A 1.6:1 Bandwidth Two-Layer Antireflection Structure for Silicon Matched to the 190-310 GHz Atmospheric Window
Fabien Defrance, Cecile Jung-Kubiak, Jack Sayers, Jake Connors, Clare deYoung, Matthew I. Hollister, Hiroshige Yoshida, Goutam Chattopadhyay, Sunil R. Golwala, Simon J. E. Radford
RResearch Article Applied Optics 1
A 1.6:1 Bandwidth Two-Layer Antireflection Structurefor Silicon Matched to the 190–310 GHz AtmosphericWindow F ABIEN D EFRANCE , C
ECILE J UNG -K UBIAK , J ACK S AYERS , J AKE C ONNORS , C LARE DE Y OUNG ,M ATTHEW
I. H
OLLISTER , H IROSHIGE Y OSHIDA , G OUTAM C HATTOPADHYAY , S UNIL
R. G
OLWALA , AND S IMON
J. E. R
ADFORD Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, CA 91125 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109 Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138 Smithsonian Astrophysical Observatory, Submillimeter Array, Hilo, HI 96720 * Corresponding author: [email protected] May 30, 2018
Although high-resistivity, low-loss silicon is an excellent material for THz transmission optics, its highrefractive index necessitates antireflection treatment. We fabricated a wide-bandwidth, two-layer antire-flection treatment by cutting subwavelength structures into the silicon surface using multi-depth deepreactive ion etching (DRIE). A wafer with this treatment on both sides has < −
20 dB ( < −
20 dB level (also in TE at 15°), reproducing previous work.Together these developments immediately enable construction of wide-bandwidth silicon vacuum win-dows and represent two important steps toward gradient-index silicon optics with integral broadbandantireflection treatment. © 2018 Optical Society of America
OCIS codes: (050.6624) Subwavelength structures; (220.4000) Microstructure fabrication; (220.4610) Optical fabrication; (310.6628) Subwave-length structures, nanostructures (350.1260) Astronomical optics http://dx.doi.org/10.1364/ao.XX.XXXXXX
1. INTRODUCTION
Optical systems at frequencies of tens of GHz to a few THz (arange termed “THz” here for brevity) benefit greatly from theuse of silicon: its high index of refraction minimizes the thick-ness and curvature of optical elements; its refractive index isachromatic; it is not birefringent; its low loss, even at room tem-perature, ensures high optical efficiency can be maintained; itshigh thermal conductivity ensures it can be cooled effectively incryogenic applications; and its strength permits it to be used forvacuum windows. Specific THz applications include securityimaging, remote sensing, and astronomical observations of thecosmic microwave background and cold, dusty sources suchas star-forming regions and dust-obscured galaxies. The highrefractive index of silicon, however, necessitates antireflection(AR) treatment. The simplest approaches, quarter-wavelengthlaminated coatings or etched structures, have only narrow band- widths, roughly 1.2:1 ( ν max : ν min ) with less than 1% reflectance.Furthermore, laminated coatings require care to avoid mechan-ical failure in applications where the optics are cooled. Thereis, therefore, a need in the THz regime for a robust, broadband( > <
1% ( < −
20 dB) reflectance over a 1.6:1bandwidth; and, use of wafer bonding to stack wafers with nomeasurable degradation in reflectance.We quote all reflectances and transmittances in power (inten-sity, not electric field) in this work. a r X i v : . [ a s t r o - ph . I M ] M a y esearch Article Applied Optics 2 A. Previous Work
The prototypical AR treatment has a quarter-wavelength layer ofdielectric material with refractive index equal to the square rootof that of the substrate. Broader bandwidths can be obtained byusing multiple quarter-wavelength layers with properly selectedindices. To maintain the advantages of silicon, any AR treatmentmust have low loss, must lack birefringence, and, for cryogenicuse, must closely match the thermal contraction of silicon. Fewmaterials meet all these requirements and also have the correctindices. Plastic coatings, such as parylene, are often used innarrow-bandwidth applications with modest reflectance require-ments [1]. Cirlex has also been used in this fashion [2]. Anotherapproach is an epoxy-based coating in which each layer’s dielec-tric constant is tuned by mixing different types of epoxy or dop-ing with strontium titanate [3]. This technique has been used toachieve wider bandwidths, yielding a reflectance of <
10% withbandwidths of 2.7:1 and 3.2:1 in two and three-layer coatings,respectively. The epoxy suffers, however, significant absorptionloss: 1% for two layers and 10% for three. Furthermore, < < −
23 dB reflectance over a 1.3:1 bandwidth. The same grouphas a prototype of a five-layer structure [8] for which measure-ments have not been reported. Smooth-sided pyramids cut witha beveled dicing saw have been used to obtain <
5% reflectanceover a 2.9:1 bandwidth [9]. In all realizations, the dicing sawapproach is limited to producing AR structures that consist ofcrossed grooves, yielding only posts, and feature sizes are lim-ited by practical saw blade thicknesses.Another method is laser machining. In one demonstration,circular holes were bored into a flat alumina sample using alaser, giving <
10% reflectance over a 1.3:1 bandwidth [10]. (Alu-mina is lossier than silicon but has a similar refractive index.)Other structures, such as sharp cones [11], concentric circulargrooves [12], and pyramids [13] have also been made with lasermachining. It is, however, difficult to control depth with lasermachining, and the process can be unacceptably slow for pro-duction fabrication.Extending to THz frequencies and increasing the bandwidthrequires finer features than conventional machining can produce.An alternative is to use a photolithographic process to etch fea-tures into the silicon surface. DRIE is a mature micromachiningtechnique that can create arbitrary patterns of deep features withaspect ratios up to 30:1. DRIE has been used in a few demon-strations of flat one-layer structures at THz frequencies [14–19].Multi-layer structures have also been designed and fabricatedat THz frequencies using DRIE. In one case, the design from [7], consisting of two layers of posts, was scaled to 850 GHz andfabricated, but test results were not presented [14]. In a secondcase, a structure using three layers of holes was demonstratedwith <
4% reflectance over a 2.2:1 bandwidth (2.5–5.55 THz) [20].DRIE, however, is not easily applicable to the curved surfacesof powered optics and seems to have only been demonstratedon such surfaces at much shorter wavelengths [21]. It is thoughtthat slumping techniques may be applicable [22, 23], though ademonstration is not forthcoming.
