QUESTION $1[$TOTAL MARKS: $40]$ Answer $8$ parts Q $1($a$)[5$ Marks$]$ Explain how the depletion layer is formed in a pn$-$junction Q $1($b$)[5$ Marks$]$ The Hall Constant$/$Coefficient for a piece of n$-$type silicon is measured as $-4\mathrm{.}2$x$10-4$ C$-1$m$3,$ calculate the concentration of majority carriers in this sample. Q $1($c$)[5$ Marks$]$ A silicon sample is doped such that one atom per million in the sample following doping is phosphorous. If the density of silicon is $2\mathrm{.}33$ g$/$cm$3$ and it has an atomic mass of $28\mathrm{.}09$ g$/$mol$,$ calculate the number of free electrons per unit volume in the doped silicon. Comment on how this compares with a typical free electron density in a metal, such as copper. Q $1($d$)[5$ Marks$]$ If a sample of GaAs has an electron effective mass of $0\mathrm{.}067$ m$0,$ and a $1$ kV$/$cm electric field is applied to it$,$ calculate the drift velocity of the electrons if the collision time is $10-13$ s