Terahertz-wave antireflectioncoating on Ge and GaAs with fused quartz

Kodo Kawase and Norihisa Hiromoto

1862 APPLIED OPTICS y V

In the terahertz-wave region, fabrication of an antireflection ~AR! coating is difficult because it must beas thick as several tens of micrometers, which is far thicker than that used in the optical region. Wediscuss a lapping method for fabricating an AR layer with a desired thickness for terahertz-wave opticaldevices. To demonstrate this method, we glued a thin fused-quartz plate to a surface of an undoped Geor GaAs wafer and polished it to a thickness of one-quarter wavelength. This reduced the reflectivity ofthe AR surface to 1y720 of the reflection of an uncoated surface, as expected from optical theory.© 1998 Optical Society of America

OCIS codes: 310.1210, 350.7420, 260.3090.

1. Introduction

Generally, one fabricates antireflection ~AR! coatingson various elements used in the optical region bydepositing a dielectric material and using a vacuumevaporation or sputtering method. However, an ARtechnique is not yet sufficiently established in theterahertz-wave region ~customary defined as 0.3–3THz, 100–1000 mm!. Moreover, to the best of ourknowledge, a technique for precisely controlling thethickness of the AR layer has not been reported.The usual coating methods for optics are not appli-cable to terahertz-wave optics because the layersmust be much thicker, by a factor of from several tensto a thousand, than that for the optical wave.

It is possible for one to make a thick SiO2 layer bya chemical vapor deposition method, using tetraeth-ylorthosilicate1 ~TEOS!. However, problems still re-main for using this method for an AR coating: Thecoating materials are very limited; deposition at lowtemperature ~below 200 °C! is difficult; and straincaused by the difference in thermal expansion or con-traction between a coated layer and a substrate isunavoidable. There is another AR-coating methodfor terahertz-wave optics that sticks a plastic film

The authors are with the Communications Research Laboratory,4-2-1 Nukui-kita, Koganei, Tokyo 184, Japan. The permanentaddress for K. Kawase is Applied Physics Department, TohokuGakuin University, Sendai 985, Japan.

Received 26 August 1997; revised manuscript received 7 Novem-ber 1997.

0003-6935y98y01862-05$15.00y0© 1998 Optical Society of America

ol. 37, No. 10 y 1 April 1998

such as polyethylene onto a substrate,2,3 but optionalcontrol of the thickness of the film is not easy withthis method.

We present a new AR-coating technique forterahertz-wave optics. A crystal or an amorphousthin plate with an adequate refractive index is gluedonto the substrate with a special adhesive, and thenits thickness is controlled by mechanical polishing.We fabricated an AR coating on Ge and GaAs wafersby using a fused-quartz thin plate, and we measuredthe transmittance and the reflectance.

The advantages of our method are as follows: ~1!Almost any crystal or amorphous material is appli-cable as a coating layer, provided that it is polishable.~2! One can obtain an AR effect at a desired centralwavelength by controlling the layer thickness in thepolishing. ~3! An anisotropic crystal can be used asa coating material at a desired crystal orientation;this is efficient for making a half- or a quarter-waveplate. ~4! The fabrication technique is usable onthermally unstable material, since all processes aredone at room temperature. This method also obvi-ates contamination of the surface to diffuse into theinside of the material. ~5! An adhesive between acoating and a substrate works as a buffer to inhibitheat stress; hence the coating can be used even atextremely low temperatures.

Applications for this coating method is extensive,as follows: ~1! The incident surface of Ge:Ga4,5 orGaAs6 far-infrared detectors can be AR coated to min-imize the Fresnel reflection loss. As a result, detec-tor sensitivity increases by a factor of approximately1.6. ~2! To improve efficiency and spectral purity,one can easily apply an external cavity to the p-Ge

1 April 1998 y Vol. 37, No. 10 y APPLIED OPTICS 1863

far-infrared laser7 if the AR coat is fabricated on theend surfaces of a p-Ge rod. ~3! As for the terahertz-wave generation in which nonlinear opticaleffects8–10 are used, the coupling efficiency increasesby AR coating the exit surface. ~4! It is easy to im-prove the transmittance of a window or a filter forterahertz wave by AR coating both surfaces.

As indicated above, we believe this AR-coatingtechnique can bring major improvements to variousterahertz-wave optics.