B. A New Approach
Combining multi-depth etching with wafer bonding may pro-vide a viable technique for broadband AR treatment for pow-ered silicon optics [24]. A multi-depth DRIE technique hasbeen previously demonstrated [25], providing a means to pat-tern layers with different refractive indices in a single wafer.Multiple wafers could then be bonded together to obtain thick,high layer-count structures needed for very wide-bandwidthAR treatments. To produce powered optics, similar techniquescould be used to create a flat-faced gradient-index (GRIN) op-tic, circumventing the challenge of AR-treating a curved sur-face. A cylindrical optic with a parabolic radial index gradient n ( r ) = n − r / ( f t ) , where n is the bulk index, f is the focallength, and t is the thickness provides the same focusing as aconventional parabolic lens. The radial index gradient could beachieved by varying the DRIE pattern across each silicon wafer.Then, as with the AR structure, several wafers could be bondedtogether to form a focusing optic of the desired thickness. TheAR structure would be integrated into the outer layers of the op-tic, including the variation of the AR treatment with radius. ThisAR-textured, GRIN silicon optic would thus present a completesolution to the problem of constructing broadband, poweredsilicon optical elements.We consider only structures that exhibit no birefringence atnormal incidence. While even non-birefringent media exhibitpolarization-dependent reflectance for non-normal incidence,such effects are minimized if the medium does not exhibit theseeffects at normal incidence. Because square grids of circularfeatures or four-fold-symmetric features (e.g., squares, crosses)are non-birefringent, we chose these as the basis for our de-sign work. There are arguments that any structure with N -foldsymmetry with N >
2. DESIGN
Our design objective was an optic with two parallel faces, aswould be used for a vacuum window, having <
1% ( < −
20 dB)reflectance across the 190–310 GHz atmospheric window (1.6:1bandwidth). Our design process consisted of multiple steps.First, we applied the well known theory of optical thin films(e.g., [27]) and the equivalent theory of transmission-lineimpedance transformers (e.g., [28]) to design AR structures with esearch Article Applied Optics 3
Fig. 1.
Example of a two-layer AR structure with two differenteffective refractive indices
Fig. 2.
Two-layer Chebyshev antireflection treatment for sili-con. Cyan solid line: A bare silicon surface has a reflectanceof 30% ( − n = < −
26 dB re-flectance over the design band, 190–310 GHz. Red solid line:Fabry-Pérot fringing slightly changes the passband and raisesthe peak in-band reflectance for a two-sided optic. Even so,it meets the design goal of < −
20 dB reflectance across thepassband. The total wafer thickness of 1 mm includes AR treat-ment on both sides.multiple quarter-wavelength layers. Second, we used finite-element analysis of one-layer microstructured silicon patterns todetermine effective indices of refraction, enabling us to chooseappropriate etch patterns for each layer. Third, we performed afinite-element analysis of the entire multi-layer optic to verifythe performance and for comparison with measurements. Whileit would be appropriate to use the finite-element analysis of thefull structure to optimize the design parameters, we did notdeem that refinement necessary for this demonstration. Finally,we analyzed the impact of expected fabrication nonidealities.We note that any interface between materials having differentindices is birefringent for non-normal incidence. The level ofbirefringence is generally small for angles less than 30° [18].Since our goal is transmissive optics such as windows and lenses,we deemed this restriction on incidence angle acceptable.
A. Multilayer AR Design
Silicon’s high refractive index, n Si = n = n , causing re- flections from the front and the rear surfaces of the AR layer todestructively interfere at the design frequency and odd harmon-ics. A single layer, however, only provides a relatively narrowbandwidth: 1.2:1 at −
20 dB reflectance and 1.1:1 at −
26 dB.Moreover, for a two-sided optic with parallel faces, suchas a vacuum window, there will be constructive interferencewhenever the total optical thickness is an integer number of halfwavelengths. To meet the design goal of < −
20 dB reflectancefor the entire optic, the reflectance from each single surface mustbe < −
26 dB to accommodate this 6 dB Fabry-Pérot fringing. Fora powered optic (curved or gradient index), we expect the Fabry-Pérot fringing to be no worse than the above 6 dB, and thusthis −
26 dB criterion is conservative and should be sufficient forpowered optics also.Multi-layer designs provide wider bandwidths. Of the manypossibilities, we focused on configurations in which all the layershave quarter-wavelength optical thicknesses. Not only is thisapproach well studied theoretically, it is well matched to our fab-rication technique. Alternate approaches, including pyramids,involve a thicker overall AR structure, more layers, or both forequivalent performance.Analogous to filter design, there is a compromise between thebandwidth and the maximum reflectance in the passband. Thereexists a technique using Chebyshev polynomials that provides,for a required bandwidth and maximum in-band reflectance,the number of layers and their refractive indices needed to meetthe requirement while providing uniform ripple through thepassband [28, 31]. There are many design tools available, in-cluding online calculators (e.g., ).Our requirement of a maximum reflectance of −
26 dB over the190–310 GHz band results in a 2-layer design with indices andthicknesses given in Table 1 and with predicted performanceshown in Fig. 2.These AR designs implicitly assume the refractive indices ofthe layers are achromatic through the frequency range of interest.Although this is true for bulk silicon, it is not strictly true formicrostructured silicon. Hence the realization of the AR designsmust be verified by finite-element analysis.
