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Jun 05, 2013
Paper is published in Journal of Physics C
“Development of near atomically perfect diffraction gratings for EUV and soft x-rays with very high efficiency and resolving power,” D. L. Voronov, E. H. Anderson, R. Cambie, L. I. Goray, P. Gawlitza, E. M.Gullikson, F. Salmassi, T. Warwick, V. V. Yashchuk, H. A. Padmore.
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Jun 04, 2013
Discounts are announced for powerful PCGrate-SX v.6.1 software
The prices of all program types from PCGrate-SX v.6.1 series w/o limitations are reduced by more than 26%, in the average.
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May 28, 2013
Presentation at Days on Diffraction 2013
The talk "Solution of 3D scattering problems from 2D ones in short waves," is presented at the DD’13 annual meeting.
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May 06, 2013
Paper is published in Journal of Applied Crystallography
“Nonlinear continuum growth model of multiscale reliefs as applied to rigorous analysis of multilayer short-wave scattering intensity. I. Gratings,” L. Goray and M. Lubov.
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Sep 18, 2012
Presentation at XTOP-2012
The talk "X-ray scattering on rough and profiled surfaces: rigorous analysis and a non-linear model of film growth," is presented at the 11th Biennial Conference on High Resolution X-Ray Diffraction and Imaging.
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Sep 17, 2012
Presentation at XTOP-2012
The talk "Development of ultra-high efficiency multilayer-coated blazed diffraction gratings for EUV and soft x-rays applications," is presented at the 11th Biennial Conference on High Resolution X-Ray Diffraction and Imaging.
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Aug 16, 2012
Discounts are announced for last PCGrate-S v.6.5 software
The prices of all program types from the updated PCGrate-S v.6.5 series are reduced by ~20%.
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Jul 25, 2012
PCGrate-S(X) v. 6.5 32/64-bit is updated
We issue PCGrate-S(X) software in the v.6.5 updated version.
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May 29, 2012
Presentation at Days on Diffraction 2012
The talk "Energy-absorption calculus for multi-boundary diffraction gratings," is presented at the DD’12 annual meeting.
more...
May 04, 2012
New Efficiency Certificate is issued online
Efficiency Certificate for a multilayer Mo4Ru6/Be blazed holographic grating in the soft x-ray–EUV range is presented.
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Paper is published in Journal of Physics C  
 
Development of near atomically perfect diffraction gratings for EUV and soft x-rays with very high efficiency and resolving power  
D. L. Voronov, E. H. Anderson, R. Cambie, L. I. Goray, P. Gawlitza, E. M.Gullikson, F. Salmassi, T. Warwick, V. V. Yashchuk, H. A. Padmore  
 
ABSTRACT  
Multilayer-coated Blazed Gratings (MBG) can offer high diffraction efficiency in a very high diffraction order and are therefore of great interest for high-resolution EUV and soft x-ray spectroscopy techniques such as Resonance Inelastic X-ray Scattering. However, realization of the MBG concept requires nano-scale precision in fabrication of a saw-tooth substrate with atomically smooth facets, and reproduction of the blazed groove profile in the course of conformal growth of a multilayer coating. We report on recent progress achieved in the development, fabrication, and characterization of ultra-dense MBGs for EUV and soft x-rays. As a result of thorough optimization of all steps of the fabrication process, an absolute diffraction efficiency as high as 44% and 12.7% was achieved for a 5250 l/mm grating in the EUV and soft x-ray regions respectively. This work now shows a direct route to achieving high diffraction efficiency in high order at wavelengths throughout the soft x-ray energy range with revolutionary applications in synchrotron science.  
© 2013 IOP Publishing Ltd. [doi:10.1088/1742-6596/425/15/152006]  
 
The paper is published in J. Phys.: Conf. Ser. Click here to download the full text.  
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PCGrate®-SX of v. 6.1 32-bit is discounted  
    
Discounts are announced for powerful PCGrate®-SX v. 6.1 32-bit software:  
 
The prices of all the types of software from the last PCGrate-SX v. 6.1 w/o limitations cut down by more than 26%, in the average. The price of updated from April 16, 2010 PCGrate-SX XML-type software is 1,999 Euros ($2,599), GUI-type - 2,999 Euros ($3,899), and Complete-type - 3,999 Euros ($5,199). We allow additional discounts for earlier and permanent Customers.  
 
