Optical Properties of Materials

A Sampling of NIST Contributions

THOMAS A. GERMER, RAJEEV GUPTA,LEONARD M. HANSSEN, AND ERIC L. SHIRLEY

Figure 1. Light scattered by a silicon wafer has a characteristic polarization thatis a signature of the scattering mechanism, in this case microroughness.

1047-6938/01/02/0039/5-$0015.00 © Optical Society of America

Optics has a wide range of applica-tions in industry and science, andthe properties of the materials that

make up optical instruments are key totheir effectiveness. Over the past century,optical instruments have increased in so-phistication and performance. The Na-tional Institute of Standards and Technol-ogy (NIST) plays an essential role in op-tics development by providing informa-tion on the optical properties of variousmaterials. These include glass for tele-scopes and cameras, semiconductors forelectronics, ultraviolet materials for pho-tolithography, and infrared materials forremote-sensing and defense applications.

NIST has developed instruments andmeasurement methods to obtain data ofthe highest level of accuracy. It providesindustry, government and academia withcalibration services and makes the physicalstandards it produces available to a widevariety of users. As part of its mission,NIST deals with the determination of op-tical properties of materials. NIST contin-ues to refine and improve its capabilities,including the development of a theoreticalbasis for understanding optical properties,to meet the future critical needs of scienceand industry.

This article will highlight steps NISThas taken to advance the field of opticalsciences and technology and give readers asense of the wide range of activities rele-vant to the broad category of "opticalproperties of materials." Specifically, thearticle will address NIST's efforts in fourareas:

• optical scatter measurements;• optical constants measurements in the

ultraviolet region that are critical forphotolithography;

• infrared filter characterization for re-mote sensing and defense applica-tions;

• improved theoretical methods thatcan help predict optical constantsfrom first-principles calculations.

These examples comprise a small portionof NIST's work in the field.

Optical scatter measurementsLight scattering has numerous negative ef-fects and positive applications, in that itcan degrade the performance of opticalsystems, enable diagnostic instruments tolocate and identify defects, and determinethe visual appearance of paints and coat-ings. The resolving power of high-quality

optical systems is often limited by scatter-ing from optical elements as well as fromthe supporting structure and baffles.Commercial software can help predict op-tical performance if the scattering func-tions for all the materials in an optical sys-tem are known. The semiconductor in-dustry uses light scattering to rapidly scansilicon wafers for defects and particulatecontaminants. As devices get smaller, de-tecting defects becomes harder. But find-ing defects–and detecting the source of theproblem–is key to producing productswith high yield.

For many years, NIST has conductedresearch on the measurement and under-standing of light scattering. During the1970s, Nicodemus defined the concept ofthe bidirectional reflectance distributionfunction (BRDF), which encapsulates theintensity scattered from a surface, as afunction of incident and scattering direc-tions.1 He further defined various con-cepts, such as directional-hemisphericalreflectance, in terms of the BRDF. Stan-dard materials, which behave like uniformscatterers over various wavelength regions,were developed. While light scattered inthe plane of incidence is easy to measure,measurement of light scattered out of theplane of incidence usually requires morecomplicated instrumentation.

It is not enough to characterize the in-tensity of scattered light: Scattering also af-fects polarization, which can yield specificinformation about the scattering sources.

Recently, NIST has led development oftheoretical models and experimental tech-niques showing how different scatteringsources—interfacial roughness, subsurfacedefects, or particulate contaminants—canbe differentiated by analyzing polariza-tion.2 Based on the Rayleigh approxima-tion, such analysis can be viewed in a sim-ple manner. When light is incidentobliquely on a surface with its electric fieldin the plane of incidence (i.e., p-polar-ized), the electric field above the surfacetends to be more normal to the surface,while that below the surface tends to bemore parallel to the surface. Therefore, asmall particle above the surface tends toradiate like an antenna normal to the sur-face, while a defect below the surface radi-ates like an antenna parallel to the surface.A viewer observing the scatter from a di-rection out of the plane of incidence needonly rotate a polarizer to determine the lo-cation of the scattering source.