B. Effective Index of Microstructured Silicon
To realize the AR designs, we need to know the effective refrac-tive index, n eff , of microstructured silicon. To our knowledge,however, there is not a comprehensive theory in the literature ofthe effective refractive index of a microstructured dielectric, evenin the zero-frequency (static) limit. Although a few models pro-vide guides for specific configurations, they are not applicablein general and are insufficient for design purposes.We therefore characterized microstructure geometries by us-ing a commercial electromagnetic finite element solver, ANSYSHigh Frequency Structure Simulator (HFSS), to calculate thecomplex reflection and transmission spectra ( S parameters). Wethen fit the spectra with dielectric slab models parameterizedby an effective refractive index, n eff , and an effective thickness, t eff . For a true “effective index” approach, it should not be nec-essary to specify both parameters. We follow [7] in using thesetwo parameters, presumably as a first-order correction to de-viations from a pure effective index model. We explored bothachromatic models with constant parameters and models with alinear frequency dependence.We modeled unit cells with microstructure features placedbetween semi-infinite vacuum and semi-infinite silicon. Weplaced the input and output ports at the interfaces to vacuumand bulk silicon. We used periodic boundary conditions at esearch Article Applied Optics 4 the cell walls to emulate an infinite grid. To avoid diffractioneffects, the grid spacing, Λ , must be considerably smaller thanthe vacuum wavelength, λ / Λ > ( n Si + cos θ ) ≈
4, for incidentangles θ ≤ ◦ [32]. This grid spacing is much smaller thanthe 100-mm wafer diameter, so the infinite array approximationshould be valid.Although we explored a variety of microstructure geometries,including linear grooves, hexagonal grids, and circular features,we restrict our attention here to square features in square gridsbecause we found the other geometries provided no additionaldesign flexibility (aside from undesired birefringence at normalincidence). We modeled straight-walled features, both posts andholes, as are produced by DRIE. We used feature depths close toone quarter of the wavelength at the target spectral band’s centerfrequency, 250 GHz. We parameterized the patterns by the fillfactor, f Si , which is the ratio of the silicon area to the unit cellarea. We calculated the spectra over the range 50–500 GHz andchose a grid spacing Λ = µ m to obtain a wavelength-to-gridratio 48 ≥ λ / Λ ≥ f Si is smaller. Holesand posts, however, are significantly different. Posts have alower effective index than holes when the fraction of silicon isthe same. Crosses, formed by indenting the corners of square fea-tures, are intermediate between square holes and square posts.The aspect ratio of their arms and the fill factor both determinetheir effective indices [33]. For holes, a simple linear model ( n eff − ) = f Si ( n Si − ) provides a reasonable design guide,although it slightly underpredicts the index when the fill factoris small, f Si < f Si > n eff − ) = f − f + f + f Si . Al-though this fit is only strictly applicable for square posts with thecell size and the frequency range we simulated, it is neverthelessa useful design guide.Three effects complicate the relation between microstructuregeometry and effective index. First, the effective thickness of themicrostructured layer differs by a few percent from the physicalthickness. The magnitude and sign of this difference depend onboth the feature geometry and the fill factor. Second, because thewavelength-to-grid ratio is frequency dependent, the effective in-dex and thickness are also frequency dependent. The magnitudeand sign of this chromaticity also depend on both the featuregeometry and the fill factor. For holes, we found a positive gradi-ent in the effective index, ≈ × − GHz − , while postsshow a negative gradient of similar magnitude. Third, in a multi-layer structure, there will be interactions at the layer interfacesthat are not captured by modeling each layer in isolation. Asa result, any wide-bandwidth, multi-layer AR design must besimulated as a whole to determine its performance.The difference between holes and posts is of great practicalimportance when choosing the geometry to use for each layer ofthe AR structure. For an effective index near that of bulk silicon,the fill factor is close to unity and thus the aspect ratio of theremoved material is critical to how feasible the structure is: itis difficult to achieve aspect ratios larger than 30:1. Holes arethus generally easier to physically realize for such high indicesbecause the fill factor at a desired index is lower than for posts.Conversely, an effective index near unity necessitates low fill Fig. 3.
Effective refractive index, n eff , of microstructured sili-con determined from HFSS calculations. The feature geome-tries, square holes, cross holes, cross posts, and square posts,all in a square grid, are parameterized by the fill factor, f Si .The widths of the cross arms are 35% of the extent of the en-closing square. Several models are shown for comparison:linear interpolation for holes, a quartic polynomial for posts,and an effective capacitor model for both holes and posts [34].factor. Because one must remove so much material, the etchingaspect ratio is no longer challenging in general. Instead, the con-cerns are now the robustness of the transversely thin structuresleft by etching and the fractional inaccuracy in their transversedimensions due to etching tolerances (in dimension and in verti-cality). For this case, posts are the better choice because one mustleave more material behind to realize a given refractive index,making the design more robust and less sensitive to fabricationimperfections. For a given fill factor, crosses have effective indexvalues intermediate between those of square holes and posts.Given the geometries of other layers, crosses may thus provide ameans to obtain a desired effective index that is less demandingof the fabrication process than holes or posts.Additionally, one must consider the relative geometry ofposts and holes on different layers, and the considerations de-pend on the manufacturing technique. Etching the entire multi-layer structure from the vacuum side alone would require thetransverse dimensions of the retained material on a given layerbe smaller than the corresponding dimensions of lower layers(greater n eff ) and larger than those of a higher layers (smaller n eff ): i.e., like a wedding cake. This constraint has the greatestimpact at the point where the design transitions from posts toholes, which is where n eff ≈ n − : it may not always be possi-ble for the post width to be compatible with the wall thicknessof the immediately underlying hole layer. (Though, for squarestructures, rotations of one layer by 45° can extend the regimeof compatibility (as we do below).) By wafer-bonding etchedstructures [24], one can circumvent this constraint by fabricat-ing subsets of the layers on individual wafers using etchingfrom both sides followed by wafer-bonding the etched waferstogether, as we plan to do for our proposed four-layer design inSection 8.The above discussion highlights the flexibility of our ap-proach. For example, in contrast, the dicing saw technique esearch Article Applied Optics 5 can only produce post structures. Furthermore, any techniquemust use wafer bonding to circumvent the above issue of layer-to-layer dimensional compatibility. Relative to dicing saw andlaser techniques, etching permits use of the thinnest wafers inconcert with wafer bonding. C. Microstructure Design and RefinementTable 1.