This version enables the calculations both multilayer resonance and any small wavelength-to-period ratio cases at very high speed using two independent solvers (Normal and Resonance) based on the rigorous boundary integral equation method (modified). The solvers have different behavior and mutually complementary capabilities for many difficult cases such as deep gratings with arbitrary border profiles including measured ones and with random roughness, gratings having any number of very thin layers, grazing incidence, x-ray—EUV ranges, echelles, etc.  
 
PCGrate®-SX v.6.1 32-bit series have three types: GUI, XML, and Complete. PCGrate®-SX v.6.1 series codes have: the minimal value of the wavelength-to-period ratio lambda/d of 2.E-13, the maximal number of propagating diffraction orders of 10,000, and the maximal number of layers of the grating surface multilayer material of 5,000. The PCGrate-SX v. 6.1 XML and PCGrate-SX v.6.1 Complete types make it possible to calculate the grating efficiency from the command line with input/output data in XML format. The PCGrate-SX v.6.1 GUI and PCGrate-SX v.6.1 Complete types make it possible to obtain the calculated data using the Graphical User Interface and work with the results including saving, coping, exporting, plotting, printing, etc. The type is determined by the HASP® HL USB key, which is shipped separately to the product.    
 
Click here to download updated PCGrate DEMO v.6.1 Complete.  
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Presentation at the Days on Diffraction International Conference, May 27 - 31, 2013, St. Petersburg, Russia  
 
Solution of 3D scattering problems from 2D ones in short waves  
L. I. Goray  
 
ABSTRACT  
The paper reports on development of a boundary integral equation technique of characterization of scattering by rough three-dimensional (3D) surfaces at a short wavelength of λ. The effect of roughness on the mirror scattering intensity can be rigorously taken into account with the model in which an uneven surface is represented by a grating with a large period of di in different perpendicular planes i, which includes an appropriate number of random asperities with a correlation length of ξi. The code analyzes the complex structures which, while being multilayer gratings from a mathematical viewpoint, are actually rough surfaces for di>>ξi. If ξi~λ and the number of orders is large, the continuous angular distribution of the energy reflected from randomly rough boundaries can be described by a discrete distribution η(#) in order # of a grating [1]. A study of the scattering intensity starts with obtaining statistical realizations of profile boundaries of the structure to be analyzed, after which one calculates the intensity for each realization, to end with the intensity averaged out over all realizations. By selecting large enough samples, one comes eventually to properly averaged properties of the rough surface; however, this approach does not involve approximations, including averaging by the Monte Carlo method. The more general case of bi-periodic gratings (or 3D surfaces) may be considered in a similar way or by expressing the solution of the 3D Helmholtz equation through solutions of the 2D equation described below, an approach which may be resorted to in some cases [2]. General equivalent rules for determination of the efficiencies of reflected orders of bi-periodic gratings from those calculated for one-periodic gratings can be found, for example, in [3]. The general approach used is based on expansion of the efficiency of a bi-grating with profile boundaries symmetric relative to the horizontal plane in a Taylor series in powers of a boundary profile depth h, with the principal terms of the series retained in the h<d case. Then the efficiencies e0,m+ and e0,n+ of the orders numbered (0,m) and (n,0) propagating in the upper (+) medium for arbitrary linear polarization of light can be defined through the leading (quadratic in h) terms of the expansion as  
 
e0,m+ = e0,1+em,2+ / R; en,0+ = en,1+e0,2+ / R, (1)  
 
where en(m),1(2)+ are the values of the efficiencies of the corresponding mutually perpendicular one-periodic gratings calculated with the position of the polarization vector left unchanged, and R is the Fresnel reflection coefficient of the grating material. For non-deterministic surface functions some modification of the general approach is required. As follows from a comparison with the results of rigorous calculations performed in [3] and by the present author, the approximate relations (1) give a high-accuracy solution for cosθihi<<di and λ<di, where θi is an incidence angle. In the cases where one minus real part of the refractive index and imaginary part of the material are small, h can be large enough.  
 
References  
[1] Goray L. I., 2010, Application of the rigorous method to x-ray and neutron beam scattering on rough surfaces, J. Appl. Phys., Vol. 108, pp. 033516-1-10.  
[2] Goray L.I., 2011, Solution of the inverse problem of diffraction from low-dimensional periodically arranged nanocrystals, Proc. SPIE, Vol. 8083, 80830L-1-12.  
[3] Petit, R., ed., 1980, Electromagnetic Theory of Gratings (Springer, Berlin).  
© 2013 `Days on Diffraction', POMI.  
 
