photoresist reflow method of microlens production part i: background and experiments

Photoresist reflow method of microlens productionPart I: Background and experiments

Feidhlim T. O’Neill, John T. Sheridan

Department of Electronic and Electrical Engineering, Faculty of Engineering and Architecture, University College Dublin,Belfield, Dublin 4, Republic of Ireland

Abstract: We present a two part study of melted microlensarrays. This first part concentrates on the production andmeasurement of microlens arrays while the second part ex-amines attempts to model the microlens profiles. In thispaper we first review some of the fabrication techniquesused over the past twenty years to produce lens arrays.Some applications of microlens arrays are then discussed.Particular emphasis is placed on the photoresist reflowmethod of microlens production that was suggested by Po-povic et al., as this was the method used to produce themicrolens examined in this study. Lenses produced usingthis method can have large deviations from the sphericalcase, i.e. the profile that would be expected from a simpleminimisation of the surface energy. These deviations havenot been explained to date in the literature, however anumber of possible causes for this deviation are given inthis paper.Therefore the fundamental questions we wish to explore

here are: (1) Why physically do dips occur? and (2) Canthe resulting surface profile be predicted? Any model de-veloped to quantitatively estimate the optical effects of sur-face shape will depend on the physical assumptions maderegarding the surface formation mechanism. However aswe shall indicate at this point only an informed guess re-garding the relative importance of a number of possiblemechanisms can be made.

Key words: Microlens – curvature – photoresist – measure-ment

1. Introduction

In this paper we review methods of production of mi-crolens. A number of the most popular methods usedover the last 20 years are described with particular em-phasis on the photoresist reflow method as this wasused to produce the lenses examined in this study. Ithas been observed that for certain parameters lensesare formed which deviate from the spherical case ex-pected from the minimisation of the surface energy,[1]. Lenses which have these deviations or “dips” are

examined in this study in an attempt to provide datawhich may enable the development of simple physicalmodels to describe the process which result in lenseshaving these dips. It is important to note that this is anextremely complex problem and to date no theory hassatisfactorily explained the formation of these dips.The complexity results from the nature of the produc-tion process. The photoresist materials are made up ofmany components and the production process involvesat least two phase changes. One theory which has beenpostulated is the curvature correction model by Abeand Sheridan, [2]. To examine the validity of this theo-ry and to attempt to produce simple polynomial mod-els it is first necessary to carry out detailed experimen-tal work in the relatively simple one dimensional caseof cylindrical lenses. Most of the experimental workcarried out in this area to date has focused on spheri-cal lenses. The cylindrical case is important as it re-duces the theoretical analysis to a two-dimensionalproblem rather than the much more complicated threedimensional spherical case.This study is split into two parts, this paper, Part I,

concentrates on describing the fabrication of microlensarrays in detail, some of the properties of the photore-sist are examined and the measurement of the surfaceprofiles of the lenses produced is discussed. The sec-ond part of the study, Part II, describes attempts tomodel the surface profiles of the lenses using analyticalmodels.

2. Microlens production methods

The study of microlenses has been an area of activityfor many years. Hooke studied the effect of melting theends of Venetian glass rods to produce microscope ob-jectives in the 17th century [3]. Since then many meth-ods have been examined for the production of micro-lenses, these include chemical process methods such asreactive ion etching [4], ion diffusion [5], deep protonirradiation [6]. Optical methods such as optical inter-ference methods, [7], and physical methods such as hotembossing, [8], and micro-machining, [9]. A chronolo-

Feidhlim T. O’Neill, John T. Sheridan, Photoresist reflow method of microlens production. Part I 391

International Journal for Light and Electron Optics

0030-4026/02/113/9-391 $ 15.00/0

Received 9 July 2002; accepted 8 September 2002.

Correspondence to: J. T. SheridanFax: ++353-1-2830921E-mail: john.sheridan@ucd.ie

Optik 113, No. 9 (2002) 391–404ª 2002 Urban & Fischer Verlaghttp://www.urbanfischer.de/journals/optik

gically ordered flow chart indicating some of the differ-ent methods used to produce the various types of mi-crolenses is shown in fig. 1. One of the more recentmethods used to produce arrays of microlens arrays isthe photoresist reflow method, suggested by Popovic in1988 [10].Some of the methods used to produce microlens ar-

rays shall now be discussed in more detail.

2.1. E-beam lithography

E-Beam lithography can be used to produce surfacemodulations in a PMMA. PMMA is used as an E-beam resist and can be spin coated onto a substrate. Toprevent charging up during the exposure the resist iscoated with a conductive metal such as Gold. The finalprofile obtained in the PMMA is proportional to theexposure time used for each region of the lens. ThePMMA resist structures are then formed by chemicallyetching the conductive metal layer and then develop-ing the PMMA layer with a suitable solvent. Thismethod was used to produce Fresnel (zone plates)lenses by Fujita et al., [11].

2.2. Photosensitive glass

There are a range of glass types which have beentermed photosensitive. It was found that when theseglasses are exposed to UV radiation and then heatedtheir colour varies. This is due to the absorption ofsmall metal colloids such as silver, copper or gold. Ithas been found that when these colloids reach a suffi-cient size they can act as nuclei for the growth of acrystalline microphase in the originally homogenousglass. If the fraction of this photoinduced phase is greatenough and the density of these regions greater thanthe original homogenous glass then a pattern isformed. Using an appropriate mask it is possible toproduce lenses using this method. The exposed regionsare more dense than the non-exposed regions and asthe glass is heated above its softening temperature thenon exposed glass is squeezed to form spherical lenses.This method was used to produce microlense arrays byBorrelli et al., [12].

2.3. Optically induced volume changesin recording materials

It has been found that when certain optical recordingmaterials are exposed to light the resulting recordingprocesses produce a volume change. This propertyhas been used to produce microlenses in a number ofdifferent materials, including photopolymers and Di-chromated Gelatin. The material is exposed to eitherUV, or in the case of dye sensitised photopolymers,visible light. The resulting surface modulation is de-termined by the exposure profile. This method has

392 Feidhlim T. O’Neill, John T. Sheridan, Photoresist reflow method of microlens production. Part I

Fujita et al. 1981, [Fuji 81]Method: Electron Beam Lithography. Lens type: Fresnel zone plates in PMMA

Borrelli et al. 1985, [Borr 85]Method: Photosensitive glass. Lens type: Biconcave and plano concave lensesproduced by exposure of photoresist to UV radiation.

