We have deposited Si-nitride thin films by remote plasma-enhanced chemical-vapor deposition using different combinations of hydrogen and deuterium source gases. In one set of experiments, NH3 and SiH4 were injected downstream from a He plasma and the ratio of NH3 to SiH4 was adjusted so that deposited films contained IR-detectable bonded-H in SiN-H arrangements, but not in Si-H arrangements. Similar results were obtained using the same ND3 to SiD4 flow ratio; these films contained only SiN-D groups. However, films prepared from ND3 and SiH4 displayed both SiN-D and SiN-H groups in essentially equal concentrations establishing that H and D atoms bonded to N are derived from both source gases SiH (D) 4 and NH (D) 3, and further that inter-mixing of H and/or D atoms occurs at the growth surface. This reaction pathway is supported by additional studies in which films were grown from SD4 and ND3 with either i) He or ii) He/H2 mixtures being plasma excited. The films grown from the deuterated source gases without H2, displayed only SiN-D bands, whereas the films grown using the He/H2 mixture displayed both SiN-H and SiN-D bands. The total concentration of N-H and N-D bonds in the films grown from the He/H2 excitation was the same as the concentration of N-D, supporting the surface reaction model. In-situ mass spectrometry provides additional insights in the film deposition reactions.