Recording ultrafine interference patterns of evanescentwaves at a silver-photoresist interface
Russell W Gruhlke
Coherent Optics Division, 2301 Lindbergh Street, Auburn, California 95603
Michael F. Becker
Department of Electrical and Computer Engineering, University of Texas at Austin, Austin, Texas 78712
Received March 14, 1991; revised manuscript received March 5, 1992; accepted March 12, 1992
We investigated the ultrafine fringe patterns that result from the interference of counterpropagating, evanes-cent surface waves that are supported in a layered silver-photoresist geometry. The surface waves that weconsidered were single-interface surface plasmons, long-range coupled surface plasmons, and short-rangecoupled surface plasmons. Calculations predicted sinusoidal intensity fringes with periodicities ranging from100 to 140 nm when the surface waves were generated by light of 488-nm wavelength. The variance ofthe fringe periodicity and other fringe properties as a function of changing silver film thickness was alsoinvestigated.
INTRODUCTION
A propagating evanescent wave interacts with a referencewave to form interference fringes that can be recorded ina holographic medium. Such evanescent-wave hologramshave many properties that are similar to those of conven-tional plane-wave holograms, but they also exhibit uniqueproperties such as spatial localization of interferencefringes to a thin, nearly two-dimensional layer and ultra-fine fringe spacing. These useful properties have beenapplied (1) to fabricate blazed, holographic surface-reliefgratings,' (2) to store holographic information in a planarformat compatible with integrated optics,2 and (3) toconstruct large-aperture holograms.2 4 Ultrafine fringespacing has prompted superresolution experiments thatrecorded the images of objects containing small featuresizes as well as experiments that demonstrated the fabri-cation of gratings with spatial periodicities less than theA/2 classical limit, where A is the free-space wavelengthof light used to generate the evanescent-wave fringe pat-tern.4 7 Bryngdahl8 has written an excellent review sum-marizing these and other advances in evanescent-waveholography.
Evanescent waves are inhomogeneous electromagneticwaves characterized by the noncoincidence of the surfacesof constant phase with the surfaces of constant amplitude.Such waves can be generated at the interface between twodifferent dielectric media upon the total internal reflec-tion of plane waves striking that interface or by diffractionfrom a grating located at the interface. Electromagneticwaves guided in a dielectric waveguide or along a metal-dielectric interface are also examples of evanescent waves.In the latter case, the electromagnetic waves are coupledto optical-frequency electron-density oscillations con-strained to the surface of the metallic layer. The coupledelectron oscillation and optical wave is called a surfaceplasmon or a single-interface surface plasmon (SISP) forthe case of a single metal-dielectric interface.9 '0 If two
metal-dielectric interfaces are in close proximity, the elec-tromagnetic fields associated with the SISP's at oppositeinterfaces can overlap and couple. This occurs in a thinmetal film (less than 100 nm in thickness) that is sur-rounded by identical dielectric material."-15 The inter-acting fields can combine in two ways to form propagatingwaves with magnetic-field profiles that possess even orodd symmetry. These excitations, commonly called long-range and short-range coupled surface plasmons (LRCSP'sand SRCSP's, respectively) have even and odd magnetic-field symmetry, respectively, and are guided along thethin metal film as evanescent surface waves. In all threecases a prism coupling technique can be used to generatethe plasmons since the momentum component, parallel tothe metal-dielectric interface, of incident light is increasedon passage through a high-refractive-index prism to per-mit plasmon-photon interaction."- 4 If the dielectric me-dium adjacent to the metal layer is a recording medium,the fringes of interfering SISP, LRCSP, or SRCSP excita-tions can be recorded. An investigation of the character-istics of such evanescent fringe patterns is the subject ofthis paper.
