Muonium reaction in semiconductors and insulators: The role of the transition state

A general scheme for the reaction of muonium with the host lattice of semiconductors and insulators is derived. We begin our considerations when the muonium has been slowed down to a kinetic energy of one to a few eV, an energy at which electron excitations across the band gap are no longer possible and the subsequent deceleration is due to elastic or inelastic processes. Elastic scattering causes energy loss in small portions, on the order of 1 parts per thousand of kinetic energy per scattering, and eventually leads to atomic muonium at an interstitial site. At these low energies, however, the muonium may stay at one site long enough, especially at the top of the diffusion barrier, to excite a local vibration of the nearest lattice atoms, e.g., a stretching or breathing mode, leading to the stopping of muonium. The configuration formed after the excitation of the local phonon is designated "transition state". This state may exist for some time and may be seen in mu SR as a fast relaxing diamagnetic signal. The decay of the transition state may lead either to interstitial atomic muonium or to a bound configuration in the neutral or positive charge state. In the present paper we apply this model to Al2O3 and to a Ge-rich SiGe alloy.