Q well, d$=20$nm$,$ n$=5*10^11$ cm$^-2,$ calculate fermi energy of this gas. sub$-$bands occupy$=?$

$2$D square metal crystal, a$=3$A$,1$ electron$/$unit cell. Area A$.$ DOS of these electrons $($per unit area, g$($E$)=$D$($E$)/$A$),$ Fermi Energy E$\_$F $($in eV relative to bottom of band$).$ Assume electrons free i$.$e m$*=$m