You are a research engineer at a start$-$up company focused on commercializing ultrasensitive silicon nanoscale field$-$effect transistors $($NanoFETs$)$ for ion sensing in cells and tissue. Knowing that yourNanoFET devices utilize n$-$type silicon nanowires that show a $500$ k$$ electrical resistance and ohmic metal$-$semiconductor contacts $($i$.$e$.,$ no electronic energy barrier at the metal$-$semiconductor interface$),$ complete the following.

$($a$)$ You have engineered NanoFETs sensitive to pH by chemically modifying the silicon surface with amine groups that have an isoelectric point of $6\mathrm{.}8($i$.$e$.,$ the pH when the surface is neutral$).$ Knowing that each $$pH $=1$ the NanoFETs show a $2\%$ change in the

nanowire$$s electrical resistance, plot out $($using MATLAB or another plotting program you are familiar with$)$ a representative current vs time trace as one of your NanoFET devices moves from outside a cell $($pH $=6\mathrm{.}8)$ to inside a cell $($pH $=4\mathrm{.}8)$ and then back to outside over a $10$ s measurement time. Assume that the source$-$drain voltage is held

constant at $1$ V$.$

You have now engineered NanoFETs $($unmodified silicon surface$)$ capable of detecting individual viral nanoparticles. Knowing that the surface of viral nanoparticles is predominantly capped by lysine groups $($isoelectric point $=9\mathrm{.}74),$ plot $($using MATLAB or another plotting program you are familiar with$)$ a representative current vs time trace for viral nanoparticles binding to the surface of the NanoFET in two different solutions $($one at a pH of $6\mathrm{.}8,$ the other at $10\mathrm{.}2).$ Assume $($i$)$ that at pH $6\mathrm{.}8$ and $10\mathrm{.}2$ a single viral nanoparticle causes an $8\%$ and $2\%$ change, respectively, in the nanowire$$s electrical resistance when bound to the nanowire surface, $($ii$)$ the source$-$drain voltage is held

constant at $1$ V$,$ and $($iii$)$ the NanoFET detects $3$ binding events cumulatively over a $10$ second sampling time at each pH$.[$Note: you will be generating $2$ different current vs time traces, one for each pH; they can both be plotted on the same graph.$]$