$1)$ When driving large capacitive loads, the best way to size an inverter chain used as a buffer is $($select the best answer$)$: $[$ Select $]["$Exponential sizing", "Quadratic sizing", "Linear sizing", "None of these is correct.", "Geometric sizing"$]$

$2)$ A unit inverter in a particular process has an input capacitance of $1$ fF and a propagation delay of $10$ ns$.$ It is necessary to size an inverter chain to drive a load of $10$ pF$.$ Assume gamma of $1.$

$($a$)$ What is the unbuffered $($ie$.$ one stage unit inverter$)$ delay to drive this load?

$($b$)$ What is the best delay of a two stage buffer and what is the sizing ratio?

$($c$)$ What is the best delay of a three stage buffer and what are the inverter sizes?

$($d$)$ What is the optimum delay possible, how many stages are necessary and what are the sizes of the inverters in the chain?