Q70 / 75 · JEE Main 2026 (05 April Shift 2) · Physics
In a semiconductor p-n diode, the doping concentrations on p-side and n-side are $10^{15}\text{ atoms/cm}^3$ and $10^{18}\text{ atoms/cm}^3$, respectively. Which one of the following statements is true ?
- AWidths of depletion region on either side of the interface are equal
- Correct answerBThe depletion region width is more on p-side compared to that in n-side
- CThe depletion region width is more on n-side compared to that in p-side
- DNo depletion region forms because of unequal doping concentrations on p and n-sides
Solution
In a p-n junction diode, the total charge on both sides of the depletion region must be equal to maintain charge neutrality.
Let $x_p$ and $x_n$ be the widths of the depletion region on the p-side and n-side, respectively. Let $N_A$ and $N_D$ be the doping concentrations on the p-side and n-side.
The charge neutrality condition is given by:
$N_A x_p = N_D x_n$
Given $N_A = 10^{15} \text{ atoms/cm}^3$ and $N_D = 10^{18} \text{ atoms/cm}^3$.
Substituting the values, we get:
$10^{15} x_p = 10^{18} x_n$
$x_p = 10^3 x_n$
Since $x_p > x_n$, the depletion region penetrates more into the lightly doped side. Therefore, the depletion region width is more on the p-side compared to that in the n-side.
Answer: The depletion region width is more on p-side compared to that in n-side
Let $x_p$ and $x_n$ be the widths of the depletion region on the p-side and n-side, respectively. Let $N_A$ and $N_D$ be the doping concentrations on the p-side and n-side.
The charge neutrality condition is given by:
$N_A x_p = N_D x_n$
Given $N_A = 10^{15} \text{ atoms/cm}^3$ and $N_D = 10^{18} \text{ atoms/cm}^3$.
Substituting the values, we get:
$10^{15} x_p = 10^{18} x_n$
$x_p = 10^3 x_n$
Since $x_p > x_n$, the depletion region penetrates more into the lightly doped side. Therefore, the depletion region width is more on the p-side compared to that in the n-side.
Answer: The depletion region width is more on p-side compared to that in n-side
Hence, the correct answer is option: 'B'.