roduction potential on the wafer scale, combinedith a wide range of applicability, has made diffrac-
ive and refractive micro-optics invaluable in the pho-onics industry. However, few techniques exist forhe fabrication of complex profiles on an optical sub-trate. In particular, the single binary lithographicask method provides neither the efficiency nor the
enerality needed by many of the latest applications.ther available methods involve use of gray-scaleasks based on either analog transmittance or digi-
al halftone. The gray-scale profile is then trans-erred to a surface height variation either throughontact lithography or through a lithographictepper.1–3 Although gray-scale masks can sculptmooth analog profiles, various gray-scale processeso have a number of different limitations. Depend-ng on the exact process, one often must directly
atch the optical density to the photoresponse curve.his means that many gray-scale masks are highlypecific to a particular design and do not provide theexibility for modifications to the fabricated elementithout one obtaining a completely new mask.
The authors are with the School of Optics, Center for Researchnd Education in Optics and Lasers, University of Central Florida,.O. Box 162700, 4000 Central Florida Boulevard, Orlando, Flor-
da 32816-2700. The e-mail address for E. G. Johnson [email protected] 20 June 2003; revised manuscript received 31 October
alftone gray-scale masks are also typically limitedn the diversity of pattern scales because of a finiteumber of discrete gray levels.A number of other fabrication methods exist but
an suffer from severe tolerance losses because oflignment difficulties. The 2N binary mask tech-ique involves use of multiple masks, each requiringseparate sequence of photoresist coating, mask
ligning, patterning, and etching. This involves aong and difficult process made ever more difficult byhe complexities in precision alignment on subse-uent masks. Additional methods have been intro-uced to utilize wafer-scale replication based on aicromolding method with an elastomeric mold.hese techniques face potential alignment problemsetween different levels and the host wafer.4An innovative method, that has varying exposure
imes and masks to sculpt complex photoresist pro-les across the wafer substrate, has recently been
ntroduced. This method, termed additive lithogra-hy, avoids many of the drawbacks encountered withther fabrication methods.5 The additive method ofithography has allowed us to form various types ofiffractive optical elements and refractive microlensrrays without compromising tolerance. The pro-uction costs are also considerably lower than that ofther techniques used to achieve similar toleranceevels. This method is easily transferable to micro-ptics of differing wavelengths and configurations.nother advantage of this approach is the ability todjust the resist profile to compensate for the etchelectivity of various substrates.Perhaps the most intriguing aspect of additive li-
hography is the ability to use a set of independent
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atterns on a single reticle to fabricate numerouseam-shaping and beam-forming elements by meansf simply controlling the exposure dose. Decompos-ng a diffractive structure to a set of more basic andundamental patterns allows for the fabrication ofiffering structures by exposure control. For exam-le, a simple basis set composed of a set of rings �Fig.� can be used to construct both a positive refractivelement and a torroidal lens element by an appropri-te change of exposure dose passed through each sub-omain aperture, as shown in Fig. 2. This wouldgain be a one-step process because all the patternsan be successively exposed with different exposureimes defined by the optical function to be realizedollowed by a single developed step to form the pat-ern on the resist.
In this paper we present the fabrication of differing
ig. 1. Reticle used as a subdomain basis for various opticalurfaces. It contains a 7 � 9 array of rings with a width of 10 �mnd a successively decreasing diameter.
ig. 2. Basis set reconstruction of �a� positive lens and �b� torroi-al lens.
icro-optic components using a single set of binaryask patterns. A single basis set of patterns with
he exposure dose as a variable is used to createarying optical functions for beam forming and shap-ng. Different patterns on a reticle are exposed suc-essively to sculpt the resist into the desired opticalunction. This allows for myriad optical elements toe created with a single reticle. We discuss theange of patterns available to the given basis set andemonstrate the optical quality of the fabricatedtructures.
