Layer-by-layer design method for multilayers with barrier layers: application to Si/Mo multilayers for extreme-ultraviolet lithography

A previous layer-by-layer multilayer design method [J. Opt. Soc. Am. A 19, 385 (2002)] is completed by adding the possibility of alternating layers with fixed thicknesses along with layers whose thicknesses are optimized for the largest possible reflectance at a desired wavelength. The previous algorithm did not allow for layers with fixed thicknesses. The current formalism is particularly suited for a multilayer design in which barrier layers of given thicknesses are used to prevent diffusion and/or reaction between the multilayer constituents. The design method is also useful both when intermixing zones develop at multilayer interfaces and when capping layers are used. The algorithm allows the design of multilayers with complex barrier layers with any number of layers of any optical constants. The optimization can be performed either for normal incidence or for nonnormal incidence with either s- or p-polarized radiation. The completed method provides a fast and accurate procedure for multilayer optimization regardless of the number of different materials used in the multilayer. The optimum layer thickness is determined by means of functions suitable for implementation in a computer code. The performance of the current algorithm is exemplified through the design of Si/Mo multilayers with intermixing layers or with barrier layers that are optimized for the largest reflectance at 13.4 nm. The use of specific barrier layers on each multilayer interface is also discussed.     

Chromium-scandium multilayer mirrors for the nitrogen K(alpha) line in the water window region

Chromium-scandium (Cr-Sc) is a promising material combination for multilayer mirrors in the water window region. A possible x-ray source for laboratory use in this wavelength range is the nitrogen K(alpha) line at 3.16 nm. High reflectivities at this wavelength can be achieved with Cr-Sc multilayer mirrors if the interfaces between adjacent layers are smooth. The growth parameters of the magnetron sputtering process for these materials have been optimized. It is shown that the reflectivity of such mirrors can be considerably improved by the application of a proper bias voltage during film growth. The high quality of the multilayer films is demonstrated with copper K(alpha) x-ray reflection and transmission electron microscopy. The reflective properties of the multilayers close to the nitrogen K(alpha) line were measured with synchrotron radiation for different angles of incidence. Reflectivities between R = 5.9% for near-normal incidence (theta = 1.5 degrees) and R = 29.6% for theta = 59.9 degrees were measured.     

Design of multilayer extreme-ultraviolet mirrors for enhanced reflectivity

We show numerically that the reflectivity of multilayer extreme-UV (EUV) mirrors tuned for the 11-14-nm spectral region, for which the two-component, Mo/Be and Mo/Si multilayer systems with constant layer thickness are commonly used, can be enhanced significantly when we incorporate additional materials within the stack. The reflectivity performance of the quarter-wavelength multilayers can be enhanced further by global optimization procedures with which the layer thicknesses are varied for optimum performance. By incorporating additional materials of differing complex refractive indices-e.g., Rh, Ru, Sr, Pd, and RbCl-in various regions of the stack, we observed peak reflectivity enhancements of as much as ~5% for a single reflector compared with standard unoptimized stacks. We show that, in an EUV optical system with nine near-normal-incidence mirror surfaces, the optical throughput may be increased by a factor as great as 2. We also show that protective capping layers, in addition to protecting the mirrors from environmental attack, may serve to improve the reflectivity characteristics.     

High-reflectivity HfO2/SiO2 ultraviolet mirrors

High-reflectivity dense multilayer coatings were produced for the ultraviolet spectral region. Thin-film single layers and UV mirrors were deposited by ion plating and plasma ion-assisted deposition high-energetic technologies. Optical characterizations of HfO2 and SiO2 single layers are made. The optical constants obtained for these two materials are presented. HfO2 and SiO2 mirrors with a reflectance of approximately 99% near 250 nm are reported.     

New layer-by-layer multilayer design method

A new layer-by-layer multilayer design method is presented. The method is demonstrated mathematically and makes possible the optimization of the multilayer for the highest possible reflectance either at normal incidence or at nonnormal incidence for s- or p-polarized radiation. With the current method multilayers can be designed regardless of the number of different materials used. The optimum layer thickness is determined by means of functions suitable for implementation in a computer code. The new multilayer design method is fast and accurate.     

Inreflectance: a new function for the optimization of multilayers with absorbing materials

A new magnitude is unveiled from the fact that a multilayer can be optimized for the largest reflectance in a layer-by-layer sequence: This magnitude has been named inreflectance. Inreflectance equals the modulus of the complex reflectance once elevated to the inverse of the complex refractive index of the next outer layer, including the inclination term. The maximization of inreflectance at every internal layer, proceeding sequentially starting with the innermost layer, results in a multilayer with the largest reflectance. At a given layer in the multilayer, inreflectance is different from reflectance when the next outer material absorbs radiation, whereas the two magnitudes are coincident when the next outer layer is transparent. The outermost layer of the multilayer is intrinsically different from the internal layers, and its optimization is performed through reflectance and not through inreflectance. Every maximum of inreflectance is found at a layer thickness that is larger than that for the reflectance maximum. The new magnitude is illustrated with some examples in the extreme ultraviolet, a spectral range in which all materials absorb radiation. Inreflectance can also be used to design multilayers in which some layers have fixed thicknesses and the rest of the layers have to be optimized taking into account the fixed layers.     

