Optimization of layered synthetic microstructures for broadband reflectivity at soft x-ray and EUV wavelengths John F. Meekins, Raymond G. Cruddace, and Herbert Gursky A technique is described which allows the thickness of each layer in a layered synthetic microstructure to yield a useful constant efficiency over a broad band of wavelengths, several hundred angstroms wide, in the soft x- ray and EUV wavebands. 1. Introduction In an earlier paper' we discussed the advantages, particularly where astronomical applications were concerned, of layered synthetic microstructures (LSMs) which, when applied to optical surfaces, would enable them to operate efficiently near normal inci- dence under exposure to soft x-ray and extreme ultra- violet (EUV) radiation. We describe there a tech- nique for optimizing the structure of a nonperiodic LSM to obtain maximum overall reflectivity over a narrow band of wavelengths, a few tens of angstroms wide. However, astronomical and other instruments often need to operate over broader ranges of wave- length, perhaps several hundred angstroms wide, and therefore in this paper we extend our analyses to deal with such applications. LSMs consist of layers of optically dissimilar materi- als, usually deposited on a substrate. When radiation is incident on the LSM, the discontinuities in the indi- ces of refraction at each of the layer boundaries cause reflected waves to be produced which interfere with one another. Among other factors, the intensity of the reflected wave depends on the magnitude of these discontinuities. In the soft x-ray and EUV bands of the spectrum, nearly all the materials are absorbing, the index of refraction is complex (n, = n + ik), and the real part of the index is often close to unity. Thus in this part of the spectrum, the contrast in the refractive indices of materials often depends on differences in the imaginary part (k) of n,. Further, because the materi- als are absorbing, the contribution to the reflectivity of The authors are with U.S. Naval Research Laboratory, E. 0. Hulburt Center for Space Research, Washington, DC 20375-5000. Received 20 May 1986. those films deep within the LSM (near the substrate) is much less than those near the top. Thus, absorption limits the reflectivity to values appreciably less than unity and low contrast materials are to be avoided. For our study, we have restricted ourselves to optimi- zations in the 100-600-A wave band and have consid- ered two combinations of materials, iridium-silicon and platinum-silicon, for which optical constants are readily available 23 and have been compiled in our ear- lier paper.' For a given angle of incidence, the reflectivity of most available materials falls as the wavelength de- creases 4 and the complex index of refraction, nc = n + ik, of materials approaches unity as the wavelength decreases. For a given wavelength, there exists a criti- cal angle of incidence, the total reflection cutoff angle 0 c (measured from the surface normal), above which intrinsically high reflectivities are obtained and below which much lower reflectivities are found. This total reflection cutoff angle for the intensity of radiation reflected at the interface between vacuum and an ab- sorbing medium can be determined from sin 2 0, = n2 - k 2 . (1) Several representative values of 0 c are given in Table I for silicon, iridium, and platinum obtained using the optical constants given by Hunter 2 and Henke et al. 3 As the wavelength decreases, 0 c increases and ap- proaches the grazing condition near 100 A. Generally, the material having the smaller Oc displays the larger reflectivity (e.g.,iridium has a higher reflectivity at 100 A than does silicon) and mirror surfaces are usually either constructed of or are overcoated with materials with the smallest c available. Multiple interference coatings can greatly improve the reflectivity of surfaces even for those cases in which the angle of incidence is smaller than O. One must be aware, however, that constructive interference coat- 990 APPLIED OPTICS / Vol. 26, No. 6 / 15 March 1987
Transcript
Optimization of layered synthetic microstructures forbroadband reflectivity at soft x-ray andEUV wavelengths
John F. Meekins, Raymond G. Cruddace, and Herbert Gursky
A technique is described which allows the thickness of each layer in a layered synthetic microstructure to yielda useful constant efficiency over a broad band of wavelengths, several hundred angstroms wide, in the soft x-ray and EUV wave bands.
1. Introduction
In an earlier paper' we discussed the advantages,particularly where astronomical applications wereconcerned, of layered synthetic microstructures(LSMs) which, when applied to optical surfaces, wouldenable them to operate efficiently near normal inci-dence under exposure to soft x-ray and extreme ultra-violet (EUV) radiation. We describe there a tech-nique for optimizing the structure of a nonperiodicLSM to obtain maximum overall reflectivity over anarrow band of wavelengths, a few tens of angstromswide. However, astronomical and other instrumentsoften need to operate over broader ranges of wave-length, perhaps several hundred angstroms wide, andtherefore in this paper we extend our analyses to dealwith such applications.
