We report the results of time-resolved and temperature-dependent stationary photoluminescence investigations of the defects responsible for emission in the visible spectral range in heavily silicon-doped Al x Ga1-xN layers grown by molecular beam epitaxy on sapphire substrates. The emission band was attributed to donor-acceptor transitions. The transitions were described using the one-dimensional configuration coordinate model taking into account the high-doping regime. An increase in Al content from 0.56 to 1 leads to an increase in the acceptor ionization energy from 1.4 to 1.87 eV. The value of the Franck-Condon shift is about 1 eV at x = 0.56-0.74 and decreases to 0.8 eV at x > 0.74. The changes in the donor-acceptor transition energy parameters with increasing silicon concentration are discussed.