Popovic et al. 1988, [Popo 88]Method: Photoresist reflow method. Lens type: plano convex lenses producedby melting islands of photoresist.

Liau et al. 1989, [Liau 89]Method: Mass transport. Lens type: Gallium Phosphide microlenses

Hutley 1990, [Hutl 90]Method: Exposure of photoresist using interference method. Lens type:Photoresist microlens arrays.

Daly 1990, [Daly 90]Method: Multiple exposure of photoresist. Lens type: Preshaped photoresistmicrolenses

Kufner et al. 1996, [Kufn 96]Method: Deep proton irradiation. Lens type: Concave and convex microlenses inPMMA

Keyworth et al. 1997, [Keyw 97]Method: Syringe application of adhesive. Lens type: Cured optical adhesivemicrolenses

Calixto et al. 1997, [Cali 97]Method: Optically induced swelling of DCG. Lens type: Plano convex DCGlenses and mirrors (when coated with aluminium)

Masuda et al. 1997, [Masu 97]Method: Variation of refractive index of liquid crytals. Lens type: Liquid crystalmicrolenses with beam steering function.

Xin-Jian et al. 1998, [Xin 98]Method: Ion bean milling. Lens type: Photoresist microlenses

Okamoto et al. 1999, [Okam 99]Method: UV curable organic polymer. Lens type: UV radiation applied toTEMA (Thioether Methacrylate) through a mask to produce convex and biconvexlenses.

Severi et al. 1999, [Seve 99]Method: Reactive ion etching. Lens type: Resist microlenses are transferred intothe silica substrate using RIE

Reyna et al. 2000, [Reyn 00]Method: Volume variation of dye sensitised gels. Lens type: Exposure of dyesensitised gels to produce temporary lenses that fade with time.

Hartmann et al. 2000, [Hart 00]Method: Hydrophobic effect. Lens type: Monomers are shaped using a patternedhydrophobic layer and then UV cured to form microlens arrays.

Lee et al. 2000, [Lee 00]Method: UV exposure of acrylic based polymer. Lens type: Arrays of lenticularlenses.

Ishii et al. 2000, [Ishi 00]Method: Ink jet fabrication. Lens type: UV curable epoxy resin is applied tot ehsubstrate using an ink jet apparatus to form microlens arrays.

Shen et al. 2002, [Shen 02]Method: Hot embossing. Lens type: Spherical rod lenses.

Fig. 1. Outline of some of the methods which have been usedto produce microlenses.

been used by Reyna et al., [20], Lee et al., [22] usingphotopolymers and by Calixto et al. in DichromatedGelatin, [16].

2.4. UV curable resins and recent Ink-Jet fabrication

Microlens arrays have been produced using UV cur-able resins and optical adhesives. The technique in-volves the controlled application of liquid drops of theUV curable material being applied to a substrate. Thedroplets are drawn into a spherical profile by the ac-tion of surface tension. The droplets are then exposedto UV radiation which cures the droplets. The con-trolled application of the resin has been achieved usingcomputer controlled syringes by Keyworth et al., [17],and also more recently using an Ink-Jet fabricationprocess by Ishii et al., [23].

2.5. Hot embossing

The hot embossing technique can be used to producepatterns in substrates. With the use of appropriate moldslens arrays can be produced. The required mold isplaced on top of the substrate and both are then placedon a heating plate. The subtrate is then heated to aboveits glass transition temperature. The soft substrate thentakes the form of the mold that it is in contact with. Anexample of the use of this method to produce microlensarrays is the work carried out by Shen et al., [24].

2.6. Hydrophobic effect

A recent method which has been used to produce lensarrays involved the application of a patterned hydro-phobic layer onto a substrate. When this substrate isdipped into hydrophilic monomer melt the monomerforms droplets in the regions which no hydrophobiclayer has been applied. Exposure of these droplets toUV light polymerises the monomer and the lenses areformed. This method has been examined by Hartmannet al., [21].

2.7. Proton beam ionisation

Proton beam ionisation method can be used to pro-duce both concave and convex lens arrays in poly-methyl methacrylate (PMMA) substrates. The PMMAsubstrate is irradiated by a proton beam through a cir-cular aperture. It can then either be developed to re-move the irradiated PMMA or exposed to a styrenemonomer vapour to form a convex lens. This methodhas been examined by Kufner et al., [6].

2.8. Reactive ion etching, R.I.E.

This method is normally used to convert photoresistmicrolens arrays into the silica substrate. It involves

exposing the lens array and substrate to a combinationof O2 and CHF3 plasmas in a vacuum chamber. Theplasma etches away the photoresist lens array and thesubstrate thus converting the photoresist pattern to thesubstrate. Accurate control of the gas mixture and RFpower supply must be achieved to assume high fidelitytransfer of the lens array to the substrate. An exampleof this method is the work carried out by Severi et al.,[4], in which careful monitoring of the lens profile andcomputerised adjustment of the gas mixtures was car-ried out.

2.9. Ion diffusion

It this method a glass substrate is exposed to metaloxides under a vacuum through a mask. The refractiveindex of the substrate is altered by the implantation ofmetal oxides and hence these lenses are known asGRIN, (GRaded INdex), lenses. The quality of thelenses produced is dependent on the profiles of themasks used and also the post exposure heat treatmentof the substrate, [42].

2.10. Mechanical milling

The techniques which have been outlined so far arenormally applied to small microlenses, (less than 1mm), however larger lenses can be produced by ma-chine milling or pressing of a negative mold, [9].

2.11. Photoresist reflow method

This method involves melting photoresist structures toform small lenses shaped by the surface tension of theliquid resist. The profiles formed by this method canbe much more complex than the simple spherical sur-faces one might expect from simple surface energyminimisation [38]. The resulting lenses can have verylarge aberrations for certain fabrication parameters.This method shall be discussed in detail below in sec-tion 4.

3. Applications of microlens arrays

Microlens arrays find applications in a large number ofareas. Some of these areas are now discussed.

