ESR Spectra of the Triplet and Singlet States of a Zn-P Two-Spin System in Si: Mathematical Modeling and Computer Simulation

摘要

A computer simulation of the ESR spectra of a Zn-P two-spin system in Si is carried out, involving solving the quantum Liouville equation supplemented with a semiempirical relaxation operator (represented by a tensor of order 4). The mathematical model employed enables one to compute ESR spectra for continuous-absorption conditions as the paramagnetic-center density is increased. Two conclusions are drawn from a comparison of the simulated spectra and previously measured ones: (i) For a model of ESR spectra to be accurate it must include both the dipole-dipole interaction between the magnetic moments and isotropic and anisotropic (vector) exchange interactions. (ii) The interaction constants are comparable with one another and so cannot be neglected. The cases are covered of a triplet and a singlet state of the ion pair, the parameter values being the same; in the latter case, the system includes a spin-0 and a spin-1/2 nucleus with two valence electrons interacting by the dipole and exchange mechanisms. Satellite lines resulting from the interactions are observed in the simulated spectrum for an extremely small natural line width.