LSMs consist of layers of optically dissimilar materi-als, usually deposited on a substrate. When radiationis incident on the LSM, the discontinuities in the indi-ces of refraction at each of the layer boundaries causereflected waves to be produced which interfere withone another. Among other factors, the intensity of thereflected wave depends on the magnitude of thesediscontinuities. In the soft x-ray and EUV bands ofthe spectrum, nearly all the materials are absorbing,the index of refraction is complex (n, = n + ik), and thereal part of the index is often close to unity. Thus inthis part of the spectrum, the contrast in the refractiveindices of materials often depends on differences in theimaginary part (k) of n,. Further, because the materi-als are absorbing, the contribution to the reflectivity of
The authors are with U.S. Naval Research Laboratory, E. 0.Hulburt Center for Space Research, Washington, DC 20375-5000.
Received 20 May 1986.
those films deep within the LSM (near the substrate) ismuch less than those near the top. Thus, absorptionlimits the reflectivity to values appreciably less thanunity and low contrast materials are to be avoided.For our study, we have restricted ourselves to optimi-zations in the 100-600-A wave band and have consid-ered two combinations of materials, iridium-siliconand platinum-silicon, for which optical constants arereadily available2 3 and have been compiled in our ear-lier paper.'
For a given angle of incidence, the reflectivity ofmost available materials falls as the wavelength de-creases4 and the complex index of refraction, nc = n +ik, of materials approaches unity as the wavelengthdecreases. For a given wavelength, there exists a criti-cal angle of incidence, the total reflection cutoff angle0 c (measured from the surface normal), above whichintrinsically high reflectivities are obtained and belowwhich much lower reflectivities are found. This totalreflection cutoff angle for the intensity of radiationreflected at the interface between vacuum and an ab-sorbing medium can be determined from
sin2 0, = n2 - k2 . (1)
Several representative values of 0c are given in Table Ifor silicon, iridium, and platinum obtained using theoptical constants given by Hunter2 and Henke et al. 3
As the wavelength decreases, 0c increases and ap-proaches the grazing condition near 100 A. Generally,the material having the smaller Oc displays the largerreflectivity (e.g., iridium has a higher reflectivity at 100A than does silicon) and mirror surfaces are usuallyeither constructed of or are overcoated with materialswith the smallest c available.
Multiple interference coatings can greatly improvethe reflectivity of surfaces even for those cases in whichthe angle of incidence is smaller than O. One must beaware, however, that constructive interference coat-
Iridium100. 0.959 0.0298 73.5 94. 533.200. 0.900 0.1000 63.4 106. 318.300. 0.775 0.1956 48.5 123. 244.400. 0.575 0.5600 7.5 112. 114.500. 0.650 0.8700 b b 91.600. 0.875 1.0750 b b 89.
Platinum100. 0.953 0.0226 72.4 108. 705.200. 0.882 0.1450 60.5 89. 220.300. 0.810 0.2270 51.0 111. 210.400. 0.687 0.5510 24.2 103. 116.500. 0.709 0.7180 b b 111.600. 0.835 0.9380 b b 102.
a Penetration depth at which the electric and magnetic fields areattenuated by e.5
b Critical angle is complex since n < k high reflectivity occurs atall angles for these wavelengths and the penetration depth at 0, is notdefined.
ings which have been designed to enhance the reflec-tivity in one wave band will depress the reflectivity inother wave bands.
II. Maximization of Reflectivity over a Broad Wave Band
When high reflectivity is desired over a broad waveband, much effort is needed in the design of an ade-quate LSM. While reducing the number of film layersin the LSM indeed increases the bandwidth, for exam-ple, compare Figs. 4 and 5 of our earlier paper,' betterbroadband performance can be produced by othermeans. Here, we describe a technique which yieldsdesigns leading to relatively high, approximately con-stant, reflectivity over the bandwidths of interest.
