The development and characterization of polymer microinjection molded gratings.
A diffraction grating (DG) is a passive optical component that diffracts polychromatic polychromatic /poly·chro·mat·ic/ (-krom-at´ik) many-colored.
pol·y·chro·mat·ic or pol·y·chro·mic or pol·y·chro·mous
Having or exhibiting many colors. light into its component wavelengths or monochromatic light into surfaces of constant phase, Fig. 1a. There are several types of diffraction gratings with different profile geometries that determine their properties. In most cases, after obtaining a master by various techniques, the gratings are manufactured by UV curing of epoxy compositions. A typical grating consists of a thick piece of float glass, having a layer of patterned UV curable cur·a·ble
Capable of being cured or healed. epoxy overlaid with a reflective coating or a refractive refractive
capacity to refract light.
a difference between the focal length of the cornea and lens, and the length of the eye, resulting in myopia or hyperopia. index-matched epoxy, in the case of transmission type gratings. As the manufacturing sequence is tedious and makes use of expensive equipment, and the final components contain a number of different materials, there have been attempts to eliminate some of the manufacturing expenses. Different techniques and materials have been investigated. Poly(methyl methacrylate) (PMMA PMMA polymethyl methacrylate. ), poly(carbonate) (PC), styrene-butadiene block copolymer copolymer: see polymer. (SBS See Small Business Server. ), cyclic olefin copolymer Cyclic Olefin Copolymer (COC) is an amorphous polymer made by several polymer manufacturers. COC is a relatively new class of polymers when compared to polypropylene and polyethylene. (COC See chip on chip. ) and other polymers have been processed by injection molding or hot embossing to fabricate such gratings (1-4).
[FIGURE 1 OMITTED]
Among all polymers suitable for optical applications COCs are preferred since they are amorphous polymers made by a catalytic reaction of ethylene and randomly distributed 3-norbornene. The latter bulky group prevents forming of crystalline sites in the bulk volume and stiffens and strengthens the polymer chain. COC has high heat resistance, is a good moisture barrier, is resistant to polar solvents, has low dissipation and dielectric loss, is highly transparent in the visible and near UV regions, and has low optical birefringence Birefringence
The splitting which a wavefront experiences when a wave disturbance is propagated in an anisotropic material; also called double refraction. In anisotropic substances the velocity of a wave is a function of displacement direction. . These properties imply that COCs are excellent candidates for optical, electronic and pharmaceutical applications (5).
In this work, COC was melt processed by injection micromolding to produce diffractive dif·fract
intr. & tr.v. dif·fract·ed, dif·fract·ing, dif·fracts
To undergo or cause to undergo diffraction.
[Back-formation from diffraction. optical components in one-step, i.e., a patterned polymer-based component, which was subsequently metallized with a reflective coating by means of thermal evaporation. Diffracted power and atomic force microscopy (AFM (Atomic Force Microscope) A device used to image materials at the atomic level. AFMs are used to solve processing and materials problems in electronics, telecom, biology and other high-tech industries. ) measurements were taken to compare the mold, an optical grating element itself, with he molded replicas. Comparison of the mold and replicas topography characteristics, collected by the AFM, was carried out through a one-way analysis of variance (ANOVA anova
see analysis of variance.
ANOVA Analysis of variance, see there ) test. Two-dimensional linear filtering of the spatial domain was used to analyze the grain sizes of the reflective aluminum coatings. Photoelasticity and boiling water tests were implemented as well.
The tooling or mold used for this study was a commercially available 12.7 x 12.7 mm ruled diffraction grating with 1200 grooves/mm and a blaze angle [alpha] = 17 [degrees]27'. As purchased the grating was coated with aluminum (Al) and had a service temperature range between -20 to + 100[degrees]C, Fig. 1b. The commercial grating was obtained from Edmund Optics Inc. It consisted of a block of float glass coated with a layer of microfeatured epoxy EPON See PON. 815 and a second layer of reflective Al. The cyclic olefin copolymer (COC) used during the study was Topas [R] 5013 supplied by Ticona. The study also involved the use of two-component Epoxy T-515 obtained from ZYMET Inc., USA, as well as the use of aluminum pellets, CAS 7429-90-5, 99.999% purity obtained from Kurt J. Lesker company, and 2-propanol (IPA IPA - International Phonetic Alphabet ), CAS 67-63-0, obtained from J.T. Baker company.
