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QPages 419-421: Q11: HC Verma: Concepts of Physics - Volume 2 Semiconductors and Semiconductor Devices Pages 419-421: Q11 Solution: The conductivity of a pure semiconductor is roughly…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently either keep ΔE in eV while using k = 1.38×10⁻²³ J/K, or assume the band‑gap is temperature‑independent; both give a wildly wrong exponent. Use k = 8.617×10⁻⁵ eV/K (or convert ΔE to joules) and insert the appropriate ΔE value for each temperature before evaluating the exponential.

The conductivity of a pure semiconductor is roughly proportional to T3/2e−ΔE/2kTT^{3/2} e^{-\Delta E/2kT} where ΔE\Delta E is the band gap. The band gap for germanium is 0.74 eV at 4 K and 0.67 eV at 300 K. By what factor does the conductivity of pure germanium increase as the temperature is raised from 4 K to 300 K?

Step-by-Step Verified Solution

**Answer:** Conductivity increases by a factor of approximately 10_. **Step-by-Step Explanation:** Given: _E = 0.74 eV at 4 K, _E = 0.67 eV at 300 K. Conductivity _ _ T^(3/2) exp(-_E/2kT). __300/__4 = (300/4)^(3/2) _ exp[-(0.67)/(2 _ 8.62 _ 10__ _ 300) + (0.74)/(2 _ 8.62 _ 10__ _ 4)] = (75)^1.5 _ exp[-12.95 + 1073] � 649 _ exp(1060) � 10_ .

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