Antireflection structure design parameters
Layers n AR t [ µ m] Shape s [ µ m]one 1.85 162 post 99one 1.85 162 hole 101two 1.39 216 rotated post 722.46 122 hole 77We fabricated three AR treatments for silicon ( n Si = s in a square gridwith Λ = µ m spacing. All layer thicknesses, t ,are one quarter wavelength at the target bandpass’scenter frequency ν =
250 GHz.
Fig. 4.
Schematic of the hole and post structures for the two-layer AR structure, neglecting the intrusions in the post wallsand other fabrication nonidealities.Combining our AR designs (Section A) with our calcula-tions of the effective index of microstructures (Section B), wedesigned both one- and two-layer AR treatments for fabrication.We directly applied the effective index calculations to obtainthe one-layer designs (Table 1). Although their fill factors arequite different, both holes and posts have similar transversedimensions and both are equally straightforward to fabricate.For the two-layer design, we applied the aforementioned con-siderations about the relative ease of fabricating holes and poststo focus on a design consisting of a layer of square posts above alayer of square holes with dimensions as given in Table 1. Wesituated the posts above the intersections of the walls of theholes in order to fabricate the structure by multi-depth etchingfrom the vacuum side alone. Even then, the posts intruded into
Fig. 5. (Left) Three-dimensional model of the two-layer ARstructure shown in Fig. 4. (Right) HFSS periodic cell used forthe simulations, now incorporating tapering of vertical wallsand cupping of the bottoms of etched features characteristicof the DRIE process (Section D). We do not show the filletedcorners or the intrusions into the posts due to the hole-etchingstep.
Fig. 6.
HFSS calculations of our nominal two-layer AR designand of the impact of fabrication nonidealities on its perfor-mance. We describe the modeled nonidealities in Section D.We show the simulated performance of the idealized structure(solid black), of the structure with any one of the nonideali-ties included (dot-dashed), and of the structure with all of thenonidealities included (dashed blue).the holes slightly. We minimized this intrusion by rotating theposts by 45°. See Fig. 4 and Fig. 5. For HFSS modeling, weallowed the 72 µ m width of the posts to extend beyond theavailable diagonal dimension of 67.9 µ m, resulting in a 2.9 µ mchamfer of the 77 µ m holes at each corner. In practice, we al-lowed the hole etch pattern to act on the post layer, resulting inright-triangular intrusions of the holes into the post walls withside length 2.9 µ m and hypotenuse 4.1 µ m. The good matchof the HFSS calculations to the data in Section 6 confirms thesedifferences do not yield discrepancies above −
20 dB reflectance.For completeness, we also modeled designs consisting of twolayers of square holes and two layers of square posts, and wefound all three designs yielded similar behavior, though withsome variation in the heights of the reflectance maxima.We did not further optimize this design for minimum in-bandreflectance or to strictly satisfy the desired 190–310 GHz banddefinition prior to manufacture. The HFSS analysis of a flat, esearch Article Applied Optics 6
Fig. 7.
SEM images of one-layer AR structures. (Top) Square posts. (Bottom) Square holes. (Left) Isometric view. (Right) Cross-section view of cleaved samples.1 mm thick wafer with the structure on both sides (Fig. 6) indi-cated the passband of the structure would be shifted to slightlylower frequency than desired, < −
20 dB over 160–280 GHz.Rather than refine the design to precisely match the desiredband, we deemed it more important to demonstrate the struc-ture could be reliably fabricated and accurately modeled. Theshift may be due to interaction between the two layers.
D. Effects of Fabrication Nonidealities
Although our DRIE process (Section 3) allows us to fabricate pat-terns that closely match our idealized rectilinear designs, SEMimages (Fig. 7 and Fig. 8) show the fabricated patterns do notperfectly reproduce the designed geometry: the bottoms of theholes, along with the spaces between the posts, show a cuppedprofile; the transverse dimension of the etch tends to expandwith depth, resulting in posts that are slightly narrower at thebottom compared to the top and holes that are slightly widerat the bottom compared to the top; and, none of the edges areperfectly sharp, but instead have a slightly rounded, or filleted,profile.To quantify the impact of these fabrication nonidealities onthe performance of our two-layer AR design, we performedcalculations using HFSS at normal incidence, assuming a 1 mmtotal wafer thickness (including the etched layers on both sides,as fabricated (Section 3)). We included the above nonidealitiesbased on their typical sizes as measured by SEM: we approxi-mated the cupped profiles at the bottom of the etched volumesusing linear pyramidal shapes with 10 µ m heights; we modeledthe horizontal dimensions of the posts/holes with linear profilesthat expanded by 4 µ m from top to bottom; and, we added a2 µ m radius fillet to all sharp edges and corners. We show the re-sults in Fig. 6. The nominal design provides < −
20 dB reflectanceover the band 160–293 GHz. The largest effects are: taperingthe holes causes one Fabry-Pérot fringe to rise a small fractionof a dB above −
20 dB; and, tapering the posts causes the band to narrow slightly, shifting the band edges inward by 2–3 GHz.When we include all the nonidealities, the effects partially cancel,with the most important result being a slight upward shift of theband edges by 1–2 GHz. Overall, these simulations indicatedthat the modeled nonidealities had noticeable but acceptablysmall effects on performance.
3. FABRICATION
A. Substrates
We used 100 mm diameter, 1 mm thick wafers < > wafers, op-tically polished on both sides and specified to have bow/warp < µ m, total thickness variation < µ m, and no more than10 particles above 0.3 µ m in size per face. The material ishigh-resistivity float-zone silicon, lightly n-type doped withphosphorus, with >
10 k Ω cm resistivity. The implied loss tan-gent should be < × − at 250 GHz and room temperature,resulting in a loss of < δ = ( πν(cid:101) (cid:101) r ρ ) − where ν is the frequency, (cid:101) the permittiv-ity of vacuum, (cid:101) r the relative permittivity of silicon, and ρ itsresistivity). Though not immediately relevant here, we note forcompleteness that the specification on minority carrier lifetimeis > B. Antireflection Structure Fabrication
Deep reactive-ion etching (DRIE) is a dry etching technique,relying on plasma-etching of bulk silicon. We employed theBosch technique because it is known to produce nearly verticalsidewalls, high aspect-ratio features, and is compatible withmass production [35]. It utilizes SF and C F as the main gases,with alternating etching and passivation steps [36]. It is compat-ible with various mask materials, including photoresist, siliconoxide/nitride, or metals. In all cases, the desired etch depthdivided by the DRIE process selectivity (the ratio of silicon tomask material etch rates) determines the mask thickness. esearch Article Applied Optics 7 Fig. 8.
