ISSN 1063-7850, Technical Physics Letters, 2006, Vol. 32, No. 3, pp. 232–237. © Pleiades Publishing, Inc., 2006.

232

¶

Introduction.

Diffractive optical elements ofmicron dimensions are now widely studied due to theirbroad range of applications such as optical signal pro-cessing, optical interconnection, optical data storage,and optical computing. A number of advanced methodshave been developed to fabricate diffractive optics forvarious applications, including holographic interfer-ence, direct laser writing, and mask alignment tech-niques. [1–5]. In these methods, the fabrication pro-cesses usually include two main steps. In the first step,the designed structures are formed in a thin photoresistfilm; the second step involves the transfer of the surfacerelief structure to the substrate by means of etching.However, the etching techniques are usually time-con-suming and expensive, especially in the case of multi-level or continuous surface relief structures.

In recent years, hybrid sol–gel (HSG) technologyhas been intensively studied as a potential alternativefor the realization of high-performance micro-opticalelements [6, 7]. The HSG materials are cost-effective,ensure good mechanical and chemical stability, andpossess high transmission characteristics over a broadwavelength range. The most important circumstance isthat sol–gel glasses offer a practically unlimited possi-bility of modifying the material properties. The majorapplication of the HSG materials is focused on the fab-rication of micro-optical elements by UV photolithog-raphy [8, 9] and electron-beam lithography [10].

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The text was submitted by the authors in English.

A number of lithographic processes involving HSGglasses on planar substrates have been described in theliterature. However, there are only a few papers aboutthe lithography process for HSG glasses on curved(e.g., lens-shaped) surfaces. The ability to fabricateoptical glass patterns on such curved surfaces would beuseful in a number of fields of optics. A laser writer hasthe ability to fabricate patterns on a curved surface [2].However, the pattern fabrication efficiency of thismethod is very low [5]. Soft lithography offers a low-cost and high-throughput patterning technique, whichhas the ability to fabricate micrometer- and evennanometer-scale patterns on curved surfaces. White-sides et al. [11] described a topographically directedphotolithography and near-field contact-mode photoli-thography. However, the patterns were mostly fabri-cated on nonglassy (photoresist or hot-cured polysty-rene) materials.

In this paper, we describe a process of fabricatingpatterns in HSG glass materials on curved surfacesbased on soft lithography. The ion etching step, whichis presently difficult to realize on curved surfaces, isavoided in this process. To our knowledge, this is thefirst report on the fabrication of glass patterns on curvedsurfaces by means of soft lithography. This techniquewill provide us a simple step to achieve glass opticalstructure on curved surface. The use of this processgreatly prolongs the life of replica gratings, especiallyin vacuum ultraviolet applications, which is explained

Low-Cost Lithographic Fabrication of Relief Patternsin a SiO

2

–TiO

2

Hybrid Sol–Gel Glass on Curved Surfaces

¶

F. Zhao

a

,

b

, Y. Xie

a

, S. Xu

b

, G. Liu

a

, S. He

c

, and S. Fu

a

a

National Synchrotron Radiation Laboratory, University of Science and Technology,Hefei, 230026 China

b

College of Material and Chemistry Technology, Changchun University of Science and Technology,Changchun, 130022 China

c

Department of Modern Mechanics, University of Science and Technology,Hefei, 230026 China

e-mail: xyj@ustc.edu.cn

Received July 7, 2005; in final form, October 15, 2005

Abstract

—We describe a low-cost method of fabricating optical patterns in a hybrid sol–gel glass on curvedsurfaces by means of soft lithography. The ion etching step, which is presently difficult to realize on curved sur-faces, is avoided in this process. Using the proposed soft lithography technique, it is possible to transfer high-quality patterns to a hybrid sol–gel glass on curved surfaces. This technique offers a low-cost and simplemethod for obtaining optical glass structures on such surfaces. The use of a sol–gel glass (replacing an epoxy)layer greatly prolongs the life of replica gratings, especially in the vacuum ultraviolet applications.