The lecture is published at IEEE Proceedings. Click here to download the full text.  
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Paper is published in Journal of Applied Crystallography  
 
Analysis of two-dimensional photonic band gaps of any rod shape and conductivity using a conical-integral-equation method  
L. I. Goray and G. Schmidt  
 
ABSTRACT  
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..  
© 2012 International Union of Crystallography. [doi:10.1107/S0021889813012387]  
 
The paper is published in JACr. Click here to download the full text.  
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Presentation at the 11th Biennial Conference on High Resolution X-Ray Diffraction and Imaging (XTOP-12), September 15-20, 2012, St. Petersburg, Russia  
 
X-ray scattering on rough and profiled surfaces: rigorous analysis and a non-linear model of film growth  
Goray L.I., Lubov M.N.  
 
ABSTRACT  
Understanding of the evolution of surface profiles and roughness of gratings, random asperities, quantum wires and dots, nanowhiskers, etc., during growth is required for further technological improvement. X-ray scattering on surfaces with different types of nano-asperities (periodic, random, and self-organized ones, as well as their combinations) is considered based on the rigorous electromagnetic theory and a non-linear continuum model of surface growth.  
It is well-known that linear continuum models of surface growth and evolution (see, for example, Ref. [1]) cannot reasonably reproduce the PSD spectra of the films deposited on a strongly profiled substrate or on a flat substrate with an rms roughness/correlation length of more than about a few nm. The linear continuum equation used in the models does not properly treat the complexity of the processes of island nucleation, growth and coalescence on profiled surfaces leading to a significant discrepancy of the predicted and measured PSD spectra [2]. The non-linear growth model proposed in the present work accounts for the non-linear growth effects and deals with a substrate that is a general rough grating with a groove spacing larger than the width/correlation length of the substrate's asperities. The temporal evolution of the surface height distribution (h(r,t) (r is the radius-vector and t is time) is a function of its derivatives and a stochastic term η(r,t):  
 
h(r,t)/∂t=f[grad h(r,t), grad2h(r,t),…] + ·(r,t).  
 
The function f is the sum of linear gradnh(r,t) and non-linear gradl([gradnh(r,t)]k), (l, k, nN), terms; the latter describes nonlinear effects and influence of the surface profile on the growth kinetics and resulting surface morphology. This model is capable simulating the growth of various crystalline, polycrystalline, and amorphous multilayers on planar and structured substrates. The model is used to predict the roughening and smoothing behaviors of Mo/Si, Al/Zr, and GaAs/AlGaAs films.  
The boundary integral equation method (MIM, Ref. [3]), where the border structure is considered as a 2D grating with wavelength λ to period d ratios of much less than one, is used to obtain absolute specular and non-specular x-ray intensities. Note that even for 1-D surfaces and, especially, in the EUV and x-ray range, finding an exact solution to the problem of scattering of electromagnetic waves from a profiled surface is extremely difficult for any rigorous method. In spite of the convergence and accuracy problems, ensemble averaging via Monte Carlo simulations is required in order to obtain scattering intensities. A generalization of MIM has been recently proposed [4] to describe rough multilayer gratings that is suitable for present calculus (see Figure).  
The authors are grateful to D. L. Voronov, Yu. V. Trushin, V. V. Yashchuk, and W. McKinney for useful discussions.  
 
References  
1. C. Herring, in The Physics of Powder Metallurgy, ed. by W. E. Kingston (McGraw-Hill, New York, 1951), 143.  
2. D. L. Voronov, E. H. Anderson, R. Cambie, E. M. Gullikson, F. Salmassi, T. Warwick, V. V. Yashchuk, and H. A. Padmore, Proc. of SPIE (2011) 8139, 81390B.  
3. L. I. Goray, J. Appl. Phys. (2010) 108, 033516.  
4. L. I. Goray, Wav. Rand. Med. (2010) 20, 569.  
© 2012 Ioffe Physical -Technical Institute of the Russian Academy of Sciences.  
 
