An InGaAs based PIN diode has to be designed for $1650$ nm with $1$ GHz bandwidth and $1$ A$/$W responsivity. Given absorption coefficient $=1105$ m$1,$ drift velocity $=105$ m$/$s$,$ anti$-$reflection coating at the surfaces and $=1,$r $=10,$ series resistance R $=1.$ Find the following $($a$)$ Quantum efficiency $($b$)$ Length of the intrinsic region $($c$)$ Transit time $($d$)$ Cross sectional area of PIN diode