3.1. Imaging

Microlens arrays have been used in a large range ofimaging applications. These include photocopier ima-ging systems, oscilloscope cameras and other “close-up” imaging systems, [25]. Recently a technique knownas microlens lithography has been proposed, [26]. Thissystem uses a 1 :1 imaging system built using microlensarrays to copy a pattern to photoresist. Advantages ofthis method include an increased depth of focus and a

Feidhlim T. O’Neill, John T. Sheridan, Photoresist reflow method of microlens production. Part I 393

larger working distance (�1 mm) than customaryproximity printing. One result of these advantages isthat no wear occurs to the mask as would occur in con-tact lithography.

3.2. Integral photography

This interesting technique was invented by GabrielLippmann in 1908. It involved using microlens arraysas the imaging system on a camera. Thereby recordingan array of images of a distant object on the photo-graphic film. The images are the object as seen fromthe position of each of the lenses. The developed filmis then projected using the same type of microlens ar-ray to form a three dimensional image of the object. Adetailed discussion of this technique has been given byStevens and Davies, [27].

3.3. Astronomy

Microlens arrays have been used as components in at-mospheric wavefront sensors, known as Shack-Hart-mann arrays, [32]. These are used to improve theimages obtainable using ground based telescopes. Theyprovide a measurement of the wavefront distortioncaused by the earths atmosphere. This information isthen used to deform either the main mirror or a smal-ler secondary mirror to remove the distortion. Thismethod can be used to produce diffraction limitedimages of stars despite atmospheric distortion. An ex-ample of optimising refractive microlens arrays for thispurpose has been shown by Artzner, [33].

3.4. Optical interconnects

Uses of microlens arrays also include the area of opti-cal interconnects. They have been used in many typesof interconnects, These include spatially variant con-nections using multiple arrays, [34], and also board-to-board and chip-to-chip connections in the electronicssector, [35].

4. Introduction to the photoresist reflow methodfor microlens production

The microlens arrays examined in this study were pro-duced using the photoresist reflow method that wassuggested by Popovic in 1988. This method will now bediscussed in detail.The reflow photoresist method involves the melting

of islands of photoresist [36]. When the islands aremelted, the liquid photoresist surfaces are pulled into ashape which minimises the energy of the system [14]. Ifgravitational effects are presumed to be negligible,[38], which for very small lenses will generally be thecase, and assuming ideal conditions, one would expectthe shape of these microlens to be well approximatedby a spherical surface. This unfortunately is not true

for all cases as will be shown later. These more com-plex profiles appear to result from the fact that themelted photoresist droplet must be formed having cer-tain physical attributes. One physical constraint is theexistence of a critical angle, qc. This is the angle atwhich the photoresist meets the solid substrate, as illu-strated in fig. 2.The magnitude of this angle is governed by the sur-

face tension of the liquid resist, the surrounding airand the substrate properties and is therefore a con-stant for a particular photoresist-substrate-air combina-tion [28]. Variations in this angle may occur if the sub-strate is non uniform or if the liquid/substrate interfacemoves [29, 30]. One result of the existence of such afixed critical angle is that there is only one particularvolume which will result in a spherical surface for agiven lens base width. Therefore if spherical lens sur-faces are required with different focal lengths it is ne-cessary to vary the width of the lenses.Deviations from the spherical surfaces have been

observed to occur when the volume used to producethe lens varies from the volume necessary to producethe spherical case [14]. This “ideal” volume must makeallowance for the effect of material evaporation duringthe production of the lenses [31].A number of possible causes have been identified and

what follows is a summary of some of these possibilities.

1. Convection

It is possible that dynamical processes such as move-ment of the resist due to the variation in pressurecaused by the curvature differences may lead to theformation of side lobes. This movement process mayalso arise because of a temperature gradient betweenthe edges of the droplet and the bulk resist.

2. Sedimentation

The resist may contain a suspended material whichmay undergo sedimentation following melting resultingin a profile with raised edges. However we know of noevidence for this.

3. Outgassing

Other possibilities include the fact that outgassing mayhave an effect on the profile formation both in redu-cing the volume of the resist and in causing localisation

394 Feidhlim T. O’Neill, John T. Sheridan, Photoresist reflow method of microlens production. Part I

Fig. 2. Critical angle.gLS ¼ Surface tension between the substrate and the liquidgLV ¼ Surface tension between the liquid and the vapourgSV ¼ Surface tension between the vapour and the substrateqc ¼ Critical angle

of gas bubbles in the resist resulting in an edge effectsimilar to that observed in baking (bread). We notethat volume changes of the resist during the meltedprocess have been observed, [9].

4. Crystalline anisotropy

It has been suggested that crystalline anisotropy canplay a part in the formation of surface profiles [39],however as the photoresists used are organic materialsand not crystalline in nature it is probable that suchanisotropy will not occur here, [2].

5. Resist boundary movement

The profile dips could occur if the experimental beha-viour of the liquid interface boundary of the resist de-viates from the expected constant stationary beha-viour. It has been noted that the contact angle of amoving liquid boundary on a surface has a differentvalue than that of the stationary case, [29]. The reflowproduction process includes a melting followed by acooling and solidification phase, it is possible that thevariation in temperature could result in a volumechange causing the boundary to move and hence vary-ing the contact angle. However the edge does not ap-pear to move, [9].

6. Shrinkage of droplet

It is known that a shrinking droplet will have a differ-ent contact angle since the surface where the liquidonce was has different properties than the original(unwet) surface. This situation could arise if the tem-perature variation in the production process causedthe liquid boundary to move. Such variations of thebase have not to our knowledge been measured.

7. Range of molecular weights

The resist may have sufficiently large a spread of mole-cular weights that it melts over a large temperaturerange [37], resulting in different sections of the micro-lens being formed at different times, perhaps causingsome profile shaping effects.

8. Variation of substrate

Variations in the substrate, roughness, curvature andconstituent materials, can lead to local variations in re-sist critical angle [28]. The identification of such effectswould require extremely accurate measurements.

9. Gravitational effects

Droplets are found to vary depending on whether theyare formed in an upright or inverted orientation how-ever for small lenses (less than 1000 mm, using standardphotoresists) the effect is known to be negligible, [38].

10. Polymeric nature of resist

The polymeric nature of the melted photoresist isthought to result in variations in the liquid boundary

profile and hence the contact angle [28]. It is possiblethat it may also affect the total profile.

