HC Verma: Concepts of Physics - Volume 2 Semiconductors and Semiconductor Devices Pages 419-421: Q14 Solution: The conductivity of an intrinsic semiconductor depends on…

QPages 419-421: Q14: HC Verma: Concepts of Physics - Volume 2 Semiconductors and Semiconductor Devices Pages 419-421: Q14 Solution: The conductivity of an intrinsic semiconductor depends on…

⚠️ Common Exam Traps & Conceptual Pitfalls

When forming the ratio σ(T2)/σ(T1)=exp[-ΔE/(2k)(1/T2‑1/T1)], students often drop the “½” in the exponent and use ΔE/k instead, which gives a temperature far from the correct value. Always keep the ΔE/(2k) factor throughout the algebra and only then take the natural log.

The conductivity of an intrinsic semiconductor depends on temperature as

\sigma = \sigma_0 e^{-\Delta E/2kT}

, where

\sigma_0

is a constant. Find the temperature at which the conductivity of an intrinsic germanium semiconductor will be double of its value at T = 300 K. Assume that the gap for germanium is 0.650 eV and remains constant as the temperature is increased. Use Planck constant

h = 4.14 \times 10^{-15} \text{ eV-s}

, Boltzmann constant

k = 8.62 \times 10^{-5} \text{ eV/K}

Step-by-Step Verified Solution

**Answer:** T = 318 K. **Step-by-Step Explanation:** Given: _E = 0.65 eV, T_ = 300 K, __ = 2__. _ _ exp(-_E/2kT). __/__ = exp[-(_E/2k)(1/T_ - 1/T_)] = 2. Taking ln: (_E/2k)(1/T_ - 1/T_) = ln2. 1/T_ = 1/T_ - (2k/_E)ln2 = 1/300 - (2 _ 8.62 _ 10__/0.65) _ 0.693 = 0.00333 - 1.84 _ 10__ = 0.003146. T_ = 318 K .

QPages 419-421: Q14: HC Verma: Concepts of Physics - Volume 2 Semiconductors and Semiconductor Devices Pages 419-421: Q14 Solution: The conductivity of an intrinsic semiconductor depends on…

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