Theoretical and experimental studies of broadband phase-controlled attosecond mirrors

We present procedures to develop and characterise chirped multilayer mirrors for attosecond pulses. The design procedure involves a simulated annealing optimisation algorithm to obtain a multilayer structure with the desired performances. The characterisation step requires the use of well-calibrated attosecond and synchrotron beam lines, allowing one to measure the amplitude and phase response of the mirror. We illustrate these approaches with a set of mirrors designed to have zero or negative dispersion. The remarkable agreement between theoretical and experimental performances validates this overall process, and demonstrates the capability of such mirrors to control the temporal profile of attosecond pulses. These tools and techniques for developing attosecond chirped mirrors will facilitate the generalisation of such components on attosecond experiments.     

Optimum weight design of fiber composite plates in flexure based on a two level strategy

This paper offers a method for weight optimization of multilayer fiber composite plates under the action of lateral loadings. The objective is to design a fiber composite plate of minimum thickness which can sustain multiple static loadings applied normal to its surface without exhibiting failure based on Tsai-Hill criterion in any of its layers. In this investigation, fiber orientation angles are treated as discrete variables, which can vary only by pre-assigned increments, while thicknesses of layers are treated as continuous variables. The optimization procedure is based on a two stage strategy; in the first of which only the fiber orientation angles for the layers are treated as variables, and in the second, only the layer thicknesses. A powerful criterion based on a load factor has been defined to find the best angle for a new layer in the first stage, and the method of center points has been used for thickness optimization in the second stage. After any angle and thickness optimization has been done, a new layer is added to the thickness and the procedure is repeated for other new layers. The end of the two stage procedure is signaled whenever the thickness of the new layer in the optimization process approaches zero; meaning that no new layers would improve the set of layers already found. In this way at the end of the optimization procedure the plate thickness would be made of a minimum number of layers whose fibers are optimally oriented, and whose thicknesses are minimal. A poor choice of layers in the stack produce near zero thickness for the respective layer, and are thus deleted from the set. A repeat process is performed after each cycle, to modify layer angles in order to compensate for errors due to approximations involved. The priorities exercised in the choice of new layers for inclusion in the set and exclusion of all the un-necessary ones, allow an optimal state of stacking sequence to be achieved. Several examples are given to demonstrate the operation of the algorithm.     

Thermally invariant dielectric coatings for micromirrors

Thermal expansion-induced curvature becomes a major effect in micromirrors as the mirror diameter exceeds 100 microm. Such mirrors are used for optical switching, scanning, and many other applications. By using multilayer coatings instead of a single metal reflector, one can use the mechanical properties of the multilayer to create mirrors with zero curvature across temperature. We demonstrate the fabrication of such thermally invariant mirrors using dielectric coatings. A semianalytic model based on free-plate elastic theory is developed that uses empirical parameters in place of the true thermal expansion coefficients of the coating materials. Micromirrors are demonstrated that maintain their design curvature to within lambda/60 for lambda = 633 nm across an operating range from 21 degrees C to 58 degrees C.     

Interference-induced enhancement in the reflectivity of three-component X-ray mirrors

The possibility of enhancing the peak reflectivity of binary multilayer periodic structures by introducing additional layers, that is, by creating three-component mirrors, is considered. The parameters of substances, for which the three-component mirrors are advantageous to the traditional binary mirrors, are determined.     

Correlation of sidelobe suppression between rugate filters and multilayer mirrors

We present the study of the correlation between refractive index profiles and the optical response of rugate filters and multilayer mirrors. The conventionally used method in multilayer mirrors for ripple suppression in the passband will be compared with a similar simple method to remove the rugate filter sidelobes without apodization. The resulting layers are compared in performance with a typical quintic matching layer. An example based on silicon oxynitride alloys with refractive indices ranging between 1.47 and 1.83 was designed and deposited.     

