Q2.

N_(A)(x)=10^(14)+10^(18)e^(-10^(4)x)

, where

x

is measured in

cm

.\

j_(n)=q\\\\mu _(n)n(E+V_(T)(1)/(n)(deln)/(delx)), and ,j_(p)^(T)=q\\\\mu _(p)p(E-V_(T)(1)/(p)(delp)/(delx))

\ i. Using the relevant equation from the equations mentioned above, demonstrate that the material must have a nonzero internal electric field

E

.\ ii. What is the value of

E

at

x=0

and

x=5\\\\mu m

?\ (Hint: In thermal equilibrium, the total electron and total hole currents must each be zero.)

Q2. A 4- m-long block of p-type silicon has an acceptor doping profile given by NA(x)=1014+1018e104x, where x is measured in cm. jn=qnn(E+VTn1xn)andjpT=qpp(EVTp1xp) i. Using the relevant equation from the equations mentioned above, demonstrate that the material must have a nonzero internal electric field E. ii. What is the value of E at x=0 and x=5m ? (Hint: In thermal equilibrium, the total electron and total hole currents must each be zero.)