GATE EC 2024 Set 1 — Question 22
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Electronic Devices → Semiconductor Physics → Temperature Dependence
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Question
For non-degenerately doped n-type silicon, which one of the following plots represents the temperature () dependence of free electron concentration ()?
Correct answer
(A) [figure]
Solution
The temperature dependence of the free electron concentration in a non-degenerately doped n-type semiconductor is characterized by three distinct physical regimes when plotted as vs :
1.Intrinsic Region (High , low ): At high temperatures, the intrinsic carrier concentration dominates over the donor concentration . Since , increases linearly as decreases (moving left on the x-axis).
2.Extrinsic or Saturation Region (Moderate ): In this range, all donor atoms are ionized (), but the temperature is not high enough for to be significant. This results in a constant carrier concentration, appearing as a plateau.
3.Freeze-out Region (Low , high ): At very low temperatures, thermal energy is insufficient to ionize the donors, and electrons 'freeze out' into the donor states. Here , which appears as a linear decrease in as increases (moving right on the x-axis).
Only plot (A) correctly captures all three of these regimes.Continue learning with Success Tracker
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