Verified Solution • 2025–26 Session moderate

QPages 419-421: Q13: HC Verma: Concepts of Physics - Volume 2 Semiconductors and Semiconductor Devices Pages 419-421: Q13 Solution: The product of the hole concentration and the conduction…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often write the relation as $n p = n_i$ instead of the correct $n p = n_i^{2}$, forgetting that the intrinsic carrier concentration must be squared. Always substitute $p = n_i^{2}/n$ when using the mass‑action law to avoid orders‑of‑magnitude errors.

The product of the hole concentration and the conduction electron concentration turns out to be independent of the amount of any impurity doped. The concentration of conduction electrons in germanium is 6×10196 \times 10^{19} per cubic metre. When some phosphorus impurity is doped into a germanium sample, the concentration of conduction electrons increases to 2×10232 \times 10^{23} per cubic metre. Find the concentration of the holes in the doped germanium.

Step-by-Step Verified Solution

**Answer:** Hole concentration = 1.8 _ 10__ per m_. **Step-by-Step Explanation:** Given: Intrinsic carrier concentration n_i = 6 _ 10__ per m_. After doping, n_e = 2 _ 10__ per m_. Using mass action law: n_e _ n_h = n_i_. n_h = (6 _ 10__)_/(2 _ 10__) = 3.6 _ 10__/(2 _ 10__) = 1.8 _ 10__ per m_. Standard answer: 1.8 _ 10__ (using different n_i).

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