PACS numbers: 85.40.Hp, 81.05.Kf

DOI:

10.1134/S1063785006030175

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LOW-COST LITHOGRAPHIC FABRICATION OF RELIEF PATTERNS 233

by replacement of the conventional epoxy layer by anHSG glass that can withstand longer high-temperatureirradiation as compared to that tolerated by epoxylayers.

Material preparation.

3-(Trimethoxysilyl)propyl-methacrylate (TMSPM, 97%) and titanium(IV) isopro-poxide Ti(OC

3

H

7

)

4

(99.999%) were obtained from Ald-rich Chemicals (USA) and used without additionalpurification. First, TMSPM is hydrolyzed on stirringfor 1 h with an 0.01 M aqueous HCl solution. In the sec-ond step, Ti(OC

3

H

7

)

4

is dissolved in isopropanol, com-plexed with acetylacetone, and then dispersed in a pre-hydrolyzed organosiloxane medium. The addition ofacetylacetone prevents the precipitation of titaniumdioxide. Tetrapropyl titanium is introduced into thematerial in order to increase its refractive index andmechanical strength. Then, the two solutions are mixedtogether and a polycondensation reaction is allowed toproceed under stirring for 30 h at room temperature.

In the next stage, a photoinitiator (IRGACURE184,CIBA) is added to render the solution photosensitive.The photoinitiator forms free radicals under UV expo-sure, which provides the crosslinking of unsaturated car-bon double bonds and thus makes the material a nega-tive-tone photoresist. The photoinitiator is 1-hydroxycy-clohexlyl phenyl ketone, which is added at an amountof 1 g per 15 ml of HSG solution. This solution is thenstirred for 30 min, until complete dissolution of thephotoinitiator. Then, the solution is filtered and spin-coated onto silicon or glass substrates. The thickness ofthe deposit depends on the spin-coating process param-eters and the solution concentration. Prior to UV expo-sure, the samples are prebaked at 90

°

C for 1 h in orderto remove excess solvent. This process is necessary todecrease the exposure time and to avoid contaminationof the photomask at the exposure stage.

Exposure of the sol–gel film to the UV light of amercury lamp with a peak emission wavelength of365 nm produces excitation of the photoinitiator. As aresult, the photoinitiator yields free radicals that inducethe polymerization of vinyl monomers via methacry-loxy side groups. In contrast to the unexposed regions,the stability and solubility properties of the exposedregions of the films change under UV irradiation, andthe refractive index of the exposed regions increasessimultaneously. After exposure, the sample is devel-oped in an aqueous ethanol solution for 6 s to removethe unexposed part, and thus the desired pattern is beobtained in the HSG glass. Finally, the sample is sub-jected to postbaking at 180

°

C for 1 h in order to stabi-lize the structure.

Fabrication of optical patterns on curved sur-faces.

The fabrication of patterns begins with the prep-aration of polydimethylsiloxane (PDMS, a polymerconsisting of two parts—a base and a curing agent) andmontmorillonite (NaMMT, a mineral available on theopen market). In order to improve the physical charac-

teristics of PDMS, the montmorillonite is introducedinto this polymer matrix so as to make it more condu-cive and facilitate the transfer of patterns onto curvedsurfaces. In our experiments, 2 wt % of montmorillo-nite was introduced into PDMS. For the preparation ofa PDMS–montmorillonite prepolymer, the componentsshould be thoroughly stirred to provide for their homo-geneous mixing.

A photoresist relief grating on a silicon substrate canbe produced by means of interference lithography or bydirect electron beam writing. The grating in the photo-resist is steamed by CF3(CF2)6(CH2)2SiCl3 for~20 min and then the PDMS– montmorillonite com-pound is poured on the grating. This structure is put intoan oven and treated at 60

°

C for about 1 h. After solidi-fication, the PDMS layer is peeled from the photoresistgrating on the silicon substrate, and thus the pattern istransferred to the PDMS layer (Fig. 1) [12]. The PDMSfilm thickness is controlled by the height of a solidframe on the substrate.

