$2.$ Current in a metal$/$semiconductor junction $(180$ pts$)-$ In lecture, we learn the saturation current $($Is$)$ in a metal$/$semiconduction junction is due to the electrons in the metal side moving to the semiconductor side and is expressed ash$34$emn$$kB$2$T$2$e$$kB$$Te$$Bn$.$ Let's work out this term now. $($a$)(40$pts$)$ The current from the semiconductor to the metal isq$$v$$n$,$ wherenis the electron density$($#$/$cm$3).$ Please show thatdn$$h$34$$(2$mn$)3/2$E$$EC$$e$($kB$$TE$$EC$+$e$$n$)$Use Boltzmann distribution instead of Fermi distribution.