The replication process or micromolding was performed by building a customized electrically-heated mold-base and mounting it on a 12 ton BOY (BOY 12A) digitally controlled micromolding machine. The mold was inserted in the mold base and the edges were sealed with the epoxy composition. Two different sets of processing conditions, i.e., "A" and "B," were chosen based on the polymer manufacturer's recommendations and previous experience with molding of COC, as seen in Table 1. A total of 30 and 40 replications were performed with A and B sets of conditions, respectively. It was noticed that subsequent moldings resulted in the structural failure of the mold's topography formed by the epoxy. This was attributed to the fact that in B set of processing conditions [T.sub.mold] was chosen to be above the maximum value of the mold's service temperature.
TABLE 1. Injection molding conditions and their influence on the resolving bare diffraction grating groove height. Setup Height (nm) Parameters A B A B [T.sub.noz] ([degrees]C) 249 291 min ~40 180 [P.sub.hold]/time (MPa/s) 7.5/3 7.5/10 max ~100 n (1/min) 200 200 [V.sub.inj] (mm/s) 100 100 [T.sub.mold] ([degrees]C) 85 116 [T.sub.sep] ([degrees]C) 70 70 Sprue Temp. ([degrees]C) 22 140
Metallization. Metallization of the bare, untreated diffraction gratings, rinsed in IPA and dried with nitrogen gas in advance, was performed by means of a physical vapor deposition This article or section is in need of attention from an expert on the subject.
Please help recruit one or [ improve this article] yourself. See the talk page for details. (PVD PVD
peripheral vascular disease
PVD Peripheral vascular disease, see there ) technique (6), i.e., e-beam induced thermal evaporation at an operating chamber pressure P ~ 1.3 x [10.sup.-7] mbar with a deposition rate of 1.0-1.4 nm/s, performed on TT6 Telemark Telemark (tĕ`ləmärk), county (1995 pop. 163,143), 5,915 sq mi (15,320 sq km), SE Norway, bordering on the Skagerrak in the east. Skien (the capital), Porsgrunn, Kragerø, and Notodden are the chief towns. evaporator by Indel Systems. The magnetized deflection of the e-beam was set so that the e-beam followed a spiral trajectory while impinging on the Al in the crucible, thus enabling uniform temperature of the melt. Metallized gratings with two different coating thicknesses were produced. i.e., 150 and 250 nm.
Molded Product Characterization
Scanning Electron Microscopy. Scanning electron microscopy (SEM) was carried out on a SEM-LEO 1550 VP equipped with a Gemini column. Prior to molding, the original commercial diffraction grating or mold tool surface was imaged while running in a variable pressure mode with a nitrogen rich environment as seen in Fig. 1b. Following the replication process, several bare polymer replicas were also inspected in the same way. To image the metallized polymer replicas, however, a standard mode of operation of the SEM was chosen as a conductive adhesive copper tape was attached at the very, non-patterned but metallized, edge of the gratings. Images with good contrast were obtained allowing for an evaluation of the achieved grain structure of the Al coating (Fig. 2). Such an approach was not possible during imaging of the molds as the copper tape could have peeled off the patterned surface during its removal after the inspection. Following imaging, all samples were scanned with an atomic force microscope atomic force microscope (AFM), device that uses a spring-mounted probe to image individual atoms on the surface of a material. Unlike the scanning tunneling microscope, which is also a scanning probe microscope, the AFM can be used on materials that do not conduct (AFM).