2. Fabrication of Antireflection Coating

Here we demonstrate our AR-coating technique us-ing Ge and GaAs substrates, which are importantmaterials for terahertz-wave optics. We selectedfused quartz as a coating material for the followingreasons: ~a! Its refractive index ~n 5 2.0! is nearlyequal to the square root of that of Ge ~n 5 4.0! orGaAs ~n 5 3.6!. The refractive indices of these ma-terials are tabulated in Ref. 11. ~b! Its absorptioncoefficient for a terahertz wave is relatively small ~a> 1 cm21!; hence the absorption in the thin-coatedlayer is negligible. ~c! It is transparent for opticalwaves; hence, merely by looking, one can easily in-spect the adhesive layer. ~d! It is also transparentfor ultraviolet ~UV! rays; consequently a UV-hardening adhesive can be used for gluing.

The conditions for the AR coating are nc ' =ns andtc > ly4nc 1 Nly2nc, where nc and tc are, respec-tively, the refractive index and the thickness of theAR coat, ns is the refractive index of the substrate, lis the wavelength of the incident terahertz wave, andN is the integer. We selected a condition of zeroorder ~i.e., N 5 0! so that the effective wavelengthrange of the AR coating would be as wide as possible.Reflectance at an AR-coated surface is expressed as

R 5 1 2 4FSnc2

ns1

ns

nc2 1 2D

1 S1ns

1 ns 2nc

2

ns2

ns

nc2Dcos2S2pnc tc

l DG21

. (1)

Figure 1 shows the reflectance of Ge and GaAs sur-

Fig. 1. Calculated reflectance of the AR surface of a Ge and aGaAs wafer coated with fused quartz.

faces coated with a fused-quartz AR layer, calculatedfrom Eq. ~1!. Center wavelengths of 172 mm for Geand 210 mm for GaAs are chosen. The reflectance ofthe AR surface of the Ge ~0.04%! is lower than that ofGaAs ~0.1%! because the refractive index of the fusedquartz ~nc > 2.0! is ideal for Ge ~ns > 4.0!.

The procedure for AR coating was as follows:First, a 3-mm diamond slurry was used to polish flatboth surfaces of a Ge or a GaAs wafer ~21 mm indiameter! so that the maximum deviation in thick-ness was less than 61 mm over the entire area. Thethicknesses of the Ge and the GaAs wafers were 2066and 585 mm, respectively, after they were polished.Optical-grade polishing was unnecessary because thewavelength is much longer in the terahertz-wavethan in the optical region. Both surfaces of a fused-quartz thin plate ~Infrasil, 20 mm in diameter and 40mm thick! were also polished flat. Pressing thefused-quartz plate as flat and as close as possible bymeans of the clamping apparatus shown in Fig. 2, weglued the plate onto the substrate with a UV-hardening adhesive ~NOA61!. Then the adhesivewas hardened by UV radiation from the upper win-dow of the clamping apparatus.

From measurements taken with a Fourier trans-form infrared spectrometer, the absorption coefficientof the adhesive was a 5 40 cm21 at around l21 5 60cm21 ~Fig. 3!, and the refractive index was n 5 1.7 atl21 5 40–120 cm21. The absorption coefficient ofthe adhesive was relatively large for the terahertzwave, but the absorption loss in the thin ~3-mm! ad-hesive layer was only approximately 1%, which isnegligible. After gluing, we again lapped the fused-quartz plate on the substrate by use of a 3-mm dia-mond slurry to adjust the center wavelength of theAR coat. During the lapping, the thickness was con-trolled by the use of a vacuum chuck holder with amechanical stop that can be preset for a desired thick-ness ~provided by Musashino Electronics Company,Ltd.!. In the demonstration, the center wavelengths

Fig. 2. Side view of clamping apparatus. The movable plate ispressed with three micrometers, and distance d is monitored bythree thickness gauges. ~The third gauge is behind the middlemicrometer.!

of the AR coatings and the coat thicknesses were l 5170 mm and tc > ly4nc 5 22 mm for the Ge wafer andl 5 210 mm and tc > ly4nc 5 27 mm for the GaAswafer, respectively. The maximum deviations inthe thickness of the AR-coated wafers were less than61 mm over the entire area of a clear aperture thatwas 20 mm in diameter.

3. Experimental Results

We measured the transmittance spectrums of AR-coated Ge and GaAs wafers with a Fourier transforminfrared spectrometer with a resolution of 0.01 cm21.Figures 4 and 5 show the transmittance of the Gewafer with and without, respectively, the fused-quartz AR coat on one side. Figures 6 and 7 alsoshow the transmittance of the GaAs wafer with andwithout, respectively, the AR coat on one side. Thedifference in the interval of the interference fringebetween Figs. 4 and 6 simply resulted from the dif-ference in thickness between the Ge and the GaAswafer. From the comparison of the interference am-plitude between Figs. 4 and 5, it is clear that the ARcoating on the Ge wafer functioned effectively. InFig. 4, the interference amplitude diminished to al-

Fig. 3. Measured absorption coefficient of the UV-hardening op-tical adhesive ~NOA61!.

