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

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 autocorrelation 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.