Analytic-Numerical Modeling and Investigation of Nanostructures' Dynamics on Material Surfaces After Laser Irradiation

Uldis Žaimis, Sharif E. Guseynov

Abstract


The work is devoted to modeling the formation and behavior of solid nano-sized particles on the surface of materials. In the simulation, it is assumed that the main processing technology of surface nanostructures is laser irradiation, which causes the Brownian motion of nanoparticles, due mainly to thermal fluctuations: if the temperature around the nanoparticles is uniformly distributed, the time average of the Brownian fluctuations is zero; however, if there is a temperature gradient around the nanoparticles, the thermal fluctuations affect the nanoparticle in different ways from different sides, and there is a force like the thermophoretic force, biasing the average position of the nanoparticle. When building a 1D model of the formation and flow behavior of nanoparticles, three important assumptions are introduced: the impact of nanoparticles on the process of irradiation is negligible; the impact of nanoparticles on each other as compared to the effect of laser irradiation on them is also negligible; and nanoparticles after laser irradiation can move both forward and backward and at every fixed period of time, moving the nanoparticles does not impose any steric constraints. Under the above assumptions, a 1D continuous model is built, implicit and explicit finite difference schemes to solve it are developed; their convergence and order of convergence are studied; an output condition ensuring the stability of the explicit difference scheme is obtained, the unconditional stability of implicit difference scheme is proven, and software for computer implementation of some of the obtained analytical and numerical results developed. 


Keywords


surface nanostructures; laser irradiation; mathematical modeling; single-phase model; explicit and implicit finite difference schemes

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References


A. Medvid, Nano-cones Formed on a Surface of Semiconductors by Laser Radiation: Technology, Model and Properties, Proceedings of the International Conferences on Nanowires Science and Technology, February 2010. Croatia: INTECH. pp. 402-424.

J. Kaupuzs, Sh. E. Guseynov, J. S. Rimshans, and A. Medvid, "Modeling of surface structure formation after laser irradiation." International Journal of Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology. pp. 49-56. 2011.

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DOI: http://dx.doi.org/10.17770/etr2015vol3.193

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