SEM images of two-layer AR structure. (Left) Top view. (Center) Isometric view. (Right) Cross-section of cleaved sample.For multi-layer AR structures, we began with the multi-stepDRIE process previously reported in [25], where the SiO maskwas patterned with steps of different thicknesses, each in pro-portion to the desired etch depths of the silicon layers. We madeone modification for this work, using a photoresist mask for theetch of the highest-index layer (closest to bulk silicon), due todifferences in process details. In particular, we found that theDRIE process has poorer selectivity between SiO and siliconthan in [25]. This may be due to the larger volumes of siliconbeing removed. This observation, along with the larger etchdepths used here (338 µ m total etch depth here, 254 µ m in [25]),would have necessitated an impractically thick SiO mask forthe last etch step, motivating the use of photoresist instead. Thatis, we used a single photoresist mask on top of a single SiO mask to fabricate our two-layer design. (For one-layer struc-tures, we used only a SiO mask.) We grew the thick ( ∼ µ m)SiO mask under water vapor at 1050 °C directly on the siliconwafers. We patterned the SiO into a mask using an InductivelyCoupled Plasma (ICP) machine with O and CHF gases andan etch rate of about 250 nm min − . We used conventional UVphotolithography to expose the photoresist mask, which wasspun on after the SiO was patterned.We etched the silicon with a Plasma-Therm VERSALINEDeep Silicon Etcher, using a modified 3-step Bosch process: pas-sivation step, etch A step, etch B step. In addition to traditionalSF and C F gases, we added Ar to each of the three stepsto keep the plasma stable during the short transitions. To pro-vide smooth surfaces and vertical sidewalls for even the largeaspect-ratio features, and to remove the large amounts of silicondemanded by our design, we optimized the gas ratio, step tim-ing, and power levels. We performed the etches at a chamberpressure of 20–35 mTorr, gas flow rates of 100–150 sccm for SF and C F and 30 sccm for Ar, inductively coupled plasma RFpower of 1500 W, and a chuck temperature of 15 °C. We alsobias the substrate with RF power (we do not supply this powervalue because it is very machine-dependent). Each step in theprocess is a few seconds long, with specific lengths dependingon the desired etch depth and calibration from test wafers. Thefirst DRIE step, using the photoresist mask, nominally providedan etch depth of 122 µ m to produce the hole features of thedeepest AR layer (but see below for a correction to this depth).The photoresist mask protected the post regions as well as thewalls between the holes. After stripping the photoresist, thesecond DRIE step etched a depth of 216 µ m more, bringing bothpatterns to their target depths. The SiO mask protected theposts during this step.During initial testing, we found that, during the second etch Fig. 9.
SEM of boundary between bonded wafers with holeAR structures. No gaps are visible at the boundary at this reso-lution, though some imperfections are present.step, which both creates the post layer and extends the holesdown to their final depth, the etch rate of the deeper hole layer,relative to that of the post layer, slowed down dramatically withtime due to its depth in the silicon. To overcome this issue, weover-etched to 190 µ m (as opposed to 122 µ m) during the firstetch step. With this change, the holes reached their final targetdepth of 338 µ m (= 122 + 216 µ m) as the post layer reached itsfinal 216 µ m depth target. Additionally, to compensate for theslight undercut during DRIE, we augmented the feature dimen-sions on the photolithographic mask by 2–3 µ m on each siderelative to the design, with the corrections determined empiri-cally by etching pathfinder wafers. Overall, we found the firststep to have an approximate silicon-to-photoresist selectivity of25:1 for an etching time of 56 min and the second step to have asilicon-to-SiO selectivity of 140:1 for an etching time of 68 min.After etching, the remaining SiO mask was removed withhydrofluoric acid and the wafer was cleaned with an O plasmafor 1 hr at 1000 W. We also performed a short thermal oxidationand etching step to improve the etched surfaces’ morphologyand smoothness [37]. We grew a sacrificial layer of SiO in an ox-idation furnace at 1050 °C using water vapor for approximately1 hr, which we then removed with the above recipe.After DRIE, we verified the depths by scanning electron mi-croscopy (SEM), shown in Fig. 7 and Fig. 8. We demonstratedgood control of all lateral dimensions (A, B and C from Fig. 4). esearch Article Applied Optics 8 Fig. 10.
Schematic of the test bench.