Fig. 4. Measured transmittance spectrum of the Ge wafer ~2066mm thick! with a fused-quartz AR coat ~22 mm thick! on onesurface. The center frequency is 58 cm21 ~5172 mm!, wheretransmittance is 57%.

1864 APPLIED OPTICS y Vol. 37, No. 10 y 1 April 1998

most nothing at the center wavelength of 172 mm~558 cm21!, where the measured transmittance was57%.

The absorption coefficient of the Ge wafer was mea-sured to be a 5 0.6 cm21 at l21 5 58 cm21, as shownin Fig. 8; therefore the transmittance within the wa-fer was T 5 exp~2ats! 5 88% for the thickness of ts 5

Fig. 5. Measured transmittance spectrum of the uncoated Gewafer ~2066 mm thick!.

Fig. 6. Measured transmittance spectrum of the GaAs wafer ~585mm thick! with a fused-quartz AR coat ~27 mm thick! on onesurface. The center frequency is 47.5 cm21 ~5210 mm!, wheretransmittance is 65%.

Fig. 7. Measured transmittance spectrum of the uncoated GaAswafer ~585 mm thick!.

2066 mm. The transmittance at the uncoated sur-face is simply given by Fresnel’s law as 4nsy~ns 1 1!2

5 64%, where ns 5 4.0. The theoretical transmit-tance of the Ge wafer with an ideal AR coating on onesurface is 57% ~64% of 88%!. This shows good agree-ment with the measured value mentioned above. Inaddition, one can estimate the reflectivity of the AR-coated surface from the interference amplitude, usingthe following equation12:

A 54~R1 R2!

1y2T2~1 2 R1!~1 2 R2!

~1 2 R1 R2 T2!2 , (2)

where A is the interference amplitude, R1 is the re-flectivity of the AR-coated surface, and R2 5 ~ns 21!2y~ns 1 1!2 5 36% is the reflectance of the uncoatedGe surface. Using Eq. ~2!, we obtain a value of R1 50.05% at the center wavelength from the measuredinterference amplitudes in Figs. 4 and 5. This valueshows good agreement with the theoretical value R15 0.04% in Fig. 1. We can therefore conclude thatthe AR coat works ideally and the reflectance ~R1! ofthe AR-coated surface decreased to approximately1y700 of the Fresnel reflection ~R2 5 36%! of theuncoated surface.

In the same manner, the AR coat fabricated on onesurface of the GaAs wafer was working properly nearthe center wavelength of 210 mm ~547.5 cm21!, asshown in Fig. 6. The measured transmittance of theAR-coated GaAs wafer was 65% at the center wave-length, and showed agreement with the theoreticalvalue of 64%. Furthermore, the reflectance of theAR-coated surface estimated from the measured in-

Fig. 8. Measured absorption coefficient of the undoped Ge.

Table 1. Theoretical and Experimental Performances of theFused-Quartz AR Coat on One Surface of Ge and GaAs

Substrate Ge GaAs

Center wavelength ~mm! 172 210Thickness of AR coat ~mm! 22 27Thickness of substrate ~mm! 2066 585Theoretical transmittance ~%! 57 64Measured transmittance ~%! 57 65Theoretical reflectance ~%! 0.04 0.10Measured reflectance ~%! 0.05 0.10

terference amplitudes in Figs. 6 and 7 was R1 5 0.1%;this value also showed good agreement with the the-oretical value shown in Fig. 1. The reflectance ~R1!of the AR surface of the GaAs wafer was reduced toapproximately 1y300 of the Fresnel reflection ~R2 532%! of the uncoated surface. The theoretical andthe measured performances of the AR coats are sum-marized in Table 1.

4. Conclusion

We have developed a terahertz-wave AR-coatingtechnique that utilizes the precise mechanical pol-ishing after a crystal thin plate is glued onto asubstrate. Based on this method, we fabricated afused-quartz AR coating on Ge and GaAs wafers.The measured reflectance of the AR-coated surfaceof a Ge wafer was reduced to as low as 0.05%,whereas that of an uncoated surface was 36%. Themeasured reflectance of the AR-coated surface of aGaAs wafer was 0.1%, whereas it was 32% for theuncoated surface. These values are consistentwith the theoretical expectations. Our techniquewill make it easy to fabricate an AR coating onvarious kinds of terahertz optical devices such assemiconductor detectors that use Ge or GaAs, p-Gelaser rods, Si-prism couplers for terahertz wave,and terahertz windows or filters.

We thank Mr. Mikio Fujiwara of the Communica-tions Research Laboratory for helping with the ex-periments and for useful discussions. Weacknowledge the support by the COE program pro-moted by the Science and Technology Agency.

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