Theory of the Sputtering Process

The mathematical methods of neutron diffusion theory are applied to the problem of cathode sputtering. The state of all particles not in thermal equilibrium with the lattice can be described by a gas-like model in which the atoms move with constant mean free path. Collisions are assumed to occur only with "fixed" lattice atoms, but binding energies are neglected. The distribution functions exhibit finite discontinuities in the energy which approximate the behavior of the correct functions. The sputtering ratio is determined by integration over the velocity direction and also over energy, thus averaging out the approximation. The resulting expression for the sputtering ratio depends upon four atomic parameters of the system. In principle all are measurable, but only the mass ratio is known with precision at the present time. The theoretical curve is fitted to the experimental data which are available for eight ion-metal combinations. The curve is found to be very sensitive to the choice of fitting parameters, and the parameters exhibit considerable internal consistency. The theory indicates certain areas of experimental research which should add to present understanding of the process.