Physics Q45 – JEE-MAIN 2026

Home Physics SemiconductorsQuestion #464

In a semiconductor p-n diode, the doping concentrations on p-side and n-side are

10^{15}

atoms/cm

^{3}

and

10^{18}

atoms/cm

^{3}

, respectively. Which one of the following statements is true?

Clue 1 of 3: Depletion Region Formation

The depletion region forms due to the diffusion of charge carriers across the p-n junction, creating an electric field and uncovering immobile ionized impurity atoms.

🧠 Full Solution Path

Step 1: Relate Depletion Width to Doping Concentration✦ Active

In a p-n junction, the total charge on the p-side of the depletion region must be equal in magnitude to the total charge on the n-side to maintain charge neutrality. This implies that the product of doping concentration and depletion width on each side is equal:

N_{A} W_{p} = N_{D} W_{n}

where $N_{A}$ is the acceptor concentration on the p-side, $N_{D}$ is the donor concentration on the n-side, $W_{p}$ is the depletion width on the p-side, and $W_{n}$ is the depletion width on the n-side.

Step 2: Apply Given Doping Concentrations○ Expand

Given doping concentrations are $N_{A} = 10^{15}$ atoms/cm $^{3}$ (p-side) and $N_{D} = 10^{18}$ atoms/cm $^{3}$ (n-side). From the relationship derived in Step 1, we can find the ratio of the depletion widths:

\frac{W_{p}}{W_{n}} = \frac{N_{D}}{N_{A}} = \frac{10^{18}}{10^{15}} = 10^{3}

💡 Teacher's Secret Hint

Remember that the depletion region extends more into the lightly doped side.

Step 3: Determine Relative Widths and Select Correct Statement○ Expand

The ratio $\frac{W_{p}}{W_{n}} = 1000$ indicates that $W_{p} = 1000 \times W_{n}$ . This means the depletion region width on the p-side ( $W_{p}$ ) is significantly larger than that on the n-side ( $W_{n}$ ). The p-side is lightly doped ( $10^{15}$ ), and the n-side is heavily doped ( $10^{18}$ ). Therefore, the depletion region extends more into the lightly doped p-side.

Comparing this conclusion with the given options:

Option 1: Incorrect, widths are unequal.

Option 2: Correct, the depletion region width is more on the p-side compared to that in the n-side.

Option 3: Incorrect.

Option 4: Incorrect, a depletion region always forms in a p-n junction regardless of doping concentration equality.

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Physics Question 45 – JEE-MAIN 2026

Clue 1 of 3: Depletion Region Formation

🧠 Full Solution Path