THEORY
The electromagnetic fields associated with the SISP, theLRCSP, and the SRCSP are all characterized by p po-larization (magnetic-field vector oriented parallel to themetal-dielectric interface) and a field amplitude thatdecays exponentially away from a single metal-dielectricinterface (SISP) or from both metal-dielectric interfacesof a metal film embedded in a dielectric (LRCSP andSRCSP). The electric-field amplitude E for all threecases is illustrated in Fig. 1 for a silver-photoresist layergeometry. If identical but counterpropagating surfacewaves interfere, a standing-wave fringe pattern is formedhaving a shape and periodicity determined by the intensity
The intensity, I(x,y) - El2, of the standing-wave fringepattern is then
I ,' si veF,1' / I I,
z=-hphotoresist
Il
lIxl>I~
In this expression G is a constant for a fixed wavelength,x the wave-number components have been expressed as k =
kxr + ikxi and k, = kzr + ikzi to account for absorption,and the terms I, and I2 are
I = (kxkx* + kzkz*)[A2 exp(-2kX,ix) + B2 exp(2k,ix)],(12)
I2 = 2AB(kzk,* - kxkx*)cos(2kxrx). (13)
The wave-number component k, for the SISP is given bythe dispersion relation
k = (/C)[8dem/(Sd + em)]1/2, (14)
L - IE 1l
IIIIIIIIII
�- -- 1E.
Fig. 1. Electric-field profile Ex for the SISP, the LRCSP, and theSRCSP as a function of the distance z from a silver-photoresistinterface.
distribution I- E12, where E is the total electric field.An expression for this distribution is determined here forstanding-wave fringe patterns contained in the dielectricregion adjacent to the metal film layer.
For each of the three types of surface wave considered,the magnetic field in the dielectric region defined byz > 0 has the general form
H+ = A exp(-kzz)exp[-i(cot - kx)] (1)
for a surface wave propagating along the +x axis and
H- = B exp(-kz)exp[-i(w)t + kxx)] (2)
for a surface wave traveling in the opposite direction.The electric-field components are determined by
E = (-ic/cos)dH,/dz,
E,= (ic/as)dH,/dx,
(3)
(4)
which are derived from Maxwell's equations. Theelectric-field components for the forward-propagatingwave, E., and E, are
In these expressions, kx and k, are the wave-number com-ponents parallel and normal to the metal-dielectric inter-face, respectively; Ed is the dielectric constant of thedielectric medium; cs is the frequency of the surface wave;and c is the speed of light in vacuum. Adding the forwardand the backward components to get the total standing-wave field, i.e., Ex= E+ + Ex -andE = E,+ + EJ, yields
E. = (ikzc/ssd)exp-kZz)exp(-iost)
X [A exp(ikxx) + B exp(-ikxx)], (9)
Ez = (kXc/cWsd)exp(-kzz)exp(- ict)
X [-A exp(ik.x) + B exp(-ikxx)]. (10)
where Ed and em are the dielectric constants of the dielec-tric and the metallic medium, respectively. The LRCSPand SRCSP dispersion relations are, respectively,'6
kz,d =-(kz,mSd/8)tanh(kz,mh/2),
kz,d = -(kzmSd/Sm)coth(kzmh/2),
(15)
(16)
where kz,d and kzm are the wave-number components nor-mal to the metal-dielectric interface in the dielectric andthe metallic medium, respectively, and h is the metal filmthickness. Equations (15) and (16) are solved numericallyin conjunction with
kzd2- kX2
+ Ed ((W2/C2) = (17)
to determine the wave-number components kx and k, forboth the LRCSP and the SRCSP. Equation (17) resultsfrom the substitution of the magnetic-field expression,Eq. (1), into the wave equation derived from Maxwell'sequations.
RESULTS AND DISCUSSION
The two dominant characteristics of the intensity pre-dicted by Eq. (11) for interfering and counterpropagatingsurface waves are (1) an exponential falloff with increasingdistance from the photoresist-silver interface and (2) a
160
^140
S, 120
._
:;100
o s._
W 448
60
LRCSP
SISP -------- >
SRCSP
20 30 40 50 60 70
Silver thickness h (nm)Fig. 2. Periodicity A of LRCSP and SRCSP interference fringesas a function of the silver film thickness h. The period associ-ated with the SISP is indicated by the arrow.
Fig. 3. Constant intensity contours of interfering, counterpropa-gating LRCSP's supported by a 30-nm-thick silver film (substrate)embedded in photoresist. From top to bottom, the ratios of theintensity to the maximum intensity represented by the curvesare 0.01, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, and 0.7.
