Simple Mathematical Models of High Energy Ion Beam Assisted Deposition Concentration Profiles in Binary Thin Films

Mathematical models of composed high energy ion beam assisted deposition (IBAD) concentration profiles of implanted component in binary thin films are described. Yields of the backscattered ions and sputtering of the deposited component are considered. A Gaussian probability density is assumed to apply to the ion range distribution. The construction of concentration profiles of various shapes is considered. These profiles should of course be constructed based on continuous changes of the process parameters, but certain technical problems can arise with this continuous parameter changes. Therefore, it has been assumed that the changes to the process parameters are discrete and proceed in several steps. The resulting mathematical models are combinations of error functions. Mathematical models can be used as regression functions for the determination of some parameters, e.g., the sputtering yield. Based on the mathematical model the gradient concentration profile of nitrogen in the SiN _x film was experimentally produced by the IBAD method, measured by Rutherford backscattering spectroscopy and compared with the mathematical model.