11. Effect of curvature of droplets

According to standard surface energy minimisation the-ory the expected shape of a droplet on a surface is asphere. It has been postulated that a further energy termmust also be included, [2]. This extra energy term is re-lated to the curvature of the droplet. It is possible thateffects due to this term are only significant when there isa large (long range) interaction between the constituentmolecules. The photoresist being an example of a situa-tion in which this extra energy may be significant as it ismade up of large (long) polymer molecules. This addedconstraint on the surface energy minimisation results indips such as those observed in the surface profiles of mi-crolenses. The polymer chain nature of the photoresistmolecules would then determine the strength of the cur-vature term in the theory of Abe and Sheridan [2].The melted microlens technique was used to fabri-

cate the lenses examined in this study and thereforethe production method is discussed in detail.

5. Initial spherical surface assumption

Using this spherical surface assumption it is possible tomake an initial approximation of the required record-ing parameters to produce a particular lens type, (focallength, numerical aperture, etc.). This approximationmust take account of the physical effects that the fabri-cation process has on the photoresist, particularly theloss of volume due to the evaporation of the solventsused in the photoresist [31]. In the procedure shown itis assumed that the system is ideal and that the contactangle can vary. The contact angle is specific to a parti-cular photoresist-substrate-air combinations. We firsttreat it as a secondary constraint on the design process.When designing lenses two parameters are normallyused to describe the lens requirements, the focallength, f, and the radius of the lens, r. When manufac-turing lenses it is necessary to produce a lens profilewith a specific radius of curvature, R. The required fo-cal length, f, is then given by,

f ¼ R

n� 1ð1Þ

where n is the refractive index of the lens material,(photoresist in this case). The central height of thelens, h, for a given lens radius, r, can be expressed interms of width and radius of curvature as,

h ¼ R�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðR2 � r2Þ

p:

These parameters can be used to calculate the volumerequired to give a spherical surface. This calculation isoutlined for two lens types, (1) cylindrical and (2) sphe-rical. The production parameter h is dependent on thethickness of the photoresist layer which is used to pro-duce the pre-melt pattern. The width of the lens, r, is

Feidhlim T. O’Neill, John T. Sheridan, Photoresist reflow method of microlens production. Part I 395

determined by the mask profile used to produce thelens array pattern desired. Two types of masks are dis-cussed here, bar grating masks and circular masks [40].A bar or Ronchi grating can be used to produce longthin rectangular lines of photoresist. A circular gratingmask can be used to produce circular islands of photo-resist or “hockey puck” like shapes. These photoresiststructures are produced in two stages, [38]: (1) Expo-sure of the photoresist to UV light through the appro-priate mask followed by (2) Development of thephotoresist layer post exposure. If the photoresist usedis a positive photoresist [36] the development stage re-moves the exposed areas of photoresist resulting in theformation of the “box” and “puck” structures depend-ing on the mask used, illustrated in fig. 3. The long thinrectangular boxes and the “pucks” are used for produ-cing the cylindrical and spherical lenses respectively.Using the production parameters given in eqs. (1)

and (2). It is possible to develop an initial design pro-cess to calculate the volume required to give a spheri-cal surface, this calculation is now outlined for the cy-lindrical case.

6. Cylindrical lens array

Let us first assume that the volume of the final cylind-rical microlens, Vcyl, is equal to the initial volume ofthe photoresist island, V0, multiplied by a volume re-duction variable, E. This can take into account the pos-sible reduction in resist volume during lens production

Vcyl ¼ V0 � E : ð3Þ

These two volumes can be expressed as follows

V0 ¼ L�W �H : ð4Þ

And

Vcyl ¼ L�A ¼ L� 12 R

2ðq� sin qÞ ð5Þ

where L is the length, W is the width and H is theheight of the photoresist before melting as illustratedin fig. 4. R is the constant radius of curvature, A is thecross-sectional area of the cylindrical lens and q is thesubtending angle illustrated in fig. 5.The subtending angle q can be expressed as

q ¼ 2 sin�1 r

R

� �¼ 2 cos�1 R� h

R

� �: ð6Þ

While the area of the segment is,

A ¼ 12

R2 2 sin�1 r

R

� �� sin 2 sin�1 r

R

� �h in o: ð7Þ

Further we note that

sin 2q ¼ 2 sin sin�1 r

R

� �h icos sin�1 r

R

� �h i; ð8Þ

which can be found using the trigonometric relation

sin 2B ¼ 2 sin B cos B : ð9Þ

396 Feidhlim T. O’Neill, John T. Sheridan, Photoresist reflow method of microlens production. Part I

After Exposure andDevelopment Stages

Substrate

Cr on GlassMask

Photoresist

“HockeyPucks” Islands

After Exposure andDevelopment Stages

Substrate

Cr on GlassMask

PhotoresistRectangularBoxes/Lines

UV light

UV light

Fig. 3. Illustration of the masks used to produce the requiredstructures used to produce microlenses in this report.

Fig. 4. The geometry of the photoresist island prior to melt-ing, typically L � W � H.

Fig. 5. Geometry of the cylindrical lens after the photoresisthas melted.

Since sin�1 r

R

� �¼ q

2¼ cos�1 R� h

R

� �, Equation (6)

can be expressed as

sin 2q ¼ 2 sin sin�1 r

R

� �h icos

q

2

� �: ð10Þ

Therefore from eq. (8),

sin 2q ¼ 2r

Rcos

q

2¼ 2

r

R

R� h

R

� �: ð11Þ

The cross-sectional area of the cylinder is thereforeequal to

A ¼ R

22 sin�1 r

R

� �� 2r

R

R� h

R

� �� �

¼ R2 sin�1 r

R

� �� rðR� hÞ

h i: ð12Þ

Substituting eq. (12) into eq. (5) we obtain an expres-sion for the volume of the cylinder of melted photore-sist, Vcyl.

Vcyl ¼ L R2 sin�1 r

R

� �� rðR� hÞ

h i: ð13Þ

Equating the volumes given in Eqs, (4) and (13), weget that,

V0 � E ¼ Vcyl ¼ L�W �H � E

¼ L R2 sinr

R

� �� rðR� hÞ

h i: ð14Þ

Since W ¼ 2r, H, is the height of resist required toform a perfect cylindrical lens, is therefore,

H ¼ 12E

R2

rsin�1 r

R

� �� Rþ h

� �: ð15Þ

So we see that given a required lens width and focallength the height of the photoresist required can bepre-determined. The plot of the thickness of the photo-resist “box” required to produce cylindrical lenses isplotted as a function of the focal length of the lens, f,and the radius of the lens, r, in fig. 6. The refractive

index of the photoresist, n, is initially taken to be 1.5.Using the above production parameters eqs. (1) and(2) it is also possible to calculate the volume requiredto give an ideal spherical surface for the case of spheri-cal lenses, this calculation is now outlined.

