Mathematical Modelling of Magnetron Sputtering Process During Thin Films Formation

The mathematical model is proposed, that allows to calculate formation of thin-film coatings at magnetron sputtering of materials, it consolidates the mathematical description of magnetic fields of ionic-plasma devices, movements of electrons of sputtered substance in electromagnetic field and its condensation on a substrate. A distinctive feature of the magnetron sputtering system compared to other diode-type sputtering systems is plasma localization near the target surface due to the transverse magnetic field and increase in the ionization intensity due to the elongation of the electron path. A three-dimensional trajectory of a particle moving in the space between the cathode and the anode are obtained. The mathematical model takes into account the effect of the space charge affecting the particle trajectory. A numerical solution of a system of equations of four acting forces on an electron in electric and magnetic fields is found. Mathematical modelling of the processes of magnetron sputtering in crossed electric and magnetic fields and numerical experiments using MatLab allow us to find the optimal modes for thin films application.