Developed profile ofholographically exposed photoresist gratings

Bernardo de A. Mello, Ivan F. da Costa, Carlos R. A. Lima, and Lucila Cescato

A simulation of the profile of holographically recorded structures in photoresists is performed. Inaddition to its simplicity this simulation can be used to take into account the effects that arise fromexposure, photosensitization, development, and resolution of positive photoresists. We analyzed theeffects of isotropy of wet development, nonlinearity of the photoresist response curve, background light,and standing waves produced by reflection at the film–substrate interface by using this simulation, andthe results agree with the experimentally recorded profiles.Key words: Holographic gratings, photoresist processing.

1. Introduction

Surface-relief structures holographically recorded inphotoresist are a subject of great interest in optics andoptoelectronics. For applications in holography forwhich the component is either directly recorded inphotoresist or embossed for replication, a linear re-sponse is desired.1 In other applications such asphotolithography, in which one can use the photore-sist as a mask to etch a substrate, a strong nonlinearresponse is more adequate to obtain an etch-resistantsquare profile.2 In each case the precise control of arecorded profile in the photoresist is desirable.Most applications of holographic recording in pho-

toresist are concerned with the fabrication of opticalcomponents. The diffraction efficiency of such com-ponents is highly dependent on the profile of thediffracting structure, and some interesting compo-nents can be obtained if the profile can be con-structed.3–7 The accurate control of a recorded pro-file in photoresists is therefore indispensable forproducing diffraction components or devices.The profile of recorded structures in photoresist

depends on several factors; light exposure pattern,

B. deA.Mello, I. F. da Costa, and L. Cescato are with the Institutode Fisica Gleb Wataghin, Universidade Estadual de Campinas, CxPostal 6165, 13081 Campinas, Brazil. C. R. A. Lima is with theDepartamento de Fisica, Centro de Tecnologia, Universidade Meto-dista de Piracicaba, Santa Barbara D’Oeste, SP, Brasil.Received 14May 1993; revised manuscript received 24May 1994.0003-6935@95@040597-07$06.00@0.

r 1995 Optical Society of America.

photoresist sensitization, and development. In suchcases, simulations are useful tools to improve theunderstanding of the effects of each process param-eter.In this paper we develop a simulation that can be

used to determine the final profile recorded in photore-sist under holographic exposures, and we use thissimulator to study the influence of some processparameters. The simulator incorporates a stringdevelopment algorithm8,9 to describe the photoresistprofile evolution, the development rate, that can beobtained either from experimental measurments orfrom the model of Mack,10 and a spatial frequencyfilter represented by a simple modulation transferfunction.

2. Model

As is well known positive photoresists are basicallycomposed of three components: a photoactive com-pound 1inhibitor2, a base resin, and a solvent.11 Thebase resin is soluble in aqueous alkaline developersand the presence of the photoactive compound stronglyinhibits its dissolution. The light neutralizes thephotosensitive compound and increases the solubilityof the film. After development in such solutions anintensity light pattern is converted into a relief struc-ture.The resulting relief profile recorded in photoresist

depends on both the exposure light pattern throughthe film and on the complete response of the photore-sist, including the development. These processescan be mathematically described, and the profile inthe photoresist can then be calculated.

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2.A. Exposure Pattern

Neglecting multiple reflections, the holographic inter-ference pattern that is inside the photoresist film,generated by the interference of two coherent beamsand their respective reflections, can be represented by1see Fig. 12

I1x, z2 5 0E1 exp3i1k1 · r24 1 E2 exp3i1k2 · r24

1 E1r exp5i3k2 · 1d 2 r246

1 E2r exp5i3k1 · 1d 2 r246 0 2 , 112

where

E1 5 E1 · y , E1r 5 2E1r · y ,

E2 5 E2 · y , E2r 5 2E2r · y , 122

k1 5 2p@l03n1cos u x 1 sin u z2 1 ikz@cos u4 , 132

k2 5 2p@l03n12cos u x 1 sin u z2 1 ikz@cos u4 , 142

and u is equal to half of the angle formed between thetwo interfering beams inside the film, n is the realpart of the photoresist refractive index, k is theimaginary part of the photoresist refractive indexwith a 5 14pk2@l0 as the absorption coefficient, x, y,and z are unit vectors in the direction of the x, y, and zaxes, respectively.

