  Muonium (Mu), a pseudo-isotope atom of hydrogen with a positively charged
muon at the place of the proton, can form in a wide range of semiconductor
materials. They can appear in different states, depending on their charge state
and microscopic site within a crystal lattice. After the Mu formation, they
undergo interactions with free charge carriers, electronic spins, and other Mu
sites, and form a dynamic network of state exchange. We identified the model of
Mu dynamics in n-type Gallium Arsenide using the density matrix simulation and
photoexcited muon spin spectroscopy technique. Fitting to the dark and
illuminated $\mu$SR data provided transition rates between Mu states, which in
turn showed the underlying mechanism of the $\mu$SR time spectra. Deduced
capture/scattering cross sections of the Mu states reflected the microscopic
dynamics of Mu. Illumination studies enable us to measure interactions between
Mu and generated minority carriers, which are unavailable in dark measurements.
The methodology we developed in this study can be applied to other
semiconductor systems for a deeper microscopic understanding of the Mu state
exchange dynamics.
