$.$ A CMOS technology is developed on a twin$-$well process. The p$-$on p$+$ substrate is used. The $n-$well has dopant concentration $Nd=1E\frac{16}{c}m3$ and the $p-$well has dopant concentration $Na=4E\frac{16}{c}m3.$ The $N+$ Polysilicon gates are used for N and $P-$channel MOSFETs respectively. The gate oxide is $100$ A thick with positive oxide charge Qox $=1E\frac{12}{c}m2$ located at the center of the gate oxide.

a$)$ Determine the energy band bending diagram of MOS capacitor of $n-$MOSFET, i$.$e$.$ channel region of $n-$MOSFET at thermal equilibrium condition.

b$)$ Determine the Vt for $n-$and $p-$MOSFETs respectively

c$)$ Is NMOSFET a depletion mode or enhancement mode device?

d$)$ Is PMOSFET a depletion mode or enhancement mode device?

e$)$ Recommend a device design solution to have both N$-$and P$-$MOSFET function as enhancement mode device. Discuss what effects your solution might have on device performance. What will new Vt be for both N $-$ and P $-$ MOSFET?