A Si p$-$n junction $($A $=6$ x $10-5$ cm$2)$ has following properties at $300$ K$.$ For Si$,$ ni $=1$E$10$ cm$-3$;

$[$Assume kBT $=0\mathrm{.}026$ eV$]$

a$)$ What is the built$-$in voltage, Vbi, of the junction? $(2$ points$)$

b$)$ What will be the energy barrier height $($absolute value, in eV$)$ in the p$-$n junction when

$($i$)0\mathrm{.}5$ V forward bias is applied? $(1$ point$)$

$($ii$)0\mathrm{.}5$ V reversed bias is applied $?(1$ point$)$

c$)$ Find the Diffusion lengths of the minority carriers for both p$-$ and n$-$side

$[$Hint: L $=$D$,$p $=$n $=10$s $(1+1=2$ point$)$

p side n side

Doping concentration: NA $=4$ x$1018$ cm$-3$ ND $=1014$ cm$-3$

Diffuson coeficient: Dn $=18\mathrm{.}7$ cm$2/$s Dp $=11\mathrm{.}7$ cm$2/$s

Mobility of charge carriers: $$p $=200$ cm$2/$V$.$s $$n $=1300$ cm$2/$V$.$s

$$n $=700$ cm$2/$V$.$s $$p $=450$ cm$2/$V$.$s