Solar-selective globular metal films

Solar-selective globular metal filmsChris M. Horwitz

School of Physics, University of Sydney, New South Wales, 2006 Australia(Received 14 August 1976; revised manuscript received 13 June 1977)

Globular metal films composed of particles with sizes of the order of the wavelength of visible light canhave interesting solar-selective properties when deposited on a metallic surface which provides the requiredhigh infrared reflectance. The geometrical nature of the absorption mechanism in these films makes theiroperation substantially independent of the materials used, and allows wide control of the cut-on wavelength.It is shown here that all-metal films can have poor broadband selective properties; however, the addition ofvery thin dielectric layers between the globules and the substrate permits surface-wave resonances, givingbroadband absorption and a higher solar selectivity. The behavior of these films is found to agree, in variousregions, with models based on interference layers, an equivalent circuit, and surface-wave propagation.

INTRODUCTION

Solar-selective surfaces are optical filters which uti-lize wavelength discrimination to convert solar radia-tion into high-temperature thermal energy (e. g., seeRef. 1). They are all reflecting in the infrared (atwavelengths greater than about 1. 5 ,m) to reduce heatloss by reradiation. Some selective surfaces are trans-parent to the solar spectrum (termed "heat mirrors":e.g., see Ref. 2); however, the majority, including theglobular films in this paper, are absorbing in this re-gion. The high infrared reflectance of these films isprovided by a metallic substrate. The films describedhere have been made with a low-temperature material(Sn), and hence would have short life at the high tem-peratures which absorbing selective surfaces must with-stand. In addition, the actual solar absorptance of thebest films described here is about 0. 8, relatively lowfor many applications. However, such a high absorp-tance combined with a low infrared emittance in a sys-tem composed of large particles of pure metal and non-absorbing dielectrics is unique. In addition, these filmselucidate the optical mechanisms of other potentiallymore absorbing selective surfaces composed of similar-ly sized particles (e.g., see Ref. 3, which deals withgranular PbS surfaces).

The globular films in this study are composed ofmetal particles with diameters of about 0. 5 pm, closeto light wavelengths. On a nonreflecting substrate theyexhibit slowly increasing absorption with decreasingwavelength 4

5; one would therefore expect moderatelyselective properties on a metal substrate. The broad-band absorption which has sometimes been observedcannot be accounted for by an interference-layer model,however, and we will find that the observed resonancesand absorption can be explained by the excitation ofsurface waves underneath the globular particles.

With many selective films the transition (cut-on)wavelength which separates the reflecting and absorbingregions is determined by the chemical nature of thematerials used, but with the Sn globular films describedhere a 5: 1 variation in cut-on wavelength will be dem-onstrated. In addition, Hetrick and Lambe5 have ob-served surface-wave resonances in globular films madeon In, confirming that these films operate in a geo-metric, material-independent fashion.

Other surfaces with roughness of the order of the

wavelength of light appear to have excellent filteringproperties7 ; however, their high scattered componentat short wavelengths gives a low solar absorptance.Rough surfaces made of globular particles overcoatedwith metal have been investigated here, and have beenfound to be poorly selective not only for the above rea-son, but also because their infrared reflectance issurprisingly low. These findings correlate with thoseof Cuomo et al. 8,9 and Grimmer et al. 10 with tungstenand nickel dendrites and "hillocks, " and it is shownhere that an equivalent-circuit model can account forsome of the observed properties.

EXPERIMENTAL METHODS

The films were formed by electron-beam evaporationof Sn onto heated substrates, from Mo or C crucibleliners. The details of this have been published pre-viously.

5 Electrically isolated Sn metal globules result.A repeatable nucleation base was generally provided byan A1203 layer; experiments have shown that MgF2layers give identical optical properties. This A1203layer also acts as a diffusion barrier, preventing inter-diffusion of the hot substrate metal and the Sn layer forfilm thicknesses as small as 5 nm.

