In heteroepitaxial GaAs grown on Si (GaAs/Si) there exist deep levels caused by various charged states of defects because of large lattice misfit and thermal expansion mismatch between GaAs and Si. The temperature-and excitation intensity-dependent near-infrared photoluminescence spectra related to the deep levels present in GaAs/Si grown by metal-organic chemical vapour deposition with different ratios of [As]/[Ga] were studied. In terms of configuration coordinate model, the Franck-Condon shifts of near-infrared emission in GaAs/Si were obtained by measuring the variation in full width at half-maximum with temperature. The band-gap shifts with temperature and with mismatch strain in GaAs/Si were considered. Taking Franck-Condon and band-gap shifts into account, the energy relations for the transitions from donor to acceptor, from conduction band to acceptor and from donor to valence band were revised. According to these transition-energy relations and the emission characteristics of GaAs/Si epilayers, three emissions were interpreted as the recombination luminescence of donor-acceptor pairs and two emissions were caused by As interstitial-Ga vacancy complex centres.