The article investigates the problems of control of dynamical systems with nonlocal terms of the convolution type using a force distributed over the area in which the motion is considered. The conditions are established under which it is possible to bring the system to complete rest with the help of a distributed force limited in absolute value. The case of one spatial variable is considered, but the proposed spectral method of research can be generalized to dimensions two and three. A connection is established between the behavior of the Fourier coefficients of the initial condition and the solvability of the control problem. The method can be used for mechanical systems with hereditary properties that arise in structural mechanics.

SWHL Nanotech team have implemented effective algorithms and developed scalable software allowing to synthesize holographic masks for various lithography applications including MEMS, MOEMS and high-end IC production. Most of the technical problems of state-of-art projection photolithography such as 3D-imaging, quality optimization were stated and solved as a completely numerical problems in the case of holographic lithography approach. Nanotech SWHL team developed effective algorithms of the holographic mask synthesis based on FFT with the complexity of O(N ln N), which allowed to synthesize holographic masks for any IC layer. We developed the continuous phase-shifting optimization method based on WFS, DFS and gradient descent, in which a hologram is synthesized not for the original pattern, but for a pattern with altered amplitude and phase distribution. Like in other RET, the holographic mask synthesized for the properly altered pattern provides a much better-quality image of the original pattern. Thus, today it is possible to use modern computing clusters for the synthesis of holographic masks and to implement them in inexpensive and sustainable devices for holographic photolithography.

The work is devoted to the construction of analytical solutions for the stress-strain state of a cylindrical hollow elastic rod with a layered structure along the radius. Earlier, the problem of finding the stress-strain state of a rod of composite material fixed at one end with the applied forces and moments of forces at the other end was considered. An approximate representation of the solutions was given, which included auxiliary problems on one fragment of the cylinder, consisting of periodically repeating similar fragments. Such auxiliary problems in the general case do not have an analytical solution. In this paper it is shown that in the presence of radial symmetry of the rod section, it is possible to construct a stress-strain state in an analytical form. In addition, tensile and bending stiffness can be presented in an analytical form. The latter circumstance allows us to set a problem of optimizing the stiffness characteristics of a rod with its fixed weight. Optimization is carried out by varying the thickness of the layers of the same materials.

We propose a scheme of maskless holography as a base of a novel lithographic technic. Maskless schemes based on reflective SLMs with planar and non-planar layouts are considered. Several effective methods of phase hologram synthesis adapted to the layouts are also introduced. These methods are based on the holographic lithography approach and calculation algorithms that have been developed by Nanotech SWHL. The aim of the work is to find the proper scheme and SLM characteristics, e.g. micromirror size, flatness, dynamic stability, etc. The non-flat optical schemes based on array of reflective SLMs will allow to achieve high NA up to 0.9 without immersion. That investigation allows to design a photolithographic tool with high diffraction efficiency and high-end capabilities.

Since the 1970s, the cost of photolithography in IC manufacturing has reached nearly 70% of the total production cost. The cost of production lithography equipment has grown almost 160 times reaching similar to$80M (193i scanner) and exceeding $200M (EUV scanner). Such high costs have caused a significant market concentration in equipment and chip manufacturing. Historically, the projection exposure technology was developed on the foundation of geometrical optics. A projection mask was a magnified stencil of the projected pattern. To achieve resolution, extensive development efforts have been made to increase the projection optics numerical aperture (NA), reduce exposure wavelength, minimize distortions of the projection lens and destructive diffraction effects. Complicated and highly costly RETs (OPC, PSM, SMO etc.) are used to suppress distortions in the pattern image induced by diffraction and aberrations of the projection optics. Sub-Wavelength Holographic Lithography (SWHL) is an unconventional imaging approach in photolithography that utilizes diffraction and interference effects to create high-quality images in photoresist, whilst decreasing exposure steps' cost, including higher resolution nodes. The ability to construct arbitrary wavefronts opens multiple opportunities like printing on various 3-D surfaces. The SWHL is capable of dramatic reduction of the lithography cost and opens new opportunities in 3D imaging. Two proof-of-concept exposure systems were designed and built to verify the SWHL capabilities: the first for imaging patterns with sub-wavelength resolution, the second for printing on 3D surfaces. The fidelity and computation efficiency of mask synthesis and RET algorithms were verified.

Sub-Wavelength Holographic Lithography (SWHL) was introduced some years ago by Nanotech SWHL GmbH as a disruptive and promising method to replace projection photolithography. SWHL is based on principles of wave optics and uses a computer-generated hologram (CGH) as a photomask for both 2D and 3D imaging. To proof the concept of SWHL first for sub-wavelength critical dimensions (CD) and then for non-flat imaging we designed two experimental optical set-ups. Both set-ups use commercially available 442nm He-Cd gas laser. The holographic masks were designed as a set of windows in an opaque chromium layer on a fused silica blank. The imaging in SWHL does not require any projection optics. Thanks to this the optical system includes only the illuminator of the mask. The illuminator design is very simple, with just a few optical elements. To demonstrate an image with sub-wavelength resolution, we use illumination with NA 0.53. For this NA we generated image with CD 250 nm that is 0.56 of the wavelength 442 nm. To demonstrate 3D imaging capability the demonstration lab tool was developed. The tool provides the illumination of holographic mask with NA 0.24. The mask generated a multi-plane image with a depth of 100 mu m and the image resolution of 2 mu m. We demonstrated both subwavelength and 3D holographic imaging in experiments and prove the concept of SWHL. All the experiments were made as computer simulations first. The comparison of the simulation and experimental results proved the reliability of our software.

The paper presents analytical estimates of the proximity of solutions to boundary value problems for elastic-creeping layered composite materials, which are widely used in construction, and must withstand loads for a long time, and the corresponding averaged model for such a material. The estimates show the possibility of using the averaged model over a long time interval for the problem of loading by a constantly acting force action. Previously, this statement was substantiated by numerical experiments comparing the solutions of boundary value problems for the effective (averaged) model and direct numerical calculation using the original model for a highly inhomogeneous layered material. Analytical estimates are based on previously obtained estimates of the proximity of solutions to stationary problems of elasticity theory. The problem under consideration is reduced to such problems using the Laplace transform in time. Next, we analyze analytically the dependence of the estimates for stationary problems with a complex parameter of the Laplace transform on this complex parameter, and the reverse transition to the original variables (time and spatial coordinate) is performed. The method used in this work for estimating the proximity of solutions for the averaged and original boundary value problems can also be used in the study of dynamic problems of viscoelasticity. It should also be noted that for the one-dimensional model considered in this work, an interesting property has been established: if the constitutive relations for various phases are written as dependences of deformations on stresses, then the coefficients for the same form of writing the constitutive relation of the averaged model are obtained as simple weighted averages of similar coefficients for individual phases.