To isolate the optical effect of this dielectric layer itis desirable to deposit Sn globules directly onto a metalsubstrate; however, Sn readily diffuses into Al at thenormal substrate temperature (180 'C), destroying theglobular film. Under some conditions Cu has beenfound to allow globular film formation. However, Snhas an inherently low diffusion rate in Ta, which hasbeen used for direct depositions with consistent resultseven though the Ta as evaporated had about 15% lowerreflectance than that of the bulk metal.

Some Sn films were overcoated with Au in a planetaryfashion at room temperature. These had similar opticalproperties to Sn films overcoated with 50 nm of A1203 ,followed by Au, indicating little interdiffusion of Sn andAu at room temperature.

Optical measurements were performed with the ap-paratus described in Ref. 5, which allowed measure-ments of total, specular, and diffuse transmittance andreflectance from 0. 2 to 2. 5 ,m, and of scattered in-tensity versus angle in this wavelength range. The an-gular distribution of the reflected scattered light ingeneral exhibited none of the diffraction structure ob-

1032 J. Opt. Soc. Am., Vol. 68, No. 8, August 1978 0030-3941/78/6808-1032$00.50 0 1978 Optical Society of America 1032

some Sn films on evaporated Ta substrates. The wave-lengths of the maxima and minima of the films withouta spacer layer scale with film thickness, as is expectedfor an interference film. In addition, the thicker filmshows good agreement with the theoretical curve excoeptat wavelengths shorter than the first reflectance maxi-mum, albeit with a lower reflectance caused by the poorTa film quality. It is thought that a different vacuumsystem layout, giving a different thickness monitor cali-bration, is the cause of the 100 nm film on Ta appear-ing similar to the earlier 70 nm films.

Figure 2(b) also shows the effect of a 10 nm spacerlayer; surprisingly, it is strong at long wavelengths andsmall at short wavelengths, destroying the agreementwith interference theory observed earlier. The firstminimum is shifted to longer wavelengths by an anom-

i 1 pm

FIG. 1. Scanning electron micrographs of a globular metalfilm (70 nm deposited Sn mass thickness). (a) As deposited;(b) overcoated with 100 nm of Au, with planetary motion.

served for films on glass substrates, approximatelyobeying an intensity cx (cosO) law, where 0 is the angleof the detector from the surface normal. Infrared spec-ular reflectance (at 30° angle of incidence) was mea-sured between 1 and 15 gm with appropriate spectro-photometers.

Transmission electron micrographs of sectionedglobular films have shown that the A1203 layer is notpermeated by the Sn globules, and hence a cermet-typelossy dielectric film cannot explain the observed prop-erties. Scanning electron micrographs have shown thateven the thickest films studied show no signs of thesnakelike structure characteristic of globular filmsformed on relatively low temperature substrates. 4,11

Figure 1(a) shows a globular film as observed in thescanning microscope, and Fig. 1(b) shows the samefilm after a thick Au coating had been applied in a plan-etary fashion. For thicker coatings, the film wouldcease to be globular.

EXPERIMENTAL RESULTS

Globules on metal substrates

In this section we compare the experimental proper-ties of globular films on reflecting substrates with thepredictions of standard interference layer theory, whichis expected to hold where light scattering by the film issmall. Previous articles (Refs. 5 and 6) have shownthat globular films on dielectric substrates possess in-terference-film properties. In particular, an effectivethickness of 160 nm and a refractive index of N= (2.4- 0.3 i) has been found to agree well with the measuredproperties of a 70 nm mass thickness Sn film on a glasssubstrate (Ref. 5). This allows calculation of the re-flectance of a globular film on a metallic substrate, andFig. 2(a) shows the calculated reflectance of a 70 nm Snfilm on a Ta substrate, with and without an A1203 spacerlayer. The comparatively thick spacer layer (20 nm)has a minor effect on the positions of the maxima andminima. Figure 2(b) shows the measured reflectance of

, o

05

- X .

