Concept:The Law of Mass Action states that under thermal equilibrium, the product of electron and hole concentrations depends only on temperature and the semiconductor material, regardless of doping levels.
Formula:$$n \cdot p = n_i^2(T) = N_c N_v e^{-\frac{E_g}{k_B T}}$$
Solution:- Increasing the majority carrier concentration through doping leads to a proportional reduction in the minority carrier concentration via recombination.
- Consequently, the product \( n \cdot p \) remains constant at a given temperature and equals \( n_i^2 \).
Why other options are incorrect:- Option A: The Law of Mass Action applies at thermal equilibrium with zero applied bias.
- Option B: \( n \cdot p \) depends on \( n_i^2 \) rather than the sum of dopant densities.
- Option D: \( n \cdot p = n_i^2 > 0 \) at any non-zero absolute temperature.
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