7. Spherical lens array

A similar argument is used to describe the design pro-cess for an ideal perfect spherical lens. The volumesbefore and after melting are related by a volume re-duction variable, E.

V0 � E ¼ VSph ¼ pr2TSph ð16Þ

where TSph is the thickness of the photoresist “puck”see fig. 7, required to produce spherical lenses and

VSph ¼ 13 ph

2ð3R� hÞ :The variables are as illustrated in fig. 7. Therefore

pr2TSph ¼ 13 ph

2ð3R� hÞ ð18Þ

Hence

TSph ¼ h2

3r2ð3R� hÞ : ð19Þ

To simplify, we eliminate R from eq. (19) using the factthat,

h ¼ R� ðR2 � r2Þ12 ð20Þ

and therefore,

R ¼ r2 þ h2

2h: ð21Þ

Substituting Equation (21) into eq. (19) gives that,

TSph ¼ h

63þ h2

r2

� �ð22Þ

where substituting from eq. (1) into eq. (20), the cen-tral height of the lens, h, can be written in terms of thefocal length, f, and the refractive index of the photore-sist, n, as

h ¼ ðn� 1Þ f �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðn� 1Þ2 f 2 � r2

q: ð23Þ

Feidhlim T. O’Neill, John T. Sheridan, Photoresist reflow method of microlens production. Part I 397

1000

1500

2000

Focal length

50

100

150

200

radius

0

20

40

Hcylindrial

1000

1500

2000

Focal length

h (µm)

f (µm)

r (µm)

Fig. 6. Thickness required for the ideal cylindrical case forcombinations of lens radius and focal length.

Fig. 7. The variables describing the production of sphericalmicrolenses.

These formulae then form the basic starting point indetermining the design parameters of the microlens ar-ray. The plot of the thickness of the photoresist “puck”required to produce spherical lenses is plotted as afunction of the focal length of the lens, f, and the ra-dius of the lens, r, in fig. 8.This section has provided us with a starting point to

identify the production parameters required to pro-duce perfect lenses. This is an initial approximationwhich assumes that the conditions are ideal and thecritical angel has no effect. However we are now ableto use the production parameters as found using thismodel to design the lenses used in this study.

8. Experimental results

In this section the experimental methods used to makeand measure the microlenses and results obtained arediscussed. Since the type of photoresist material usedto produce the lenses is critical, we first describe thephotoresist used in this study.

8.1. The Photoresist

The photoresist used in this study was Shipley S1800series resist. This resist is a positive photoresist systemthat is engineered to satisfy the microelectronics indus-try requirements for advanced IC device fabrication.This resist has therefore high resolution and is suitablefor high fidelity replication of the mask profiles and

therefore the lens pitch. The various parameters whichare necessary to describe the action of the photoresistin contact with the substrate are outlined in point formin table 1. The absorbance spectra of the photoresist isshown in fig. 9, [36].The production of uniform lens arrays required a

high degree of control over the recording parameters.One of these parameters is the initial photoresist thick-ness prior to the melting process. The resist is coatedonto the substrate using a spin coating process inwhich the resist thickness is controlled by the spin rateand spin duration used. The experimental data ob-tained in the production of the microlenses is com-pared to the official Shipley data in fig. 10.This information made it possible to produce the in-

itial structures used to produce the cylindrical andspherical microlens arrays.

8.2. Optical examination of the lens arrays

The production method is illustrated with photographsof the resist cylinders before and after melting, (fig. 11).The non-uniformity of the lenses produced using the

398 Feidhlim T. O’Neill, John T. Sheridan, Photoresist reflow method of microlens production. Part I

1000

1500

2000

2500

3000

focal length

50

100

150

200

radius

0

10

20

30

40

Tspherical

1000

1500

2000

2500

3000

focal length

h (µm)

f (µm)

r (µm)

Fig. 8. Thickness required for the ideal spherical case for var-ious combinations of lens radii and focal lengths.

Table 1. Summary of the photoresist physical parameters.

S1800 Series

Absorption 320–450 nm (maximised at 436 nm)

Viscosity 3.5710�5 m2 s�1

Density 1.02 g cm�3

Fig. 9. The absorbance spectra of the S1800 series photore-sist.

0

0.5

1

1.5

2

2.5

3

2000 3000 4000 5000 6000 7000Spin Speed (RPM)

Thi

ckne

ss(m

icro

ns) Shipley data

sheet

ExperimentalData

Fig. 10. Graph showing the thickness of the Shipley 1818Photoresist thickness as a function of spin rate for experimen-tal and theoretical cases.

reflow method is illustrated in these microscope pic-tures and also examined using a Linnik interferometer,(fig. 12). They show a raised section of the lens profileall around the lens perimeter, this is shown to be � 0.2microns. These lenses are however at the extremes ofthe range for which the reflow method is used, f /# ffi26, (where r = 200 mm).Having once again, [1], observed the fact that the

melted photoresist reflow method can result in non-spherical surface profiles in the previous section wenow examine the profiles obtained in more detail.

8.3. Lens profile measurements

Three techniques were used to measure the profiles ofthe microlenses: (a) TallyStep, (b) Dektak and (c)AFM. The results of these measurements are now dis-cussed.

8.4. TallyStep profilometry

The surface profile both the melted microlenses andalso the structure of the developed plates prior to themelting stage, are measured using a Taylor and Hob-son TallyStep device. The equipment uses a stylus witha �2 mm chisel head as a contact with the sample. Thisdevice is designed to allow the accurate measurementof step height, (�0.1 mm) on the 5 mm scale, however itwas found to be out of calibration. An attempt wasmade to calibrate the device using an old standard andit was found to have an accuracy of �2.4% on the5 mm scale.

