GATE EC 2017 Set 2 — Question 39
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Electronic Devices → P-N Junction & Diodes → Junction Formation & Depletion
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Question
An abrupt junction (located at ) is uniformly doped on both and sides. The width of the depletion region is and the electric field variation in the -direction is . Which of the following figures represents the electric field profile near the junction?
Correct answer
(A) [figure]
Solution
For an abrupt junction, the charge density in the depletion region is constant on the -side (negative charge due to acceptor ions) and constant on the -side (positive charge due to donor ions).Poisson's equation relates the electric field to the charge density :
1.On the -side (from to ): The charge density (a constant negative value). Therefore, is constant and negative. This implies that the electric field decreases linearly as increases.
2.On the -side (from to ): The charge density (a constant positive value). Therefore, is constant and positive. This implies that the electric field increases linearly as increases.
The electric field is zero at the edges of the depletion region ( and ) and reaches its maximum magnitude at the metallurgical junction ().Combining these observations, the electric field profile across an abrupt junction is triangular, with the peak at and linearly decreasing to zero at the depletion region boundaries. The total width of the depletion region is .- Option (A) correctly depicts this triangular electric field profile, with the maximum field at and linearly decreasing to zero at the edges of the depletion region, which spans a width .
- Options (B) and (D) show rectangular profiles, which are incorrect for an abrupt junction.
- Option (C) shows an inverted triangular profile, which is also incorrect.
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