Dielectric functions of molecular-beam-epitaxy-grown $Ga1−xMnxAs$ thin films

We have measured the dielectric functions of a series of molecular-beam-epitaxy-grown $Ga1−xMnxAs$ thin films directly deposited on GaAs (100) substrates. Initially, x-ray diffraction experiments were employed to determine the alloy compositions of these samples. A rotating analyzer spectroscopic ellipsometer was used subsequently to measure the complex reflection ratio for each of the films in the energy range between 0.9 and $6.5eV$⁠. By modeling the ellipsometric data in the transparent region, we were able to determine the film thickness precisely. Extending the analysis into the absorption region, we were able to identify the dielectric functions for each of the $Ga1−xMnxAs$ samples in the energy region of our measurement. All of the dielectric functions displayed the critical point structures related to the higher-order electronic transitions. To determine the characteristics associated with the higher-order electronic transitions, we fit the dielectric functions with a model that incorporates the energy band structure near critical points as well as discrete and continuum exciton states associated with each critical point. This enabled us to determine that both $E1$ and $E1+Δ1$ critical points blueshift slightly in the $Ga1−xMnxAs$ alloy system as Mn is incorporated into the lattice.