Technological parameters of a MOS capacitor are given in table below, together with the values of the relevant physical parameters.

a$)$ Determine the value of the flat$-$band voltage.

b$)$ Calculate the charge density at the onset of strong inversion. Identify the type and origin of this charge.

c$)$ Calculate the value of the threstiold voltage.

d$)$ Calculate the charge density in the inversion layer at $\backslash (\backslash$mathrm$\{$V$\}\_\{\backslash$mathrm$\{$O$\}\}=5\backslash$mathrm$\{$~V$\}\backslash ).$

In CMOS $($complementary MOS$)$ integrated circuits, it is required to provide equal absolute values of the threshold vollages of MOS structures on P$-$type and N$-$type substrates. Determine the value of the donor concentration $\backslash ($ N$\_\{$D$\}\backslash ),$ necessary to provide an N $-$substrate MOS structure with the absolute value of the threshold voltage equal to the threshold voltage of the P $-$substrate MOS structure considered above. The values of all other parameters should remain the same.