I

I~~i I I _I _I I I06 I 2

X (Q m)4

0 51

(a)

6 0o

(b)

X (jm)

I 0f

I

FI.2.0 5L / 2\\~ (C)0 6 1 2 4 6 10

X (/,m)

FIG. 2. (a) Calculated reflectance of a 70 nm mass thicknessSn film (with an effective thickness of 160 nm), on (1) a Tasubstrate and (2) 20 nm of A1203 on a Ta substrate. (b) Ex-perimental total reflectances of films on Ta substrates: (1)50 nm mass thickness of Sn, (2) 100 nm Sn, (3) 100 nm Sn on10 nm A1203. (c) Calculated and experimental total reflectancesof 70 nm mass thickness Sn films on Al substrates: (1) cal-culated, (2) calculated with a 20 nm A1203 spacer layer, (3)measured with a 20 nm A1203 spacer layer.

1033 J. Opt. Soc. Am., Vol. 68, No. 8, August 1978

(a)

(b)

Chris M. Horwitz 1033

I,I,

/ I

II 21

/ I

(a)

I I I I06 1 2 4

. (am)

051-

(b)

1-R

Ir

0.5Vo0oil-

l l I l I I I I06 1 2 4

X (jtm)

FIG. 3. Measured total and scattered reflected light from Snfilms on various substrates. The solid lines are scattered;dashed lines are the total reflectance. (a) Ta substrate, 100nm mass thickness Sn film: (1) without a spacer layer, (2)with a 10 nm A12 03 spacer layer. (b) 70 nm mass thicknessSn film with a 20 nm A1 20 3 spacer layer, on (1) a glass sub-strate, (2) an Al substrate.

alously large amount, and a second long-wavelengthminimum is evident. This is caused by scattering pro-cesses; Fig. 3(a) shows that a scattering resonance oc-curs when a spacer layer is added. From these obser-vations we conclude that the interference model is notsatisfactory at wavelengths shorter than the first re-flectance maximum, due to scattering in the globularfilm. In addition, a scattering resonance, present whena thin dielectric spacer layer is inserted, causes inter-ference models to fail in the intermediate wavelengthregion around the first reflectance minimium.

The small scattering resonance observed with Ta sub-strates can be enhanced with a substrate of lower op-

0-2 -

01 -

0.01

L

I I I1 2 5 10 20

X ( Jm)

FIG. 4. Power-law plot of the long-wavelength reflectanceloss of globular films vs wavelength (20 nm Al? O0 spacer layer,Al substrates). Deposited Sn mass thicknesses of (1) 236 nm,(2) 100 nm, (3) 20 nm; (4) reference line corresponding to X-3law.


tical loss, such as Al. Figure 2(c) shows the calculatedreflectances of an Sn film on an Al substrate with andwithout a spacer layer, and the measured total reflec-tance of an Sn-AI 203-Al stack. Again, a double reso-nance at long wavelengths is present; Fig. 3(b) showsthat strong scattered light resonances can be observedwhich correlate with reflectance minima, and that scat-tering commences at approximately double the wave-length of that for a globular film on glass.

We now use interference layer theory to analyze thelong-wavelength performance of globular films. Weapproximate them as a single uniform layer on a per-fectly reflecting substrate, ignoring the thin spacerlayer. Then for a globular film of refractive indexN= (n - ik) and thickness 1, the reflectance loss (absorp-tion) can be shown, from the equations given by Ramoet al. (Ref. 12, p. 349) for 1 - R - 1, to be

2A1 -R =1+ (I - n2) (1ko )2 + A'(1

where

A=- (nk) (lko)3

and

ko =27r//X

the free-space wave number. This formula is accurateto within 20% for values of (1 - R) up to 0. 1, and n up to

02F

oil -

o0*oI

05

0 2 F

0.1


R

0.6 1 2 3X ( p m)

FIG. 5. Effect of perfect vs Al substrates at short wavelength,for a thin (20 nm deposited Sn) globular film, on a 20 nm A1203spacer layer. (1) Reflectance (calculated) for perfect sub-strate, (2) for Al substrate, (3) total measured reflectance onAl substrate.

