Review:%20Depletion%20Region%20Recombination

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Review Depletion Region Recombination

• Flat Quasi-Fermi Level (QFL)
• ? Requires rate limiting recombination is slow
  compared to thermal diffusion

Assuming knkp s v , Flat QFL ?We get for
recombination in the bulk at position x,
Note, Vapp lt 0 here
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Review Depletion Region Recombination
-Substitute definitions and
divide top and bottom by
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Review Depletion Region Recombination
Maximum occurs when n(x) p(x)
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New Material Recall we desire UTOTAL
Continue with Udr,max, recalling we want to solve
for UTOTAL, as
We need definition for n(x) and p(x)
You can show that
Nm concentration of e- for max
U, n(xm)p(xm) Xm position where nnm
In region 1, xltxm Exp (-) so n(x)ltn(xm) ?
More band bending In region 2, xgtxm Exp ()
so n(x)gtn(xm) ? Less band bending
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Calculating UTOTAL Back to Math
Substituting in for n(x) and p(x)
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Calculating UTOTAL
For normally doped Si with KnKp (assumed) UMAX
is strongly peaked away from W, so we can extend
the integral from W ? 8.
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Calculating UTOTAL
After a change of variables,
Recognizing that
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UTOTAL
Substituting for UMAX , we obtain
A 2 There are e- s and hs recombining. It
is as if you lose half of the voltage to the
other carrier.
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UTOTAL Everyone Does it Differently

• Note Nate and Mary quote a different value.

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Quasi-Neutral Region
Ionized donor atoms neutralized by injection of
electrons into CB.
p(x) has not changed before injection
of electrons, p(w)ltp(w) despite flat bands
Concentration gradient causing holes to diffuse
away from W into the bulk.
Need to understand Diffusion/Recombination/Generat
ion equations ? Assume No Generation
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Diffusion-Recombination
Diffusion
Putting it together
Need Boundary Conditions
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Diffusion-Recombination
Assume no recombination in D.R. or at S.S.
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Diffusion-Recombination
After the math
You tell me.
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Diffusion-Recombination
We only have p(x), so lets take region where
flux only due to holes at xW
Evaluate at xW
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Schockley-Read-Hall
Trapped states can be caused by metal
impurities, oxygen, or dopants
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Schockley-Read-Hall
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Schockley-Read-Hall
LLI Lower Level Injection of Electrons and
holes from photons
For n-type
HLI Generate more electrons and holes than We
had in our lattice
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Schockley-Read-Hall
Assuming LLI of n-type
Leaving us with
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Schockley-Read-Hall
Solving yields
For HLI, same assumptions
HLI decays twice as slowly
LLI Wait for hole carriers to recombine
HLI hole e- carriers must recombine ? twice
as long