Surface-relief diffractive optical elements ~DOE’s!have found numerous applications in optical sys-tems.1 These computer-designed micro-optical com-ponents, which manipulate light through theirunique diffraction characteristics, can improve theperformance of optical systems and increase systemcompactness. DOE’s are usually realized ascontinuous-relief microstructures, e.g., by direct-write electron-beam lithography or direct laser writ-ing, or as binary or multilevel reliefs, mostly bysemiconductor fabrication technology. In general,the optical performance ~particularly the efficiency! ofcontinuous reliefs is superior to that of their binarycounterparts.2 One important feature of DOE’s istheir ability to be replicated by techniques such asembossing, casting, or molding.3–10 Although themanufacturing cost of one original DOE is usuallyrelatively high, the unit cost for large quantities ofone specific DOE can be dramatically reduced, pro-vided good replication can be made. A method withhigh potential for mass production of DOE’s is injec-
F. Nikolajeff, S. Jacobsson, and S. Hard are with the Departmentof Microwave Technology, Chalmers University of Technology,S-412 96 Goteborg, Sweden. Å. Billman, L. Lundbladh, and C.Lindell are with Toolex Alpha, Box 1176, S-172 24 Sundbyberg,Sweden.
Received 20 February 1996; revised manuscript received 23 Sep-tember 1996.
tion molding.11–14 In this paper, we describe the pro-cess of replicating continuous-relief DOE’s byconventional compact disc ~CD! injection-moldingtechniques, report on replicated DOE’s, and discussthe fidelity of the process.
2. Design and Original Fabrication
Two typical continuous-relief DOE’s, a linear blazedgrating and a fan-out element, were chosen as teststructures. The blazed grating had a period of 20mm. A 3 3 3 fan-out element, with a periodicity of;18 mm, was iteratively calculated with a modifiedGerchberg–Saxton phase-retrieval algorithm with-out phase quantization. To fabricate original ele-ments, we used the direct-write electron-beamlithography system ~JEOL, Model JBX-5DII! atChalmers University. A circular ~98-mm-diameter!quartz substrate with a 10-nm top layer of chromewas first spin coated with a positive e-beam resist,NANO PMGI ~Microlithography Chemical Corp.!, toa resist thickness of 2.8 mm. The layout of theDOE’s on the substrate had to be made with consid-eration of the chosen molding process, which left anannulus between the 18- and 40-mm radii availablefor DOE exposure ~see also Section 5!. Two identicalgratings and two identical fan-out elements werethen exposed, one in each quadrant, on the circularsubstrate. Each DOE occupied an area of 2.6 mm 32.6 mm. In the e-beam exposure we used an accel-eration voltage of 50 kV with a beam current of 5.0nA. The number of exposure doses was 64, andthese compensated for the proximity effect. Finally,the exposed substrate was successively developed in
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a PMGI 101 ~Microlithography! developer. A totaldevelopment time of 10 min resulted in relief depthsof ;1 mm.
3. Replication
To sustain the high pressure and temperature in themold process, a copy of the original microstructure inthe form of a metal stamper has to be made. Thefirst step in this process is to form a conductive coat-ing on the resist surface. In conventional CD man-ufacture, Ag is sputtered on the photoresist, but Aghas shown to be insufficiently adhesive to e-beamresists. We therefore sputtered a 100-nm Au layerwithout any nonadhesion problems. A first-generation Ni master can then be produced by elec-troplating in a Ni sulfamate bath. The plating wasdone with a commercial optical disc-plating system~Toolex Alpha P 250!. A Ni thickness of 300 mm wasobtained after a 3-h plating, during which the platingcurrent was ramped from 0.5 to 15 A. We then eas-ily separated the Ni copy from the original resistmicrostructure by merely knocking on the backside ofthe quartz substrate. In the separation procedurethe resist microstructure is destroyed and some of theresist may stick to the Ni master. We thus usedplasma etching in O2 of the Ni master to remove anyremaining resist. To make the backside of the Nimaster very flat ~if there are small bumps on the Nimaster it will be destroyed by the high pressure in themold!, we used the standard technique of lapping~with a Toolex Alpha PML-300 lapping machine!.The Ni stamper was finally inserted into a ToolexAlpha MD 100 injection-molding machine. This is acommercial machine that is built with high precisionfor mass production of optical discs of various for-mats. By use of the process data shown in Table 1,several thousand DOE replicas were molded as 80-mm-diameter CD’s in poly~carbonate! ~Makrolon CD2005yMAS 130!. The cycle time for production ofoptical discs is typically only 3 s. We used a longertime ~;10 seconds! to minimize shrinkage of the rep-licated DOE’s.
4. Results
Original and replicated DOE’s were characterized byoptical measurements and an atomic force micro-scope ~AFM!.
A. Blazed Gratings
In Fig. 1, AFM images of both original and replicatedgratings are shown. The faint lines across the grat-ings are due to field stitching in the original e-beam
Table 1. Mold Data for a Toolex Alpha MD 100 Injection MoldingMachine to Replicate Continuous-Relief DOE’s in the Form of CD’s
MaterialPressure
~MPa!
