Progress Toward Corrugated Feed Horn Arrays in Silicon

J. Britton,∗ K. W. Yoon, J. A. Beall, D. Becker, H. M. Cho, G. C. Hilton, M. D. Niemack, and K. D. IrwinQuantum Sensors Group, NIST, Boulder, CO 80305, USA

AbstractWe are developing monolithic arrays of corrugated feed horns fabricated in silicon for dual-polarization single-mode operation

at 90, 145 and 220 GHz. The arrays consist of hundreds of platelet feed horns assembled from gold-coated stacks of micro-machined silicon wafers. As a first step, Au-coated Si waveguides with a circular, corrugated cross section were fabricated; theirattenuation was measured to be less than 0.15 dB/cm from 80 to 110 GHz at room temperature. To ease the manufacture ofhorn arrays, electrolytic deposition of Au on degenerate Si without a metal seed layer was demonstrated. An apparatus formeasuring the radiation pattern, optical efficiency, and spectral band-pass of prototype horns is described. Feed horn arraysmade of silicon may find use in measurements of the polarization anisotropy of the cosmic microwave background radiation.

Imaging detectors at millimeter wavelengths can nowbe built with hundreds of pixels.[1] However, parallelgains in free-space coupling optics have lagged.

At NIST we are pursuing monolithic arrays of corru-gated platelet feed horns made with Si. Each layer inthe stack is a Si wafer with photolithographically de-fined apertures. Once assembled and coated with Au,these horn arrays are expected to feature the same lowloss, wide bandwidth, minimal side lobes and low cross-correlation as electroformed horns.[2, 3] Moreover, rel-ative to metal corrugated arrays [4], Si horn arrays areexpected to have the following benefits: (a) a thermal ex-pansion matched to Si detectors, (b) lower thermal mass,and (c) a straightforward development to arrays of thou-sands of horns. The formermost of these considerationsmeans that detector-horn alignment at room tempera-ture should be maintained at low temperature (Table I).Silicon is also convenient due to the availability of highresolution wafer-scale Si etch tools.

To demonstrate the feasibility of this approach we fab-ricated W-band (WR10) waveguides out of Si and mea-sured their transmission characteristics from 80 to 110GHz. The Si platelets were machined in 75 mm diameterSi wafers by use of photolithography and deep reactiveion etching (DRIE). In 250 µm thick Si, for example, fea-tures can be reproduced with ∼ 5 µm lateral resolutionthrough the full wafer bulk (∼ 50 : 1 aspect ratio). Side-wall roughness for etched apertures is less than 1 µm.[5]Tools for applying this process to wafers 150 mm in di-ameter are currently being installed at NIST.

With the aim of easing the eventual manufacture ofhorn arrays, we demonstrated electrolytic deposition ofAu films directly on degenerate Si. Tests of film adhesionand waveguide performance are reported.

An apparatus was constructed to measure the far-fieldradiation pattern and cross polarization of feed horns byuse of a vector network analyzer.

∗Electronic address: britton@nist.gov

Figure 1: Photograph of an assembled circular waveguideafter electroplating with Au. Visible in the figure are fea-tures for joining the Si waveguide with other standard metallicwaveguide components: A) clearance holes for 4 − 40 screwsand C) four holes for stainless alignment dowels. Arrow Bidentifies the waveguide channel. The shiny surface is driedepoxy used to hold the stack together. The annulus surround-ing the waveguide (B) is an artifact of the electroplating pro-cess and is not functional.

I. CIRCULAR WAVEGUIDES

A pair of waveguides with circular cross section wereassembled from platelets 380 µm thick. The wave-guide apertures were sized to be single mode from 80to 110 GHz. One waveguide was smooth-walled (2.21mm diameter; 4.0 mm length) and one was corru-gated (2.1/5.55 mm diameter, alternating every 380 µm;11.5 mm length). The corrugation depth was one half-wave deep. A metal seed layer (Ti:Au 100 nm:500 nm)was deposited on platelets mounted on an orbital plat-form canted at 45. Platelets were stacked on alignmentpins and adhered with two-part epoxy applied to theiredges. Platelet alignment accuracy was ±10 µm. Sub-sequent electrolytic plating of the assembled stack in-creased the Au thickness to 3 − 5 µm on flat surfaces

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cp/(J · g−1 ·K−1) α/(1× 10−6/K−1)at 77 K at 293 K

Al 0.336 23.1

Mg 0.488 8.2

Be 0.080 11.3

Cu 0.195 16.5

Si 0.18 2.6

Table I: Comparison of materials for horn arrays. Where, cp

is specific heat and α is coefficient of thermal expansion.[6]

(less in the corrugations). Figure shows a photograph ofone waveguide structure.

