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The concept of the diffusive approach is as follows
When the kinetic energy of the sputtered particle becomes lower then some threshold, for example thermal energy of gases, the particle is regarded to be "THERMALIZED", and the Monte Carlo trace is stopped for that particle.
After the thermalization, the diffusion of the particle is ruled under the Poisson's equation.
And the points where the thermalization occurs are treated as the source of particle flow in the Poisson's equation.