Scattering from small amounts ofroughness can be understood in a similarway: it behaves as if dipoles are created bythe field above the surface yet radiate frombelow the surface. Figure 1 shows the po-larization of light scattered by micror-oughness when the substrate has the opti-cal constants of silicon. Experimentalmeasurements have confirmed that thelight scattered by different sources indeedfollows the predictions of the respectivetheories. The technological implications ofthe NIST findings have resulted in im-

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February 2001 ■ Optics & Photonics News 39

Figure 2. Measured refractive indices of fused silica samples at 193.39 nm and 20° C from three dif-ferent suppliers (A, B, C).

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proved detection of defects on siliconwafers. Future work in scatterometry in-cludes the development of methods tocharacterize coatings and films. Recent re-sults, for instance, have shown that light-scattering ellipsometry can be used to ex-tract the roughness of both interfaces of adielectric film.3

Optical constants measurementsin the ultraviolet regionSince it was founded in 1901, NIST* hasserved U.S. national needs related to opti-cal materials. Early on, NBS was responsi-ble for much of the domestic optical glassproduction and for characterizing variousapplications, including bomb sights.4

NIST's current mission—to enhanceAmerican economic competitiveness andtechnological development—has placedthe agency at the heart of the semiconduc-tor industry, in the arena of photolithog-raphy.

A key problem in fabricating high-pre-cision optics that transmit in the ultravio-let (UV) is characterizing the optical prop-erties of transmissive materials such as theindex of refraction, its dependence on

wavelength and temperature, and trans-mittance. The need for accurate data con-tinues to increase, especially as optical sys-tems are designed to achieve higher reso-lution and to operate at shorter wave-lengths (e.g., 157 nm). Accurate data havebecome indispensable, especially to to-day's microelectronics industry, which israpidly extending photolithography to thedeep ultraviolet. Projection optics for li-thography must be able to achieve diffrac-tion-limited performance with high nu-merical apertures and extremely widefields of view. Under these design rules,optical constants of materials must beknown to a few parts per million.

The most accurate measurements ofthe index of refraction of solid materialsin the UV can be performed using theminimum deviation method. Thismethod works by fabricating a prism withan accurately known apex angle, andmeasuring the minimum deviation angleof a monochromatic beam of light thatpasses through the prism. An NIST team,for instance, used this method to obtainhigh-accuracy values of the index and itsdependence on wavelength and tempera-ture. The accuracy of the measurementsmade around the wavelength of 193 nmwas sufficient to distinguish betweengrades of fused silica that were produced

by different manufacturers, pointing theindustry to the need for better materialspecifications5 (Fig. 2). The technique hasbeen extended to shorter wavelengths tomake critically needed measurements ofthe index of refraction for calcium fluo-ride and other materials around the wave-length of 157 nm.

As the wavelength of interest for pho-tolithography becomes shorter, all the de-sign parameters become more stringent—requiring increasingly accurate characteri-zation of the optical properties of trans-missive materials. The NIST team, usingan interferometric technique based on aUV Fourier transform spectrometer andthe broadband radiation from an in-housesynchrotron source, is at the forefront ofindex of refraction measurements. An ac-curate count of the fringes produced in aflat, plane-parallel piece of optical materi-al has the potential of yielding a value ofthe index of refraction with an accuracy ofa few parts per million.

Infrared filter characterizationFourier Transform (FT) methods for opti-cal properties characterization in the in-frared offer a number of well-known ad-vantages including high spectral resolu-tion and signal-to-noise ratio. However,FT methods are also prone to numeroussources of measurement error6 that gener-ally require correction prior to FT process-ing. Hence, FT spectrophotometry's appli-cation to accurate characterization of opti-cal materials and components, and gener-ation of reference data and standard arti-facts, requires a thorough evaluation of allthe important sources of error as well asthe subsequent development and imple-mentation of methods for reduction ofthose errors.