As in many other optimization techniques, a nu-merical measure is needed which positively correlateswith undesirable features. Minimization of this mep-sure then produces the most desirable configuration.Of the many functional forms possible for this mea-sure, we choose one which places high emphasis onundesirable characteristics,
P E ('max - 4 (2)
where A,\ is the reflectivity for a randomly polarizedincident beam (i.e., we set x to the average of thereflectivities for the two polarization states, transverseelectric and transverse magnetic), max is a test valuewhich is incrementally varied during optimization(minimization of p2), and the summation is taken onlyover those wavelengths for which Aid < max. Becauseof the extremely nonlinear relationship between re-
Table II. Film Thicknesses of Iridium-Silicon LSM Optimized for the 300-600-A Band
flectivity and film thicknesses, minimization of thismeasure is accomplished by taking numerical deriva-tives and interatively varying the film thicknesses.This particular choice of the measure was made be-cause we desire the reflectivity to be approximatelyconstant at the highest value which can be reachedover the wave band. During the optimization, thisvalue is unknown, so to obtain a reasonable measure ofperformance we adopt a test value max which is equalto or just larger than the highest reflectivity(5^) foundduring the last iteration. Since obtaining a reflectivityhigher than this test value should incur no penalty, therestricted summation is incorporated. The fourthpower (in lieu of the second power) arises because eachterm in the summation has been weighted by thesquare of its difference from the test value to empha-size the low reflectivities within the wave band (thosewhich are least desirable). The thicknesses of each ofthe film layers is allowed to vary freely during theoptimization calculation, but the number and compo-sition of the layers is fixed. Note that, if in the courseof optimization the total thickness becomes much larg-er than the penetration depth (e.g., those shown inTable I), the deeper layers do not contribute substan-tially to the reflectivity of the LSM and thereforevariations of the deeper layer thicknesses produce lit-tle change in p2. This insensitivity of p2 to the deeperlayer thicknesses may indicate that several of the lay-ers should be removed from the design.
We have performed a number of calculations foreach combination of materials, varying the total num-ber of layers and seeking a satisfactory compromisebetween increasing the LSM reflectivity and reducingits complexity. Thus in the case of the iridium-siliconcombination, where maximum reflectivity is sought inthe 300-600-A band, we have settled on seven layers asproviding a good compromise. The optimum thick-nesses of the layers are summarized in Table II for twoangles of incidence, 0° and 200. The reflectivities areshown in Figs. 1 and 2. The relatively flat response towavelength is evident, in marked contrast to the resultof a narrowband optimization, for example, Fig. 3 inRef. 1. The integrated reflectivity, S ?xdX, between300 and 600 A is 56 A for the LSM represented in Fig. 1to be compared with a value of 49 A for the narrowbandLSM.
Fig. 1. Reflectivity of a seven-layer iridium-silicon LSM optimizedfor normally incident 300-600-A radiation.
a:
00 30 4 5
a:~~~~~~~~a
0.20
300 350 400 450 500 550 600WAVELENGTH (Angstroms)
0.20 5
a: 0.10
0.05
300 350 400 450 500 550 600WAVELENGTH (Angstroms)
Fig.2. Reflectivities of seven-layer iridium-silicon LSMs for radia-tion incident at 200 and for three polarization modes: (a) LSMoptimized over the 300-600- wave band for 200 angle of incidence;(b) LSM optimized over the 300-600- wave band for normal inci-
dence (LSM design of Fig. 1).
dence, the reflectivity of these broadband LSMs re-mains high. Figure 2(b) shows the reflectivity of theLSM optimized for normal incidence, when operatedat an angle of incidence of 200. The correspondingcurves of Fig. 2(a) show the improvement that may beobtained, particularly at the shorter wavelengths,when the LSM is optimized for the 20° angle of inci-dence. Also in Fig. 2 we illustrate the effect on thereflectivity of polarizing the light in either the trans-verse electric (TE, electric vector parallel to the sur-
I-
0JU 0.1
w Q-jIL
a:
100 200 300 400 500 600WAVELENGTH (Angstroms)
Fig. 3. Reflectivity of a seventeen-layer platinum-silicon LSMoptimized for normally incident 100-300-A radiation.
Table Ill. Film Thicknesses of Platinum-Silicon LSM Optimized for the100-300-A Band
face) or transverse magnetic (TM, magnetic vectorparallel to the surface) mode. The integrated reflecti-vities (300-600 A) for the three polarization modesshown in Fig. 2(a) are 46, 58, and 64 A.