. Approach
ith the additive method of lithography we use anxposure time control while transferring each pat-ern of the multilevel diffractive structure. This isimilar to a 2N technique commonly used to form suchiffractive elements; the exposure times add up asuccessive patterns are transferred to the resist withifferent exposure doses. Contrary to the 2N tech-ique, there is no etching or developing of the sampleetween exposures. A substrate is typically placedn a wafer stepper and the machine is programmedith the desired exposure times for each lithographicask exposure as well as the exact locations and
izes of the patterns to be successively exposed. Thetepper automatically exposes the first pattern, shiftshe wafer and the aperture as needed, exposes theecond pattern, and repeats the process. Once allhe patterns have been exposed, developing the resistroduces the desired pattern on the resist. Reactiveon etching can then be used to transfer the pattern tohe substrate. Although the additive process can beerformed on any type of lithographic system, thetepper system provides accurate and easy control ofattern-to-pattern alignment and thus is the pre-erred tool for this process. Fabrication with the 2N
ype of process requires that the resist show a linearehavior between threshold and saturation becauseuccessive exposures add up to form the multilevelrofile.5 By using a orthogonal basis set of binaryatterns, i.e., individual patterns do not overlap eachther, for fabricating a specific class of beam-shapinglements, we can eliminate this need for linearity inhe resist while making the process more flexible.
To fabricate a set of refractive or diffractive ele-ents with a single set of independent binary pat-
erns, the first step is to realize a basis set of patternshat can be used to represent these diffractive ele-ents in two-dimensional �2-D� space. A refractive
ens can be represented in two dimensions by a col-ection of consecutive rings. The third dimensionan then be added to the structure by lithographicxposure control. This is true for both positive andegative lenses because both can be easily split in twoimensions to be represented by consecutive rings.ome or all of these rings can also be used to repre-ent other beam-shaping elements that can be easilyroken down to this basis set of rings. The sameings can be used to represent diffractive lenses asell as a variety of other beam-shaping elements.
he rings can be easily patterned on the substrate atspecific location with a stepper system.From this we can postulate the existence of a litho-
raphic pattern basis set. A large collection of ringsnd circles of varying sizes can theoretically be usedo fabricate a wide range of rotationally symmetriciffractive and both positive and negative refractivelements. Specifically, for a 5� stepper system, aingle mask with rings and circles of diameters rang-ng up to 1250 �m on the mask can be used to fabri-ate virtually any rotationally symmetric elementith a 250-�m diameter. Such an approach has al-
eady been taken to fabricate arrays of positive andegative lenses together on a single wafer.6
. Micro-Optical Element Design and Fabrication
sually diffractive lenses are designed by means ofarying the widths of each of level within a zone whileeeping the level heights equal. Another method toabricate such lenses would be to fix the widths ofhese rings and vary the heights. We can representlens profile in two dimensions with a set of consec-tive rings all having the same widths. Thus theumber of rings in each zone as well the level heightsf each of these rings will vary. Now all we need tonow is the optical function we wish to realize andnd the height corresponding to each of the rings thatill lead to the sculpted form on the resist to allow
abrication in the manner illustrated in Fig. 2. Weemonstrate this through the fabrication of a diffrac-ive positive and negative lens.
The first step is to fit the resist response curve so aso have a relationship between the developed resistepth and the exposure time. Unlike the 2N tech-ique in which linearity is an automatic requirementecause of the exposure addition, use of a basis set ofndependent patterns to form diffractives can be eas-ly handled with any response curve. The only re-uirements are that the response curve within theias and saturation region can be fitted and that aumerical relation can be determined between theeveloped resist depth and the exposure time. Thiss because each pattern is independent and the expo-ures do not add up. The idea is to add up thesendividual patterns with varying exposures so as toculpt the resist to represent the optical function.The focal length of a microlens is given as1
f �R
n � 1, (1)
here R is the radius of curvature of the lens and ns the refractive index of the material on which the
icrolens is to be fabricated. The height of the re-ractive microlens is given as
H � R � �R2 � �D�2�2�1�2, (2)
here D is the aperture size of the lens.The height H is generally quite high. The fabri-
ation of such lenses typically needs to be performedn thick resists, of the order of 10 �m or more. The
lternative to this is to fabricate a diffractive struc-ure, which can be as easily undertaken with a thinesist such as Shipley PR1813. A refractive micro-ens can be easily converted to a diffractive structureepresenting a mod 2� or its multiples for the specificavelength of operation. By fixing the step widths
o be w, which is the same as the width of each ring,e can easily calculate the level heights for the lens
o be fabricated, while the wavelength, index, andperture size will tell us the number of zones in theiffractive structure. Thus, if we use rings havingidths of 2 �m each, we will need 63 ring patterns to
orm a lens with an aperture size of 252 �m.The height H for a diffractive structure will then be
Hdif �m�
�n � 1�, (3)
here m gives the order where the refractive heights taken mod 2m�.
