P$1.(20$ points$)$ An ideal MOS structure with di $($insulator $($SiO$2)$ thickness$)=4\mathrm{.}5$ nm exhibit Vi $($Voltage across insulator$)=0\mathrm{.}42$ V at $1$ V gate bias $($applied VG$).$ Calculate s $($semiconductor surface potential$),$ Qs $($charges in the semiconductors$),$ Es $($electric field in the semiconductor surface$),$ and Ei $($electric field in the insulator$).($Assume T $=300$K$,$ the dielectric constant of Semiconductor, s$,$ is $11\mathrm{.}70,0=8\mathrm{.}85$x$10-14$ F$/$cm$,$ sio$2=3\mathrm{.}90)$