r 5 xx 1 z z 152

is the coordinate of any point inside the photoresistfilm with its origin at the air–photoresist interface, E1andE2 are the amplitudes of the electrical fields of theincident waves that are transmitted through theair–photoresist interface, Er1 and Er2 are the complexamplitudes of the waves reflected at the film–substrate interface 1including the phase of the reflec-tion and the losses that are due to the absorption ofthe incident wave in the film2, and d 5 dz with dequal to the film thickness.The light intensity pattern given by Eq. 112 contains

two sinusoidal fringe patterns: one in the x direc-tion 1produced by the interference between two incom-ing waves2 and another in the z direction, which iscalled a standing wave 1produced by the interferencebetween each incoming wave and its reflection at thefilm–substrate interface2. The neglected multiple

Fig. 1. Schema of the interfering waves on photoresist filmshowing the incident and reflected beams.

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reflections may be represented by a term that multi-plies both sinusoidal fringe patterns.12 This termdepends on the film thickness and on the reflectivityof both interfaces. This does not change the relativeintensity between the two sinusoidal patterns, butrather the total amplitude, similar to changes in thelight intensity. For glass substrates the effect ofmultiple reflections can be neglected completely.For high reflectivity substrates, however, the mul-tiple reflections can strongly reduce the total energyinside the film if the film thickness is not chosenappropriately.The contrast of the principal interference pattern is

better when E1 5 E2 and any perturbation on theinterference pattern that is due to vibrations orthermal drifts may be represented by a differencebetween E1 and E2. Any light scattering or preexpo-sure can be considered by adding a background lightintensity 1Ib2 to Eq. 112.In holographic exposures the photoresist is gener-

ally not completely exposed because the requirementsof homogeneity and the quality of the wave frontgenerally result in the use of low irradiance in thevisible 1blue-violet2. In such cases the absorption isvery poor 3at 450 nm the absorption coefficient 1a2 ofthe unexposed positive photoresists is approximatelyten times smaller than that for UV light 1365–405nm2134 and the irradiance is low, requiring longexposure time to saturate the material. In suchcases changes in the intensity pattern during expo-sure because of bleaching 1absorption coefficient andrefractive-index changes2 can be neglected, so that thetotal exposure energy 1E2 can be found directly bymultiplying the irradiance of Eq. 112 by the exposuretime 1Dt2. For UV exposures for which these ap-proaches are not valid, the exposed energy must becalculated by integration of Eq. 112 during exposuretime, taking into account photoresist bleaching.9

2.B. Photoresist Response

Although the response of photoresist film to lightexposure is frequently described by the function ofthe photoresist solubility rate 1V 2 versus exposureenergy 1E2, its overall response also depends on thedevelopment process that introduces other nonlineari-ties. To complete the description of the photoresistresponse we must also consider the effect of the limitof the spatial frequency response. Therefore wedivide this subsection into three parts.

2.B.1. V X E CurveThe V X E curve 3photoresist solubility rate 1V 2 versusexposure energy 1E24 represents the response of thephotoresist film to uniform light exposures, whichdepends on the resist–developer system that includessuch variables as developer concentration, tempera-ture, and prebake conditions. This curve can beexperimentally measured by using several tech-niques.1,11,14 Figure 2 shows examples of such curvesfor Shipley AZ-1350J photoresist films developed byimmersion in NaOH solutions for different concentra-

tions and for AZ-1400 films immersed in ShipleyAZ-351 developer. These measurements were per-formed by monitoring the development with a He–Nelaser. When the film thickness changes the intensityof the He–Ne laser presents maxima and minimafrom which the development rate depth can be calcu-lated along the film depth.14The photosensitization process was mathemati-