[FIGURE 2 OMITTED]
Scanning Prode Microscopy. Scanning probe microscopy (SPM SPM - Sequential Parlog Machine ) was performed in air with Digital Instruments Dimension 3000 AFM in TappingMode[TM]. It was used to collect quantitative data about the surface topographies of the mold and both the bare and metallized polymer replicas. The probe used was an Antimony antimony (ăn`tĭmō'nē) [Lat. antimoneum], semimetallic chemical element; symbol Sb [Lat. stibium,=a mark]; at. no. 51; at. wt. 121.75; m.p. 630.74°C;; b.p. 1,750°C;; sp. gr. (metallic form) 6. (n) doped Tapping Mode Etched Silicon Probe, Aluminum coated (TESPA), for enhanced laser detection signal with nominal spring constant k = 42 N/m, nominal resonant frequency f = 320 kHz, tip radius of curvature ROC < 10 nm (max ROC = 15 nm), and tip height h = 10 - 15 [micro]m. Prior to section analysis, the data was modified to eliminate unwanted features from the scan lines by using a polynomial polynomial, mathematical expression which is a finite sum, each term being a constant times a product of one or more variables raised to powers. With only one variable the general form of a polynomial is a0xn+a filter. It removed the Z-offset between scan lines, and the tilt and the bow in each scan line, by calculating a third order, least-squares fir for the selected segment and subtracting it from the scan line. The samples were oriented in such a way that they were scanned across the grooves in the fast X-direction. To ensure proper scanning of the sample topography, the feedback parameters setpoint amplitude (SA), integral gain (IG), proportional gain (PG), and scan rate (SR) were set so that the trace and retrace scans looked identical. They were regularly monitored throughout the scanning process. The mold, a bare grating, and two metallized gratings were scanned at 10 different 5 X 5 [micro]m locations each. As criteria for judging the quality of replication of the surface topography of the samples, the following parameters obtained by the section analysis were considered--the root-mean-square deviation of the z-values (RMS); the mean roughness of the roughness curve relative to the center line ([R.sub.a]); the maximum height ([R.sub.max]) defined as the difference between the highest and lowest points on the cross-sectional profile; the 10-point mean roughness ([R.sub.z]) defined as the difference between the five highest peaks and the five lowest valleys; the pitch (horizontal) distance and the peak-to-valley (vertical) distance. The quantitative data was statistically analyzed via oneway analysis of variance (ANOVA), a robust procedure that determines if groups (mold and replicas) are similar or not in the measured characteristics.
Diffracted Power Measurements. An industry standard approach for measuring the efficiency of a grating is by calculating the absolute efficiency in a Littrow configuration in which the incident and diffracted rays are in auto collimation collimation /col·li·ma·tion/ (kol?i-ma´shun)
1. in microscopy, the process of making light rays parallel; the adjustment or aligning of optical axes.
2. . In any other off Littrow configuration, the efficiency of a grating element decreases (17). The grating that was utilized as a mold in this study had two major maxima at around 500 nm and 1600 nm according to the manufacturer's specification. A different and less difficult to implement testing approach was used in our experimental setup as seen in Fig. 3. An infrared (IR) tunable laser (Agilent 8164A) was used to generate monochromatic IR light n the range between 1460 and 1580 nm. A single mode fiber was used as a waveguide waveguide, device that controls the propagation of an electromagnetic wave so that the wave is forced to follow a path defined by the physical structure of the guide. to a monochromator unit in which the gratings were mounted. At the exit slit of the monochromator, an IR power photodetector A device that senses light. It uses the principle of photoconductivity, which is exhibited in certain materials that change their electrical conductivity when exposed to light. See photoelectric, photocell and photodiode. (InGaAs detector) detected the diffracted light from a grating under test. It was connected to a power meter (Newport, Model 2832C) and calibrated for the used wavelength, which measured the diffracted power. As it was difficult to attach every single grating at the same exact location on the mount fixture, only normalized diffracted power values were reported as seen in Fig. 4. This approach allowed for the comparison between the output diffracted power curves of the commercial grating and molded polymer replicas since any deviation of the grooves shape would change the shape of the curve. The whole surface of the grating was illuminated with a monochromatic light with six different wavelengths, thus forming diffracted surfaces of constant phase (wave-fronts). Ten molded polymer gratings were optically characterized along with the commercial grating.
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
Grain Size Quantification Analysis. Grain size quantification analysis was determined by two-dimensional linear filtering of the spatial domain. It was implemented to quantify the grain sizes of the metal reflective coatings on the original grating, i.e., the mold, and on the molded and metallized gratings with 150 and 250 nm Al films. The procedure was performed via WSxM[R] and Matlab. First, matrix convolution convolution /con·vo·lu·tion/ (-loo´shun) a tortuous irregularity or elevation caused by the infolding of a structure upon itself. of the original SPM images was implemented. The procedure is a neighborhood operation in which each output pixel of the resulted convoluted image matrix is a weighted sum of the neighboring input pixels of the original SPM image. The weights were defined by a convolutin kernel K chosen to be a 5 X 5 matrix with the following elements:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII ASCII or American Standard Code for Information Interchange, a set of codes used to represent letters, numbers, a few symbols, and control characters. Originally designed for teletype operations, it has found wide application in computers. ] (1)
The matrix convolution operation yielded an improved edge enhancement and sharpened boundaries of the surface topography, i.e., the Al grains. Second, the convoluted images were converted to binary ones, with black and white pixels. The black regions constituted the background and the white regions (the grains) constituted the foreground of the binary images. Third, the area measured by the number of the white pixels was calculated via a built-in procedure in MATLAB. The latter calculates the area of an individual pixel by looking at its two-by-two neighborhood. Two SPM 256 X 256 pixel images of 5 X 5 [micro]m scanned areas of the mold and the metallized gratings were processed and the average pixel size areas per group were found and used to measure the grain size distribution.
