Instability at the Melting Threshold of Laser Irradiated Silicon as the Underlying Origin of the Ripples Formation
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INSTABILITY AT THE MELTING THRESHOLD OF LASER IRRADIATED SILICON UNDERLYING ORIGIN OF THE RIPPLES FORMATION
AS THE
M. COMBESCOT, J. BOK AND C. BENOIT A LA GUILLAUME *Groupe de Physique des Solides de l'Ecole Normale Supdrieure, 24 rue Lhomond, 75231 Paris Cedex 05, France Groupe de Physique des Solides de l'Ecole Normale Supdrieure, Tour 23, Universitd Paris VII, 2 place Jussieu, 75221 Paris Cedex 05,
France
ABSTRACT The increase of reflectivity associated with a strong decrease of the laser penetration depth at the melting threshold of laser irradiated silicon induces a symmetry breaking with formation of a mixture of solid and liquid regions. We present a steady state solution in the case of solid and liquid stripes and we show that the liquid regions are slightly hotter than solid ones in contradiction with the previous idea of an undercooled liquid. The pattern size has to be smaller than a critical value of the order of the laser penetration depth, and can be selected by additional interference and diffraction effects.
In recent studies, liquid and solid ripples appearing at the melting threshold of laser irradiated silicon have been observed, often linked with interference and diffraction effects [1]. In this communication, we are concerned by the underlying mechanism which produces from a spatially uniform laser irradiation a spontaneous symmetry breaking leading to a regular set of liquid and solid regions. Some authors [2,3] have realized the importance of the change in reflectivity at melting but as it goes in the wrong direction (less energy enters in the liquid than in the solid regions), they have conclude that the liquid was undercooled, invoking surface tension effects. Besides reflectivity increase, there is another very important consequence of melting, not considered up to now, which is the strong decrease of the laser penetration depth (which can go from % 1 p to ^ 100 A for %O0.5 1a). It is true that less heat enters a liquid region but as this heat is deposited in a region 100 times thinner than in the solid, the liquid surface should finally be hotter than the solid one, in contradiction with the idea of an undercooled liquid. In order to compensate for the decrease of absorbed energy in the liquid, a lateral heat flow is necessary from the solid region to the back of the liquid one, leading to an heat flow pattern shown on Fig. Ia in a 2 dimensional situation (liquid stripes). This compensation is only possible if the liquid and solid stripes widths are not too large compared with the laser penetration depth in the solid. Finally, as liquid and solid coexist at the surface, one expects an average surface temperature close to the melting one, and, consequently, a ratio liquid-to-solid area such that the resulting mean reflectivity leads to Tm at the surface. We will outline now [31 the mathematical derivation of the above intuitive results and restrict to the simplest case i.e. the stripes formation. For that we consider a 2 dimensional problem containing the main physical aspects i.e. di
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