2. Thus at long X a X-3 dependence is expected, andFig. 4 shows the good agreement obtained. The long-wavelength ripple on the curves may be caused by asmall population of large globules, since the nature ofthe ripple varies with deposition parameters (e. g., de-position rate).

Although an interference model is adequate for theabove results they are also compatible with a Rayleigh-scattering model, which has a X-4 law if all scatteredradiation is absorbed [see Eq. (3)]. However, the scat-tering hypothesis breaks down in the case of thin globu-lar films, where (based on the observed particle sizes)it predicts a transition wavelength which is shorter thanthat observed. Interference theory correctly accountsfor the behavior of thin globular films in the transitionwavelength region if the optical properties of the Al sub-strate are taken into account, as Fig. 5 shows. Thetransition wavelength is longer than that for a perfectlyreflecting substrate, and agrees well with the experi-mental results.

We now consider the effect of varying the A120 3 spacerlayer thickness. Figure 6 shows the total reflectanceof films on Al substrates, with spacer layer thicknessas the parameter. Clearly the thickest spacer layerscause the greatest departures from interference layerpredictions. The subsidiary maxima and minima onthe curves, most evident in the total reflectance curvesfor the thickest spacer layer, have successive wave-number ratios of 1: 1. 2: 2.3: 2. 7: 3. 1, etc. This maybe compared with interference layer theory which pre-dicts corresponding ratios of 1: 2 :3 :, etc.

Overcoated globular films

When globular metal films are overcoated with a high-ly reflecting metal such as Au, an all-metal structurewith micron scale roughness results. This differs fromthe all-metal films without a spacer layer consideredearlier because the smooth, highly reflecting substrateis no longer a large fraction of the area presented to

incoming radiation [see Fig. 1(b)]. The specular op-tical properties of such films, Au-coated with bothstationary and planetary substrate motion, are shown inFig. 7. Note that the total (specular+diffuse) reflec-tance of these films at short wavelengths is appreciablyhigher than that of the films considered previously;however, this is not as significant as the long-wave-length performance. The high reflectance loss evidentat long wavelengths cannot be caused by scattering be-cause of the relatively small particle sizes. In addi-tion, the X-1 dependence cannot be explained by simpleinterference layer models. In the following section wewill investigate this behavior further.

THEORETICAL MODELS

Choice of models

The experimental results have shown that the short-wavelength reflectance is dominated by the nature of theglobule profile, since it is almost independent of thesubstrate and the scattered component is large. Wenave also found that interference layer theory satisfac-torily accounts for the long-wavelength behavior ofmetal-backed globular films. Thus we require appro-priate models for the intermediate wavelength behavior

R

3

( a )0.51-

0.5

0.6 1 2 3X ( Pm)

R

( b )

0.6 1 2 3X (Pm)

FIG. 6. Measured total (a) and specular (b) reflectance vswavelength of 70 nm deposited Sn films on Al substrates withA1203 spacer layer thicknesses of (1) 5 nm, (2) 10 nm, (3) 30nm.


1l

1

Chris M. Horwitz

1 -

0.5F

0.2 F

0.1 I I I I I I I I I0.6 1 2 4 6 10

X ( Jim)

FIG. 7. Power-plot of reflectance loss vs wavelength of a 70nm deposited Sn globular film, overcoated with Au. (1) Plane-tary substrate motion, (2) stationary substrate.

of metal-backed films, and for the long-wavelength be-havior of overcoated films.

In the former case, we will employ surface-wave("creeping wave") models. Some scattering propertiesof globular particles can be inferred from the exact re-sults available for isolated metal spheres (Mie scatter-ing) and isolated metal hemispheres on a conductingplane. 13 The former treatment shows that at shortwavelengths, resonances around particles can be set upwhich can be visualized as creeping waves, and whichhave similar wavelength ratios to those observed inFig. 6 (Ref. 14, p. 129). However, neither of the abovetreatments can account for the observed interferencelayer properties or for the effect of spacer layer thick-ness. In the previous treatment of glass-backed globu-lar films5 calculations on an analogous periodic wiregrating proved useful; however, the corresponding cal-culations for a wire grating spaced above a conductingplane are not available.