In the case of the platinum-silicon combination wehave examined a more difficult task, that of obtaininguseful reflectivity at normal incidence in the 100-300-A wave band. We found seventeen layers to be neces-sary and obtained the optimum thicknesses shown inTable III. The reflectivity of this LSM for normallyincident radiation is given in Fig. 3. Again, the result-ing LSM has a better overall performance in the select-ed broadband than does the narrowband LSM opti-mized in Ref. 1 for maximum reflectivity at 200 A (seeFig. 4 of Ref. 1). The integrated reflectivities of thesetwo LSMs at normal incidence in the 100-300-A bandare 8 and 5 A, respectively. The reflectivity of theoptimized Pt-Si LSM fluctuates significantly over theselected wave band (100-300 A), unlike the result ob-tained for the Ir-Si LSM optimized between 300 and600 A (Fig. 1). This more complicated interferencepattern is a consequence of the greater number oflayers in the Pt-Si LSM.
Fig.4. Reflectivitiesofseventeen-layer platinunradiation incident at 20' and for three polarizatioioptimized over the 100-300-A wave band for 200,(b) LSM optimized over the 100-300-A wave bar
dence (LSM design of Fig. 3).
The reflectivities of this LSM at andence of 200 are given in Fig. 4(b).optimizing the LSM for an angle of in[Fig. 4(a)] is to increase the integratslightly, for example, from 8.8 to 9.5 A fcand from 4.7 to 5.1 A for the TM mode.
The curves in Figs. 3 and 4(a), which operating at the angles of incidence fwere optimized, 0 and 20", respectprominent features which occur at tllengths. For example, each shows a '125 A and a null at -333 A. This occtreflectivity calculations employ a chara((see Ref. 1) for the Pt-Si combination, trigonometric functions with an argumEX, where h is the layer thickness, n iindex of refraction, 0 is the angle of incthe material), and X is the wavelength inoptimization calculations have maintairthe curves in Figs. 3 and 4(a) at a fixedkeeping h cosO approximately constantble III a systematic increase in layer thiobserved as the angle of incidence is inc:to 20°.
However, in the curves of Fig. 4(b) ahave moved systematically to shorteiThis is because the values of h in the ax
0.3 -
: 0.2
100 200 300 400 500 600WAVELENGTH (Angstroms)
Fig. 5. Reflectivities of a seven-layer platinum-silicon LSM opti-mized for 100-300-A radiation with an angle of incidence of 600.
o cosO/X are fixed (00 incidence columhn in Table III), sothat critical values of the argument will be reached atshorter wavelengths as the angle of incidence is in-creased.
Benefits may be derived also from the use of LSMsat large angles of incidence, near the grazing condition.To illustrate this, we show in Fig. 5 the reflectivity of aseven-layer Pt-Si LSM optimized over the 100-300-A
500 600 band for an angle of incidence of 600. The thicknessesof the seven layers are given in Table III. This angle,
i-silicon LSMs for 60° is the critical angle, 0c, for platinum at 200 A (seea modes: (a) LSM Table I), so that at longer wavelengths the reflectivityangle of incidence; is essentially determined by straightforward reflectionid for normal inci- from the outer platinum layer, which acts like a mirror.
In addition, useful efficiency is maintained at shorterwavelengths, reaching down to 100 A, due to the con-structive interference in the LSM. In this manner the
angle of inci- response of an optical surface operating at large anglesThe effect of of incidence may be extended to shorter wavelengths.
cidence of 200 The response of the LSM to the degree of polariza-ed reflectivity tion of the radiation can be significant, as pointed outr the TE mode by Spiller,6 who considered the use of LSMs as polar-
imeters. As the angle of incidence increases awaylescribe LSMs from the normal incidence condition, the reflectivity ofor which they TM polarized radiation decreases and reaches a mini-tively, display mum at the polarizing angle which, for these materialshe same wave- and wavelengths, is close to 450. Thus, while thesharp spike at reflectivity of TE polarized radiation may increase asirs because the the angle of incidence increases, the reflectivity ofcteristic matrix randomly polarized radiation decreases as the polariz-which contains ing angle is approached. When the angle of incidenceent 27rnch cosO/ exceeds the polarizing angle, the reflectivity of TMs the complex polarized radiation again contributes substantially toidence (within the reflectivity of randomly polarized radiation. Thevacuum. The sensitivity of the reflectivity to polarization at largeied a feature in angles of incidence is illustrated in Fig. 5.wavelength by. Thus in Ta- III- Conclusions.ckness may be A technique has been described which allows thereased from 00 thickness of each layer in an LSM to be optimized, to
yield a useful, approximately constant efficiency over aall the features broad band of wavelengths, several hundred ang-
wavelengths. stroms wide, in the soft x-ray and EUV wave bands.rgument 27rnch The usefulness of such LSMs, if they can be construct-
ed successfully, appears to be greatest near the normalincidence condition, but they may have applicationalso in extending the response of near grazing inci-dence optics both to shorter wavelengths and to largergrazing angles.
