$($b$)$ An engineer uses a step$-$and$-$repeat aligner printing system to fabricate a patterned image with a minimum linewidth of $\backslash (0\mathrm{.}5\backslash$mu $\backslash$mathrm$\{$~m$\}\backslash ).$ The exposure source is a mercury arc lamp with a wavelength of $436$ nm $.$

$($i$)$ Calculate the numerical aperture $($NA$)$ value of the lens and the depth of focus $($DOF$)$ of the image. Assume the process dependent factor, $\backslash ($ k$\_\{1\}=0\mathrm{.}9\backslash )$ and $\backslash ($ k$\_\{2\}=\backslash )0\mathrm{.}75.$

$($ii$)$ Describe how would the resolution and DOF be affected if the exposure source is replaced by an excimer laser.

$($iii$)$ State three optical enhancement techniques that the engineer can adopt to further improve the resolution of the image.

$(10$ Marks$)$

$($c$)$ A lift$-$off process is a common technique that is used to create metal patterns on a silicon wafer. Explain with the aid of a diagram the steps involved in a lift$-$off process.