Photoelasticity Measurements. Photoelasticity measurements were carried out with a standard Strainoptics PS-100 polarimeter polarimeter: see polarization of light. . It was used to observe the direction of stress and to measure the retardation and the stress magnitude of a chosen point of interest (POI) located at a close distance to the gate of the polymer gratings (Fig. 5). The measurement technique of choice was chosen to be Senarmont analyzer rotation method, requiring plane polarizers with clockwise rotation of the analyzer filter. Only polymer replicas produced by B processing conditions were evaluated since their grooves were well replicated.
[FIGURE 5 OMITTED]
Boiling Test Analysis. Boiling test analysis was implemented to test the adhesion strength of the Al coatings to the polymer substrate. For the purpose, a simple boiling water delamination delamination /de·lam·i·na·tion/ (de-lam?i-na´shun) separation into layers, as of the blastoderm.
1. A splitting or separation into layers.
2. testing was performed. Two metallized gratings, one with 150 nm and a second one with 250 nm Al were immersed into boiling deionized water with temperature T ~ 100 [degree]C for a time t = 120 s. Following that the components were left to cool down to room temperature, blow dried with nitrogen gas and imaged with SEM while running in a variable pressure mode with a nitrogen rich environment to detect defect formation.
RESULTS AND DISCUSSIONS
The results after replication with the two sets of molding conditions were found to be quite different. Molding with type A conditions led to a very poor replication of the grating profile as seen from AFM measurements in Fig. 6. The replicated groove height was not uniform, and values between 40 and 100 nm were measured on single components. It was assumed that the [T.sub.mold] and [T.sub.noz] were lower than those required for a full profile replication. Therefore, their values were accordingly increased in type B setup and 30 gratings were injection molded (Table 1). Additionally, the channel from the end of the nozzle to the gate, i.e., the sprue sprue, chronic disorder of the small intestine caused by impaired absorption of fat and other nutrients. Two forms of the disease exist. Tropical sprue occurs in central and northern South America, Asia, Africa, and other specific locations. bushing, was also heated to a temperature above [T.sub.g] of the polymer, which is ~ 130 [degree]C by inserting cartridge heaters. The achieved effect was similar to using heated extension of the nozzle. AFM measurements of the profiles confirmed the improved replication as seen in Fig. 7.
[FIGURE 6 OMITTED]
[FIGURE 7 OMITTED]
The two-dimensional linear filtering revealed that the average calculated pixel area of the polymer gratings versus that of the mold were 73% and 63% for the 150- and 250-nm Al coated components, Fig. 8. In other words Adv. 1. in other words - otherwise stated; "in other words, we are broke"
put differently , the commercial grating's coating, deposited under different conditions than those of the present study, had finer grain sizes. In addition, it can be inferred that the smaller grains, i.e., in the case of the 150-nm Al coating, covered the area better than the larger ones, i.e., in the case of the 250-nm Al coating.
[FIGURE 8 OMITTED]
The data collected from the AFM measurements was statistically analyzed and the probability P-value was calculated for each measured parameter (Table 2). The accepted level of significance was chosen to be [alpha] = 0.05. Any P-value smaller than [alpha] suggests that the groups are not statistically similar in the measured parameter. The mold profile was compared with that of the bare replicas (Fig. 6) and that of the metallized replicas (Fig. 7). The results were then represented with box plots. As seen in Fig. 9, a box plot consists of a box and whisker lines for each group number. The box has horizontal lines at the lower quartile Quartile
A statistical term describing a division of observations into four defined intervals based upon the values of the data and how they compare to the entire set of observations.
Each quartile contains 25% of the total observations. , median, and the upper quartile values. The whiskers See metal whiskers. are lines that extend from each box and represent the extent of the rest of the data. The dot in the middle of the lower whisker line is placed if there are not outliers. The notches graph a robust estimate of the uncertainly about the sample means and could be used for box-to-box comparison.
