Why do extrinsic semiconductors behave like intrinsic semiconductors at very high temperatures?
-
ADrive-in diffusion of dopants and carriers
-
BBand-to-band transition dominates over impurity ionization
-
CImpurity ionization dominates over band-to-band transition
-
DBand-to-band transition is balanced by impurity ionization
-
ETrapping of carriers prevents conduction
Answer
Correct Answer: Band-to-band transition dominates over impurity ionization
Explanation
Introduction / Context:Semiconductor classification (intrinsic vs extrinsic) depends on which mechanism supplies the majority of carriers. At moderate temperatures, doping dominates. At very high temperatures, intrinsic excitation across the band gap surpasses dopant contribution. This explains why extrinsic semiconductors appear intrinsic at high T.
Given Data / Assumptions:
- Extrinsic semiconductor initially doped with donors or acceptors.
- Temperature increase leads to thermal generation of electron–hole pairs.
- Band-to-band excitation increases exponentially with T.
Concept / Approach:The intrinsic carrier concentration ni grows rapidly with temperature (ni ∝ T^(3/2) exp(−Eg/2kT)). At high enough T, ni ≫ Nd (donors) or Na (acceptors). Thus, the conduction resembles that of intrinsic material regardless of initial doping.
Step-by-Step Solution:
Start: At low T, extrinsic carriers dominate, conductivity set by doping.As T rises, ni increases exponentially.When ni surpasses dopant density, intrinsic carriers dominate conduction.Thus, band-to-band transitions dominate over impurity ionization at very high T.Verification / Alternative check:
Silicon with Nd ≈ 10^15 cm−3: at ~600–700 K, ni ~ 10^15 cm−3, so extrinsic → intrinsic crossover happens.Why Other Options Are Wrong:
Impurity ionization dominates: true only at lower T, not at very high T.Drive-in diffusion: refers to fabrication process, irrelevant here.Balanced processes: misleading; intrinsic eventually dominates, not balance.Trapping: not the cause of intrinsic behavior.Common Pitfalls:
Forgetting the exponential dependence of ni; confusing freeze-out at low T with intrinsic dominance at high T.Final Answer:
Band-to-band transition dominates over impurity ionization