Concept:The intrinsic (I) layer in a PIN photodiode expands the depletion width \( W \), which increases the volume available for photon absorption and lowers junction capacitance (\( C = \epsilon A / W \)), enabling faster switching speeds.
Formula:$$W \approx W_I \implies C_j = \frac{\epsilon_s A}{W_I} \downarrow \quad \text{and} \quad \eta_{\text{absorption}} = 1 - e^{-\alpha W_I} \uparrow$$
Solution:- The thick intrinsic layer creates a wide depletion region under reverse bias.
- This larger volume absorbs a higher fraction of incident photons, increasing quantum efficiency.
- The wider depletion layer also reduces junction capacitance, lowering the \( R C \) time constant and enabling response speeds into the gigahertz range.
Why other options are incorrect:- Option A: The bandgap \( E_g \) remains an intrinsic material property and is not eliminated.
- Option B: PIN diodes operate capacitively and do not act as inductors.
- Option C: PIN photodiodes are optical sensors operated in reverse bias.
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