Assertion A Analysis: Photodetector Depletion Region

Assertion A states that a large depletion region width (W) is desired in a photodetector.

• Purpose: Maximizing photon absorption within the depletion region is crucial.
• Mechanism: Electron-hole pairs generated by absorbed photons are efficiently separated by the electric field in the depletion region. Absorption in neutral regions yields fewer useful carriers.
• Verdict: Assertion A is correct.

Reason R Analysis: Depletion Width and Junction Capacitance

Reason R states that a wider depletion region width (W) leads to small junction capacitance.

• Capacitance Formula: The junction capacitance ($C_J$) is related to the depletion width ($W$) by the approximate relation $C_J \propto \frac{\epsilon A}{W}$, where $\epsilon$ is the permittivity and $A$ is the junction area.
• Relationship: As $W$ increases, $C_J$ decreases.
• Verdict: Reason R is correct.

Evaluating the Connection

Both Assertion A and Reason R are independently correct statements:

• Assertion A highlights the benefit of a wide depletion region for photon absorption.
• Reason R explains that wider depletion regions lead to lower junction capacitance, which benefits detector speed.
• However, the primary goal stated in A (efficient photon absorption) is achieved by having a wide depletion region, not *because* the capacitance is reduced. Lower capacitance is a related physical characteristic, but not the direct explanation for why absorption efficiency necessitates a large $W$.

Conclusion

Since both statements are true but Reason R does not explain the primary reason behind Assertion A, the correct option is that both are correct, but R is not the correct explanation for A.