Unless otherwise indicated, all devices are double$-$gate silicon at $T=300k.$

$10\mathrm{.}1$ An N$-$channel silicon JFET has a gate doping of $5{10}^{18}c{m}^{-3},$ a channel doping of ${10}^{17}c{m}^{-3},$ and width $a=0\mathrm{.}2m.$ Determine:

a$)$ the pinchoff voltage.

b$)$ the gate bias required to make the width of the undepleted channel equal to $0\mathrm{.}15m$ at $V_D=0.$