C. Wafer Bonding
As explained in Section B, wafer-bonding of patterned siliconwafers is integral to our approach for constructing broadband,antireflection-textured, gradient-index silicon optics. We employa standard process, “hydrophilic fusion bonding” (also knownas “hydrophilic direct bonding”) [23, 38], which has been usedin prior work on one-layer AR structures [14].Prior to bonding, we performed cleaning and oxidation stepsto ensure a high-quality bond. We began by using a 1:1 mix-ture of sulfuric acid (H SO ) and hydrogen peroxide (H O )(also known as Piranha solution) for about 10 minutes to re-move organic residues, followed by a long rinse under water.We followed this with a 1 hr O plasma clean. We then grewa thin ( ∼
500 nm) layer of SiO via a 1 hr exposure to watervapor in an oxidation furnace at 1050 °C with a nitrogen atmo-sphere. Finally, immediately before the initiation of the bond,we performed a two-step cleaning process with solutions ofRCA-1 (H O/H O /NH OH (5:1:1)) heated to 80 °C and RCA-2(H O/H O /HCl (4:1:1)) heated to 70 °C to remove any remain-ing organic and/or metallic particles.Next, to initiate bonding, we aligned the two silicon wafersusing a contact mask aligner with backside capabilities andbrought them into contact, forming van der Waals bonds be-tween the wafers. We allowed the wafers to rest for at least 12hours at room temperature to provide time for any bubbles todissipate and to release surface tension between the two wafers.We strengthened the still temporary bond by bringing the twowafers to 450 °C for at least 12 hours. After this step, we in-spected the wafer pair under an IR microscope for any remain-ing bubbles or voids. Unsatisfactory inspection results wouldhave led us to separate the wafers and restart the process, but we had no such failures during bonding of the sample reported onin Section 7. Finally, we proceeded to create a chemical bond [39]between the wafers by heating them to 1050 °C. Since the qualityof the bond increases for longer annealing times, we annealedour wafers for 1–3 days in a dry environment (no water vapor).The thermal oxide layer grew to a thickness of 0.4–1 µ m duringthis step. We show a cross-section of a bonded wafer in Fig. 9.
4. MEASUREMENT SETUP
We used a scalar spectrometer (Fig. 10) to measure the reflectanceand transmittance of samples between 75 GHz and 330 GHz.The signal generation chain begins with a frequency synthesizeroutputting a 20–40 GHz signal that is amplitude modulated(10 Hz for the data shown here). We amplify and triple thissignal, with the tripler having sufficiently high output powerbetween 75 and 115 GHz. We follow the tripler with an isolatorto mitigate standing waves, a W-band amplifier, a directionalcoupler to provide a monitor signal, and finally a rectangularfeedhorn for measurements in the 75–115 GHz band (designatedas “Band 1”). We use a lookup table based on the measurementsof the monitor signal to power-level the W-band signal and, forthe higher-frequency bands, protect the doubler/tripler. Theoutput signal is polarized normal to the optical bench and hence,relative to the sample, normal to the plane of incidence or TE. Formeasurements at higher frequencies, we employ another isolator,either a doubler (to reach “Band 2”: 140–220 GHz) or a tripler(to reach “Band 3”: 220–330 GHz), and a band-appropriate rect-angular feedhorn. Fig. 10 shows, in dark red, the power levels atvarious points in the multiplier chain as well as the band-specificpower at the output of the chain. Fig. 10 also lists identifyinginformation for each element of the setup. esearch Article Applied Optics 9
Fig. 11.
Top view of the test setup.We attenuate the signal emitted by the generation chain withan Eccosorb ® HR-10 foam absorber (attenuation increasing from −
10 dB in Band 1 to about −
20 dB in Band 3) to mitigate stand-ing waves. A parabolic mirror then collimates the beam anddirects it to the sample. We mount the samples to be measuredin a translating support that makes a 15° angle with the incidentbeam. The support has three measurement locations for sam-ples and two calibrator locations, one used for a mirror and theother with no element (for full transmission). To measure thetransmission of a sample, we calculate the ratio of the powertransmitted by the full transmission calibrator and by the sam-ple, while the reflectance is the ratio of the power reflected by thesample and by the mirror. For both the reflection and transmis-sion arms, we focus the signal from the sample via a parabolicmirror to a feedhorn coupled to a Schottky diode power detec-tor. We monitor the diode voltages with lockin amplifiers. Weuse band-appropriate feedhorns and diode detectors. To reduceunwanted reflections, we cover all flat surfaces with the samefoam absorber as used above (see Fig. 11).In order to accurately evaluate the intensity distribution andwavefront of the beam along the optical path, especially at thesample and at the receiving horn positions, we used Feko ® tosimulate the propagation of the beam (Fig. 12). The simulationuses the Multi-Level Fast Multipole Method (MLFMM) solver,which is based on the method of moments. In addition to ba-sic Gaussian-beam propagation calculations (which can be per-formed without the use of electromagnetic simulation software),it is possible to use the real, imperfectly Gaussian shape of thebeam emitted by the horn for each of the three bands. The simu-lation also accounts for the transformation of the beam by theparabolic mirrors and the slight truncation of the beam by thedifferent elements (mirrors, sample).The setup suffers modest systematic effects arising from themodification of the beam propagation by the sample. Because ofthe 15° incidence angle, a 1 mm thick silicon sample shifts thebeam transversely by 0.19 mm. Additionally, as detailed in [40,41], when a Gaussian beam passes through a flat dielectric slab(even at normal incidence), the waist position of the transmittedbeam differs from that of the incident beam. For our setupand our typical silicon sample thickness of 1 mm, this effectartificially shortens the distance between the beam waist andthe post-sample parabolic mirror (in the transmission arm only) Fig. 12.
Propagation of the Gaussian beam along the opticalpath of the test setup at 100 GHz (Band 1) using Feko ® . Thisfigure is the combination of the near-field patterns given bytwo simulations, one with no sample and one with a perfectlyreflective sample. See text for details.by 0.7 mm. We used Feko ® to quantitatively evaluate thesetwo effects, finding a 0.4% reduction in power received at thetransmission-arm detector at 100 GHz and 0.5% at 300 GHz.For the reflection arm, the effect only occurs for the componentof the signal reflected from the backside of the sample, so itmodulates an already small reflectance by a few percent relative.(It would be more important for samples with higher reflectance.)The sub-1% systematic error on the transmission measurementwas not important for this work, as we relied entirely on thereflectance measurement to quantify the effectiveness of theAR structure specifically for the above reason: multiplicativesystematic uncertainties are much less important for the near-zero reflectance.
5. ONE-LAYER SAMPLE MEASUREMENTS AND COM-PARISON TO FINITE-ELEMENT ANALYSIS
Table 2.
