It is shown that taking into proper account certain terms in the nonlinear continuum equation of thin-film growth makes it applicable to the simulation of the surface of multilayer gratings with large boundary profile heights and/or gradient jumps. The proposed model describes smoothing and displacement of Mo/Si and Al/Zr boundaries of gratings grown on Si substrates with a blazed groove profile by magnetron sputtering and ion-beam deposition. Computer simulation of the growth of multilayer Mo/Si and Al/Zr gratings has been conducted. Absolute diffraction efficiencies of Mo/Si and Al/Zr gratings in the extreme UV range have been found within the framework of boundary integral equations applied to the calculated boundary profiles. It has been demonstrated that the integrated approach to the calculation of boundary profiles and of the intensity of short-wave scattering by multilayer gratings developed here opens up a way to perform studies comparable in accuracy to measurements with synchrotron radiation, at least for known materials and growth techniques.
Combined computer simulations of the growth of multilayer mirrors and their exact differential reflection coefficients in the soft-x-ray-EUV range have been conducted. The proposed model describes the variation of the surface roughness of the multilayer Al/Zr mirror boundary profiles taking into account a random noise source. Theoretically calculated Al/Zr boundary profiles allow one to know real rough boundary statistics including rms roughnesses and correlation lengths and, to obtain rigorously EUV specular and diffuse reflection coefficients. The proposed integrated approach opens up a way to performing exact theoretical studies similar in accuracy to results obtained by quantitative microscopy investigations of nanoreliefs and synchrotron radiation measurements.
The main obstacle of implementing numerical simulations for the prediction of nucleation and epitaxial growth is the variety of physical processes with a considerable difference in time and spatial scales. During the growth of nanostructures and epitaxy deposition of atoms, surface and bulk diffusion, nucleation of two-dimensional and three-dimensional clusters, transitions from two dimensional to three dimensional growth, stress relaxation occur. Thus, it is challenging to describe all of them in the framework of a single physical model. In the present work a multi-scale simulation of the epitaxial growth of silicon carbide nanostructures on silicon using three numerical methods, namely Molecular Dynamics, kinetic Monte Carlo, and the Rate Equations was implemented. Molecular Dynamics was used for the estimation of kinetic parameters of atoms and stress fields at the surface, which are input parameters for the other simulation methods. Kinetic Monte Carlo simulations allowed investigating basic nucleation processes and the transition from two dimensional nucleation to three dimensional cluster growth as well as the ordering of nanoclusters. Furthermore the influence of impurities on the nucleation of nanoscale SiC was studied. The energy barriers values obtained in Molecular Dynamics and the physical model used in the rate equation simulations was validated by Kinetic Monte Carlo. The Rate Equation simulation allowed studying the growth process at larger time scales taking into account the surface stress fields. As a result, a full time scale description spanning over a large substrate area of the morphological and structural surface evolution during SiC formation on Si was developed.
Growth of subsurface cobalt clusters during the deposition of cobalt on copper substrate has been studied through kinetic modeling. It is shown that, in comparison with reverse transposition, the formation of subsurface clusters is caused by a strong dissociation of surface cobalt clusters and preferential transposition of surface cobalt atoms to subsurface copper layers. Cobalt clusters’ size distribution functions are calculated for the different deposition times. Values of the migration energy of cobalt atoms in subsurface layers of copper, and the binding energy of subsurface cobalt atoms with the subsurface cobalt cluster are estimated.
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