HYBRID MODELING OF DEPOSITION PROFILES IN MAGNETRON SPUTTERING SYSTEMS

A three-dimensional hybrid model for calculating sputter deposition profiles has been developed. Both Monte Carlo methods and methods of statistical physics have been used. Due to the negligible mutual interaction of the sputtered particles, the Monte Carlo simulation is only carried out by a point sputtering source. The point source deposition profile and the point source thermalization profile resulting from the Monte Carlo simulation are integrated over all relevant point sources. The spatial distribution of the thermalized particles enters in the well known diffusion equation as a source term. The stationary distribution of concentration of the thermalized particles results in the time invariant solution of the diffusion equation. Therefore, the flux of thermalized particles to the substrate is available. The evaluated model takes into consideration the pressure of the working gas, the initial energy and angular distribution of the sputtered particles, the masses of the working gas atoms and the sputtered particles, the emissivity of the target and the geometry of the sputtering system, and is applicable to all common sputter processes. To verify the model silicon layers have been deposited from a planar magnetron target at an argon pressure of 1.1 and 4.0 Pa. The simulations are in good agreement with experimental data. It is shown that the unexpected decrease in uniformity with increasing pressure is an effect of the pressure dependent source term.