For overcoated globular films the region of interest

is at long wavelengths, away from the region wherescattering can occur. Thus the surface can be modeledwith an equivalent circuit (for examples of the approach,see Ref. 15, Sec. 5.18), and we will show that i simpli-fied circuit model can predict large losses, comparablewith those observed.

Surface-wave model

Scattering processes can redistribute energy fromthe normal interference processes into waves aroundthe globules, as shown in Fig. 8(a). These surfacewaves can themselves be modeled using interferencetechniques, using the formally equivalent structureshown in Fig. 8(b). A hypothetical substrate with awave impedance of infinity provides zero reflectionphase shift and unit reflectance, and the refractive indexN2 of the upper structure can be taken to be that givenearlier for globular films. Note that a given incidentwave can always excite a vertically polarized surface-wave mode due to the close spacing of globules; hori-zontally polarized modes should not propagate becausethe configuration would correspond to a waveguide be-yond cutoff.

Waveguide theory can be used to estimate N1 by treat-ing the surface wave as a TEM mode traveling betweentwo infinite conducting planes separated by a distance a[Fig. 8(a)]. With a Sn upper plane and a perfectly con-ducting lower plane, N1 can be found using the equationsgiven in Ref. 12 (p. 379), by iteration. Figure 9 showsthe results obtained at X= 1.3 Am, for optical constants

a(nm)103

102

N2

Ni ( a)

- / , , , / ' '

N1

10

7N'~-_..T

r& ~ - I

51 b)

NONsub` °

FIG. 8. (a) Cross-sectional view of a globular film showingsurface wave ray path around globule, with a perfectly re-flecting substrate and a spacer layer thickness of "a. "I N1 isthe refractive Index oxperioncod by a horizontally traveling,vertically polarized wave. (b) Formally equivalent ray pathfor surface wave used in calculations of surface-wave reflec-tidn coefficient.


0.1 1 2 5 10n , k

FIG. 9. Theoretical transmission-line propagation constantsvs plate separation "a, " with dielectric filler refractive indexas parameter. X = 1. 3 ,um, and conducting plate indexN = (2. 7 - 8. 1 i), corresponding to Sn. Other plate assumed tobe perfectly conducting.


R

0.4 0.6 4 6

FIG. 10. Calculated reflectance vs wavelength using the sur-face-wave interference scattering model, of incoherent glob-ules of radius r= 0. 2 gim, on a perfectly reflecting substrate.The upper refractive index N2 = (2. 45 - 0. 2 i), and the surfacewave indexN 1=(1) (3-0.8i), i.e., a . 5 nm, (2) (2-0.li),i.e., a. 50nm.

close to those of Sn and various refractive indices ofthe medium between the parallel planes ( . 1.7 for A1203 ).It has been found that N1 does not vary greatly withwavelength for values of a- 5 nm.

We assume that scattering affects interference andsurface-wave processes in a simple linear fashion,giving the total reflectance:

R= (1 -S)I+SW, (2)

where I is the standard interference layer reflectance[in the structure of Fig. 8(a)], Wis the surface-wavereflectance [Fig. 8(b)], and S is the fraction of incidentlight scattered by the globules, for a given globule size.In the following calculations the scattering term wasextended from the long wavelength result for a metalsphere (Ref. 14, p. 90) to give a plausible scatteringfunction,

S=3.71 c 4(1+0.24CE2 - -.. ) for a<0.7

=1 for ca>0.7,

resonance around the globules) are 1: 1.4: 1. 9: 2.4: 2. 9,etc., a good agreement with experiment in view of theapproximations employed.

