Intrinsic Semiconductor Conduction – Rankers Physics
Topic: Semiconductor Physics
Subtopic: Properties of Semiconductors

Intrinsic Semiconductor Conduction

Assertion (A): The probability of electrons to be found in the conduction band of an intrinsic semiconductor at a finite temperature decreases exponentially with increasing band gap.
Reason (R): It is more difficult for the electrons to jump to the conduction band from the valence band if the band gap between them is large.
 
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution:

Assertion (A) is true: The probability of finding electrons in the conduction band is proportional to \(e^{-E_g / (2kT)}\), decreasing exponentially with band gap \(E_g\).


Reason (R) is true: A larger band gap means more energy is required for electrons to jump. Reason (R) correctly explains Assertion (A).

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