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Presentation at the 11th Biennial Conference on High Resolution X-Ray Diffraction and Imaging (XTOP-12), September 15-20, 2012, St. Petersburg, Russia  
 
Development of ultra-high efficiency multilayer-coated blazed diffraction gratings for EUV and soft x-rays applications  
Voronov D.L., Anderson E. H., Cambie R., Goray L.I., Gullikson E.M., Salmassi F., Warwick T., Yashchuk V.V., Padmore H.A  
 
ABSTRACT  
We report on recent progress achieved at the Advanced Light Source (ALS) on development, fabrication, and characterization of ultra-high efficiency multilayer-coated blazed gratings (MBG) suitable for EUV and soft x-ray applications. As diffraction elements, MBGs have several important advantages compared with sinusoidal or laminar gratings. First, with blazed gratings most of the incoming radiation m ay potentially be diffracted into one specific, desired, diffracted order. Second, use of high efficiency multilayer coatings potentially allows extending the advantages of normal incidence grating spectrometer designs to EUV and soft x -ray wavelengths. In order to realize this potential, the MBG must have a nano-period structure with an ideal saw-tooth groove profile, coherently replicated over the entire structure and ensured to have an extremely low micro-roughness of the substrate's and multilayer's interfacial surfaces.  
Using e-beam and interference lithography techniques followed by wet anisotropic etching of silicon [1], we fabricated saw-tooth substrates with groove densities up to 10,000 lines/mm having near-atomically plane groove facets. The multilayers are deposited on the substrates by magnetron sputtering in Argon. With cross-sectional transmission-electron microscopy (TEM), we show that careful optimization of the deposition parameters [2] allows us to avoid significant smoothing of the groove profile and increase of the surface roughness. This observation is in excellent agreement with the results of diffraction measurements. An absolute efficiency of 44% was achieved for the first blazed order of a 5250 lines/mm MBG (consisting of 30 Mo/Si bilayers) at a wavelength of 13.1 nm. Simulations of diffraction efficiency of soft x-ray MBGs, based on the integral method for solving Maxwell's equations for a periodic structure [3], show that the efficiency of an optimized grating relative to the reflectance of the multilayer can approach 100%.  
We also discuss a route to achieving high diffraction efficiency in high order at wavelengths throughout the soft x-ray energy range with revolutionary applications in synchrotron science.  
The authors are grateful to R. M. Feshchenko, V. V. Kondratenko, Y. P. Pershin, A. G. Ponomarenko, and A. V. Vinogradov for very useful discussions. The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, Material Science Division, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231 at Lawrence Berkeley National Laboratory.  
 
References  
1. D. L. Voronov, E. H. Anderson, R. Cambie, S. Dhuey, E. M. Gullikson, F. Salmassi, T. Warwick, V. V. Yashchuk, and H. A. Padmore, Nucl. Instr. and Meth. (2011) A649(1), 156.  
2. D. L. Voronov, E. H. Anderson, E. M. Gullikson, F. Salmassi, T. Warwick, V. V. Yashchuk, and H.A. Padmore, Opt. Lett. (2012) (in press).  
3. PCGrate® software (http://www.pcgrate.com/about/pcgrates/sxseries).  
© 2012 Ioffe Physical -Technical Institute of the Russian Academy of Sciences.  
 
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PCGrate®-S update of v. 6.5 32/64-bit is discounted  
    
Discounts are announced for updated PCGrate®-S(X) v. 6.5 32/64-bit software:  
 
The prices of all the types of software from the last PCGrate-S v. 6.5 cut down by more than 20%, in the average. The price of updated from July 25, 2012 PCGrate-S XML-type software is 2,499 Euros ($3,124), GUI-type - 3,499 Euros ($4,374), and Complete-type - 4,999 Euros ($6,249). We allow additional discounts for earlier and permanent Customers.  
 
This version enables the calculations both multilayer resonance and small wavelength-to-period ratio cases at very high speed using two independent solvers based on the modified boundary integral equation method, i.e. Penetrating and Separating. The solvers have different behavior and mutually complementary capabilities for many difficult cases such as deep and shallow rough gratings and mirrors with very thin layers, grazing incidence, x-rays, and photonic crystals.  
 