References1. J. F. Meekins, R. G. Cruddace, and H. Gursky, "Optimization of
Layered Synthetic Microstructures for Narrowband Reflectivityat Soft X-Ray and EUV Wavelengths," Appl. Opt. 25, 2757(1986).
2. W. R. Hunter, Sachs/Freeman Associates, Inc.; private commu-nication (1984).
3. B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, and B. K.Fujikawa, "Low-Energy X-Ray Interaction Coefficients: Pho-
toabsorption, Scattering, and Reflection," At. Data Nucl. DataTables 27, 1 (1982).
4. G. Hass and W. R. Hunter, "New Developments in Vacuum-Ultraviolet Reflection Coatings for Space Astronomy," in SpaceOptics, Proceedings, Ninth International Congress of the Inter-national Commission for Optics, Santa Monica, CA, 1972, B. J.Thompson and R. R. Shannon, Eds. (National Academy of Sci-ences, Washington, DC, 1974), p. 525.
5. M. Born and E. Wolf, Principles of Optics-ElectromagneticTheory of Propagation, Interference, and Diffraction of Light(Pergamon, Oxford, 1980), p. 616.
6. E. Spiller, "Multilayer Interference Coatings for the VacuumUltraviolet," in Space Optics, Proceedings, Ninth InternationalCongress of the International Commission for Optics, SantaMonica, CA, 1972, B. J. Thompson and R. R. Shannon, Eds.(National Academy of Sciences, Washington, DC, 1974), p. 581.
Fortieth Anniversary of the Office of Naval Research
The year 1986 saw the fortieth anniversary of the founding ofthe Office of Naval Research on 1 August 1946 by PresidentTruman. This was the first permanent federal agency devotedto funding basic research at American universities. DuringWorld War II research sponsorship came mainly from industrialand philanthropic sources. The development of federal spon-sorship at the universities is reviewed in vol. 38, no.3 (1986) ofthe Naval Research Review.
By the early 1950s, Europe had recovered sufficiently thatthere began to be once again major research contributions,mainly from Britain, France, and Germany. The ONR LondonOffice began to report significant developments in its EuropeanScientific Notes. The Office of Naval Research played animportant role in the support of basic research at universitiesduring this period, and many of the students, who would go outto become industrial scientists or university faculty members inthe rapidly expanding university community, were supported asgraduate students by ONR funding. It is possible that thisinvestment in people had a greater multiplying effect than theindividual scientific research results obtained by the funding.
In 1975 ONR established a liaison office in Tokyo to reporton research developments throughout the Far East area. TheOffice of Naval Research Far East Scientific Bulletin is its
publication. ONR has now been joined in sponsorship of theBulletin by the Air Force Office of Scientific Research. TheJuly to September 1986 issue, vol. 11, no.3, has many articlesof interest, including a historical account by George B. Wright
from which the above was extracted. Hajime Karatsu dis-cusses U.S. and Japanese approaches to semiconductors andpoints out that in Japan quality control is not just for a fewspecialists but is the concern of everyone for total qualitycontrol. In his review, which includes many examples, hementions persistence and patience as bases for the Japanesesuccess.
The status of the Japanese supercomputer project, startedin 1982, is given. It has a goal of creating a computer capableof performing 10 billion floating point operations (10 Gflops).Strong emphasis is placed on research and development ofGaAs and high electron mobility transistors. An article on thin-film silicon technologies in Japan notes a greater developmentemphasis on providing multilayered structures for 3-D integra-tion than in the U.S.A.
Symposia are reported: Seoul, Korea, on physics of semi-conductors and applications; Beijing, China, on compositematerials and structures; and Tokyo, Japan, solid-state devicesand materials. Research programs are summarized at theShanghai Institute of Technical Physics, the Nagoya WaterResearch Institute, physiological engineering at Toyohashi Uni-versity, physiological research at Japan's Marine Science andTechnology Center.
The Bulletin can be obtained by subscription from the Super-intendent of Documents, Attn: Subscription, GovernmentPrinting Office, Washington, DC 20402. Domestic rate, $13.00;foreign, $16.25; single copy, domestic, $4.50; foreign, $5.65.
