Acoustic substrate expansion in modelling dry laser cleaning of low absorbing substrates

Acoustic expressions have been derived for the thermal expansion of substrate surfaces due to irradiation by an exponential laser pulse. The result of acoustic effects on three substrates (silicon, glass and silica) with different absorptions has been calculated. It has been shown that for substrates having relatively low absorptions, like silica and glass, acoustic considerations substantially reduce thermal expansion of the substrate caused by irradiation by nanosecond laser pulses relative to a quasi-static expansion model. In particular, the expansion of the substrate occurs over a much longer time frame than when the quasistatic approximation holds. Consequently, acceleration of the substrate surface is greatly reduced and laser cleaning threshold fluences for particle removal are increased. The predictions of the model of Arnold et al. when developed for acoustic considerations give reasonable agreement with experimentally found threshold fluences for alumina particles on silica and glass substrates although it underestimates the ratio of the threshold cleaning fluences of silica and glass. This could be due to the model underestimating the contribution of surface expansion to the laser cleaning process. The influence of multiple reflections in the substrate and departure from one dimensionality in the heat conduction on the threshold fluence was found to be insignificant. Thermal contact between the particle and the substrate was also found to have little effect on laser cleaning threshold fluences. Another mechanism that may enhance surface expansion is the 3D focussing of radiation by the particles.