$($d$)(4$ pts$)$ Based upon the periodic table shown below $($from Group II to VI$),$ which

element$($s$)$ can be doped into Si to make it into an $n-$type semiconductor? Include all

possible doping elements from this table.

$($e$)(4$ pts$)$ Which of the two is more ductile, a $HCP$ metal or an $FCC$ metal? Give your

reasoning.

$($f$)(4$ pts$)$ Derive the twist angle $()$ during the torsion test in terms of elastic modulus and

the dimension of the specimen and the loading parameter.

nent

igle of twist