The rotationally symmetric optical function �r�an be written as
�r� � exp�ikd�r��n � 1��, (4)
here d�r� is the height of the resist at the position r,nd n is the refractive index of the medium. Theeight of the resist to be developed off at the positionis then given as
h�r� � H � d�r�, (5)
here H is the total height of the diffractive or re-ractive lenses to be fabricated. The problem now iso calculate the time required to sculpt this height�r�. �The fit relating the exposure time to the de-eloped resist across the linear region of the resist isiscussed elsewhere.5 The fit is given as � 0.299h,here is the exposure time in seconds to obtain
esist height h in micrometers after the resist haseen biased.�Thus the optical function �r� can be written in
erms of the exposure time as
p � exp�ik�n � 1��H � �3.344p A�� , (6)
here p is the exposure time corresponding to aeight hp�r� for the pth ring. The factor A is used todjust for etch selectivity. A � 1 would represent antch selectivity of 1:1.Thus if we use N rings to form a rotationally sym-etric micro-optic element, then the phase function
ealized can be written as
� � �p�1
N
p, (7)
here N � 63 in our case.The transmittance of the pth ring of outer diameter
p is
tp� x, y� � cyl�� x2 � y2�1�2
D � � cyl�� x2 � y2�1�2
D � D � , (8)
p p p�1
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s
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here p � 1, 2, 3 . . . 63 and Dp � 2wp � 20p for theiven basis set with a ring width w � 10 �m. For anmaging system, the image intensity distribution isiven as7
I� x, y� �
�s
as Is� x, y�
�s
as
, (9)
here as is the strength of the source and Is�x, y� ishe intensity in the image plane due to each sourceoint and is written as
Is� x, y� � �� ���
�
P��, ��T�� � �s, �
� �s�exp��i2���x � �y��d�d��2
. (10)
ere T�� � �s, � � �s� is the spectrum of the reticleransmittance t�x, y� and P��, �� represents the trans-ittance in the pupil plane.The cutoff spatial frequency of this imaging system
s then �1 � ��NA�� where � is the partial coherenceactor and NA is the numerical aperture. A com-letely coherent source distribution can be repre-ented as a single source with � � 0, whereas � � 1or a fully incoherent source.
The smallest linewidth that can be resolved on theubstrate with such a system is then ���1 � ��NA.In the case of our 5� GCA stepper the NA equals
.38, � � 0.6, and � � 436 nm. This gives the valuef the minimum-resolvable feature on the substrateo be 717 nm. Thus it is possible to represent theicro-optic function to be fabricated with a muchner basis set of rings with widths of approximately�m on the reticle, as opposed to the coarser basis set
onsisting of 10-�m-wide rings that we are currentlysing. This would result in 800-nm features on theubstrate, as opposed to the 2 �m that our currentasis set produces.However, although a finer basis set can provide a
etter representation of the optical function, there istrade-off in terms of fabrication time. In our case
he rings forming the basis set had a width of 10 �mn the reticle; thus, to fabricate micro-optic elementsith a 252-�m diameter on the substrate, 64 expo-
ures had to be performed and the fabrication timeor each element was approximately 36 s. It is pos-ible to increase the throughput if we expose multipleings simultaneously. For example, if we fabricate aeticle that allows us to expose a 10 � 10 array ofings of the same size simultaneously, we can in-rease the throughput by 2 orders of magnitude.his would result in a fabrication time of approxi-ately 0.36 s for each element.Now the problem is to choose the optical function to
e fabricated, set it on the grid used for the basisunction, determine the heights hp�r�, and calculate thexposure time by use of the previous numerical fitbtained from the response curve of the photoresist.
nce the exposure time for each of the ring patterns isnown, fabrication can begin. An aperture is openedn the stepper over the reticle area containing thepecific ring, which is then exposed with a specifiedose calculated earlier. The overlay of each ring withespect to the earlier exposed ring pattern is easilyontrolled by use of the pass shift features on a stepper.ll 63 patterns as well as the bias pattern were placedn a single reticle. To change the specifications of theens to be fabricated, it is a matter of our simply eval-ating the exposure times for each ring in the set. Bylteration of the exposure doses, it is possible to shapeositive and negative lenses of differing f-numbers,ocal lengths, and other design specifications. All thisan be done by use of a single reticle in a single-steprocess with high fabrication tolerance and low cost.