Dimensions of one-layer AR structures
Shape Posts ( n eff = n eff = [ µ m ] Width [ µ m ] Depth [ µ m ] Width [ µ m ] Design 162 99 162 101Measured 157 top: 97base: 93 171 top: 99base: 101We compare the design and measured (by SEM) dimen-sions for the two one-layer single sided wafers. The topand base dimensions of the posts and holes are the widthat the top of the structures (toward vacuum) and at thebase (toward bulk silicon), respectively. All layers use a125 µ m cell size (grid spacing).In order to validate the fabrication technique and the testsetup, we first fabricated and measured two one-layer AR struc-tures, one with square holes and one with square posts (seeFig. 7). We optimized the designs for maximum transmission at250 GHz, resulting in the dimensions given in Table 2. We fabri-cated these structures using DRIE as described in Section 3. SEMmeasurements of a cleaved wafer confirmed that the dimensions esearch Article Applied Optics 10 Fig. 13.
Reflectance and transmittance measurements of sili-con wafers with one-layer AR structures. We compare to theresults of finite element calculations using the design (dashedline) and measured (solid line) dimensions (Table 2) and 15°incidence angle. (Top) A single layer of square posts on oneside of a wafer. (Middle) A single layer of square holes on oneside of a wafer. (Bottom) A single layer of square holes on bothsides of a wafer. Note the upper two panels use linear verticalscales while the bottom uses a logarithmic vertical scale to em-phasize the low reflectance. We discuss possible explanationsof the modest discrepancies between simulation and data inthe text.of the fabricated structures were close to the design dimensions(within ±
6. TWO-LAYER SAMPLE MEASUREMENTS AND COM-PARISON TO FINITE-ELEMENT ANALYSIS
Our two-layer design, presented in Fig. 4 and Fig. 5, consistsof a top layer of square posts ( n eff = 1.39) and a bottom layerof square holes ( n eff = 2.46), designed for a bandpass centeredon 250 GHz. We used the multi-depth DRIE process describedin Section 3. We measured both samples with our test bench,and we cleaved and analyzed one of these samples with a SEM(Fig. 8) to obtain accurate dimensions. The two sets of opticalmeasurements were quite consistent, indicating reproducibil-ity of the AR structures. We updated the HFSS simulationsdescribed in Section C using the dimensions derived from theSEM measurements (see Table 3) so that discrepancies wouldinform us about differences between theory and measurement,as well as random variations across the wafer, rather than beingdominated by the mean differences between the designed andfabricated structures. Table 3.
Dimensions of two-layer AR structure
Shape Posts ( n eff = n eff = µ m] WidthC [ µ m] DepthT2 [ µ m] WidthB [ µ m]Design 216 72 122 77MeasuredFace 1 228 top: 71base: 66 112 top: 82base: 83MeasuredFace 2 210 top: 71base: 65 121 top: 82base: 84We compare the design and measured (by SEM) dimensionson each face of the cleaved wafer. The top and base dimen-sions of the posts and holes are the width at the top of thestructures (toward vacuum) and at the base (toward bulksilicon). The letters (B, C, T1, T2) refer to the dimensionsin Fig. 4. All layers use a 125 µ m cell size (grid spacing; di-mension A). The thickness of the wafer is 996 µ m, which iswithin the range provided by the manufacturer, Waferpro ® ,(1000 ± µ m).Fig. 14 shows the reflectance and transmittance results of oneof the tested samples, compared with both the original and up-dated HFSS simulations. The sample shows < −
20 dB reflectanceover the band 187–317 GHz, meeting our 190–310 GHz designgoal. The measured reflectance agrees very closely with thesimulation incorporating the SEM measurements, with discrep-ancies only below −
20 dB. An alternate technique that measuresreflectance at normal incidence, not described here, agrees withthese measurements to better than 1 dB precision after correctingfor the incidence angle (black crosses in Fig. 14).The remaining discrepancies with the simulation probablyarise from small nonidealities created by the etching process.We modeled some of these effects in Section D to characterizetheir magnitude, but we expect our model for these effects isonly approximate. In addition, because the HFSS simulationsassumed periodic boundary conditions, they could not accountfor systematic or random variations with position. In particular, esearch Article Applied Optics 11
Fig. 14.
Reflectance and transmittance measurements of a silicon wafer with two-layer AR structures on both sides compared tofinite-element simulations. (Left) Linear vertical scale. (Right) Logarithmic vertical scale. We show finite-element calculationswith the design dimensions (dashed line) and with the dimensions measured from SEM images (solid line), as listed in Table 3.Both calculations incorporate the 15° angle of incidence of the measurement as well as the actual wafer thickness (996 µ m). Thesechanges result in a shift of 3 GHz and some differences in the in-band reflectance relative to the design calculation shown in Fig. 6.The black crosses show the reflectance measurement of the same wafer at normal incidence between 200 GHz and 330 GHz, with analternate technique, as mentioned in the text.we determined that the etch depth varies by ±
10% from thenominal value, shallower at the center and deeper at the edge,and the taper angle of the walls also varies slightly with radius,from 0° at the center to no more than 1° at the edge, though wehave not precisely characterized the range. All these unmodelednonidealities seem to only produce features below our −
20 dBspecification and thus do not merit further modeling.The measurements do show a roughly 8 GHz shift relative tothe original
HFSS model, as measured below 100 GHz (the shiftmust be measured well away from the desired passband becausethe phasing of the Fabry-Pérot fringing can significantly movethe passband edges, as defined by the −
20 dB transmissionpoints). This shift is largely due to the differences betweenthe etched and design dimensions ( ± transmittance are likely due to mea-surement systematics, motivated by the observation that thedeviations are not monotonically increasing with frequency. Wedescribed in Section 4 systematic effects in the test setup at thislevel. The obvious alternative explanations, loss and scattering,would not yield such non-monotonic behavior. Moreover, as weexplained quantitatively in Section 3, the loss expected giventhe high resistivity of the bulk silicon is much smaller than theobserved deviation from unity transmittance. It may be possibleto use alternative measurement techniques to reduce these trans-mittance systematics, but they do not have a significant effect onthe reflectance measurement.