[FIGURE 9 OMITTED]
TABLE 2. P-value statistics results obtained from the one-way ANOVA test. Criterion Mold and bare Mold and coated replica 5, p-value replicas and 16, p-value RMS 0 < [alpha] 0.2649 [R.sub.a] 0 < [alpha] 0.8458 [R.sub.max] 0 < [alpha] 0.9250 [R.sub.z] 0 < [alpha] 0.0343 < [alpha] = 0.05 Peak-to-valley 0 < [alpha] 0.1903 Pitch 0.3422 0.7131
It is clearly visible that the replica's groove height distribution is statistically different from that of the mold, which was confirmed by the very small p-value from the ANOVA analysis. The outliers suggest that some scanned areas had acceptable groove heights. The difference between the two medians, though, is ~20 nm, a very small value, and was improved to about ~5 nm after metallization of the grating, resulting in statistically more equal mold and metallized micromolded gratings as seen in Fig. 10. The pitch values distribution for the two groups is similar, with group two having larger sample distribution, median, and upper quartile than group one, suggesting that the polymer-structured grooves underwent shrinkage. The calculated RMS, [R.sub.a], [R.sub.max], and [R.sub.z] P-values were found to be zeros due to the fact that the polymer did not replicate the surface topography formed by the finite Al grains size. This finding was attributed to the low value of [T.sub.mold]. Therefore, the original and replicated surfaces were not statistically equal. It was estimated by AFM measurement of the mold that the grain size is ~40 nm. In addition, it is worth indicating that the mold is actually a diffraction grating, which exhibits its highest efficiency (from manufacturer's specification) at [lambda] ~ 500 nm. As a general rule, an optical surface's roughness should be less than [lambda]/10 in magnitude (7). The metallization of the grating, on the other hand, changed the distribution of the parameters toward improving the statistical similarity between the two groups. The RMS and [R.sub.a] box-plot statistics could be regarded as regarded as criteria for estimating the smoothness of the diffractive coatings. Group one was with narrower distribution than group two, which suggests that the Al coatings were deposited with different conditions. Indeed, SEM imaging, coupled with AFM surface plot construction and two-dimentional linear filtering, unambiguously revealed that the metallized polymer gratings had larger grain sizes. The [R.sub.z] and [R.sub.max] statistics could be used to estimate the height distribution (saw-tooth profile height or the micro-topography) coupled with the grain size variation (nano-topography). The [R.sub.max] statistics revealed a P-value smaller than the accepted level of significance, which is attributed to the variations in the microtopography. Finally, the AFM measurements illustrate that, at least for the 150-nm coated gratings, the PVD preserved the pitch distribution and changed (toward improving) the peak-to-valley distance of the polymer gratings.
[FIGURE 10 OMITTED]
The diffracted power measurement showed that the replicated micromolded gratings had the same response to the IR radiation regardless of the thickness of the coating. This can be attributed to the fact that their geometry and surface imperfections are similar. The lower value of the local minima, compared with that of the mold and observed around 1550 nm, might be due to the larger grains, the scattering losses from the surface, and due to the reduced patterned surface area of the replicas (the mold was inserted into the mold fixture and the gaps between the walls and its edges were sealed with an epoxy, thus also covering some of the patterned area of the mold which was not transferred onto the replicas). Despite this, the shape of the curves is similar, which strongly suggests that the geometry profile of the original and replicated gratings is comparable.
The photoelasticity measurements of the bare gratings revealed that the higher stress levels were primarily concentrated only around the gae, which suggests the future implementation of a different gate design and location. The stress level distribution among the molded components was identical. The calculated retardation and stress value (maximum for the entire area) at the point of interest (POI) were R = 370.5 nm and [sigma] = 92.625 MPa, respectively. The observed isoclinic lines, i.e., the lines that connect points with the same direction of stress were found to spread out of the gate toward the edges. The highest order fringe observed at the POI was n = 1.05 (blue color).
Finally, SEM imaging of the coated gratings that underwent boiling testing, as seen in Fig. 11, revealed that no delamination occurred on the interface formed by the patterned COC surface and the Al coating. Interestingly, the Al film coherence was destroyed by the boiling water, which formed surfaces with spikes having a large surface area. The spikes are believed to be formed of A1/[Al.sub.x] [O.sub.y] since some oxidation inevitably occurred during testing. Two-dimensional Fourier transform was used to assess the geometric characteristics of the spatial domain (SEM) images before and after the boiling test (Fig.12). Because the image in the Fourier domain is decomposed into its sinusoidal sinusoidal /si·nus·oi·dal/ (si?nu-soi´dal)
1. located in a sinusoid or affecting the circulation in the region of a sinusoid.
