Hydrogenated silicon nitride films of 100-300 nm in thickness were prepared on GaAs and Si wafers by plasma enhanced chemical vapor deposition. The number of Si and N atoms in the film was measured by Rutherford backscattering. The number of H atoms was determined by an energy recoil detection (ERD) technique. A zero dose extrapolation method was employed to eliminate the effect of undesirable decrease in ERD count during ion-beam irradiation. The atomic density was determined by dividing the number of atoms by the film thickness obtained from ellipsometry. Infrared absorption cross sections of the Si-H and N-H bonds were obtained by using a correlation curve between IR band areas and the number of hydrogen atoms from ERD. The density of chemical bonds such as Si-Si, Si-N, Si-H and N-H was obtained by equating the atomic density with the absorption cross-section of the bonds. Investigation of the refractive index of films with different chemical structures suggests that a concept of the bond refraction can explain a relatively high refractive index (1.8-2.3) and low density (2.1-2.7 g/cm-3) of the Si-rich silicon nitride films, as compared with a stoichiometric compound Si3N4. The etch rate of the silicon nitride film in buffered oxide etchant solution showed a linear relation against the density of silicon atoms that were not bonded to hydrogen.