Quadratic Zeeman Effect of Donor Lines in Silicon and Germanium. I. Theory

Abstract

Calculation of the quadratic Zeeman shift of donor lines of silicon and germanium has been undertaken in the effective mass theory framework. The energies are obtained by the perturbation method up to second order and a very small interaction between two sublevels m = 1 and m = −1 is found theoretically. The Zeeman patterns (phosphorus in silicon) for different configurations show crossing or noncrossing of the levels and sublevels, depending upon the chosen configuration. The results predict that for germanium, the p0 lines exhibit a splitting due to the anisotropic shift of these lines for some configurations. This theory can also be used for shallow impurities wherever the electron effective mass possesses ellipsoidal symmetry.