Kuramoto-Sivashinsky equation for modulation of surface relief of molten layer and formation of surface periodic microstructures under pulsed laser irradiation of solids

A closed nonlinear two dimensional equation of Kuramoto-Sivashinsky type for the thickness of the laser pulse induced viscous molten layer is derived in the long wavelength and weak nonlinearity approximation. Linear stability analysis shows that under the condition that the temperature gradient at the surface is directed from the surface to the bulk, the surface instability sets in that leads to formation of surface relief structures with wavelength proportional to the thickness of the liquid layer. Computer simulations predict the subsequent formation of lamellar and disordered, quasihexagonal structures of surface relief when the time of irradiation is increased. Obtained results are used for the interpretation of experimental data on formation of lamellar and quasihexagonal surface relief microstructures upon multiple nanosecond pulse laser irradiation of silicon in water confinement.