. Experimental Results
e fabricated the diffractive lenses using a set of ringatterns fabricated on a single reticle as shown inig. 1. The pattern set contains rings of constant0-�m widths with the inner radius incrementallyecreasing by 10 �m. There are 63 rings on theeticle so that the outer diameter of the largest ring is260 �m and the smallest structure is a circle with aiameter of 20 �m. On a 5� stepper the aperture ofhe largest lens that can be fabricated with this ret-cle is 252 �m. We fabricated mod 2� and mod 4�iffractive lenses for operation at 632.8 nm. As de-cribed above, a set of rings of this form constitutes aasis set for rotationally symmetric patterns. Onhe basis of this, we used the same reticle to fabricatehe torroidal lenses shown in Fig. 3. To further dem-nstrate the flexibility of this fabrication approach welso formed lenses for operation at 1550 nm.Figure 4 shows a lens that was designed for a focal
ength of 2 mm to operate at a wavelength of 632.8m, which sets the resist depth at 0.988 �m for a mod
ig. 3. Mod 4� torroidal lens for a 632.8-nm �a� 3-D profile �b� 2-Drofile.
� structure and 1.976 �m for a mod 4� structure.sing the numerical fit from the resist response data,e calculated the exposure doses for the desired lens
unction. We biased the resist with an exposure of.37 s using a 252-�m circular aperture on the reticle.he rings were then exposed individually with thealculated exposure time. The stepper aperture set-ing was used to individually expose the rings, andhe wafer pass shift was used to align the successivexposures to the previous exposures.The 2-D and three-dimensional �3-D� profiles for a
ositive and a negative lens designed for operation at550 nm are shown in Fig. 5. We fabricated theseenses for a focal length of 2 mm again using the sameing basis set reticle. The maximum height mea-ured for both the positive and the negative lens was.45 �m. Once exposed and developed, all these
ig. 4. Positive diffractive lens for 632 nm with a focal length ofmm. Mod 2� �a� 3-D profile, �b� 2-D profile; mod 4� �c� 3-D
enses can then easily be etched into the substrate byreactive ion etcher with 1:1 etch selectivity between
he substrate and the resist �a slightly different se-ectivity can be used with these lenses to compensateor exposure depth error and ensure that the lensorks at the desired wavelength�.After fabricating the lenses, we placed them on an
ptical bench using light coming out of an optical fibers the incident beam. The substrates were placedith the lens side away from the fiber. The sub-
trates were 1 mm thick and the fiber was 5 mmway. The torroidal lens gives the expected ring-haped output beam at the best focus, as demon-trated in Fig. 6. The diffractive lenses had a sharpocus at 3 mm from the lens, as demonstrated in Fig.. Figure 8 shows the spot size in micrometers plot-
ig. 5. Mod 2� lens with for 1550 nm with a focal length of 2 mm.ositive lens �a� 3-D profile, �b� 2-D profile; negative lens �c� 3-Drofile, �d� 2-D profile.
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ed as a function of position for the mod 2� as com-ared with the ideal theoretical lens. The spot sizet the focal point was 14.5 �m for the mod 2� lens and7 �m for the mod 4� lens. The diffraction efficiencyas observed to be 88% for the mod 2� lens and 87%
or the mod 4� lens. Note that none of the opticallements had antireflection coatings, which suggestshat one could obtain significantly higher diffractionfficiency than the measured values.Standing waves8 can cause variations of the resist
epth and add to a roughness and profile variation ofhe fabricated structure. If the exposure time dif-erence between the successive exposures with theings is very small, the effect can be more pro-ounced. In this case the diffractive element can beculpted by the above method but by means of in-reasing the exposure dose over the entire set of pat-erns by a small factor and adjusting the etchelectivity between the substrate and the photoresistppropriately to obtain the desired optical componentn the substrate. Thus we can compensate the ex-osure dose for etch selectivity and vice versa while
Fig. 6. Intensity pattern produced by a torroidal lens.
Fig. 7. Normalized intensity distribut
sing additive lithography. It is possible to use theame set of patterns and simply adjust the exposureose of each pattern calculated from the numerical fitEq. �2�� to fabricate beam-shaping diffractives or re-ractives to cater to different specifications.