8.4.1. Alignment

The surface profiles of the cylindrical lenses were mea-sured using the TallyStep instrument. This instrument

Feidhlim T. O’Neill, John T. Sheridan, Photoresist reflow method of microlens production. Part I 399

Fig. 11. Images of lenses with diametersof 400 mm, pre- and post-melt, Magnifica-tion � 10, (Mag. � 10), clearly showingedge effects.

Mag×20 Mag×60

Fig. 12. Images of the same lens arrayobtained using a Linnik interferometer.Diameter 400 mm, Mag. � 20 and Mag.� 60, l = 540 nm.

suffers from alignment difficulties, however it wasfound that manual alignment should give an error of1.5% or less. This corresponds to a 10 degree miss-alignment. The angular deviation from the sample truevalue, 15 degrees, is shown in fig. 13.

8.4.2. Profile obtained

The profiles obtained using this method show markeddeviation from the cylindrical profile predicted by thesimple energy minimization approach. This deviation ismost noticeable for lenses which have large f /#, i.e.lenses formed where the ratio of the thickness of the

resist prior to melting to the width of the lenses issmall. Typical experimental profiles for four differentcylindrical lenses are compared to the theoretical sphe-rical solution, for qc ¼ 15�, and are shown in fig. 14.The TallyStep device produces an output using a rec-

tilinear recorder. A large number of profiles were mea-sured using this method, [43]. To enable mathematicalfits to be carried out using this data it was necessary totransfer the data to standard spreadsheet format. Alarge number of the profiles obtained were found to beslanted, probably due to misalignment of the measure-ment device. This slant was removed by rotating thetraces numerically using Mathematica, [41]. This stepwas necessary in order to fit the experimental datawith the polynomial models that shall be discussed inthe second part of this paper. An example of this pro-cess is shown in figs. 15 and 16.The profiles were then normalised with respect to

the lens radius, r, and fitted using the polynomial mod-els discussed in the second part of this paper, [44].

8.4.3. Critical angle measurement

The theoretical model for melted microlens surfaceprofiles relies on a number of parameters. One of

400 Feidhlim T. O’Neill, John T. Sheridan, Photoresist reflow method of microlens production. Part I

0

2

4

6

8

10

12

14

16

0 20 40 60 80 100Deviation from perpendicular incidence (degrees)

Cri

tical

Ang

le(d

egre

es)

Fig. 13. Angular deviation from the example true value, 15degrees, due to misalignment.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

-1 -0.5 0 0.5 1

Normalised Width

Nor

mal

ised

Hei

ght

300500D A25

2600 A80

4700H A250

4700I A800

Spherical (Theoretical)

Fig. 14. Normalised graphs of four different pitch cylindricallens profiles produced experimentally and the theoretical per-fect “sphere” for qc = 15�.

0

0.5

1

1.5

2

2.5

0 100 200 300 400 500 600

X postion (microns)

Hei

ght(

mic

rons

)

Fig. 15. Typical initial slanted profile. Cylindrical lens profile(A250 profile 21800K).

0

0.5

1

1.5

2

2.5

0 100 200 300 400 500 600

X position (microns)

Hei

ght(

mic

rons

)

Fig. 16. Profile with slant removed. Cylindrical lens profile(A250 profile 21800K).

these is the contact angle, i.e. the angle the melted li-quid makes with the substrate. Careful measurementof this angle was attempted using the TallyStep and aconfirmation of the results was attempted using theother two profilometry methods used in this study, theDektak and AFM. The results provide a first estimateapproximate reading so as to provide initial param-eters for the theoretical model.The TallyStep translation motor was calibrated using

a number of photoresist gratings. The pitch of thesesgratings having previously been measured using theoptical microscope. The results of this calibration wereplotted and are shown in fig. 17.The critical angles obtained are dependent on the

substrate properties and also on the temperature atwhich the resist is melted. The average critical anglesobtained for a range of different melting temperaturesand orientations are shown in table 2. The values ob-tained were between 5� � qc � 19.65�.Table 2 also shows the results obtained by melting

the photoresist in an inverted orientation. There wasno apparent change in the profiles obtained using thismethod, which is as expected due to the low volume ofresist used to produce each lens. However the differ-ences observed in the critical angle may be caused by anumber of effects.

First the substrates used were green float glass and itis likely that some differences in the surface, (i.e. flat-ness, roughness), were present. Some differences in themelting process may also have occurred. Furthermorethe properties of the resist are known to vary slightlywith changes in storage temperature and humidity,[45].This experiment does illustrate the effect that the

melting temperature has on the critical angle. It isknown that the surface tension is a function of tem-perature. Normally it is assumed that the photoresistwill solidify at the same temperature regardless of themelting temperature. However as the resist is heated,variation in the composition may occur causing the so-lidification point to vary. The variation in the resistcomposition itself could also result in the variation incritical angle we have observed. The experimental dataobtained is shown in fig. 18.Confirmation of the above results was attempted

using two separate profilometry techniques. The firstbeing Dektak profilometry and the second AtomicForce Microscopy. We outline both of these in moredetail in the next section.

8.5. Dektak profilometry

A second profilometer, a Vecco Dektak 3 profil-ometer, was used to validate the TallyStep results. Itprovides more accurate measurement than the olderTallyStep device and has a lateral dynamical range ofup to 50 mm. It was calibrated to have an accuracyof 0.8%. Some of the profiles obtained using thismethod were also found to be tilted due to misalign-ment. Therefore they were rotated in a similar man-ner to the TallyStep traces prior to estimating thecritical angle and comparing the profiles. These Dek-tak measurements were obtained for a set of micro-lens arrays which were far from the spherical case.

Feidhlim T. O’Neill, John T. Sheridan, Photoresist reflow method of microlens production. Part I 401

y = 20.494x + 0.0813R

2

= 1

0

10

20

30

40

50

60

70

0 0.5 1 1.5 2 2.5 3 3.5

Speed (A.U.)

Mic

rons

/Div

.

Fig. 17. TallyStep translation motor calibration.

Table 2. Average critical angles obtained experimentallyusing three different photoresists with both normal (right sideup) and inverted (upside down) orientations

Photoresist Melting Temperature Orientation Critical Angle

S1828 160 normal 10.95

S1818 120 normal 19.65

S1818 160 normal 9.15

S1818 160 inverted 8.6

S1818 170 inverted 7.7

S1818 150 inverted 8.6

AZ4562 160 normal �5.0

y = -0.2431x + 48.344

R2 = 0.9357

0

5

10

15

20

25

110 120 130 140 150 160 170 180Temperature (degrees C)

Cri

tical

Ang

le(d

egre

es)

Fig. 18. Temperature dependence of the critical angle usingthe S1818 photoresist.