Waveguide loss was measured by use of a vector net-work analyzer (VNA). A short followed the device undertest so that a S11 reflection measurement gave twice thesingle-pass loss. We observed less than 0.15 dB/cm lossin both the corrugated and not corrugated waveguides(Fig. 2). We also measured the transmission (S12) forthe waveguides and observed attenuation consistent withthe S11 measurements.

It is instructive to compare the loss in our circularcorrugated waveguides with the expected loss α for thefundamental (TE10) mode of a hollow rectangular wave-guide due to finite wall conductivity. An expression forα is

α =λ0

b λg

√π

λ0ησ

(1 +

(λg

λc

)2(1 + 2

b

a

))×8.676 dB/m,

(1)where λ0 = c/f is the free-space wavelength, c is thespeed of light, f is the frequency, λg = λ0/

√1− (λ0/λc)2

is the guided wavelength, λc = 2 a is the waveguide cutoffwavelength, η =

√µ0/ε0 is the intrinsic impedance of the

material filling the waveguide, σ is the conductivity, anda and b are the width and height of the waveguide crosssection.[7] For f = 100 GHz, σAu = 2.05 × 10−8 Ω · m(at 273 K), aWR10 = 2.54 mm and bWR10 = 1.27 mm,λ0 = 3 mm, λg = 3.7 mm, λc = 5.1 mm (fc = 59 GHz),η = 377Ω and α = 0.027 dB/cm. Note that the surfaceresistance of Au drops by over a factor of 10 from roomtemperature to 10 K.[8] The excess conduction loss weobserve may be caused by metal surface roughness andscattering into non-propagating modes.[9] In our guidesthe latter is expected to dominate and therefore we donot expect a large reduction in loss if the waveguides weretested at 10 K.

To test whether the waveguide attenuation plotted inFig. 2 was limited by plating thickness, an additionallayer of Cu 3 to 5 µm thick followed by Au 1 to 2 µmthick was deposited (as measured on flat, superficial sur-faces; e.g., location B in Fig. 3). Following this treat-ment there was no change in attenuation. This is to beexpected because the skin depth of bulk Au at 100 GHzand 273 K(78 K) is 90 nm (43 nm).[6, 10]

Figure 2: Attenuation for waveguides with circular cross sec-tion as determined by S11 measurements on a VNA. The base-line (0 dB) was established by measuring S11 without a testwaveguide installed. The vertical axis scaling relies on a cal-ibration performed by the VNA manufacturer in 2008. Thetheory curve shows attenuation at room temperature due tofinite conductivity of the waveguide walls assuming the bulkresistivity of Au (σAu = 20.5× 10−9 Ω ·m; see Eq. 1).

II. ELECTROLYTIC PLATING OF DEGENER-ATE SI

Low transmission losses in our Si waveguides were ob-tained by electroplating with Au, a chemistry that re-quires that the target surface be initially conducting. Inthe devices described in the previous section, we achievedthis by e-beam evaporation of a Ti:Au (100 nm:500 nm)seed layer prior to electroplating. This step could beeliminated by use of degenerate Si as a substrate mate-rial. Degenerate Si with a bulk resistivity of less than50 × 10−6 Ω · m is available commercially. For such awafer with a substrate thickness of 100 µm, the sheet re-sistance is 100 × 10−3 Ω/, equivalent to a 200 nm Auseed layer.[6] On test chips made of Si we successfullydemonstrated Au deposition based on a recipe by Llona,et al.[11]

The electrolytic deposition rate depends on geome-try via the local electric field and degree of depletionof the plating solution. Corrugated waveguides have re-cesses that might plate more slowly than exposed sur-faces. To test this we microfabricated, then electroplated,Si test structures (Fig. 3) with linear trenches whose as-pect ratios (depth/width) varied from 0.44 to 8.75. Aftersnapping a sample wafer perpendicular to a row of suchtrenches, the deposition thickness was measured fromSEM micrographs near the bottom of the trenches. Overthis range of aspect ratios, the plating rate diminishedfrom 1/2 to 1/5 (C to D in Fig. 3) of the rate at the topsurface (B in Fig. 3).