R. W Gruhlke and M. F. Becker
300
iM 200.0
E0
Q 100S._
SRCSP
h=30 nm
0 100 200 300Distance along substrate (nm)
Fig. 6. Constant intensity contours of interfering, counterpropa-gating SRCSP's supported by a 30-nm-thick silver film (substrate)embedded in photoresist. From top to bottom, the ratios of theintensity to the maximum intensity represented by the curvesare 0.01, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, and 0.7.
cc)
Cu
I-.0
a
!n
.0C'-
r)SCu.U,
0 100 200 300Distance along substrate (nm)
Fig. 4. Constant intensity contours of interfering, counterpropa-gating LRCSP's supported by a 50-nm-thick silver film (substrate)embedded in photoresist. From top to bottom, the ratios of theintensity to the maximum intensity represented by the curvesare 0.01, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, and 0.7.
300
icC
Q200
.0a,
0 100 200 300Distance along substrate (nm)
Fig. 5. Constant intensity contours of interfering, counterpropa-gating LRCSP's supported by a 75-nm-thick silver film (substrate)embedded in photoresist. From top to bottom, the ratios of theintensity to the maximum intensity represented by the curvesare 0.01, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, and 0.7.
'iC)
.0a0
S.4
0 100 200 300Distance along substrate (nm)
Fig. 7. Constant intensity contours of interfering, counterpropa-gating SRCSP's supported by a 50-nm-thick silver film (substrate)embedded in photoresist. From top to bottom, the ratios of theintensity to the maximum intensity represented by the curvesare 0.01, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, and 0.7.
cCCZ
(n.0
a0C)
.)
100 200
Distance along substrate (nm)Fig. 8. Constant intensity contours of interfering, counterpropa-gating SRCSP's supported by a 75-nm-thick silver film (substrate)embedded in photoresist. From top to bottom, the ratios of theintensity to the maximum intensity represented by the curvesare 0.01, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, and 0.7.
Vol. 9, No. 8/August 1992/J. Opt. Soc. Am. A 1283
periodic variation along the x axis. These characteristicscan be imprinted into the photoresist layer since a varia-tion in exposure intensity causes a corresponding variationin photoresist thickness upon the subsequent processingand development of the exposed photoresist layer. Thusthe development of a photoresist layer exposed to SISP,LRCSP, or SRCSP interference fringes should result in athin, corrugated photoresist layer adjacent to the metalfilm substrate.
The fringe spacing of the intensity undulation along thex axis predicted by Eq. (11) is equal to /kr and can bedetermined by solving one of the dispersion equations[Eqs. (14)-(16)] in conjunction with Eq. (17) for k,. As-suming that the free-space wavelength of the laser lightgenerating the interfering surface waves is equal to 488 nmand using the values em = -9.12 + i.3 and Ed = 2.76 forthe dielectric constants of silver'7 and Shipley microposit1400 photoresist, respectively, the spatial periods of thefringe patterns generated by interfering SISP's, interfer-ing LRCSP's, and interfering SRCSP's were calculated.These values are plotted as a function of the silver filmthickness h in Fig. 2. The prominent feature of thisgraph is the divergence of the LRCSP and the SRCSPfringe spacing as the silver film thickness decreases. Thisdivergence is caused by the increasing degeneracy of theSISP mode as coupling between SISP's on opposite sides ofthe metal film increases with decreasing metal film thick-ness to form LRCSP's and SRCSP's. The LRCSP period-icity increases slightly while the SRCSP periodicitydecreases more sharply to values less than 100 nm forsilver film thicknesses less than 30 nm. With increasingsilver film thickness, both the LRCSP and the SRCSPfringe spacings converge asymptotically to the fringe spac-ing of the SISP, which is roughly equal to A/4 (or 122 nm).It is important to note that regardless of silver film thick-ness each periodicity predicted in Fig. 2 is less than theclassical limit A = A/2 (or 244 nm) for conventional, plane-wave holography.
