ISSN 10274510, Journal of Surface Investigation. Xray, Synchrotron and Neutron Techniques, 2014, Vol. 8, No. 3, pp. 444–455. © Pleiades Publishing, Ltd., 2014. Original Russian Text © L.I. Goray, M.N. Lubov, 2014, published in Poverkhnost’. Rentgenovskie, Sinkhrotronnye i Neitronnye Issledovaniya, 2014, No. 5, pp. 39–51. 444 INTRODUCTION Progress in the manufacture of Xray multilayer diffraction gratings and mirrors with preselected boundary shapes and assigned subatomic roughnesses is related first of all to the holographic and litho graphic methods used in the production thereof, advances in material chemistry, the advancement of vacuum techniques and technology for preparing and treating Si plates, and achievements in nanometrology. Further investigations are urgent because there is a necessity to create uptodate highresolution and highefficiency components for optical and electronic devices (including those for 6.Xnm lithography) and Xray freeelectron lasers and develop resonant inelas tic Xray scattering, soft Xray and extreme UV (EUV) astrophysics, Xray microscopy, and other fields of application. The comparison of scattering intensities measured with the help of synchrotronradiation (SR) sources and Xray freeelectron lasers with data calcu lated via rigorous methods becomes more and more important for shortwavelength optics. It should be emphasized that microscopy methods, such as transmission electron microscopy (TEM), atomicforce microscopy (AFM), and nearfield scanning optical microscopy, are finding wide applica tion in qualitative research into the evolution of thin film boundary profiles. The first approach is expensive and destructive, and the other two techniques make it impossible to determine the boundary profiles of the internal layers of prepared samples. Moreover, only the local characteristics of a formed structure can be studied with the use of microscopy methods. The most universal approach to examination of the morphology and composition of layers is the reflecto metry (scatterometry) method, including its short wavelength variant whereby the nanorelief character istics of practically all thinfilm materials can accu rately be determined in an integrated way [1]. When solving the imperfectly and ambiguously defined inverse problems of reflectometry [2], it is especially important to have a universal and rigorous method for solving a direct problem and information on the recovered relief and/or refractive indices of the mate rials, which are employed as an initial approxima tion.Despite the substantial progress in the develop ment of accurate numerical methods for examining wave diffraction by arbitrary boundary asperities achieved in the last few years [3], the Xray and neu tron scattering intensities have only recently been ana lyzed by means of asymptotic and approximate approaches: the Kirchhoff scalar integral method, the Born approximation, the distortedwave Born approx Nonlinear Continual Growth Model of Nonuniformly Scaled Reliefs as Applied to the Rigorous Analysis of the Xray Scattering Intensity of Multilayer Mirrors and Gratings L. I. Goray a, b and M. N. Lubov a, c a St. Petersburg Academic University–Nanotechnology Research and Education Centre, Russian Academy of Sciences, St. Petersburg, Russia b Institute for Analytical Instrumentation, Russian Academy of Sciences, St. Petersburg, Russia c Ioffe Physical Technical Institute, Russian Academy of Sciences, St. Petersburg, Russia Received May 30, 2013 Abstract—It is revealed that certain terms entering into the nonlinear continual equation describing thin film growth enable its application to the simulation of the surfaces of multilayer mirrors and gratings with a large height and/or jumps of boundaryprofile gradients. The proposed model characterizes both variations in the power spectraldensity function of the surface of Al/Zr multilayer mirrors and the smoothing and shift of the boundaries of Mo/Si and Al/Zr gratings grown on Si substrates with triangular groove profiles by means of magnetron and ionbeam deposition. Rigorous calculations indicate that the intensities of diffuse Xray scattering by Au mirrors, which have similar boundary profiles with Gaussian and exponential autocorrela tion functions, differ substantially from each other. Computer simulation of the growth of Mo/Si and Al/Zr multilayer gratings is performed. On the basis of the calculated boundary profiles, the absolute diffraction efficiencies of the Mo/Si and Al/Zr gratings are found via the integral equation method in the extreme UV region. It is demonstrated that the proposed comprehensive approach to calculations of the boundary profiles and the intensities of shortwavelength scattering from multilayer mirrors and gratings makes it possible to carry out studies comparable in accuracy to measurements based on synchrotron radiation. DOI: 10.1134/S1027451014030057