Abstract: In this work we present a generic approximate graphic 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 graphic method are described. By graphically plotting two wrapping step functions facing each other, one for the positive hole-acceptor and one for the negative electron-acceptor, we have the crossing point that renders the Fermi level and majority carrier density. Using the graphic 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 graphic method presented in the work will help guide the design, adjustment, and improvement of the multiply doped semiconductors. Comparison of this approximate graphic method with previous work on compensation, and with some experimental results is made. Future work in the field is proposed.

Key words: Multiple Donors, Multiple Acceptors, Majority Carrier Density, Fermi Level, Graphic Method