Deformation patterns in thin films under uniform laser irradiation

Abstract

The mechanical behavior of thin films subjected to laser irradiation is described by a dynamical model that is based on coupled evolution equations for the deformation and vacancy density fields. Lattice vacancies are generated in a thin layer as a result of shallow absorption of electromagnetic laser radiation. The strain field associated with lattice dilatation due to vacancies is shown to couple with bending and stretching mechanical deformation fields. The dynamical model developed here is an extension of the work of Emel'yanov in two respects: ͑1͒ the coupling between the diffusion and mechanical deformation fields is rigorously developed with additional cross-field contributions; ͑2͒ new equations for reduced dynamics are derived from this model, and are used to analyze the physical conditions for the onset of a deformational instability. For a given material, the threshold for this instability is correlated mainly with laser power. We also show that, although the instability threshold and critical wavelengths are given by the linear part of the dynamics, the selection and type of deformation patterns induced by this instability require a nonlinear formulation. Both numerical and analytical analysis are performed here. According to the relative importance of nonlinearities arising from the defect or from the bending dynamics, square or hexagonal planforms are shown to be selected. Furthermore, it appears that one-dimensional gratings are always unstable in isotropic systems. The results for square patterns are consistent with experimental observations, while those for hexagonal and one-dimensional gratings show the importance of anisotropies on their final selection. ͓S0163-1829͑97͒03847-2͔

On certain problems of deformation-induced material instabilities

“…The derivation of the deformation dynamics of a thin film on a substrate, in the presence of a spatially varying defect concentration field has already been presented in Walgraef, Ghoniem, and Lauzeral (1997). The evolution equation for the film bending coordinate can be adapted to the present case where various structural defects (vacant sites, deposited atoms and adatoms, islands, grains, etc.)…”

“…Finally, if E 0 stands for the self-energy of deposited atoms, then E 0 % h with h % 0.3b 3 K, where b is the Burgers vector magnitude and K the bulk elasticity modulus. The components of the in-plane stress tensor r ij are given by Walgraef et al (1997) …”

Development of efficient solar cells with the use of multifunctional multitextures

“…That is why a comprehensive model in article [17] was improved, originally devised for the n-type silicon, in order to explain the formation of macropores in silicon of the p-type conductivity. According to this model, the formation of pores is suppressed if the charge transfer is carried out by predominant thermo-electron processes, which is sensitive to the height of the barrier and is not sensitive to its width.…”

Modeling Laser Effects on the Final Optics in Simulated IFE Environments

“…the lateral dimensions (corresponding to the x and y directions) are much larger than the thickness, as can be seen in Fig.(31). Its dynamics is governed by coupled evolution equations for vacancy density, C, and its neutral plane transverse deflection, ξ, (Emel'yanov, 1992;Walgraef et al, 1997a). The kinetic equation for vacancy density may be written as…”

“…These defects may include vacancies, interstitials, microvoids, transmutation-defect clusters and dislocation loops and tangles. Walgraef, Ghoniem and Lauzeral (1997c) developed a dynamical model that is based on coupled evolution equations for the deformation and vacancy density fields. On the one hand, strong laser irradiation generates an excess of defects in the surface layer; on the other hand, the defect field gives rise to strong deformation of the subsurface layer of the material.…”