1.47 eV; μ_n = 0.720 m²/(V · s); μ_p = 0.020 m²/(V · s); n_i = 1.4 × 10¹² m⁻³.]

Expert Solution & Answer

To determine

The intrinsic electrical conductivity of GaAs at 125°C.

Answer to Problem 81AAP

The intrinsic electrical conductivity of GaAs at 125°C is 1.81×10−4 Ω−1⋅m−1.

Explanation of Solution

Write the expression for the conductivity of GaAs 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) K=273 K

(125°C+273) K=398 K

Write the expression for the conductivity of GaAs at 398 K.

σ398 K=σ300 Ke(−Eg2kT300 K)e(−Eg2kT398 K) (II)

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

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, 1.4×1012 m−3 for ni, 0.720 m2/V⋅s for μn and 0.020 m2/V⋅s for μp in Equation (II).

σ300 K=(1.4×1012 m−3)(1.6×10−19 C)(0.720 m2/V⋅s+0.020 m2/V⋅s)=(2.24×10−7 C⋅m−3)(1 A⋅s1 C)(0.74 m2/V⋅s)(1 V/A1 Ω)=1.65×10−7 Ω−1⋅m−1

Substitute 1.65×10−7 Ω−1⋅m−1 for σ300 K, 1.47 eV for Eg, 8.62×10−5 eV/K for k, 398 K for T398 K and 300 K for T300 K in Equation (II).

σ398 K=(1.65×10−7 Ω−1⋅m−1)e(−1.47 eV2(8.62×10−5 eV/K)300 K)e(−1.47 eV2(8.62×10−5 eV/K)398 K)=(1.65×10−7 Ω−1⋅m−1)e(−28.42)e(−21.42)=(1.65×10−7 Ω−1⋅m−1)4.54×10−134.982×10−10=1.81×10−4 Ω−1⋅m−1

Thus, the intrinsic electrical conductivity of GaAs at 125°C is 1.81×10−4 Ω−1⋅m−1.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

The intrinsic electrical conductivity of GaAs at 125°C.

Answer to Problem 81AAP

The intrinsic electrical conductivity of GaAs at 125°C is 1.81×10−4 Ω−1⋅m−1.

Explanation of Solution

Write the expression for the conductivity of GaAs 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) K=273 K

(125°C+273) K=398 K

Write the expression for the conductivity of GaAs at 398 K.

σ398 K=σ300 Ke(−Eg2kT300 K)e(−Eg2kT398 K) (II)

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

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, 1.4×1012 m−3 for ni, 0.720 m2/V⋅s for μn and 0.020 m2/V⋅s for μp in Equation (II).

σ300 K=(1.4×1012 m−3)(1.6×10−19 C)(0.720 m2/V⋅s+0.020 m2/V⋅s)=(2.24×10−7 C⋅m−3)(1 A⋅s1 C)(0.74 m2/V⋅s)(1 V/A1 Ω)=1.65×10−7 Ω−1⋅m−1

Substitute 1.65×10−7 Ω−1⋅m−1 for σ300 K, 1.47 eV for Eg, 8.62×10−5 eV/K for k, 398 K for T398 K and 300 K for T300 K in Equation (II).

σ398 K=(1.65×10−7 Ω−1⋅m−1)e(−1.47 eV2(8.62×10−5 eV/K)300 K)e(−1.47 eV2(8.62×10−5 eV/K)398 K)=(1.65×10−7 Ω−1⋅m−1)e(−28.42)e(−21.42)=(1.65×10−7 Ω−1⋅m−1)4.54×10−134.982×10−10=1.81×10−4 Ω−1⋅m−1

Thus, the intrinsic electrical conductivity of GaAs at 125°C is 1.81×10−4 Ω−1⋅m−1.

Answer 8

Expert Solution & Answer

To determine

The intrinsic electrical conductivity of GaAs at 125°C.

Answer to Problem 81AAP

The intrinsic electrical conductivity of GaAs at 125°C is 1.81×10−4 Ω−1⋅m−1.

Explanation of Solution

Write the expression for the conductivity of GaAs 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) K=273 K

(125°C+273) K=398 K

Write the expression for the conductivity of GaAs at 398 K.

σ398 K=σ300 Ke(−Eg2kT300 K)e(−Eg2kT398 K) (II)

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

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, 1.4×1012 m−3 for ni, 0.720 m2/V⋅s for μn and 0.020 m2/V⋅s for μp in Equation (II).

σ300 K=(1.4×1012 m−3)(1.6×10−19 C)(0.720 m2/V⋅s+0.020 m2/V⋅s)=(2.24×10−7 C⋅m−3)(1 A⋅s1 C)(0.74 m2/V⋅s)(1 V/A1 Ω)=1.65×10−7 Ω−1⋅m−1

Substitute 1.65×10−7 Ω−1⋅m−1 for σ300 K, 1.47 eV for Eg, 8.62×10−5 eV/K for k, 398 K for T398 K and 300 K for T300 K in Equation (II).

σ398 K=(1.65×10−7 Ω−1⋅m−1)e(−1.47 eV2(8.62×10−5 eV/K)300 K)e(−1.47 eV2(8.62×10−5 eV/K)398 K)=(1.65×10−7 Ω−1⋅m−1)e(−28.42)e(−21.42)=(1.65×10−7 Ω−1⋅m−1)4.54×10−134.982×10−10=1.81×10−4 Ω−1⋅m−1

Thus, the intrinsic electrical conductivity of GaAs at 125°C is 1.81×10−4 Ω−1⋅m−1.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

The intrinsic electrical conductivity of GaAs at 125°C.

Answer 12

Answer to Problem 81AAP

The intrinsic electrical conductivity of GaAs at 125°C is 1.81×10−4 Ω−1⋅m−1.

Answer 13

Explanation of Solution

Write the expression for the conductivity of GaAs 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) K=273 K

(125°C+273) K=398 K

Write the expression for the conductivity of GaAs at 398 K.

σ398 K=σ300 Ke(−Eg2kT300 K)e(−Eg2kT398 K) (II)

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

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, 1.4×1012 m−3 for ni, 0.720 m2/V⋅s for μn and 0.020 m2/V⋅s for μp in Equation (II).

σ300 K=(1.4×1012 m−3)(1.6×10−19 C)(0.720 m2/V⋅s+0.020 m2/V⋅s)=(2.24×10−7 C⋅m−3)(1 A⋅s1 C)(0.74 m2/V⋅s)(1 V/A1 Ω)=1.65×10−7 Ω−1⋅m−1

Substitute 1.65×10−7 Ω−1⋅m−1 for σ300 K, 1.47 eV for Eg, 8.62×10−5 eV/K for k, 398 K for T398 K and 300 K for T300 K in Equation (II).

σ398 K=(1.65×10−7 Ω−1⋅m−1)e(−1.47 eV2(8.62×10−5 eV/K)300 K)e(−1.47 eV2(8.62×10−5 eV/K)398 K)=(1.65×10−7 Ω−1⋅m−1)e(−28.42)e(−21.42)=(1.65×10−7 Ω−1⋅m−1)4.54×10−134.982×10−10=1.81×10−4 Ω−1⋅m−1

Thus, the intrinsic electrical conductivity of GaAs at 125°C is 1.81×10−4 Ω−1⋅m−1.

Answer 14

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Calculate the intrinsic electrical conductivity of GaAs at 125°C. [ E g = 1.47 eV; μ n = 0.720 m 2 /(V · s); μ p = 0.020 m 2 /(V · s); n i = 1.4 × 10 12 m −3 .]

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Answer to Problem 81AAP

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