Equation (11) was evaluated to determine constant in-tensity contours and thus the photoresist exposure distri-bution caused by the interference fringes. This was doneby choosing a value for the ratio of the intensity to themaximum intensity and then solving Eq. (11) to determinethe locus of points (x, z) at which this intensity ratiooccurs. Nine intensity ratios, 0.01, 0.05, 0.1, 0.2, 0.3, 0.4,
0.5, 0.6, and 0.7, were used. It was also assumed that theelectric-field strength of counterpropagating waves wasequal, i.e, A = B in Eq. (11). Figures 3-8 display the pre-dicted constant intensity contours resulting from the in-terference of coupled surface waves supported on a silverfilm of thickness h (h = 30, 50, and 75 nm), and Fig. 9shows the intensity contours resulting from the interfer-ence of SISP excitations at a single silver-photoresist in-terface. The intensity contours positioned from the topto the bottom in each figure represent the loci of points(x, y) at which the ratios of the intensity to the maximumintensity are equal to 0.01, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6,and 0.7, respectively.
Each constant intensity contour can be characterized bya periodicity, a contrast or peak-to-trough distance, and apenetration distance defined as the maximum distance ofthe contour from the silver-photoresist interface. Thecontour periodicity is dependent only on the type of sur-
300
S SISP
: 200
.a
0 100 200 300
Distance along substrate (nm)Fig. 9. Constant intensity contours of interfering, counterpropa-gating SISP's supported at a silver-photoresist interface. Fromtop to bottom, the ratios of the intensity to the maximum inten-sity represented by the curves are 0.01, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5,0.6, and 0.7.
face wave interfering and the metal film thickness h.These dependencies are indicated in Fig. 2 and are dis-cussed above. The striking feature evident in Fig. 3-9 isthe variance in the contrast of the intensity contours asthe thickness of the silver film changes. For example, theSISP, LRCSP, and SRCSP intensity contours are roughlyequivalent if the silver film thickness is large; i.e., h =75 nm (Figs. 5, 8, and 9). But for a smaller silver filmthickness, h = 30 nm (Figs. 3 and 6), the variation of theSRCSP contours is barely discernible (peak-to-troughdistance of 15 nm) while the LRCSP contours are verypronounced (peak-to-trough distance of 160 nm). Withdecreasing silver film thickness, the contrast of the SRCSPcontours decreases by a factor of 1/4 while the contrast ofthe LRCSP contours more than doubles. This trend re-sults from decreased (increased) attenuation as the LRCSP(SRCSP) electromagnetic fields are expelled from (drawninto) the metallic film as the film thickness h is decreased.The decrease in the SRCSP field contrast predicted forsilver films c30 nm thick greatly reduces the potential forforming ultrafine gratings with spacings less than 100 nm.In general, the penetration of electromagnetic fields intothe photoresist layer is small for all three surface-wavetypes considered. For relatively thick silver film layers(h > 50 nm) the intensity contour representing 30% of themaximum intensity penetrates only 40 nm into the pho-toresist layer for all three surface-wave types considered.As the silver film thickness decreases to 30 nm, theLRCSP contours penetrate nearly twice as far into thephotoresist layer, while the SRCSP contour penetration ishalved. Although these surface-wave field penetrationsinto the photoresist layer seem small, it should be notedthat surface-wave intensities at the silver-photoresist in-terface can be several orders of magnitude larger than theintensity of a plane wave striking that same interface. 8
CONCLUSION
We investigated the shape and the periodicity of interfer-ence fringes generated in a photoresist layer by counter-propagating, evanescent surface waves supported by
R. W Gruhlke and M. R Becker
1284 J. Opt. Soc. Am. A/Vol. 9, No. 8/August 1992
an adjacent thin silver film. The counterpropagatingsurface-wave pairs considered were either single-interfacesurface plasmons (SISP's), long-range coupled surfaceplasmons (LRCSP's), or short-range coupled surface plas-mons (SRCSP's). By calculating constant intensitycontours, we predicted the fringe distributions to be quasi-sinusoidal with fringe spacings less than the classical A/2limit, where A is the wavelength of the light generating thesurface waves. For A equal to 488 nm and a silver filmthickness equal to 30 nm or more, the periodicity valuesvaried between 100 and 140 nm: the values centeredabout A/4.