InjectionTemperature
~°C!
ToolTemperature
~°C!
CycleTime
~s!
Poly~carbonate!~Tg 5 144 °C!
6 360 120 '10
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manufacture. Figure 2 shows profilometer traces ofthe gratings. To measure at equivalent positions ofthe original and the replica, we first located the samecorner of the square grating area and then used anoffset of 500 mm in both the x and the y directions.We estimated the positioning error to be ;20 mm.Figures 1 and 2 indicate that the shape of the gratingis well preserved in the replication process. How-ever, because the AFM traces measure at only spe-cific lines and we know that the relief depth of theoriginal grating may differ by approximately 63%over the grating area ~mostly because of an unevenresist layer and drift in the electron current duringthe e-beam exposure!, we refrain from drawing anyquantitative conclusions from the AFM scans. Tocompare the gratings quantitatively, we chose tomeasure the grating deflection angles. Such a mea-surement both serves as an integrated measure overthe whole illuminated grating area and partly showsthe optical performance of the grating. This mea-surement was done after the replicas had been pro-duced, and because the original had been destroyedin the electroforming process, as described above, we
Fig. 1. AFM image of ~a! the original linear blazed grating fab-ricated by e-beam lithography ~grating period 20 mm!, ~b! the grat-ing replicated by injection molding.
used the Ni master and a CD replica with a sput-tered layer of Al to measure reflected orders. Thefidelity of the electroforming process is high andmajor dimensional changes in the replication chainare most likely to occur during the molding step,4 sowe assume no change in the grating period betweenthe original and the Ni master. The gratings wereilluminated perpendicularly with a He–Ne laserbeam ~l 5 633 nm!. At a distance of 188 cm fromthe grating, the 25 order was centered on a CCDcamera, and we measured the position of the 15order by scanning a 300-mm-wide slit in front of aphotodiode. We found the deflection angle of thereplicated grating to be 0.15° 6 0.01° larger thanthat of the original. This increase in the anglecorresponds to a decrease in the grating period of1.6%, which is reasonable, considering that Makro-lon has a linear thermal expansion coefficient of0.7 3 1024 K21 between 23 and 80 °C. We alsomeasured the transmitted diffraction efficiency ~de-fined here as the measured intensity in one orderdivided by the sum of the intensities in all measur-able orders! in the first order, again using a He–Nelaser ~l 5 633 nm!. The efficiency measurementwas first done with the original before it was repli-cated, and then with one of the replicas. A differ-ence in diffraction efficiency between the originaland the replicated gratings is to be expected fromthe difference in the index of refraction of thee-beam resist ~n 5 1.54! and poly~carbonate! ~n 5
Fig. 2. AFM profilometer trace of ~a! the original grating shown inFig. 1~a! and ~b! the replicated grating shown in Fig. 1 ~b!.
1.58!. The 11 efficiency was 90% for the originaland 94% for the replica. Assuming a perfectlyblazed structure ~Fig. 2 shows that the deviationfrom a triangular shape is very small!, we use sca-lar diffraction theory to calculate the diffraction ef-ficiency of a grating for different relief depths.15 Atypical grating depth of the original that was mea-sured with the AFM was 960 nm, which would givea diffraction efficiency of 89.7%. It is reasonable tobelieve that the shrinkage of poly~carbonate! isequally large in all dimensions. Assuming the re-lief depth of the replicated grating to be 1.6% lowerthan that of the original, we predict a diffractionefficiency of 94.2% for the replica. These two cal-culated values both agree well with our measure-ments.
B. Fan-Out Elements
The fan-out element was designed to give an array of3 3 3 equally intense spots. A commonly chosenquality measure to characterize a fan-out element isthe uniformity error, which is defined as
U 5Pmax 2 Pmin
Pmax 1 Pmin,
where Pmax and Pmin represent the powers of thebrightest and the faintest spots, respectively. Theuniformity error is sensitive to any kind of fabrica-tion error and is therefore also a good measure ofthe replication fidelity. In Fig. 3 we show thecomputer-simulated uniformity error as a functionof phase scale factor, in which a phase scale factorof 1 corresponds to a phase of 2p for the designedfan-out element. The measured uniformity errorof the original was U 5 34% ~l 5 633 nm!. UsingFig. 3, we find the corresponding simulated phasescale factor. We then predict the uniformity errorof a replicated fan-out element by compensating forthe difference in the index of refraction and assum-ing a 1.6% shrinkage in one dimension. In doingso, from Fig. 3 we predict a uniformity error of theCD replica of U 5 19%. The measured value was17%. The good agreement between theoretical and
Fig. 3. Computed uniformity error as a function of the phase scalefactor for the designed 3 3 3 fan-out element. A phase scale factorof 1 corresponds to a phase of 2p.