The results obtained using this method are comparedwith the other two profilometry method used in sec-tion 9.

8.6. Atomic force microscopy, AFM

The third method used to examine the microlens pro-files was carried out using a Burleigh instruments“Vista” scanning probe microscope. This instrumenthad a number of limitations which restricted its appli-cation when applied to the measurement of the micro-lens profiles. The maximum range of the instrumentwas 5 mm and so it could only be used on the thinnestsamples (A800 cylindrical lenses and the A400sphspherical lenses). The maximum lateral dynamicalrange was 40 mm and so it was only possible to mea-sure the edges of the profiles of these lenses. Thiscoupled with the limited accuracy of this system, esti-mated to be �10% using a calibration standard, meant

that its applicability to this study was limited to esti-mates of critical angles.The edge profile of a sample cylindrical lens is

shown in fig. 19. The profiles obtained using this meth-od, were slanted, once again probably due to misalign-ment of the substrate.Therefore the profile data was rotated using Mathe-

matica before estimates of the critical angle weremade, the rotated profile corresponding to fig. 20 isshown in fig. 21. The results obtained are discussed inthe next section.

9. Comparison of the profilometry results

The majority of the profiles obtained during this studywere measured using the TallyStep instrument and at-tempts were made to verify these results using the two

402 Feidhlim T. O’Neill, John T. Sheridan, Photoresist reflow method of microlens production. Part I

40

40

0 0

1.76

Y direction(microns)

X direction(microns)

Hei

ght

(mic

rons

)

Fig. 19. AFM profile of cylindrical lens (A800).

0

200

400

600

800

1000

1200

1400

1600

0 5000 10000 15000 20000 25000 30000 35000

X direction (nm)

Hei

ght(

nm)

Fig. 20. Cross-sectional profile of the cylindrical lens takenfrom AFM measurement.

5 10 15 20 25 30

0.5

1

1.5

Width (Microns)

Hei

ght(

Mic

rons

)

Fig. 21. Rotated AFM data. Angle used to level the data was2.5�.

-0.5

0

0.5

1

1.5

2

2.5

0 10 20 30 40 50 60 70 80 90

X position (Microns)

Hei

ght

(Mic

rons

)

Dektak

AFM

TallyStep

Fig. 22. Comparison of the edge profiles of the cylindricallens (17800G A800).

instruments discussed above. The results of this com-parison are shown in table 3.We can see from the comparison shown in fig. 22

that there are significant differences between the re-sults obtained using the three methods. However thevalue of qc was always found to be in the range 7.3� �qc � 24�. The polynomial models were fitted to theprofile data using a critical angle of 15 degrees which iswithin this range.

10. Conclusions: Microlens experiments

In this paper the production of microlens arrays hasbeen discussed. The fabrication technique used in thisstudy, the photoresist reflow method, has been dis-cussed. The fabrication of microlens arrays has beendescribed and the resulting profiles measured. Devia-tions from the ideal spherical case have been observed,and estimates of the critical angle have been given.Some of the properties of the photoresist used havebeen examined as the photoresist is critical to the typeof profiles obtained.The profile data obtained using the methods de-

scribed in this paper shall be used in the Part II. toexamine a number of analytic models which are devel-oped to predict the microlens surface profile.

Acknowledgements. The authors would like to Dr. M. Hutleyand Mr. N. Turner who facilitated access to the microlens pro-duction facilities at The National Physical Laboratory U.K. Wealso wish to thank Dr. D. Daly for kindly providing experi-mental data and his Doctoral thesis. The authors would alsolike to thank Prof. I. Samuel and also Mr. J. Lawrence at TheUniversity of St. Andrews, Scotland for providing the access tothe AFM and Dektak profilometers. We would also like tothank Dr. H. J. Byrne for providing access to the spectroscopicfacility at the FOCAS group at the Dublin Institute of Tech-nology, Ireland.

References

[1] Sheridan, JT, Schwider, J, Streibl, N, Haselbeck, S, Eisner, M,Heissmeier, M, Falkenstorfer, O: Modelling and measure-ment ofmeltedmicrolens shapes, Optik 97 (1994) 174–180

[2] Abe, S, Sheridan, JT: Curvature correction model of dro-plet profiles. Phys. Lett. A 253 (1999) 317–321

[3] Hooke, R: Micrographia. The Royal Society of London,1665

[4] Severi, M, Mottier, P: Etching selectivity control duringresist pattern transfer into silica for the fabrication of mi-crolenses with reduced spherical aberration. Opt. Eng. 38(1999) 146–150

[5] Iga, I, Kokubun, Y, Oikawa, M: Fundemetals of Microop-tics. Academic Press, London 1984

[6] Kufner, M, Kufner, S: Fabrication of monolithic inte-grated fiber-lens connector arrays by deep proton irradia-tion. Microsystem Technol. 2 (1996) 114–118

[7] Hutley, MC: Optical techniques for the generation of mi-crolens arrays. J. Mod. Opt. 37 (1990) 253–265

[8] Fu, YQ, Bryan, NKA: Novel one-step method of microlensmold array fabrication. Opt. Eng. 40 (2001) 1433–1434

[9] Daly, DJ: The fabrication and measurement of meltedphotoresist microlenses. Doctoral Thesis, Kings CollegeLondon, U.K. 1998

[10] Popovic, ZD, Sprague, RA, Connell, GAN: Technique formonolytic fabrication of microlens arrays. Appl. Opt. 27(1988) 1281–1288

[11] Fujita, T, Nishihara, H. Koyama, J: Fabrication of microlenses using electron-beam lithography. Opt. Lett. 6(1981) 613–615

[12] Borrelli, NF, Morse, DL, Bellman, RH, Morgan, WL:Photolytic technique for producing microlenses in photo-sensitive glass. Appl. Opt. 24 (1985) 2520–2525

[13] Liau, ZL, Diadiuk, V, Walpole, JN, Mull, DE: Galliumphosphide microlenses by mass transport. Appl. Phys.Lett. 55 (1989) 97–99

[14] Daly, D, Stevens, RF, Hutley, MC, Davies, N: The manu-facture of microlenses by melting photoresist. Meas. Sci.Technol. 1 (1990) 759–766

[15] Masuda, S, Takahasi, S, Nose, T, Sato, S, Ito, H: Liquid-crystal microlens with a beam steering function. Appl.Opt. 36 (1997) 4772–4778

[16] Calixto, S, Scholl, MS: Relief optical microelements fabri-cated with dichromated gelatin. Appl. Opt. 36 (1997)2101–2106

Feidhlim T. O’Neill, John T. Sheridan, Photoresist reflow method of microlens production. Part I 403

Table 3. Comparison between the results obtained using the three profilometry methods.

