Verified Solution • 2025–26 Session moderate

QPages 416-417: Q5: HC Verma: Concepts of Physics - Volume 2 Semiconductors and Semiconductor Devices Pages 416-417: Q5 Solution: When an electron goes from the valence band to the conduction…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often incorrectly assume that because the average thermal energy $kT$ is less than the band gap $E_g$, no excitation can occur. You must recognize that energy exchange follows a statistical distribution, allowing a small fraction of high-energy collisions in the tail to bridge the gap.

When an electron goes from the valence band to the conduction band in silicon, its energy is increased by 1.1 eV. The average energy exchanged in a thermal collision is of the order of kTkT which is only 0.026 eV at room temperature. How is a thermal collision able to take some of the electrons from the valence band to the conduction band?

Step-by-Step Verified Solution

**Answer:** A single thermal collision cannot provide 1.1 eV directly. The electron absorbs energy from multiple collisions over time, or it gains energy from the electric field and then is excited by a collision. **Step-by-Step Explanation:** The average thermal energy kT is only 0.026 eV at room temperature, much less than the 1.1 eV band gap. However, the energy distribution of collisions is statistical. A small fraction of collisions involve much higher energies (in the tail of the Maxwell-Boltzmann distribution). Additionally, electrons can gain energy from an applied electric field before being scattered into the conduction band .

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