Numerical estimates of metal atom energy in reactive sputter deposition of TiN and TaN thin films

In this study, a model was proposed for the energy transfer from the sputtered Ti and Ta atoms to the background gases in Ar and N2 mixtures. For elastic collisions, an energy-dependent Lennard-Jones radius was used. For inelastic collisions, the excitation cross sections for heavy Ti and Ta atoms were based on the scaling of the corresponding electron impact cross sections. Under typical low pressure sputtering conditions, the average energy and the energy distribution of the Ti and Ta atoms were calculated with the collision number. The calculated average energy and mean free path of the Ti and Ta atoms leaving the target are over 20 eV and 12 cm, respectively. The metal atoms reach equilibrium with the background gas at about 2 to 3 times the thermal speed. The elastic energy transfer dominates over the inelastic transfer and the model could be simplified to elastic only.