Q$.5$

$($a$)$ If a metal with a work function of $4\mathrm{.}65$ eV is deposited on a $\backslash ($ p $\backslash )-$type semiconductor with a work function of $4\mathrm{.}85$ eV $,$ and electron affinity of the semiconductor is $4\mathrm{.}05$ eV $,$ determine and explain briefly whether this junction is a Schottky barrier or an ohmic contact. If this junction is used in a FET, does it have a linear $\backslash ($ I$-$V $\backslash )$ characteristic in both biasing directions?$(4$ marks$)$

$($b$)$ Assuming that the bandgap of the semiconductor in part $($a$)$ is $1\mathrm{.}1$ eV $,$ draw the energy diagram of the metal$-$semiconductor contact in part $($a$).$ Please include the numerical value of the built$-$in voltage and barrier height on the diagram. What are the main merit and limitation of a Schottky barrier diode compared to a $\backslash ($ p$-$n $\backslash )$ junction diode? Explain your answer.