Concept:The Mass Action Law states that under thermal equilibrium, the product of the equilibrium electron concentration \( n \) and hole concentration \( p \) is constant for a given semiconductor at a fixed temperature, independent of dopant concentration.
Formula:$$n \cdot p = n_i^2 = N_c N_v \exp\left(-\frac{E_g}{k T}\right) = \text{constant} \quad (\text{at fixed } T)$$
Solution:- Adding donor impurities increases electron concentration \( n \), which increases the recombination rate and suppresses hole concentration \( p \).
- The product \( n \cdot p \) remains equal to \( n_i^2 \) at that temperature.
Why other options are incorrect:- Option B: The Mass Action Law applies to thermal equilibrium (zero applied voltage).
- Option C: Neither carrier concentration drops to zero due to continuous thermal generation.
- Option D: \( n_i^2 \) increases with temperature as \( T^3 e^{-E_g / kT} \); it is not inversely proportional.
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