Standard artifacts for infrared trans-mittance (neutral-density filters) andwavelength/wavenumber calibration havebeen developed at NIST's FTIR (Fouriertransform infrared) SpectrophotometryLaboratory.7 In the process, primarysources of error, including detector systemnon-linearity and sample-interferometerand sample-detector inter-reflections,have been evaluated and minimized.8

Several systems employing differentmethods for the determination of thecomplex index of refraction measure-ments have been developed and estab-lished. These include absolute spectraltransmittance and reflectance, ellipsome-try, and spectral fringe analysis techniques(also used in the ultraviolet, as described

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40 Optics & Photonics News ■ February 2001

Figure 3.Transmittance of a 4 �m narrow-band filter at 25 K. Measurements were re-quired from 1.6 �m to 80 �m for use with a cryogenic cavity radiometer.This plot is thecombined result of six separate measurements covering different sections of the spec-trum, as determined by the spectral ranges of the detectors, beam splitters, sources,blocking filters, and regions of high transmission of the sample filter. Regions where thenoise level determines the base level of the measurement appear as structure that ex-tends to the bottom of the plot (i.e., to 0).

* Originally known as the National Bureau of Standards(NBS).

above).9 The laboratory uses multiplemethods of measurement for much of itswork because this allows for method com-parisons, validation of uncertainties, andmethod refinement—all of which yieldhigher-accuracy results.

A critical component of many sensorand radiometer systems is the filters usedto define the spectral regions of interest. Inthe infrared, such systems are used in nu-merous defense and remote-sensing sys-tems on the ground, in the atmosphere, orin space. Often, the detectors are sensitiveover a much broader spectral range thanthe filter passband. Even at low levels, forinstance, the out-of-band transmittance ofthe filters can trigger incorrect and misin-terpreted results when integrated over thecomplete detector range. In the worst-casescenario, such transmittance can renderthe measurement useless. Knowledge ofthe in-band spectral transmittance isequally important for sensors looking atinfrared flux that varies rapidly within thefilter passband—in the short-wavelengthpart of a Planckian blackbody distribu-tion, or adjacent to atmospheric absorp-tion lines. Furthermore, most infraredbandpass filters have both an angular de-pendence and a temperature dependence.

NIST has developed a methodology forcharacterizing infrared narrow-band fil-ters at temperatures from 10 K to 300 Kfor frequently used incident-beam geo-metries, and employed it to support anumber of Department of Defense,NASA, and National Oceanic and Atmo-spheric Administration programs.10 Anexample of combined in- and out-of-bandfilter measurements in semi-log format isshown in Fig. 3. Through the use of trans-fer standard neutral density filters andpassband blocking filters, the out-of-bandtransmittance can be measured down tolevels of 10-5 to 10-7, depending on thewavelength. Use of the supplementary fil-ters allows sample and reference measure-ments to be made at the same time thatoperation of the cryogenic detectors inlinear regimes is being maintained. Thein-band transmittance level is measured tohigh accuracy at ambient conditions usingcustom absolute transmittance–reflect-ance instrumentation. It is important totake the time to select the right measuredinterferogram type and to pay attention tothe details of the phase correction andapodization functions used in the FT pro-cessing that produces the final spectra. Theambient results are used to calibrate meas-

urements obtained with optical cryostatsat the required temperature and angle. Of-ten, additional measurements are per-formed to characterize the temperatureand incident-angle dependencies.

NIST filter-characterization results areused to help DoD and NASA contractorsassess their performance. The results alsohelp filter manufacturers design and fabri-cate filters critical to several satellite sen-sor systems. Finally, accurate filter trans-mittance data are used to improve thequality of the measurements made by thesensor systems themselves.

