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QPages 419-421: Q15: HC Verma: Concepts of Physics - Volume 2 Semiconductors and Semiconductor Devices Pages 419-421: Q15 Solution: A semiconducting material has a band gap of 1 eV. Acceptor…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often flip the inequality when converting the energy‑temperature criteria ($kT$ < threshold vs $kT$ > threshold) and thus label the wrong temperature regime as “forbidden” or “maximum population.” Always solve $kT = E_{crit}$ for $T$ first, then check whether the condition requires $T$ to be above or below that value before assigning the temperature range.

A semiconducting material has a band gap of 1 eV. Acceptor impurities are doped into it which create acceptor levels 1 meV above the valence band. Assume that the transition from one energy level to the other is almost forbidden if kTkT is less than 1/50 of the energy gap. Also if kTkT is more than twice the gap, the upper levels have maximum population. The temperature of the semiconductor is increased from 0 K. The concentration of the holes increases with temperature and after a certain temperature it becomes approximately constant. As the temperature is further increased, the hole concentration again starts increasing at a certain temperature. Find the order of the temperature range in which the hole concentration remains approximately constant. 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:** Temperature range: 20 K to 230 K. **Step-by-Step Explanation:** Given: Band gap = 1 eV, acceptor level = 1 meV above valence band. Condition 1: kT > (1/50) _ 1 eV = 0.02 eV _ T > 0.02/8.62 _ 10__ = 232 K (transition forbidden below this). Condition 2: kT < 2 _ 1 meV = 2 meV _ T < 0.002/8.62 _ 10__ = 23 K (maximum population above this). The constant range is between these: approximately 20 K to 230 K .

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