Then, the PDMS layer with the pattern (peeled fromthe photoresist grating) is transferred to a concave lenssurface. The transfer process is performed in severalsteps as depicted in Fig. 2. First, the PDMS film with athickness of 100

µ

m is transferred onto a planar trans-parent glass substrate. Using a circular solid frame witha width of 1 mm, a thickness of 1mm, and a diameter of30 mm (which is smaller than the lens sphere diameter,50 mm), the PDMS film is pressed tightly to the glasssubstrate, so that a sealed chamber is formed betweenthe PDMS film and the glass substrate (Fig. 2A). Sec-ond, HSG material is spin-coated onto the lens surfaceat 3000 rpm (note that the HSG film should not be pre-baked). Third, air is pressurized into the sealed cham-ber and the plane PDMS membrane will acquire aspherical shape. When the radius of the sphericalPDMS membrane is equal to the radius of the lens sur-face, air pressurization is stopped. Thus, the micro-structure of the PDMS membrane surface is transferredto the HSG material (Fig. 2B). Fourth, after 30 min, the

PhotoresistSi

PDMS

PDMS

A

B

C

Fig. 1.

Transfer of a relief pattern formed in a planar photo-resist layer (on a flat silicon substrate) to a PDMS layer (seetext for explanations).

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HSG material becomes a gel. The assembly is put on ahot plate at 90

°

C and prebaked for 15 minutes. Aftercooling to room temperature, the HSG film is exposedfor 30 min to UV light of a mercury lamp with a peakemission wavelength of 365 nm. This irradiation leadsto polymerization and stabilization of the HSG film(Fig. 2C). Fifth, after polymerization and stabilizationof the HSG glass, the PDMS membrane is allowed todeflate, and the PDMS film is peeled from the surfaceof the polymerized and stabilized HSG glass. This pro-cess does not deform the microstructure of the HSGglass because PDMS is still soft, whereas the HSGmaterial is hard. Sixth, the HSG glass structure on theconcave lens surface is postbaked in the oven at 180

°

Cfor ~60 min (Fig. 2D).

The deformation of a PDMS membrane during thetransfer process was studied by computer simulationusing Finite Element Analysis software (ANSYS). Fig-ures 3 and 4 show computer images of a deformedmembrane. The simulation showed that the PDMSmembrane forms a sphere under air pressure.

In terms of the mechanical theory, the surface stressof the PDMS membrane can be described as follows.Let us consider a random area element

∆

S

on a spheri-cal PDMS membrane centered at point

O

a having aradius of

R

(Fig. 5a). This element can be simplified toa two-dimensional system as depicted in Fig. 5b. The

force balance equations in this system can be written asfollows:

(1)

If the thickness of the spherical element under con-sideration is

h

, the stress in this element can beexpressed as

(2)

where

(3)

Using expressions (1)–(3), we obtain the followingrelation:

. (4)

If the area of the element is infinitesimal, we canassume that sin(

θ

)

≈ θ

, in which case the above formulasimplifies to

(5)

F θ( )cos F^ θ( )cos=

2F θ( )sin N=

N p∆S p 2Rθ( )2.= =⎩⎪⎨⎪⎧

σ FS---

N2 θ( )sin-------------------

2Rθh-------------------

N4Rθh θ( )sin------------------------------,= = =

N p∆S p 2Rθ( )2.= =

σ pRθh θ( )sin-------------------=

σ pRh

-------.=

Air

ForceA

B

C

D Heat

UV

HSG layer

Air

Air

Force

ForceForce

ForceForce

Lens

Fig. 2.

Formation of a relief pattern on a curved substrate surface with the aid of a PDMS layer (see the text for explanations).