cally represented by Dill et al.11 who wrote the inhibi-tor concentration,m1x, z2, as a function of irradiance:

m1x, z2 5 exp32CI1x, z2Dt4 , 162

where I1x, z2 is given by Eq. 112, Dt is the time ofexposure, and C is the kinetic exposure rate con-stant.8Using the inhibitor concentration m1x, z2, Mack10

described the dissolution rate of the photoresist in adeveloper 1V 2 by

V 1x, z2 5 Vmax

1a 1 1231 2 m1x, z24n

a 1 31 2 m1x, z24n1 Vmin , 172

where Vmax is the dissolution rate of the fully exposedphotoresist, Vmin is the dissolution rate of the nonex-posed photoresist, and

a 51n 1 12

1n 2 1211 2 mth2

n, 182

Fig. 2. V X E experimental curves for the AZ-1350J photoresistdeveloped at different dilutions of NaOH in deionized water 1solidcurves2 and for the AZ-1400 photoresist developed at differentdilutions of AZ-351 developer 1dashed curves2. Both developerswere kept at a room temperature of approximately 23 °C. Thefilms were homogeneously exposed to the line l 5 0.4579 µm of anAr laser. Taking into account the changes in the developmentrate along the z direction, the values were averaged along the 1-µmthickness of the films.

where a is a function of the inhibitor concentrationthreshold mth at the onset of dissolution, and n is thenumber of molecules of the product of the photoreac-tion that reacts with the developer to dissolve a resinmolecule.Equation 172 gives a theoretical relation between the

dissolution rate of the photoresist 1V 2 and the expo-sure energy E 5 I1x, z2Dt.

2.B.2. DevelopmentIf the developer acts only in the z direction, as can beassumed for the case of anisotropic reactive ionetching, the remaining photoresist thickness, z1x, t2,can be obtained by a simple integration of the dissolu-tion rate V1x, z2:

z1x, t2 5 z1x, t02 2 e0

t

V 1x, z2dt. 192

Otherwise when the exposed resist is immersed in adeveloper solution such as for wet development, thephotosensitized resist is dissolved across the wholeresist–developer interface. Assuming that this disso-lution occurs only at this interface, the mass trans-port proceeds in the direction normal to it. Neglect-ing the small effects of induction and adhesion thatoccur at the first and last skin layer of photoresist1.0.1 µm2,10,14 the changes in the surface that are dueto the dissolution can be described by

≠r

≠t5 2V 1r2n , 1102

where r is the vector that describes each point of thephotoresist surface given by Eq. 152, n is the unitvector that is perpendicular to the photoresist sur-face:

n 5 sin1w2x 1 cos1w2z , 1112

w is the angle between the n unit vector and the z axis,shown in Fig. 3, and V 1r2 5 V 1x, z2 is the dissolutionrate of the photoresist in the developer given by Eq. 172or by the experimental V X E curve.Substituting Eq. 1112 into Eq. 1102, one can itera-

tively describe the time evolution of position vector rof each surface point as

r1t 1 Dt2 5 r1t2 2 V 3r1t24 · Dt1sin wx 1 cos wz 2, 1122

where w is calculated from the preceding surfacecurve at time t for the same point r of the surface.

Fig. 3. Schema of the resist–developer interface with vector nperpendicular to the interface at each point r and time t.

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The surface profile at each time is represented byan array of r vectors.8 Starting from the array attime t, we apply Eq. 1122 to each point of the array andobtain the surface array at time t 1 Dt. Figure 4illustrates this iterative computing and the evolutionof points r during the development time. The samefigure shows that surface points are created or elimi-nated as the neighboring points became closer orfurther away from each other. This procedure can beused to maintain the same precision along the surfaceand to eliminate unnecessary calculations.

