Concept:In the extrinsic exhaustion temperature range, all donor impurity atoms are fully ionized (\( N_D^+ \)), while intrinsic thermal generation across the bandgap remains negligible compared to \( N_D \), keeping majority carrier concentration constant at \( n \approx N_D \).
Formula:$$n(T) \approx N_D = \text{constant} \quad (\text{for } T_{\text{freeze-out}} < T < T_{\text{intrinsic}})$$
Solution:- Above freeze-out (\( \sim 100\text{ K} \)), thermal energy ionizes all donor impurity states.
- Below the intrinsic transition temperature (\( \sim 450\text{ K} \)), intrinsic carrier generation is negligible compared to \( N_D \).
- Throughout this exhaustion range, the electron concentration remains constant at \( n \approx N_D \).
Why other options are incorrect:- Option A: Exponential carrier increase occurs in the high-temperature intrinsic range (\( T > 500\text{ K} \)).
- Option B: Carrier concentration drops toward zero only at deep cryogenic temperatures (carrier freeze-out near 0 K).
- Option C: Carrier concentrations vary monotonically with temperature, not periodically.
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