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LOW-COST LITHOGRAPHIC FABRICATION OF RELIEF PATTERNS 235

0 0.76128 0.152256 0.228384 0.3045120.38064 0.114192 0.19032 0.226448 0.342576

MW

X

Y

Z

Fig. 3.

Computer-simulated image (top view) of a PDMS membrane (gray gradations correspond to various displacement in the

Z

axis direction).

XZ

Y

MW

0 0.76128 0.152256 0.228384 0.3045120.38064 0.114192 0.19032 0.226448 0.342576

MX

Fig. 4.

Computer-simulated image (side view) of a PDMS membrane (gray gradations correspond to various displacement in the

Z

axis direction).

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From this relation, we may conclude that deforma-tion of a pattern on the PDMS film is determined bythree factors: air pressure

p

, curvature radius

R

, andfilm thickness

h

. It is obvious that the air pressure isuniform everywhere on the surface. The curvatureradius and thickness are also uniform according to theresults of simulations for a PDMS membrane formedon a spherical surface. Therefore, the deformation isuniform over a PDMS membrane surface. Thus, thegrating pattern is transferred from a plane substrateonto a lens surface with uniform deformation.

Using the method described above, a grating withrelief surface is obtained on the concave lens surfacewith a curvature radius of 50 mm. Figure 6 shows thetypical scanning electron microscopy (SEM) images ofa grating fabricated in a SiO

2

–TiO

2

hybrid sol–gelglass. The period of the grating is 10

µ

m. Figure 6a pre-sents a general view of the grating, while Fig. 6b showsthe relief of separate lines. As can be seen from theseSEM images, a planar lithographic pattern has beentransferred to the SiO

2

–TiO

2

hybrid sol–gel glass layeron a curved lens surface with high quality.

The grating on a concave lens surface makes it pos-sible to focus and diffract light beams by one opticalelement (Fig. 7). Therefore, the total losses in an opticalsystem can be reduced by decreasing the number ofoptical elements. In this study, we used the grating pat-tern as an example in order to demonstrate a low-costtechnique proposed for the fabrication of glass patternson curved surfaces. Therefore, only the basic perfor-mance characteristics of the obtained optical elementare presented. Figure 8a shows the focus distribution in

∆

S

O

R

Fp

θ

F

*

R

O

(a) (b)

N

=

p

×

∆

S

Fig. 5.

Schematic diagrams of (a) a small area element and (b) force balance on the PDMS membrane surface.

NONE LEI 5.0 kV

×

300 10

µm NONE LEI 5.0 kV ×1.000 10 µm

Fig. 6. SEM images of a grating transferred from a planar substrate to a concave surface: (a) general view of the grating; (b) therelief of separate lines.

Fig. 7. Interaction (focusing and diffraction) of a parallellight beam with optical elements containing (a) convex and(b) concave surface gratings formed in an HSG glass layer.

(a) (b)

(a) (b)

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LOW-COST LITHOGRAPHIC FABRICATION OF RELIEF PATTERNS 237

the case of reflection diffraction, while Fig. 8b showsthe analogous distribution in the case of diffuse diffrac-tion (for a beam transmitted through the element). Forthe light with a wavelength of 632.8 nm, the diffractionefficiency is 76%, which is the same as that for the grat-ing on a planar substrate.

Conclusions. We described a low-cost method forfabricating lithographic optical structures in an HSGglass on a concave lens surface. Using the HSG glass,it is possible to obtain glass structures on curved sur-faces without ion etching. The soft lithography pro-vides a means of obtaining fine patterns on curved sur-faces. Thus, the proposed technique offers a low-costand simple means of fabricating optical glass structureswith curved surfaces. This technique greatly prolongsthe life of replica gratings, especially in vacuum ultra-violet applications by replacing the conventional epoxylayer by an HSG layer.

Acknowledgments. This study was supported bythe National Natural Science Foundation of China(project nos. 10402039 and 10272098).

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Fig. 8. The patterns of focus distribution showing the optical performance of (a) concave and (b) convex gratings formed in an HSGglass layer.

(a) (b)