2.B.3. ResolutionThe isotropy of wet development introduces strongernonlinearities than those arising from photosensitiza-tion processes. These nonlinearities generate a pro-file that is rich in tips and that can be represented byhigh-spatial-frequency harmonics.When the spatial frequency becomes higher, the

photoresist does not record as well, as thin tips do notappear in the experimental profiles. This phenom-enon, generally called loss in resolution, occurs be-cause of several effects such as chemical diffusion ofphotoactive9 and developer species, dependence of thedevelopment rate on surface curvature,15 mean dis-tance between photosensitive molecules,16 and thesize of the smallest particle of photoresist that isremoved by the developer. The modeling of eacheffect separately complicates the simulation becauseit is not always possible to distinguish the effect thatlimits the resolution and constitutes a problem formost of the profile simulations.9,17 In this way aninteresting approach is to describe the loss of theresolution of the complete process as a high-spatial-frequency filter.Although the complete process of the photoresist

does not behave like a linear system, its limitedfrequency response can be assumed to be a linearspace-invariant filter 1LSIF2.18,19 A LSIF can be com-pletely described by its modulation transfer function1MTF2, which represents the filter response for eachspatial sinusoidal signal. Although each step of theprocess has its intrinsic resolution limit, we candefine a MTF for the complete process 1includingdevelopment2.The complete response of the photoresist can then

be treated as a cascade of a nonlinear response of thephotoresist and the LSIF. So if we calculate theprofile in the photoresist that results from the expo-sure and development processes, the final profile can

Fig. 4. Schema of numerical computing of the surface. Note thatsurface points are created or eliminated as necessary.

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be obtained by applying a MTF to each spatialharmonic of the profile and then synthesizing thefinal profile again.Assuming a simplified MTF as illustrated in Fig. 5,

this procedure can be numerically performed. ThisMTF corresponds to a linear cut in the response,starting at the period L2 and finishing at L1. L2corresponds to the smallest dimension that can berecorded without cut off, and L1 is the smallestdimension that can be recorded at all.Figure 6 illustrates the effects of this filter applica-

tion on the profile of a grating.

3. Results and Discussion

The simulation described above was performed byusing a simple IBM PC-compatible microcomputerand was used to compute the profile of gratingsrecorded holographically in films of Shipley AZ-1400photoresist on glass and Si substrates under wetimmersion development. The initial film thick-nesses were assumed to be much larger than theperiod of the gratings so that the substrate was notreached.For filtering purposes the simple MTF function

proposed above was employed. The initial and finalcutoff periods were determined by comparing thesimulated profiles with those obtained by scanningelectron microscope 1SEM2 photos of the cross sectionof gratings with periods of 0.8 and 1.6 µm, recorded inAZ-1400 photoresist films on glass and Si substrates,respectively, in linear conditions. The shapes werecompared taking into account the definitions of stand-ing waves for glass substrates and edges for Sisubstrates. This comparison leads to cutoff periodsof L2 5 0.6 µm and L1 5 0.1 µm. These periodsprovide information about the smallest structuredimension that can be recorded by this technique.This limit depends only on the intrinsic limit of thephotoresist and the wet development process and noton the exposure pattern or stability of the holographicsetup.20Figure 7 shows the evolution with development

time for the computed cross section of relief holo-graphic gratings. These were recorded on glass sub-strates using the same exposure energy and twodifferent development conditions: 1a2 for a nonlin-ear V X E curve 1corresponding to low concentration ofthe developer and high-exposure energy2, 1b2 for alinear V X E curve 1corresponding to high concentra-tion of developer or small exposure energies2, and 1c2

Fig. 5. MTF of a spatial frequency filter, which we assumed to bea simple function that decays linearly with the period fromL2 to L1 .

the same as 1b2 with a light background. The refrac-tive index and the absorption coefficient used in thecomputations were, respectively, n 5 1.67 and a 50.08 µm21 at l 5 0.4579 µm for Shipley AZ-1400photoresist. For the glass substrate a value of n 51.51 was assumed. For such values there are noobservable effects from the light decay through thefilm because of absorption and from the standingwaves because of reflection at the photoresist–glassinterface.As described by Austin and Stone,2 the develop-

ment in strong nonlinear conditions 3Fig. 71a24 pro-duces a squarelike profile even for sinusoidal patternexposures. On the other hand, the isotropy of wetdevelopment produces a narrowing of the top of thestructures.21 This effect is particularly pronouncedfor linear development conditions and long develop-

Fig. 6. Example of the application of the MTF filter in a resultingsurface relief with 1dashed curve2 and without 1solid curve2 a filter.

