Fermi Level vs. Carrier Concentration and
Doping of Donor and Acceptor Impurities


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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:
    1. 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.
    2. 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)].
    3. 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.
    4. Miscellaneous:


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    Copyright (c) C.R.Wie, SUNY-Buffalo, 1996-1997