Equivalent circuit model

To describe the long-wavelength performance ofovercoated globular films, we represent the idealizedrectangular globular structure shown in Fig. 11(a) bythe simplified equivalent circuit of Fig. 11(b), wherer, represents the equivalent resistance of the metal onthe top faces, and r 2 that of the side walls and bottom.Cl is the capacitance between two adjacent top faces,given by16

C1 = EdK(l - k2)1"2/2K(k), (4)

where k=t/(2d+t), E0 is the free-space permittivity,d, t as in Fig. 11(a), and K(u) is the complete ellipticintegral of modulus u. Note that the capacitance of thelower face (of width t) has been ignored, making thismodel valid only for small t relative to d and h.

The values of L and C2 (pertaining to the gap betweentwo globules) can be estimated from low-frequency ap-proximations to be [with h as in Fig. 11(a)],

C2 =Eodh/t and L=i 0 th/d, (5)

where go is the permeability of free space. These val-ues give a resonant frequency which is smaller than thatof a x/4 cavity by a factor of 2/,r. Numerical calcula-tions using the integral equation approach of Maystre17

applied to lamellar gratings [which have a cross sectionsimilar to that of Fig. 11(a)] have given a factor of2. 2/Tr, in close agreement with the present model. 18

The (complex) metal resistances are derived in astraightforward manner from the surface impedances ofthe metals, Z, (Ref. 12, p. 288):

NZs=10(N2- 1)

width I E-rxditacIE (6)

(3)

where ! = 27rr/N. The above scattering formula assumesno cooperative effects between globules; in fact, somenearest neighbor interaction has been observed in globu-lar films. 5

Figure 10 shows the resultant calculated reflectanceof an incoherent array of globules with radius r= 0. 2,um, on a perfectly reflecting substrate. Values of N1have been chosen to correspond to large and smallspacer layer thicknesses, with a dielectric filler indexbetween that of air and A1203 (the surface wave propa-gates in both media because of the rounded globulecross section). A range of values for the radius, asfound in practice, would smooth out the resonances inFig. 10; however, even without this smoothing the be-havior is similar to the experimental results of Fig. 6,with a higher average reflectance at intermediate wave-lengths for the thick spacer-layer case. In addition,for the thick spacer layer, successive wave-numberratios of maxima and minima in reflectance (caused by

E

h--A ~ tHtI

r2JL

(a)

(bI

FIG. 11. (a) Idealized model of an overcoated globular tilm(repeated indefinitely into the page). h is the globule height,d the globule diameter, and t the distance between globules.(b) Equivalent circuit used to describe the above structure atlong wavelengths. Symbols are defined in the text.

1037 J. Opt. Soc. Am., Vol. 68, No. 8, August 1978 Chris M. Horwitz 1037

1-R1

0.5 1.

0.2

0.1 1-

n.01 I I - I1 2 5 10

) ( Pm)FIG. 12. Calculated equivalent-circuit reflectance loss vswavelength on a power law plot, for d= 0.2, h=0.2, t=0.05pum, and a structure with (1) Au top and side walls, (2) Au top,Sn side walls.

where N = (n - ik) = metal refractive index, and 770 is theimpedance of free space. The reflectance R followsfrom the mismatch between i10 and the impedance of theequivalent circuit, ZL-

In the following calculations, the value of h has beenchosen to give a resonant wavelength close to the peakabsorption wavelength observed. It. has been found thatvariation in d and t does not affect the results greatly,and Fig. 12 shows typical results. It is clear from thefigure that an Au structure can give surprisingly largeabsorption; however, a structure with Au top faces andSn side walls has relatively high absorption approachingthe experimental data, indicating that the Au coatinghas not covered the sides of the globular particles.

The fixed value of h(O. 2 gim) used in Fig. 12 can onlybe an average value, since the rounded globule profileresembles a "tapered waveguide" to incoming radiation.This may account for the experimentally observedbroadband absorption in Fig. 7.