Fig. 7. Evolution of the computed profiles with the developmenttime for photoresist films on glass substrates exposed to aninterference pattern of 0.8-µm period at l 5 0.4579 in threedifferent conditions: 1a2 strong nonlinear V X E condition, 1b2linear V X E curve, 1c2 linear V X E curve with a light background.The V X E curves assumed in each case are shown on theright-hand side for each case. The energy that corresponds to theexposed interference pattern is indicated in the V X E curves andwas the same for the three cases. The profiles are equally spacedby the same developing time for each case.

ment times 1deep gratings2. In these cases a strongshift from the expected sinusoidal profiles is observed3Fig. 71b24. Figure 8 shows SEM photographs of thecross section of a deep photoresist grating recorded inAZ-1400 photoresist film on glass substrates. Theexposures were performed in a self-stabilized holo-graphic setup22 at l 5 0.4579 µm. The total expo-sure energies were 150 mJ@cm2 3Fig. 81a24 and 200mJ@cm2 3Fig. 81b24, respectively, and both gratingswere developed in AZ-351 developer diluted 1:3 indeionized water for 1 min. These conditions corre-spond approximately to a linear V X E curve. Notethe strong narrowing of the peaks as described by themodel.Figure 71c2 shows the same recording in linear

conditions as that shown in Fig. 71b2 but with back-ground light. Note that, because of the effects ofisotropy, the maximum aspect ratio 1depth@period2 ofthe resulting grating depends strongly on backgroundlight and not only on isotropy itself as proposed byZaidi and Brueck.23 This fact indicates that the useof high-stability holographic setups is indispensablein order to realize high aspect ratio gratings. Somegrating profiles that are recorded in nonstable condi-tions, as, for example, holographic recording inside

Fig. 8. SEM photos of the cross section of deep relief gratings of0.8-µm period, recorded in a photoresist film on glass substrateswith exposure energies of 1a2 150 mJ@cm2 and 1b2 200 mJ@cm2.

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liquids,24 exhibit the characteristic shape shown inFig. 71c2.Note also that the nonlinearity of the V X E curve

produces effects that are opposite isotropic ones 1anenlargement of the top of the structures2. Thus thenonlinear conditions of theVXE curve should be usedto produce high aspect ratio gratings and to preservethe sinusoidal form in deep gratings, particularly inthe presence of background light.Figure 9 shows the same evolution curves as those

in Fig. 7 but for Si substrates 1n5 4.58, a 5 3.57 µm212developed in nonlinear and linear conditions. Thosedeveloped in linear conditions were done so with andwithout background light. Note that, as described inthe literature,12,23 the standing waves produce energynodes so strong that the gratings rapidly assume asquarelike profile that develops as a sidewall struc-ture 3Fig. 91b24. Figure 10 shows a SEM photographof the cross section of a photoresist grating. Thiswas recorded in AZ-1400 photoresist film on Si sub-strates using the same experimental conditions aswere used for Fig. 8 1illustrating this squarelikeprofile2.The nonlinear development conditions amplify the

enlargement of the peaks caused by standing waves,producing a lateral etch under the nodes of thestanding waves. Such an effect can be useful forpreparing shadow masks for lift-off processes. This

Fig. 9. Evolution of computed profile gratings of 1.6-µm periodexposed at l 5 0.4579 µm in photoresist films over Si substrates forthree different conditions: 1a2 strong nonlinear V X E condition, 1b2linear V X E curve, 1c2 linear V X E curve with a light background.As in Fig. 7, the V X E curves assumed in each case are shown on

the right-hand side for each case. Although the energy of theinterference pattern was the same as that used for glass sub-strates, here it corresponds to a higher energy inside the filmbecause of reflection on the Si substrate. Because of strongchanges in the energy along the film thickness 1standing waves2,the profiles are not equally spaced by the same developing time butare the same for each case.