7. IMPACT OF WAFER BONDING ON PERFORMANCE
Our overall approach (Section B) to producing broadband,antireflection-textured, gradient-index silicon optics involveswafer-bonding of patterned wafers using the technique de-scribed in Section C. As a first step toward demonstration of theprocess with etched wafers, we fabricated wafers with one-layerAR structures on one side (both the hole and post designs ofSection 5), bonded the unpatterned faces together, and tested their
Fig. 15.
Reflectance and transmittance measurements of one-layer AR structures on two bonded silicon wafers compared tofinite-element calculations using the design (dashed line) andmeasured dimensions (plain line) (Table 2), for a 15°angle ofincidence. (Top) Square posts. (Bottom) Square holes.performance. We show the bonded interface in Fig. 9 and thereflectance and transmittance results in Fig. 15.The sample using holes shows excellent performance: thebandwidth over which we observe < −
20 dB reflectance is com-parable to that of the sample employing a one-layer structureon both sides of a single wafer (Fig. 13). The agreement with esearch Article Applied Optics 12 theory is also good, though the Fabry-Pérot pattern shows somedeviations in the frequency band of interest. The sample usingposts does not perform as well, with a Fabry-Pérot interferencemaximum rising up above −
20 dB near the center of the desiredband. The measured dimensions partly explain the degradedperformance. Even then, the Fabry-Pérot pattern shows the samekind of discrepancy in the desired band as we see in the waferwith holes. These discrepancies are probably caused by varia-tions of the structures’ dimensions over the surface of the wafers,as explained in Section 6. We believe they are not germane tothe quality of the wafer bond: it was observed in [14] that a gapbetween wafers causes a distinctive, double-Fabry-Pérot pattern,which we do not observe here. We think it is reasonable to con-clude that such effects, if present, are well below our −
20 dBcriterion. Overall, this successful demonstration of wafer bond-ing is a necessary (but not sufficient) condition for bonding ofpatterned faces, our planned technique for structures requiringfour or more layers, to yield acceptable performance.
8. APPLICATION OF OUR WORK TO FUTURE DEVEL-OPMENT EFFORTS
We have demonstrated the fabrication and optical performanceof a two-layer, two-geometry (post and hole) antireflection struc-ture on flat silicon suitable for THz applications. While this tech-nique provides a 1.6:1 bandwidth, which is sufficient to cover,for example, the 190–310 GHz atmospheric window, broaderbandwidths and/or focusing optics are desirable for a range ofapplications. Our techniques can be expanded to achieve thesegoals by bonding together multiple wafers with such patternedstructures. We have already demonstrated that adequate opticalperformance is maintained after wafer-bonding of unpatternedsilicon surfaces. Bonding of patterned surfaces is, therefore, anatural, although likely nontrivial, extension of our techniques.To this end, we have designed a straw-person four-layer struc-ture that would employ bonding of patterned wafers (Fig. 16).HFSS calculations indicate it will have a 4:1 bandwidth, whichwould be sufficient to cover, for example, the atmospheric win-dows at 125–170 GHz, 190–310 GHz, and 335–355 GHz. Thetop two layers use round and square posts, while the bottomtwo layers use square holes. The large etch depths of the postlayers, along with the manner in which they intrude into thehole layers, make it impossible to fabricate the entire structurevia multi-depth etching of a single wafer from the vacuum side.Instead, we would pattern the two hole layers into a substratesilicon wafer via multi-depth etching as we have demonstratedhere, pattern the higher-index post layer into a thin silicon wafer,bond the patterned faces together, and then etch the lower-indexpost layer into the vacuum side of the bonded structure. Evenbroader bandwidths should be possible using similar techniques.For example, a seven-layer design would be capable of coveringa 6:1 bandwidth, which is sufficient for all of the atmosphericwindows between 80 and 420 GHz .We anticipate the patterned structures we have demonstratedhere can also be used to fabricate a gradient-index focusing optic.Obtaining adequate optical performance may require extremeaspect ratios for the features near the center and edges of thelens, and such features may be realizable by bonding patternedsurfaces in the same manner as described above. Based on ourcurrent straw-person designs, the bonding surfaces for someof the structures will likely be smaller than those used for theantireflection structures, and thus adequate bonding may bemore challenging to realize.
Fig. 16.
Schematic of a straw-person four-layer AR design, ne-glecting fabrication nonidealities. The features labeled T3 andT4 on the left would be patterned on one silicon wafer whilethe feature labeled T2 would be patterned on a separate sili-con wafer. The two patterned surfaces would then be bondedand the feature labeled T1 would then be patterned to pro-duce the final geometry. This AR structure would provide 4:1bandwidth (see text).
9. CONCLUSIONS
We have successfully demonstrated a 1.6:1 bandwidth antireflec-tion structure on a flat silicon wafer. A silicon wafer patternedwith this structure on both sides shows < −
20 dB reflectance overthe spectral band 187–317 GHz at 15° angle of incidence in TE po-larization. We believe observed deviations from unity transmis-sion are not due to loss or scattering but rather to measurementsystematics. We have also demonstrated that wafer-bonding ofunpatterned faces introduces no degradation in optical perfor-mance observable above the −
20 dB level (also in TE at 15°).These are important steps in the development of broadband,antireflection-textured, gradient-index optics.
Funding.
NASA (NNX15AE01G)
Acknowledgment.
We performed this work at the California In-stitute of Technology, the Caltech Submillimeter ObservatoryHilo office, the Harvard-Smithsonian Center for Astrophysics,and the MicroDevices Laboratory of the Jet Propulsion Labora-tory (operated by the California Institute of Technology under acontract with the National Aeronautics and Space Administra-tion).The authors thank A. Bose for early, pathfinding HFSS sim-ulation work, K. McClure for contributions to the HFSS toler-ancing simulations, K. Yee for performing the wafer-bondingsteps, J. Wong for contributions to the test setup control code,E. Padilla for undertaking preparatory measurements of the two-layer structures, C.-Y. E. Tong for participation in the Fig. 14alternate technique measurements, and T. Macioce for contri-butions to the text of the paper. C. de Young acknowledgessupport from an SAO Internship. D. Bisel, K. Deniston, andS. Stoll provided able administrative support. esearch Article Applied Optics 13
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