Question # $2/6$ Biased Schottky Diode $(10$ points$)$

A Schottky barrier is formed between a metal having ${}_m=4\mathrm{.}4V$ and a N $-$type $)$ semiconductor. The doping is such that $E_c-E_{Fs}=0\mathrm{.}2eV.$ The bandgap is $E_g=1\mathrm{.}1eV$ at room temperature.

a$)$ Draw the equilibrium band diagram including the local vacuum level, showing a numerical value for $q{V}_0$ the builtin potential. Give the direction of the diode symbol.

b$)$ Draw the band diagram with $0\mathrm{.}2$ V forward bias and $-0\mathrm{.}5$ V reverse bias. Show the depletion charges in the semiconductor and the metal charge.