Grating MaskUsed

AFM Dektak TalyStep

CentralHeight

Width qc CentralHeight

Width qc CentralHeight

Width qc

17800G A800 �1.7 N/A 24 1.941 436 14, 10 1.8 398 23

17800G A800 �1.85 N/A 24

17800G A250 N/A 1.9 140 7.3, 7.2, 11 1.85 125 24

17800G A25 N/A N/A (cusping) cusping

17800A A80 N/A 5.0 55 14.5, 16 5.6 51 N/A

17800A A80 N/A 14.0

17800B A400sph

N/A �1 (cusping) 410 1.8 395 N/A

17800B A400sph

N/A �1 412

[17] Keyworth, BP, Corazza, DJ, McMullin, JN, Mabbott, L:Single-step fabrication of refractive microlens arrays.Appl. Opt. 36 (1998) 2198–2202

[18] Xin-Jian, Y, Xin-Yu, Z, Yi, L, Xin-Rong, Z: Microlens ar-rays formed by melting photoresist and ion beam milling.Proc. S.P.I.E. 3276 (1998) 249–253

[19] Okamoto, T, Mori, T, Karasawa, T, Hayakawa, S, Seo, I,Sato, H: Ultraviolet-cured polymer microlens arrays.Appl. Opt. 38 (1999) 2991–2996

[20] Reyna, A, Quiroga, D, Calixto, S: Dynamical optical mi-croelements on dye sensitised gels. Appl. Opt. 39 (2000)3948–3954

[21] Hartmann, DM, Kibar, O, Esener, SC: Characterisationof a polymer microlens fabricated by use if the hydropho-bic effect. Opt. Lett. 25 (2000) 975–977

[22] Lee, HJ, Park, KS: Self-developed formation of relief op-tical microlens by dry photopolymer. Mol. Cryst. Liq.Cryst. 349 (2000) 19–22

[23] Ishii, Y, Koike, S, Arai, Y, Ando, Y: Ink-jet fabrication ofpolymer microlens for optical-I/O chip packaging. Jpn. J.Appl. Phys. 39, Part 1 (2000) 1490–1493

[24] Shen, X-J, Pan, L-W, Lin, L: Microplastic embossing pro-cess: experimental and theoretical characterizations. Sen-sors and Actuators A 3323 (2002) 1–6

[25] Anderson, RH: Close up imaging of documents anddisplays with lens arrays. Appl. Opt. 18 (1979) 477–484

[26] Volkel, R, Herzig, HP, Nussbaum, P, Dandliker, R: Micro-lens array imaging system for photolithography. Opt. Eng.35 (1996) 3323–3330

[27] Stevens, RF, Davies, N: Lens arrays and photography.Jour. Photographic Science 39 (1991) 199–208

[28] de Gennes, PG: Wetting: Statics and dynamics. Rev. Mod.Phys. 57 (1985) 827–863

[29] Voinov, OV: Dynamic edge angles of wetting uponspreading of a drop over a solid surface. Jour. Appl.Mech. Tech. Phys. 40 (1999) 86–92

[30] Sekimoto, K, Oguma, R, Kawasaki, K: Morphological sta-bility analysis of partial wetting. Ann. Phys. 176 (1987)359–392

[31] Jay, TR, Stern, MB: Preshaping photoresist for refractivemicrolens fabrication. Opt. Eng. 33 (1994) 3552–3555

[32] Lindlein, N, Pfund, J, Schwider, J: Algorithm for expand-ing the dynamic range of a Shack-Hartmann sensor byusing a spatial light modulator array. Opt. Eng. 40 (2001)837–840

[33] Artzner, G: Microlens arrays for Shack-Hartmann wave-front sensors. Opt. Eng. 31 (1992) 1311–1321,

[34] Hutley, MC, Savander, P, Schrader, M: The use of micro-lenses for making spatially variant optical interconnec-tions. Pure Appl. Opt. 1 (1992) 337–346

[35] Craft, NC, Feldblum, AY: Optical interconnects based onarrays of surface-emitting lasers and lenslets. Appl. Opt.31 (1992) 1735–1739

[36] Shipley Microposit S1800 series photo resists data sheet,Shipley Ltd, Herald Way, Coventry, CV3 2RQ, U.K.

[37] Elias, H-G: An introduction to polymer science. VCHPublishers, New York 1997

[38] Schilling, A, Merz, R, Ossmann, C, Herzig, HP: Surfaceprofiles of reflow microlenses under the influence of sur-face tension and gravity. Opt. Eng. 39 (2000) 2171–2176

[39] Marks, LD, Heine, V, Smith, DJ: Direct observations ofelastic and plastic deformations at Au(1,1,1) surfaces.Phys. Rev. Lett. 52 (1986) 656–658

[40] Compugraphics International Ltd., (Total Mask Solu-tions), Eastfield Industrial Estate, Glenrothes, Fife, Scot-land, KY7 4NT, U.K.

[41] Wolfram, S: The Mathematica Book, 4th edition. WolframMedia/Cambridge University Press, Cambridge 1999

[42] Klug, R, Brenner, K-H: Implementation of multilens mi-cro-optical systems with large numerical aperture bystacking of microlenses. Appl. Opt. 38 (1999) 7002–7008

[43] O’Neill, FT: Holographic and refractive optical elementarrays. Doctoral Thesis, University College Dublin, Ire-land 2002

[44] O’Neill, FT, Sheridan, JT: Photoresist reflow method ofmicrolens production Part II: Analytic Models. submittedto Optik 113 (2002) 405–419

[45] Garbut, I: Private communications, National Physical La-boratory 2000

404 Feidhlim T. O’Neill, John T. Sheridan, Photoresist reflow method of microlens production. Part I