The adhesion of Au electrolytically deposited on de-generate Si was investigated. Three tests were conducted:

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Figure 3: (top) Schematic view of a test chip for electrolyticplating of Au directly on degenerate Si (0.5 cm2). The Siwas 400 µm thick, B-doped (p-type), σ = 10 × 10−6 Ω · m.(bottom) Trenches were deep etched into the Si surface tomimic the aspect ratio (depth/width) of corrugations in awaveguide. The trench depth is about 175 µm deep. Fromright to left, the widest trench is 400 µm wide, the narrowestis 20 µm wide. (B) denotes the top surface of the chip withzero aspect ratio, while (D) marks a trench with an aspectratio of 8.75. Disregard (A). A waveguide with corrugationsλ/4 deep repeated N times per λ has an aspect ratio of N/2.In our waveguides we aim for N = 4.

chips were (a) scratched with stainless forceps, (b) dippedrepeatedly in liquid nitrogen, and (c) snapped in half. Nodelamination of the Au was observed for the successfuldeposition recipe (Fig. II).

Figure 4: Micrograph of a degenerate Si electroplated withAu in cross section.

III. HORN TESTING APPARATUS

Desired characteristics of feed horns include low losses,wide bandwidth, minimal side lobes and low cross corre-lation of orthogonal polarizations. We built an appara-tus to measure these parameters for horns we fabricated(Fig. 5). It consists of two horns: a fixed transmitter(Tx) and a receiver (Rx) that pivots about the trans-mitter’s phase center. The Rx horn is a commerciallymanufactured corrugated metal horn for G-band (WR5).According to simulation, its cross polarization is less than

Figure 5: Schematic of feed horn test setup. It consists oftwo horns: a fixed transmitter (Tx) and a receiver (Rx) thatpivots about the transmitter’s phase center.

Figure 6: Photograph of a corrugated Si feed horn prior tometallization. This horn was designed for 145 GHz. Corruga-tions are visible in the central aperture as they extend down-ward into the stack. See Fig. for an explanation of the visiblehole pattern.

30 dB and side lobe amplitude is less than 25 dB at 150,180 and 220 GHz. A vector network analyzer is used tomeasure S12 (amplitude and phase) as a function of an-gle (φ) and frequency. We use a 0or 90 twist precedingthe Tx horn to measure H-plane and E-plane mode pat-terns. Cross polarization measurements use 45 twistsbefore the Tx horn and after the Rx horn. To confirmproper operation of the system we use a pair of identicalmetal horns. Return loss (insertion loss) will be measuredwith the horn face pressed against a microwave absorber(metal plate). This apparatus is assembled and testingis underway.

IV. CONCLUSION

In this proceeding we reported on progress toward fab-rication of corrugated millimeter-wave feed horn arraysmade of Si and a testing facility for evaluating the per-

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formance of millimeter-wave horns. Next steps includetesting a 145 GHz Si feed horn (already designed andfabricated, Fig. 6) and demonstrating plating of a hornfabricated from degenerate Si. In 2009 we plan to build aprototype 75 mm diameter feed horn array, and in 2010we plan to build a 150 mm diameter feed horn array with640 channels (50 to 100 corrugations). Matching detec-tors and refractive optics will permit characterization ofthe imaging characteristics of these horn arrays.

V. ACKNOWLEDGMENTS

K. W. Yoon acknowledge support from the NationalResearch Council. This work was supported by NIST

through the Innovations in Measurement Science pro-gram. We thank Robbie Smith and Christian Wigginswho provided assistance developing the recipe for elec-trolytic plating of degenerate Si (Custom Microwave,Inc., Longmont, CO). This proceeding is a contributionof NIST and is not subject to U.S. copyright.

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