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NaN089
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Homework Statement
a. The densities of electrons and holes required for the Fermi levels in
both the p- and n-type Ge to enter the bands. That is, in n-type Ge the Fermi
level coincides with the bottom of the conduction band and for p-type Ge the
Fermi level coincides with the top of the valence band. [[I know how to do this but I have given this question so that question (b) is comprehensible.]]
b. Hence calculate the fraction of ionised dopants and the total density of
dopants required for (a) above.
c. For the situation depicted in Esaki’s figure 2 below calculate the
densities of electrons and holes on either side of the junction as well as the
total densities of dopants.
d. Estimate the width of the depletion region and compare your
calculation with Esaki’s estimate
Homework Equations
for a:
n(Ec)= Nc.e^(-((Ec-Ef))/(k.T))
p(Ev)= Nv.e^(-((Ef-Ev))/(k.T))
for b:
N+D = (ND)/(1+ gD*exp((Ef-ED)/(k.T))
N-A = (NA)/(1+ gA*exp((EA-Ef)/(k.T))
The Attempt at a Solution
for a:
Putting Ec-Ef= 0, we get nc=Nc and the similar for holes.
for b:
I have used the equations for N+D and N+A to find the dopants, but I do not know how to find the fraction of them. Next, the density is found for the condition Ec-Ef= 0.
for c:
I believe that we need the Fermi energy to find the solutions.
Ef==KT*ln{[(1/4)*[e^(Ed/KT)]*([(1+(8Nd/Nc)e^(deltaEd/KT))^(1/2)]-1)}
Is this the correct formula to find the Fermi energy?
Thanks