A simple graphical method for determining densities and energy levels of donors and acceptors in semiconductor from temperature dependence of majority carrier concentration

The purpose of this study is to propose a simple graphical method for accurately determining the densities and energy levels of donors and accepters with different energy levels in a semiconductor from the temperature dependence of majority carrier concentration n(T). For this purpose, a function S(T,E-ref) is defined as S(T, E-ref) = n(T) exp(E-ref/kT)/kT, where k is the Boltzmann constant and E-ref is a parameter which varies a peak temperature of S(T, E-ref). Since S(T, E-ref) has peaks corresponding to the energy levels of impurities which produce majority carriers, the density and energy level can be evaluated using each peak in the S(T, E-ref) curve. This method can be used to investigate how many kinds of impurities, which produce majority carriers, exist in a semiconductor. Moreover, the density of all impurities, which produce minority carriers, carl be determined,since we can simulate the dependence of S(T, E-ref) on this density.