Numerical Calculation Of The Fermi Energy In Single-Doped And Co-doped Semiconductors

Fermi level is a very important physical parameter in material science. The energy level below E F is filled with electrons, but there is no electron to fill above the energy of E F at absolute zero. Under certain temperature, the statistical distribution of electrons on every quantum-state is determined by the locations of Fermi level. If we know the Fermi level, we can ascertain many important characters of materials. Fermi level is more important to semiconductor. There are many ways to calculate the Fermi level, but they are not accurate enough or not fit to all kinds of doping conditions semiconductors.In this article, the author tries to calculate Fermi level numerically at any request accuracy. According to the conditionn of electroneutrality, formula of electron's concetration and formula of hole's concentration, we deduce the general equation of electroneutrality when both donors and acceptors exist at the same time. Then we use Simpson procedure to evaluate the Fermi integral. Then we use the QBASIC language, adopt the segmentation method to solve the equation of electroneutrality with the help of computer, and figure out the Fermi energy. We draw the graphics about the relation of E F vis. T under different circumstances, and test the accuracy of the procedure. In the end, we discuss simply about the varied patterns of concentration and temperature of free carriers in co-doped semiconductors.