CONCLUSIONS

We have found that, while film scattering is small,globular metal films behave like interference films, andhave a cut-on wavelength closely proportional to thefilm thickness. In addition, globular filmns oi a metalsubstrate exhibit interference-film properties even forwavelengths as short as their first reflectance maxi-

mum. However, if the globules are electrically isolatedfrom the underlying metallic substrate, unusual selec-tive properties result which are compatible with a sur-face-wave model. The broadband absorption caused bysurface waves can be high over a 4: 1 wavelength range,and appears to be limited at short wavelengths by therounded globule profile. A useful area for further de-velopment of these films would be in the construction ofglobular films with a lower inherent reflectance at shortwavelength; for instance, a scaled-down version of thedendritic structures described in Refs. 8-10.

Other geometric structures without a dielectric inter-mediate layer (for instance, metal-coated globularfilms), while showing selectivity, demonstrate that veryrough all-metal surfaces are not as suitable for use asselective absorbers because of their higher reflectedscattered light, and because of their lower infrared re-flectance due to long-wavelength resonant absorption.

ACKNOWLEDGMENTS

I would like to thank Professor C. N. Watson-Munrofor his support and guidance in this work, Dr. R. C.McPhedran for his discussions during the preparationof this material, and I. T. Ritchie for the use of histhin-film calculation routines. I am grateful to the Syd-ney University Energy Research Centre and the ARGCfor funds, and Professor H. Messel for the provision ofresearch facilities in the School of Physics. This workwas done with the aid of a CSIRO Postgraduate Student-,;hip.

1A. B. Meinel and M. P. Meinel, Phys. Today, Feb. 1972,p. 44.

2J. C. C. Fan, F. J. Bachner, and R. A. Murphy, Appl.Phys. Lett. 28, 440 (1976).

3D. A. Williams, T. A. Lappin, and J. A. Duffie, Trans.ASME 85A, 213 (1963).

4E. A. Allen, G. D. Scott, K. T. Thompson, and F. Veas, J.Opt. Soc. Am. 64, 1190 (1974).

'C. Al. Horwitz, Internal Report No. SP75/3, presented atI. S. E. S. Conference, Los Angeles, Calif., July 1975; C. M.Horwitz, J. A. Beunen, and R. C. McPhedran, "Interferenceand Diffraction in Globular Metal Films," J. Opt. Soc. Am. 68,1023-1031 (1978).

6R. E. Hetrick and J. Lambe, Phys. Rev. B 11, 1273 (1975).7H. E. Bennett, J. Opt. Soc. Am. 53, 1389 (1963).8J. J. Cuomo, J. F. Ziegler, and J. M. Woodall, Appl. Phys.

Lett. 26, 557 (1975).9J. J. Cuomo, J. M. Woodall, and T. H. Di Stefano, in Pro-

ceedings of the American Electroplaters Society Symposium,Atlanta, Ga., 1976, p. 133 (American Electroplaters' So-ciety, Inc., Winter Park, Fla., 1976).'OD. P. Grimmer, K. C. Herr, and W. J. McCreary, in Ref.

9, p. 79."1 H. P. Singh and L. E. Murr, Philos. Mag. 26, 649 (1972).12S. Ramo, J. R. Whinnery, and T. van Duzer, Fields and

Waves in Communication Electronics (Wiley, New York,1965).

13V. Twersky, I.R.E. Trans. AP-5, 81 (1957).14M. Kerker, The Scattering of Light (Academic, New York,

1969).15N. Marcuvitz, Waveguide Handbook, M.I. T. Radiation Lab-

oratory Series (McGraw-Hill, New York, 1951).t6 Amnerican Institute of Physics Handbook, edited by D. E.

Gray (McGraw-Hill, New York, 1963), p. 5-1g.t7D. Maystre, Opt. Commun. 8, 216 (1973).18R. C. McPhedran (private communication, 1976).

1038 J. Opt. Soc. Am., Vol. 68, No. 8, August 1978 Chris M. Horwitz 1038

Documents

Solar-selective globular metal films