2. shaped like or pertaining to a sine wave. components, it is easy to examine the geometric structure in the spatial domain. The dominating direction of the vertical regular pattern (grooves) seen from the insets, is shown as a horizontal line on the transformed images. It is constructed by dots or reflexes which from the images' characteristic frequencies. Within a single domain area, the integrity of the grooves was lost, as seen from the decreased number of reflexes important to note that although no treatment of the gratings was done in this work, formation of new carbony1 and carboxyl carboxyl /car·box·yl/ (kahr-bok´sil) the monovalent radical —COOH, occurring in those organic acids termed carboxylic acids.
n. groups on COC surfaces via pretreatment pretreatment,
n the protocols required before beginning therapy, usually of a diagnostic nature; before treatment.
n See predetermination. with oxygen rf plasma leads to an increase of the adhesion strength between COC and metals and might be used if required (6).
[FIGURE 11 OMITTED]
[FIGURE 12 OMITTED]
Injection micromolding with cyclic olefin copolymer was used to replicate polymetric ruled diffraction gratings with two different processing conditions. Characterization of the mold, an optical element itself, and a number of molded replicas revealed that higher melt mold temperatures are vital for improving the fidelity of replication. Statistical analysis confirmed that for improved replication of the nanotopography, formed by the Al grains, even further increase of their values is necessary. It also unveiled that the polymer material had experienced small shrinkage. Two-dimensional linear filtering of the topographic imaged revealed that the Al coating with 150-nm thickness had smaller grains than that with a 250-nm coating and that the mold had finer grain sizes. The diffractive power measurements showed performance of the micromolded and metallized gratings to be similar to that of the commercial optical grating. A boiling test in deionized water showed good adhesion between the untreated COC and A1 surfaces. These results strongly suggest that COC and injection micromolding could be used for manufacturing of low cost diffraction gratings. Furthermore, the same approach could be used for the manufacture of transmission diffraction grating in which there will be no need for index-matching epoxy. also one may envision patterning diffraction grating profiles right on moldable polymetric microfluidics-based platforms to integrate spectroscopy analysis capability into the device.
The authors would like to acknowledge BOY Machines Inc. for providing the injection micromolding machine, TICONA for supplying the COC 5013S polymer, and Dr. B. S. Ooi and his graduate students at Lehigh University for their assistance and discussions pertinent to the power measurements of the diffraction gratings.
(1.) C.-H. Chang, R.K. Heilmann, R.C. Fleming, J. Carter, E. Murphy, M.L. Schattenburg, T.C. Bailey, J.G. Ekerdt, R.D. Frankel, and R. Voisin, J, Vac. Sci. Technol. B, 21, 2755 (2003).
(2.) R. Wimberger-Friedl, J. Inj. Mold. Tech., 4, 78 (2000).
(3.) W.R. Hunter, M.P. Kowalski, J.C. Ride, and R.G. Cruddace, Appl. Opt., 40, 6157 (2001).
(4.) K. Monkkonen, J. Hietala, P. Paakkonen, E.J. Paakkonen, T. Kaikuranta, T.T. Pakkanen, and T. Jaaskelainen, Polym. Eng. Sci., 42, 1600 (2002).
(5.) G. khanarian and H. Celanese, Opt. Eng., 40, 1024 (2001).
(6.) D. Nikolova, E. Dayss, G. Leps, and A. Wutzler, Surf. Interface Anal., 39, 689 (2004).
(7.) Palmer and E. Loewen, Diffraction Grating Handbook 6th ed., Newport, Rochester (2005).
Correspondence to: J.P. Coulter: e-mail: email@example.com
Contract grant sponsor: National Science Foundation: contract grant number: NSF NSF - National Science Foundation grant DMI-0423506.
DOI (Digital Object Identifier) A method of applying a persistent name to documents, publications and other resources on the Internet rather than using a URL, which can change over time. 10.1002/pen.21162
Published online in Wiley InterScience (www.interscience.wiley.com).
[C] 2008 Society of Plastics Engineers
A.K. Angelov, J.P. Coulter
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, Pennsylvania 18015