To demonstrate the full range of flexibility of thisrocess, we also fabricated refractive microlenses onR1813 resist using the same reticle. Figure 9hows the microscope image at 50� of an array oficrolenses. Each individual lens is 40 �m in diam-
ter and is fabricated with ten rings successively pat-erned. The array is a close-packed structure withlternating rows of positive and negative lenses.he 3-D profile of the lenses measured with a Zygo
nterferometer can be seen to the right. The align-ent of the lenses in the array is automatically taken
are of by the wafer stepper system once the positionf each of the rings is fed into the process control andhe pass shift made available. This demonstrateshe ease with which additive lithography can realize
t the focal point of the diffractive lens.
ig. 8. Comparison of theoretical and fabricated spot size �inicrometers� as a function of distance from the diffractive lens.
icro-optic functions with very small features andaintain a high alignment tolerance. It also dem-
nstrates the feasibility of combining various well-hosen patterns to obtain highly complex opticalunctions through simple exposure control.
. Conclusion
lthough new and innovative micro-optical systemsre constantly in demand, continuous advances andevelopments in the processes used to fabricate themre an unchanging requirement. Previous fabrica-ion techniques have been effective for a number ofifferent applications but tend to have limitationsnd drawbacks in other areas. The additive methodf lithography provides an innovative advance on therevious methods and not only simplifies a previouslyedious and expensive process, but also supplies nu-erous additional degrees of freedom and flexibility
o the fabrication process.The additive process thus improves on other pro-
esses because the amount of time spent in pattern-ng and etching each pattern individually is reduced.t also alleviates the need for more complex maskshile providing much better alignment tolerances.umerous micro-optics can be fabricated for varyingavelengths and applications with a simple set ofatterns on a single reticle or multiple reticles. Andded advantage to the additive method of lithogra-hy is the compensation for etch selectivity of varyingubstrates through a variation of the resist profile.An optical surface basis set for a variety of rota-
ionally symmetric patterns has been designed and
ig. 9. Microlens array with alternating rows of positive andegative lenses in a hexagonal arrangement. �a� Microscope im-ge and �b� 3-D profile showing both the negative and the positiveenses.
ith the additive lithographic method, this basis setas allowed us to obtain positive and negative refrac-ive and diffractive lenses designed for multiple focalengths and operating wavelengths. It has also beensed to form torroidal-shaped lenses.The process allows unprecedented flexibility, withinimal processing time and expense. Tolerance isot sacrificed, and variations to patterns for differentperating wavelengths can be obtained with negligi-le additional development time for small variationso the resulting element. Varying types of patternuch as positive and negative refractive elements canasily be incorporated together on a single wafer byse of a single lithographic reticle. Arbitrary pat-erns such as a combination refractive–diffractiveens, or a lens with a diffractive grating incorporatedn top of it, can be easily combined to form the samelement under this method. Although in a produc-ion environment a specific reticle may be desirous forapid fabrication of large microlens arrays, the addi-ive method provides a superb alternative for devel-pment and prototyping.Thus subdomain masking gives additive lithogra-
hy a wide range of flexibility unavailable to otherabrication processes. It allows one to perform pro-otyping and testing of a vast set of possible designsithout the cost of new photolithographic reticles.abrication time is of the order of other lithographicrocesses for most cases and is substantially better inany others. This means that subdomain masking,
n conjunction with additive lithography, can providehighly cost-effective method for micro-optical fabri-
ation.
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Stauffer, M. Rossi, and E. B. Kley, “Micro-optical elements witharbitrary surfaces,” in Diffractive Optics and Micro-Optics, OSATechnical Digest �Optical Society of America, Washington, D.C.,2000�, pp. 234–236.
. A. G. Poleshchuk, “Techniques for formation of the surface pro-file of diffractive optical elements,” in Optics and Lasers inEngineering �Elsevier Science, Amsterdam, The Netherlands,1998�, Vol. 29, pp. 289–306.
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. M. Pitchumani, H. Hockel, W. Mohammed, and E. G. Johnson,“Additive lithography for fabrication of diffractive optics,” Appl.Opt. 41, 6176–6181 �2002�.
. M. Pitchumani, H. Hockel, J. Brown, W. Mohammed, and E.Johnson, “Additive lithography for refractive micro-optics,” inMicromachining Technology for Micro-Optics and Nano-Optics,E. G. Johnson, ed., Proc. SPIE 4984, 1–9 �2003�.
. A. K.-K. Wong, ed., Resolution Enhancement Techniques in Op-tical Lithography, Vol. TT47 of the SPIE Tutorial Texts �SPIE,Bellingham, 2001).
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