PCGrate®-S v.6.5 32/64-bit series have three types: GUI, XML, and Complete. PCGrate®-S v.6.5 series codes have the minimal value of the wavelength-to-period ratio lambda/d of 0.02 and the maximal number of layers of the grating surface multilayer material of 20. The PCGrate-S v. 6.5 XML and PCGrate-S v.6.5 Complete types make it possible to calculate the grating efficiency from the command line with input/output data in XML format. The PCGrate-S v.6.5 GUI and PCGrate-S v.6.5 Complete types make it possible to obtain the calculated data using the Graphical User Interface and work with the results including saving, coping, exporting, plotting, printing, etc. The type is determined by the HASP® HL USB key, which is shipped separately to the product.    
 
Click here to download updated PCGrate DEMO v.6.5 Complete.  
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PCGrate®-S(X) update of v. 6.5 32/64-bit is available  
    
PCGrate®-S(X) v. 6.5 32/64-bit software is updated. A few minor bugs were fixed in updated PCGrate®-S(X) v. 6.5 32/64-bit series. The software is available for update as from July 25, 2012.  
Important: input and output data formats (grt- and pcg- types) were not changed !  
   
Click here to download updated PCGrate DEMO v.6.5 Complete.  
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Presentation at the Days on Diffraction International Conference, May 28 - June 1, 2012, St. Petersburg, Russia  
 
Energy-absorption calculus for multi-boundary diffraction gratings  
L. I. Goray  
 
ABSTRACT  
A general energy-balance criterion for multi-boundary lossy periodical objects (general gratings) has been derived and verified numerically. In the general case, the difference A = 1  R  T e 0 is called the absorption coefficient in the given diffraction problem with the sums of reflected and trans-mitted energies R and T, respectively. In addition to being physically meaningful, this expression is useful as one of the accuracy tests for computational codes. The energy criterion in the lossless case says A = 0. In the lossy case, one needs an independently calculated quantity to compare with A. For such a quantity, we use the absorption expression defined as the sum of volume or surface integrals. The equation for the absorption A of an electromagnetic field by a multilayer grating can be derived directly from Maxwell's equations [1], or by the variational principle [2], or by applying the second Green's identity to boundary functions for the contours in the upper and lower media [3]. By definition, the first part of integrals in the expression of A is 1  R, and the second, T, vanishes if the lower medium is absorbing or the lower boundary is perfectly conducting. The absorption expression in the explicit form which is based on scattering amplitude matrices has been added to the previous study to treat closed and separated boundaries, e.g. photonic crystals [4]. The sum A + R + T is actually the energy balance for an absorbing grating, and the extent to which it approaches unity is a measure of the accuracy of calculations. Maxwell equations being valid in the sense of distributions, the proposed general energy-balance criterion is valid in the same sense. The connection of the derived expression with the optical theorem and its application to non-periodical surfaces is discussed.  
 
References  
[1] Goray L.I., 2010, Application of the boundary integral equation method to very small wavelength-to-period diffraction problems, Waves Random Media, Vol. 20, pp. 569-586.  
[2] Goray L.I. and Schmidt G., 2010, Solving conical diffraction grating problems with integral equations, J. Opt. Soc. Am. A, Vol. 27, pp. 585-597.  
[3] Goray L.I., Kuznetsov I.G., Sadov S.Yu., and Content D.A., 2006, Multilayer resonant subwave-length gratings: effects of waveguide modes and real groove profiles, J. Opt. Soc. Am. A, Vol. 23, pp. 155-165.  
[4] Goray L.I. and Schmidt G., 2012, Analysis of two-dimensional photonic band gaps of any rod shape and conductivity using a conical-integral-equation method, Phys. Rev. E, Vol. 85, pp. 036701-1-12.  
© 2012 `Days on Diffraction', POMI.  
 
The lecture is published at IEEE Proceedings. Click here to download the full text.  
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New Efficiency Certificate is issued online  
    
Efficiency Certificate for a multilayer Mo4Ru6/Be blazed holographic grating in the soft x-ray-EUV range is presented. The complete results of the grating efficiency investigation and all relevant information about the computation and measurement processes can be obtained from the downloading page (Cert_2400_holo-blaz_MoRu-Be_soft-X-ray--EUV.zip file). Various files both *.xlsx (MS Excel® 2010) and *.grt, *.ggp, *.ri, *.ari, & *.pcg (PCGrate®-S(X)™ v.6.1) formats relating to this grating efficiency certification are included in the package. You can view the later by the PCGrate Demo v.6.1 Complete (updated on the 16th April, 2010).  
   
 
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