The calculations also indicated that the shape and theperiodicity of the fringe patterns vary significantly withchanges in the silver film thickness. The fringe spacingof the LRCSP interference pattern increases slightly withdecreasing silver film thickness, while the periodicity ofthe SRCSP interference pattern decreases more sharply tovalues less than 100 nm over the same range of silver filmthickness. Thus metal film thickness can be used as aparameter to control holographic fringe spacing. Boththe electromagnetic-field contrast and the penetrationinto the photoresist layer diverge for the LRCSP andSRCSP interference patterns with decreasing silver thick-ness. The contrast and the penetration of the SRCSP be-come negligible for values of silver film thickness less than30 nm. Unfortunately, this negates some of the potentialfor forming ultrafine fringe grating structures. However,sufficient contrast in intensity exists for other combina-tions of silver film thickness and type of surface wave forthe fabrication, using the argon-ion laser, of ultrafinegratings with periodicities ranging between 100 and130 nm. The fabrication of grating structures of evensmaller periodicity with other laser sources may be pos-sible for application to the miniaturization of optical andelectronic devices.
REFERENCES
1. J. Cowan, "Blazed holographic gratings-formation by sur-face waves and replication by metal electroforming," in Peri-
odic Structures, Gratings, Moire Patterns, and DiffractionPhenomena I, C. H. Chi, E. G. Loewen, and C. L. O'BryanIII, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 240, 5-12(1980).
2. W Lukosz and A. Wuthrich, "Hologram recording and read-out with the evanescent field of guided waves," Opt. Commun.19, 232-235 (1976).
3. S. Suinov and V Suinov, 'Angular and polarization depen-dences of the diffraction efficiency of evanescent-wave holo-grams," Sov. J. Quantum Electron. 9, 1046-1048 (1979).
4. 0. Bryngdahl, "Holography with evanescent waves," J. Opt.Soc. Am. 59, 1645-1650 (1969).
5. H. Nassenstein, "Superresolution by diffraction of subwaves,"Opt. Commun. 2, 231-234 (1970).
6. H. Nassenstein, "Interference, diffraction and holographywith surface waves I," Optik (Stuttgart) 29, 597-607 (1969).
7. H. Nassenstein, "Interference, diffraction and holographywith surface waves II," Optik (Stuttgart) 30, 44-55 (1969).
8. 0. Bryngdahl, "Evanescent waves in optical imaging," inProgress in Optics, E. Wolf, ed. (North-Holland, Amsterdam,1973), Vol. 11, pp. 167-221.
9. R. Ritchie, "Surface plasmons in solids," Surf. Sci. 34, 1-19(1973).
10. W Steinmann, "Optical plasma resonances in solids," Phys.Status Solidi 28, 437-459 (1968).
11. G. Kovacs and G. Scott, 'Attenuated total reflection angularspectra of a Ag film bounded by dielectric slabs," Can.J. Phys. 56, 1235-1247 (1978).
12. Y Kuwamura, M. Fukui, and 0. Tada, "Experimental obser-vation of long-range surface plasmon polaritons," J. Phys.Soc. Jpn. 52, 2350-2355 (1983).
13. J. Quail, J. Rako, and H. Simon, "Long-range surface plas-mon modes in silver and aluminum films," Opt. Lett. 8, 377-379 (1983).
14. A. Craig, G. Olson, and D. Sarid, "Experimental observationof the long-range surface plasmon polariton," Opt. Lett. 8,380-382 (1983).
15. R. W Gruhlke, W R. Holland, and D. G. Hall, "Optical emis-sion from coupled surface plasmons," Opt. Lett. 12, 364-366(1987).
16. A. Otto, "Excitation by light of co+ and Co surface plasmawaves in thin metal layers," Z. Phys. 219, 227-233 (1969).
17. P. B. Johnson and R. W Christy, "Optical constants of thenoble metals," Phys. Rev. B 6, 4370-4379 (1972).
18. W H. Weber and G. W Ford, "Optical electric-field enhance-ment at a metal surface arising from surface-plasmon excita-tion," Opt. Lett. 6, 122-124 (1981).
