ENERGY LEVELS OF DONOR INPURITIES IN THE PRESENCE OF A MAGNETIC FIELD

JOSE JESUS RODRIGUEZ NUNEZ, Purdue University

Abstract

This work is devoted to the calculation of energy levels of donor impurities in the presence of an uniform external magnetic field. We use a variational technique. We have studied the lowest energy levels 1S, 2S, 2P('0), 2P('+), 2P('-). Every state is represented by a wave function which has two variational parameters. Our method makes use of the Effective Mass Equation (E.M.E.) since the central cell corrections appear to be negligible as shown experimentally. Theoretically, the fact that the core region is small and the wave function spread causes a small correction to the binding energy. For the states 1S, 2P('0), 2P('+), 2P('-) we have been able, after taking partial derivatives with respect to the two variational parameters, to express one variational parameter in terms of the other. This reduces the number of variational parameters from two to one. Next, we searched for the minimum of the energy by simple plotting. However, the state 2S does not allow this simplification, since we must also require that the states 1S and 2S be orthogonal. This is done by adding an extra parameter, A, which is a function of four parameters; two of these belong to the 1S state and the other two to the 2S state. The additional parameter A contributes terms proportional to A and A('2) to the energy of the 2S state. Because of this, we minimize numerically in two dimensions. We give numerical results for several values of the coupling constant. Next, we have extended our method to the case of three variational parameters for the low-lying energy levels. We derive expressions for the energy and give numerical results for the ground state as function of magnetic field. Finally, we compared our results with other relevant theoretical work in the literature.

Degree

Ph.D.

Subject Area

Condensation

COinS