Approximate graphical method of solving Fermi level and majority carrier density of semiconductors with multiple donors and multiple acceptors

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Abstract

We present a generic approximate graphical method for determining the equilibrium Fermi level and majority carrier density of a semiconductor with multiple donors and multiple acceptors compensating each other. Simple and easy-to-follow procedures of the graphical method are described. By graphically plotting two wrapping step functions facing each other, one for the positive hole-ionized donor and one for the negative electron-ionized acceptor, we have the crossing point that renders the Fermi level and majority carrier density. Using the graphical method, new equations are derived, such as the carrier compensation proportional to NA/ND, not the widely quoted NA - ND. Visual insight is offered to view not only the result of graphic determination of Fermi level and majority carrier density but also the dominant and critical pair of donors and acceptors in compensation. The graphical method presented in this work will help to guide the design, adjustment, and improvement of the multiply doped semiconductors. Comparison of this approximate graphical method with previous work on compensation, and with some experimental results, is made. Future work in the field is proposed.

Original languageEnglish (US)
Article number062001
JournalJournal of Semiconductors
Volume32
Issue number6
DOIs
StatePublished - Jun 2011

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Electrical and Electronic Engineering
  • Materials Chemistry

Keywords

  • Doping
  • Fermi level
  • carrier density
  • compensation
  • graphical method
  • ionization

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