Theory of thermal sputtering

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Abstract
An energetic ion which is incident on a solid target causes a momentary temperature increase in the impact region, i.e., a so-called thermal spike occurs. Such spikes are capable of causing (or supplementing) disordering, precipitation, crystallization, electronic excitation, stoichiometry change, desorption, and sputtering, it being the contribution to sputtering that we consider here. The approach used is compatible with modern damage-distribution theory. Thus the temperature profile left by the incident ion is taken as a three-dimensional Gaussian with parameters appropriate to power-law scattering, and is used as the initial condition for solving the heat-conduction equation. Let us write this solution as T = T(t, y), where t is time and y is a dimension parallel to the target surface. The vaporization flux from a solid surface is taken as pn ½ (2πkT)−½ where p, the equilibrium pressure of a vapor species containing n atoms, can be written as poexp (−L/T), po and L are constants largely independent of temperature, and <m 2> is the mean mass per atom of target. The thermal sputtering coefficient then follows as Both integrations can be carried out, with the final result taking the form where T ∞ is the macroscopic target temperature, cΔT o is the maximum temperature increase at x = y = 0, p is to be evaluated at T = T ∞ + cΔT o, λ is the mean atomic spacing of the target, and teff is a quantity with units of time.