Design, fabrication, and analysis of chirped multilayer mirrors for reflection of extreme-ultraviolet attosecond pulses

Chirped Mo/Si multilayer coatings have been designed, fabricated, and characterized for use in extreme-ultraviolet attosecond experiments. By numerically simulating the reflection of the attosecond pulse from a multilayer mirror during the optimization procedure based on a genetic algorithm, we obtain optimized layer designs. We show that normal incidence chirped multilayer mirrors capable of reflecting pulses of approximately 100 attoseconds (as) duration can be designed by enhancing the reflectivity bandwidth and optimizing the phase-shift behavior. The chirped multilayer coatings have been fabricated by electron-beam evaporation in an ultrahigh vacuum in combination with ion-beam polishing of the interfaces and in situ reflectivity measurement for layer thickness control. To analyze the aperiodic layer structure by hard-x-ray reflectometry, we have developed an automatic fitting procedure that allows us to determine the individual layer thicknesses with an error of less than 0.05 nm. The fabricated chirped mirror may be used for production of 150-160 as pulses.     

Design of X-ray supermirrors

A new approach is proposed for the design of wide band-pass multilayer optical elements operating in the hard X-ray spectral region. The method, based on the combination of analytical and numerical methods, solves the inverse problem consisting of inferring the composition profile of a depth-graded multilayer coating. The key feature of our approach consists in using an analytical expression for the depth-distribution of the period as initial solution for direct computer calculations. This allows a global minimization of the merit function and a many-fold decrease of the computer run time. Simulations of two particular cases are presented: a constant reflectivity over a wide spectral range and a complicated reflectivity profile. The best choice of material pairs for composing a depth-graded multilayer structure is discussed from the viewpoint of maximum achievable reflectivity and least number of bi-layers. Features of depth-graded multilayer mirrors, which are distinctive from conventional periodic mirrors, are examined. The factors influencing the optical quality of broad-band multilayers are also considered.     

Damping behavior of Al/SiCP multilayer composite manufactured by roll bonding

High damping materials comprising good mechanical properties as structural materials and high damping capacity for vibration loading are the best solutions for vibration problem. In current study, functionally graded material from composite sheets with different percentages of reinforcement was manufactured by hot rolling process. The damping behavior of base alloy composite including different percentages of SiC particles and Al/SiC_P multilayer composite sheets was studied at room temperature conditions. The Al/SiC_P composites were found to exhibit higher damping capacity compared to Al alloy. The damping capacity increased by increase in the percentage of reinforcement. Furthermore, Al/SiC_P multilayer composite sheet provided higher damping capacity in comparison to Al alloy. Therefore, damping capacity enhanced by increasing the number of layers. The main source for damping behavior in composite materials is dislocation damping whereas in stepwise multilayer composite sheets, it comes from boundary conditions between layers.     

Properties of Laser Mirrors at Non-normal Incidence

For laser mirrors made out of lossless periodic dielectric mutlilayers, having a basic period of two layers (ZnS and MgF₂) with different refractive indices and equal effective optical thicknesses, both the reflectivity at the stopband centre and the width of the stopband are calculated as a function of the angle of incidence for radiation polarized perpendicular or parallel to the plane of incidence. The results of computer calculations for mirrors with up to 20 layers are presented in a number of graphs and are discussed in detail. The graphs simplify the design of laser mirrors according to prescribed specifications and make it possible to distinguish between a maximum or a minimum of the spectral reflectivity at the centre of the stopband.     

遗传算法在双层微穿孔结构优化设计中的应用

影响双层微穿孔结构的参数很多，其声阻抗及吸声系数的计算复杂。以双层微穿孔板的吸声学为优化目标，穿孔率、孔径及空腔深度为优化参数，研究基于遗传算法对双层微穿孔结构进行优化设计。通过计算程序，验证了该算法的可行性和有效性。写以前的算法比较表明，经优化过的双层微穿孔板的吸声效果有明显的提高。     

Modeling and in situ identification of material parameters for layered structures based on carbon nanotube arrays

We test and model the mechanical response of a multilayer composite structure composed of alternating layers of aligned carbon nanotubes and copper foils under compression. We employ a bistable mass-spring model to capture the three-phase hysteretic response of the loading curve with excellent agreement with the experimental observations. An in situ identification procedure is proposed to quantify the material parameters corresponding to the mesoscopic scale of the structure. We refine the results using a genetic algorithm and compare the response of two different models based on three and four springs in series. The localization of deformation can be accurately captured by these simplified models, which hold promise for the design of novel materials with tailored deformation responses.     

Laser-Generated Lamb Waves Propagation in Multilayered Plates Composed of Viscoelastic Fiber-reinforced Composite Materials

The propagation characteristics of laser-generated Lamb waves in multilayered fiber-reinforced composite plates with different fiber orientations and number of layers have been investigated quantitatively. Considering the viscoelasticity of the composite materials, we have set up finite element models for simulating the laser-generated Lamb waves in two types of the multilayered composite plates. In the first type, different fiber orientations are adopted. In the second one, different number of layers are considered. The results illustrate the occurrence of attenuation and dispersion, which is induced by the viscoelasticity and multilayer structure, respectively.