602 APPLIED OPTICS @ Vol. 34, No. 4 @ 1 February 1995

effect is less pronounced in linear conditions becauseit favors the narrowing of the top of the structures.The presence of background light attenuates the

effect of the standing waves, particularly in linearconditions for which the effect of the narrowing ofpeaks caused by isotropy is larger.

4. Conclusions

In spite of its simplicity, the simulation that we havedeveloped here is a good description of the recordedprofile on photoresists under holographic exposures.Our simulation takes into consideration only themore effective process effects in the profile, such asphotosensitization response of the photoresist, stand-ing waves, isotropy of wet development, and the cutoffof high-spatial-frequency harmonics. Other effects,such as changes in the dissolution ratio, multiplereflections, the ending of film, or different light pat-terns, that have not been treated in this simulationcan be easily introduced.The simulation can be used to study the influence of

experimental conditions on the shape of the profileand can be used to optimize holographic recordings.To exemplify the potential of our device it was used tocompute the resulting profile of AZ-1400 photoresistfilms on glass and Si substrates. The strong influ-ence of isotropy of wet development on the shape ofphotoresist gratings on glass substrates has beenshown. We amplified this effect by using lineardevelopment conditions and background light, but weattenuated the effect by using nonlinear developmentconditions. For exposures on high-reflectivity sub-strates such as Si wafers, the standing waves stronglyinfluence the shape of the relief profiles. If the initialfilm thickness is conveniently chosen, this effect canbe used to produce squarelike profiles that are moreresistant for use as a mask for etching or as shadowmasks for lift-off processes. If the experimental con-ditions are well known, in particular the V X E curve,the simulation can be used to fit the experimentalprofiles.An additional use of the model is the evaluation of

the resolution limit of photoresist processing. The

Fig. 10. SEM photograph of the cross section of a holographicgrating of 1.6-µm period recorded on a Si substrate.

resolution limit produces an attenuation effect of theinterference pattern that is similar to backgroundlight and causes the collapse of the peaks. In termsof sinusoidal harmonics this effect can be explained asa decay of the amplitude of the higher-spatial-frequency harmonics. Such a limit is difficult toobtain from direct measurements because of mechani-cal vibrations on holographic setups.20 The standingwaves, however, are high-spatial-frequency light sig-nals that are quite insensitive to vibrations. Thusthe fitting of the profile of standing waves can be usedas a method to evaluate the resolution limit of photo-sensitive materials and processes, as has been illus-trated in this paper.

The authors thank Hiran M. de Carvalho and theCentro de Pesquisas e Desenvolvimento of Telebrasfor the SEM photographs, Jaime Frejlich for manyfruitful discussions, and the technicians, Joao Petru-cio Medeiros da Silva and Aparecida do Carmo daSilva Almeida. We acknowledge the financial sup-port of the Financiadora de Estudos e Projetos,Fundacao de Amparo a Pesquisa do Estado de SaoPaulo, the Conselho Nacional de Pesquisa, and theFundcao de Apoio a Pesquisa da Universidade Meto-dista de Piracicaba.

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13. AZ-1400 and AZ-1350 photoresists 1Shipley, Newton, Mass.,19842.

14. L. Cescato and J. Frejlich, ‘‘Real-time optical techniques formonitoring of etching process,’’ in Trends in Electrochemistry1Council of Scientific Research Integration@Research Trends,Sreekanteswaran, Trivandrum, India, 19922, 201–213.

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20. M. S. Sthel, C. R. A. de Lima, and L. Cescato, ‘‘Photoresistresolution measurement during the exposure process,’’ Appl.Opt. 30, 5152–5156 119912.

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