Fermi Level vs. Carrier Concentration and
Doping of Donor and Acceptor Impurities
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A snapshot of the applet is:
All magenta-colored horizontal bars (i.e., Ef and scroller) may be mouse-dragged.
After becoming sufficiently familiar with the inter-relationship between
the Fermi level (Ef) and the electron (n) and hole (p) concentrations,
users may use the donor/acceptor impurity panels to learn how to use the
doping of impurities to control the carrier concentrations (n & p)
and thus the Fermi level.
Fermi level in a Semiconductor band gap:
This
applet shows a simple relationship of the Fermi level position in the
band gap and the carrier concentration in the bands. Answer the following
questions:
- Move up and down the Ef using the scrollbar.
Observe the changes in carrier concentrations n
and p. (If you click on the
"show parameter" button, you will see the numbers.) Ei
is very close to the midgap. Does this applet make it
clear that when Ef is closer to Ec
(ie, when Ef is
above Ei) than to Ev,
the material is n-type, and when Ef
is closer to Ev (ie, when Ef
is below Ei)
the material is p-type. Before using
this applet, did you have an immediate association between the relative
position Ef and the type of the material? Did
this applet help in anyway ? Make concrete comments.
- Record the values of Ef, n,
and p at a series of different Fermi level
positions. By plotting the data using computer or on a graph paper,
find the mathematical relationship between n and
Ef - Ei, and
between p and Ef -
Ei. [ie, report your procedure
and results for n = f(Ef
- Ei) and p =
g(Ef - Ei)].
- Display the donor and acceptor panels by clicking on the appropriate
buttons. This time, instead of moving Ef to
control n and p,
CHANGE THE DOPING LEVEL Na or Nd
and observe that Ef, n,
and p are controlled by Nd
and/or Na. This is what actually
happens in real semiconductors. Compensation: set Na
to a certain value like 2E17, and set Nd within
a factor of 10 of Na (ie, anywhere between
0.1Na and 10Na). Find the majority carrier concentration and verify
the carrier compensation (ie, n = Nd
- Na or p =
Na - Nd). Explain
physically why this happens.
- Miscellaneous:
- The 2nd question is to 'reverse engineer' or 're-engineer' your learning:
That is, first learn conceptually and
then develop mathematical (or physical) models based on the conceptual
understanding. Make some specific comments whether
and how this objective has been accomplished in this applet and how this
applet can be improved further toward this goal.
For this applet, make suggestions on how it can be improved to increase
the efficiency and quality of learning.
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Copyright (c) C.R.Wie, SUNY-Buffalo, 1996-1997