Improving theoretical methodsfor optical constants predictionsIt is often helpful to compare measure-ment results with the results of theoreticaland numerical modeling. For instance,theoretical analysis can help determinewhether features of a given spectrum areintrinsic to a material or are extrinsic arti-facts resulting from impurities, defects or

the measurement apparatus itself. NIST isworking to improve researchers’ ability topredict optical properties of materials(e.g., optical constants) from first princi-ples—an effort that complements labora-tory measurements and their refinements.

In contrast, the use of empirical modelswith adjustable parameters that can be fitto measured optical properties allows forsensible extrapolation of measurement re-sults to infer properties that were not actu-ally measured, e.g., the value of the refrac-tive index at a given wavelength. However,a first-principles approach can enable re-searchers to anticipate the optical proper-ties of materials before they are measured.

Although the overall systematic trendsare impressive, it is doubtful that modelingwill ever be able to achieve the same levelof accuracy now realized in measurementsof optical constants. Consider, for in-stance, the dielectric function for periclase(magnesium oxide, or MgO) in Fig. 4,where measured11 and theoretical valuesare shown. It is important to note thequalitative and quantitative correspon-dence of spectral features. Even a qualita-tive accounting for spectral features re-quires detailed numerical analysis of theoptical excitation process that was realizedonly recently at NIST12 and independentlyby others.13

Much of the work on first-principlesmodeling of optical constants has empha-sized the visible and ultraviolet regions ofthe spectrum and the role of electron in-ter-band transitions. However, the indexdispersion throughout the infrared regionis equally relevant, especially in view of therapid pace of developments in infraredtechnologies. One of NIST's goals is to de-velop a predictive model for optical con-stants in the far-infrared region, where op-tical absorption is governed by single- andmulti-phonon processes.

To achieve this goal, two criteria mustbe met. First, we must understand thecomplex, anharmonic inter-atomic forcesthat govern lattice dynamics.14 Second, wemust be able to solve the equations of mo-tion for the dynamical system of atoms vi-brating in a lattice, which is governed bysuch forces, to determine the response tolight in detail. Such a solution presents po-tentially unsolvable problems that mustnonetheless be addressed within wiselychosen approximations. One way to ad-dress this could be to treat multi-phononexcitations statistically and to limit one’sevaluation to various moments of the ab-

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February 2001 ■ Optics & Photonics News 41

0

2

4

6

8

10

12

5 10 15 20 25 30

Photon Energy (eV)

Theory

Measured

MgO

Figure 4. Imaginary part of the dielec-tric function (�2) for MgO as a functionof photon energy. Measured and ab ini-tio spectra are shown to the samescale,but with shifted baselines, to facil-itate visual comparison of spectral fea-tures.

sorption spectrum instead of attemptingto describe the total dynamical system.

The work highlighted in this article il-lustrates but a few of the challenges facingNIST scientists in the field of optical prop-erties of materials. It represents only asnapshot of NIST's efforts to maintain akey role in optics in general and to developthe skills, knowledge, and experience nec-essary to accomplish the task today and inthe future.

References1. F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I.W. Gins-

berg, and T. Limperis,“Geometrical Considerationsand Nomenclature for Reflectance,” NBS Mono-graph 160, (National Bureau of Standards, Gaithers-burg, 1977).

2. T.A. Germer,“Angular dependence and polarizationof out-of-plane optical scattering from particulatecontamination, subsurface defects, and surface mi-croroughness,” Appl. Opt. 36, 8798-805 (1997).

3. T.A. Germer,“Measurement of roughness of twointerfaces of a dielectric film by scattering ellipsom-etry,” Phys. Rev. Lett. 85, 349-52 (2000).

4. R. C. Cochrane,“Measures for Progress:A Historyof the National Bureau of Standards,” (U.S. G.P.O.,Washington, D.C.), pp. 186.

5. R. Gupta, J. H. Burnett, U. Griesmann, and M.Wal-hout,“Absolute refractive indices and thermal coef-ficients of fused silica and calcium fluoride near 193nm,” Applied Optics 37, 5964 (1998).

6. F. J. J. Clarke and J. R. Birch,“Fifty categories of ordi-nate error in Fourier transform spectroscopy,”Spec. Europe 7, 16-22 (1995).

