Verified Solution • 2025–26 Session moderate

QPages 419-421: Q4: HC Verma: Concepts of Physics - Volume 2 Semiconductors and Semiconductor Devices Pages 419-421: Q4 Solution: The band gap for silicon is 1.1 eV. a) Find the ratio of the…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often read “the ratio becomes one‑tenth of the value at 300 K” as the ratio itself being 0.1, instead of recognizing it must be (original ratio)/10 ≈ 4.3. Always compute the new ratio as $R_{new}=R_{300}/10$ before solving $T=E/(kR_{new})$ to avoid a ten‑fold temperature error.

The band gap for silicon is 1.1 eV. a) Find the ratio of the band gap to kTkT for silicon at room temperature 300 K. b) At what temperature does this ratio become one tenth of the value at 300 K? Silicon will not retain its structure at these high temperatures.) Use Planck constant h=4.14×10−15 eV-sh = 4.14 \times 10^{-15} \text{ eV-s}, Boltzmann constant k=8.62×10−5 eV/Kk = 8.62 \times 10^{-5} \text{ eV/K}.)

Step-by-Step Verified Solution

**Answer:** (a) Ratio = 43 (b) T = 3000 K. **Step-by-Step Explanation:** Given: Band gap = 1.1 eV, T = 300 K. (a) Ratio = E/(kT) = 1.1/(8.62 _ 10__ _ 300) = 1.1/0.02586 = 42.53 � 43. (b) For ratio to be one-tenth: E/(kT) = 4.253.
T=1.14.253×8.62×10−5=1.13.666×10−4=3000 KT = \frac{1.1}{4.253 \times 8.62 \times 10^{-5}} = \frac{1.1}{3.666 \times 10^{-4}} = 3000 \text{ K}

All Questions in this Chapter

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