JEE Mains 2026 APR 5th Shift 2 Q45 p n Junction Depletion Region Option 2 #jeemain2026

[00:00:00]JEE Mains, 5th April 2026 shift 2.

[00:00:03]Question 45.

[00:00:06]This question deals with a PN junction diode with unequal doping concentrations.

[00:00:10]Here is a PN junction.

[00:00:12]The P side is lightly doped with 10 to the power 15 atoms per cm³ and the N side is heavily doped with 10 to the power 18 atoms per cm³. Notice how the depletion region extends much more into the lightly doped P side.

[00:00:27]Here is the full question. In a semiconductor PN diode, the doping concentration on the P side is 10 to the 15 atoms per cm³ and on the N side is 10 to the 18 atoms per cm³. Which statement is true?

[00:00:40]Option one, depletion widths on either side are equal.

[00:00:44]Option two, depletion width is more on the P side.

[00:00:47]Option three, depletion width is more on the N side. Option four, no depletion region forms.

[00:00:54]The key concept is charge neutrality in the depletion region.

[00:00:58]At the PN junction, the total charge exposed on the P side must equal the total charge on the N side. This gives us the condition NA * XP = ND * XN, where XP and XN are the depletion widths on the P and N sides, respectively. The depletion region always extends more into the lightly doped side.

[00:01:18]Step one. Apply the charge neutrality condition. NA * XP = ND * XN.

[00:01:24]Substituting 10 to the 15 * XP = 10 to the 18 * XN.

[00:01:29]Step two.

[00:01:31]Solving XP = 10 to the 18 / 10 to the 15 * XN, that is XP = 1,000 * XN.

[00:01:39]The depletion width on the P side is a thousand times wider than on the N side.

[00:01:44]The correct answer is option two. The depletion region width is more on the P side compared to the N side.

[00:01:50]G tip, in a PN junction, always [clears throat] remember the depletion region extends more into the lightly doped side. This comes directly from the charge neutrality condition.

[00:02:00]Also, higher doping means thinner depletion width on that side. This is a frequently asked concept in JEE semiconductors.

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