The question asks to evaluate two statements, Assertion A and Reason R, regarding a $p^+-n$ junction and choose the correct option.

Assertion A Analysis: Depletion Width in $p^+-n$ Junction

In a semiconductor junction, the depletion width on each side ($W_n$ for n-side, $W_p$ for p-side) is inversely related to the square root of the doping concentration on that side, assuming the built-in potential and permittivity are constant. Specifically:

• $W_n \propto \sqrt{\frac{N_A}{N_D(N_A + N_D)}}$
• $W_p \propto \sqrt{\frac{N_D}{N_A(N_A + N_D)}}$

For a $p^+-n$ junction, the doping concentration on the p-side ($N_A$) is much greater than the doping concentration on the n-side ($N_D$), i.e., $N_A \gg N_D$. This implies:

• $\frac{W_n}{W_p} = \sqrt{\frac{N_A}{N_D}} \gg 1$

Therefore, $W_n > W_p$. The depletion width is indeed larger on the n-side (less doped) compared to the p-side (heavily doped). Assertion A is correct.

Reason R Analysis: Doping Concentration Effect

The depletion width ($W$) of a $p-n$ junction is given by $W = W_n + W_p$. The expressions for $W_n$ and $W_p$ show an inverse relationship with the doping concentrations ($N_D$ and $N_A$). For instance, $W_n \approx \sqrt{\frac{2 \epsilon_s (V_{bi} - V)}{q N_D}}$ and $W_p \approx \sqrt{\frac{2 \epsilon_s (V_{bi} - V)}{q N_A}}$ (under certain approximations). If the doping concentration on either side increases, the corresponding depletion width decreases. Thus, as doping concentration increases, the depletion width reduces. Reason R is correct.

Relationship between Assertion A and Reason R

Assertion A states that the depletion width is larger on the n-side than the p-side in a $p^+-n$ junction. This is because the n-side is lightly doped ($N_D$) while the p-side is heavily doped ($N_A \gg N_D$). Reason R explains the general principle that higher doping concentration leads to a reduced depletion width. Since the p-side is heavily doped, its depletion width is smaller, and conversely, the lightly doped n-side has a larger depletion width. Therefore, Reason R correctly explains why Assertion A is true. R is the correct explanation of A.

Conclusion

Both Assertion A and Reason R are correct statements, and Reason R provides the correct explanation for Assertion A.