Verified Solution • 2025–26 Session moderate

QPages 419-421: Q10: HC Verma: Concepts of Physics - Volume 2 Semiconductors and Semiconductor Devices Pages 419-421: Q10 Solution: Let denote the energy gap between the valence band and the…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often plug ΔE in electron‑volts while using $k_B=1.38\times10^{-23}\,$J/K, producing a nonsensical exponent; always convert $k_B$ to eV/K ($k_B\approx8.62\times10^{-5}\,$eV/K) or ΔE to joules before evaluating $e^{-\Delta E/(2k_BT)}$.

Let ΔE\Delta E denote the energy gap between the valence band and the conduction band. The population of conduction electrons and of the holes) is roughly proportional to e−ΔE/2kTe^{-\Delta E/2kT}. Find the ratio of the concentration of conduction electrons in diamond to that in silicon at room temperature 300 K. ΔE\Delta E for silicon is 1.1 eV and for diamond is 6.1 eV. How many conduction electrons are likely to be in one cubic metre of diamond?

Step-by-Step Verified Solution

**Answer:** Ratio = 7.15 _ 10___. Conduction electrons in diamond � 0. **Step-by-Step Explanation:** Given: _E_Si = 1.1 eV, _E_diamond = 6.1 eV, T = 300 K. Concentration _ exp(-_E/2kT). Ratio = exp[-(6.1 - 1.1)/(2 _ 8.62 _ 10__ _ 300)] = exp[-5.0/0.05172] = exp(-96.67) = 7.15 _ 10___. Since the ratio is extremely small, the number of conduction electrons in diamond is essentially zero .

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