We present a study on magnetotransport in films of the topological Dirac semimetal Cd$_{3}$As$_{2}$ doped with Sb grown by molecular beam epitaxy. In our weak antilocalization analysis, we find a significant enhancement of the spin-orbit scattering rate, indicating that Sb doping leads to a strong increase of the pristine band-inversion energy. We discuss possible origins of this large enhancement by comparing Sb-doped Cd$_{3}$As$_{2}$ with other compound semiconductors. Sb-doped Cd$_{3}$As$_{2}$ will be a suitable system for further investigations and functionalization of topological Dirac semimetals.
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