7. S. G. Kaplan and L. M. Hanssen, Infrared Transmit-

tance Standards 2053, 2054, 2055, and 2056, NISTSpecial Publication 260-135 (2000); D. Gupta, L.Wang, L. M. Hanssen, J. J. Hsia, and R. U. Datla, Poly-styrene films for calibrating the wavelength scale ofinfrared spectrophotometers - SRM 1921, NISTSpecial Publication 260-122 (1995).

8. S. G. Kaplan, R. U. Datla, and L. M. Hanssen,“Testingthe radiometric accuracy of Fourier transform in-frared transmittance measurements,” Appl Opt. 36,8896-908 (1997).

9. S. G. Kaplan and L. M. Hanssen,“Infrared regular re-flectance and transmittance instrumentation andstandards at NIST,” Anal. Chim.Acta 380, 303-10(1998); S. G. Kaplan and L. M. Hanssen,“FT-IR-basedellipsometer using high-quality Brewster-angle po-larizers,” Proc. SPIE 3754, 285-93 (1999); S. G. Ka-plan, L. M. Hanssen, U. Griesmann, and R. Gupta,“Fourier transform refractometry,” Proc. SPIE3425, 203-12 (1998).

10. Z. Zhang, L. M. Hanssen, and R. Datla,“High-optical-density out-of-band spectral transmittance meas-urements of bandpass filters,” Opt. Lett. 20, 1077-9(1995); S. G. Kaplan and L. M. Hanssen,“Characteri-zation of narrowband infrared interference filters,”Proc. SPIE 3425, 48-55 (1998).

11. D. M. Roessler and D. R. Huffman, in Handbook ofOptical Constants of Solids II, ed. E. D. Palik (Acad-emic Press, San Diego, 1998), pp. 919-55.

12. L. X. Benedict, R. B. Bohn, and E. L. Shirley,“Opticalabsorption of insulators and the electron-hole in-teraction: an ab initio calculation,” Phys. Rev. Lett.80, 4514-7 (1998),“Theory of optical absorption indiamond, Si, Ge, and GaAs,” Phys. Rev. B 57, R9385-7 (1998).

13. S.Albrecht, L. Reining, R. Del Sole, and G. Onida,“Abinitio calculation of excitonic effects in the opticalspectra of semiconductors,” Phys. Rev. Lett. 80,4510-3 (1998); M. Rohlfing and S. G. Louie,“Elec-tron-hole excitations in semiconductors and insula-tors,” Phys. Rev. Lett. 81, 2312-5 (1998); J.W. van derHorst, P.A. Bobbert, M.A. J. Michels, G. Brocks, and P.

J. Kelly,“Ab initio calculation of the electronic andoptical excitations in polythiophene: Effects of intra-and interchain screening,” Phys. Rev. Lett. 83, 4413-6(1999).

14. A. Debernardi, S. Baroni, and E. Molinari,“Anhar-monic phonon lifetimes in semiconductors fromdensity-functional perturbation theory,” Phys. Rev.Lett. 75, 1819-22 (1995);A. Debernardi,“Anhar-monic effects in the phonons of III-V semiconduc-tors: first principles calculations,” Solid StateComm. , 1-10 (2000).

Thomas A. Germer, Rajeev Gupta, Leonard M.Hanssen, and Eric L. Shirley work in the Optical Tech-nology Division, NIST, Gaithersburg, Maryland.

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42 Optics & Photonics News ■ February 2001

Correction:The article "Using Color to Un-derstand Light Transmission,"published in OPN, Vol. 11, No. 8,pp. 44-50, August 2000, has beenposted on the OSA web site athttp://www.osa.org/pub_svc/opn/gevarticle/ because several of thefigures in the original article wereblurred. For best results, we sug-gest that readers download the ar-ticle and print it using a qualitycolor printer. The article can alsobe viewed using a MAC-basedsystem.