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measured values once again suggests that theshape of the diffractive microstructure is well pre-served. Note that, in designing the original fan-out element, we model the proximity effect by threeparameters,16 and if the actual value of any of thesethree parameters is different from what we assume,the uniformity errors will not be exactly as predict-ed.17 It can also be noted that we could probablyhave reached a lower uniformity error of the replicaif we had developed the original element for alonger time ~which would result in deeper reliefdepth!.
Taking another replica, produced some hundredreplicas later, we found the uniformity error to beU 5 16%. The similar uniformity errors for the two
Fig. 4. Ni master that has been used for the injection molding ofDOE’s, which are seen as small square areas. The original DOE’swere exposed on a circular 98-mm-diameter substrate by e-beamlithography. The wetlike look of the Ni master is caused by itsprotective laquer ~which is removed before the Ni master is used!.
Fig. 5. Injection-molded CD ~80 mm in diameter! with differentkinoforms, each giving a far-field diffraction pattern in the form ofa logotype.
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replicas indicate that the replication fidelity is stableover a large number of molded discs.
5. Discussion and Conclusions
This study focused on the replication practicality andfidelity of conventional injection molding ofcontinuous-relief e-beam-written DOE’s.
First we make some comments about the manufac-ture of the original: The DOE areas we exposedwere 2.6 mm in diameter, and the DOE’s had peri-odicities of 20 mm or less and a relief height of ;1 mm.The periodicity must not be understood as the mini-mum feature size of a continuous-relief DOE. Togive an indication of what resolution is needed infabricating blazed gratings, we computer simulatedthe generation of a blazed grating by adding sinewaves of successively higher spatial frequencies, vi-sually comparing the result with Fig. 2. To obtainvisual similarity, we found that the computed gratingat least needed a highest spatial frequency of period2 mm. To fabricate a sine wave with a 2-mm period,the effective electron-beam diameter has to be nowider than approximately half that value, i.e., 1 mm.
The proximity effect, i.e. a scattering of the expos-ing electrons within the resist layer that broadens theeffective beam diameter, makes it difficult to manu-facture deep blazed microstructures with very shortperiods, although the e-beam manufacture of blazeddiffractive structures with submicrometer periodicityin thin resist films has been demonstrated.16,18
The particular e-beam lithography system we usecan accept a wafer size up to 5 in. ~12.7 cm! indiameter. With this limitation, the conventionalinjection-molding equipment we used allows a max-imum diameter of 22 mm of the replicated DOE’s.Larger-area DOE’s would require another methodfor manufacturing the original or a modification ofthe mold equipment ~e.g., let the center hole of thereplicated disc become smaller!.
Next we make some comments about the limita-tions of injection molding: Deep micro-optical com-ponents have been replicated by injection moldingwith good results, although they were refractive, notdiffractive.19 The relief depth of injection-moldedDOE’s can probably extend to several hundredmicrometers without severe degradation in opticalperformance. Rather, it is the aspect ratio, thewidth-to-depth ratio, that will limit the fidelity ofinjection-molded DOE’s.4 This is especially true formicrostructures with sharp edges, such as 2p phase-modulated DOE’s usually have. With very demand-ing aspect ratios ~say a width-to-depth ratio of 1:10!,embossing in an UV-curable laquer might give a bet-ter result.3 Shallow continuous-relief gratings witha period length of only a few micrometers have beeninjection molded with good results,14 and injectionmolding is probably capable of nanometer precisionfor shallow structures.
Strain and birefringence might limit the opticalperformance of large-area molded DOE’s. Themanufacturer of the injection-molding equipmentused in this study states that the birefringence is less
than 20 nm for a 1.2-mm-thick optical disc over itsfull area ~diameter 57 mm!. When hot embossing orUV embossing is used to replicate DOE’s in a polymerfilm on a glass or quartz substrate ~possibly followedby an etch step to transfer the replicated structureonto the underlying substrate!, replicas with lowerstrain and higher thermal and mechanical stabilitythan injection-molded DOE’s have can be achieved.20
Our results show that conventional injection-molding equipment can replicate blazed continuous-relief diffractive structures with a periodicity of 20mm, a depth of 1 mm, a well-preserved shape, and1.6% one-dimensional shrinkage. The stability inreplication fidelity was kept over many hundred rep-licated elements.
For demonstration purposes we have also fabri-cated a CD with several different kinoforms, eachgiving a diffraction pattern in the form of a logotype.The Ni master used for these kinoforms is shown inFig. 4, and one of the replicated CD’s is shown in Fig.5.
We acknowledge Ove Ohman, Pharmacia Biotech,for Au sputtering of the original DOE, Olle Larsson,Industrial Microelectronics Center, for plasma etch-ing, Anna-Karin Holmer, Chalmers University ofTechnology, for help with the optical measurements,Laurent Krummenacher, Institute of Optical Re-search, for the AFM images, and finally Jan-Olof Yx-ell, Chalmers University of Technology, for taking thephotographs. This work was supported by grantsfrom the Swedish Board for Technical Development.
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