$2.$ As shown in the figure below, the sacrificial layer is removed by undercutting through the access hole. The top structural layer is uniform with $\backslash (2\backslash$mu $\backslash$mathrm$\{$~m$\}\backslash )$ thick. The length of the sacrificial layer is $\backslash (100\backslash$mu $\backslash$mathrm$\{$~m$\}\backslash ).$ During the release, the structural layer is also exposed to the sacrificial etch. Assume that the sacrificial layer etch proceeds at a uniform rate $\backslash (\backslash$mathrm$\{$R$\}=1\backslash$mu $\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$min$\}\backslash ),$ and the etch has a selectivity of $\backslash (600$: $1\backslash ).$

$($a$)$ Calculate the time required to remove the sacrificial layer.

$($b$)$ Calculate the profile of the walls inside the channel.

$($c$)$ What is the final shape of the channel.

$($d$)$ What is the minimum and maximum thickness.