APPLIED PHYSICS LETTERS 93, 261102 共2008兲
Partial confinement photonic crystal waveguides S. Saini,a兲 C.-Y. Hong, N. Pfaff, L. C. Kimerling, and J. Michel Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
共Received 14 August 2008; accepted 9 December 2008; published online 29 December 2008兲 One-dimensional photonic crystal waveguides with an incomplete photonic band gap are modeled and proposed for an integration application that exploits their property of partial angular confinement. Planar apodized photonic crystal structures are deposited by plasma enhanced chemical vapor deposition and characterized by reflectivity as a function of angle and polarization, validating a partial confinement design for light at 850 nm wavelength. Partial confinement identifies an approach for tailoring waveguide properties by the exploitation of conformal film deposition over a substrate with angularly dependent topology. An application for an optoelectronic transceiver is demonstrated. © 2008 American Institute of Physics. 关DOI: 10.1063/1.3059553兴 Photonic crystal 共PC兲 waveguides are “defect” regions that interrupt one-dimensional 共1D兲, two-dimensional, or three-dimensional periodicity in the refractive index of a composite medium1–4 and guide wavelengths of light otherwise inhibited by the photonic band gap.5–13 Actual PC waveguides with a finite number of periodic layers have a finite magnitude reflectivity within their stop band. They are characterized by a complex propagation wave vector and therefore loose optical power per unit length of propagation.14–18 High power waveguide applications have recently exploited the unique ability to confine light within hollow air defect regions, where optical power density can be increased by orders of magnitude.9–12,16 The key design concern is to ensure the presence of a complete photonic band gap for propagation constant values lying above the light line.14 For such a design at the wavelength of interest, all angles of light will lie within the periodic medium’s stop band and be reflected;6,7 we refer to this reflection at all angles as complete optical confinement. In this letter we report the results for a 1D PC waveguide that exploits the properties of partial confinement—the presence of an incomplete band gap above the light line—in order to design for an integrated device application.19 The PC structures investigated were grown by plasma enhanced chemical vapor deposition 共PECVD兲 on silicon 共Si兲 and quartz wafer substrates in a Si complementary metal-oxide semiconductor-compliant clean room. Thickness values of the deposited periodic layers were confirmed by transmission electron microscopy 共TEM兲 using a JEOL 2010. Reflectivity measurements were done using a Carey 5E UV-visible-NIR dual-beam spectrophotometer. 共The visible light source was a tungsten halogen lamp transmitted through a linear polarizer with a spot size of ⬃1 cm2; reflected light was detected by a Hamamatsu R928 photomultiplier tube.兲 Refractive index and film thickness were calibrated with a KLA-Tencor-Prometrix UV-1280 ellipsometer 共 = 633 nm兲. Theoretical reflectivity plots were calculated by means of the transfer matrix method. Figure 1 shows a 1D photonic band diagram calculated for a periodic structure comprised of alternating layers of a兲
Electronic mail:
[email protected].
0003-6951/2008/93共26兲/261102/3/$23.00
silicon oxide 共SiO2 with refractive index of n1 = 1.453, film thickness of t1 = 180 nm兲 and silicon-rich silicon nitride 共Si-rich Si3N4, i.e., SiNx with n2 = 2.2, t2 = 115 nm兲. The band diagram shows 共in regions shaded blue兲 modes of light that can propagate through the PC—dubbed low-dielectric 共confined to n1 regions兲 or high-dielectric states 共confined to n2 regions兲—for both transverse magnetic 共TM兲 and transverse electric 共TE兲 incident polarizations. The propagation constant  represents the horizontal projection of incident light on the PC 共see schematic below band diagram兲. The angular frequencies of light and  have been plotted in units renormalized to 2c / L 共c is the free space speed of light兲 and 2 / L, respectively; L = t1 + t2 = 295 nm. We observe the light line to be above the Brewster line14 for TM polarization, affirming a complete photonic band gap for certain wavelengths of light when confined to the air defect. The center of the first photonic band gap at = 0.28共2c / L兲 共i.e., ⬇ 1054 nm兲 exhibits a complete confinement: all values of  that lie above the light line are within the photonic band gap, resulting in defect state modes
TM mode r r E
B
r k
r k β
θ
normal
nn22 nn11
TE mode r
r B
E
r k
substrate
FIG. 1. 共Color online兲 Photonic band diagram for a 1D PC comprised of SiO2 共n1 = 1.453, t1 = 180 nm兲 and SiNx 共n2 = 2.2, t2 = 115 nm兲. Left and right plots show the band diagram for TM and TE polarizations, respectively. Polarization orientation is depicted below with respect to a schematic of a finite PC.  is the component of the incident wave vector parallel to the surface of the PC; is the angle the incident wave vector makes with the normal.
93, 261102-1
© 2008 American Institute of Physics
Downloaded 06 Jan 2009 to 117.32.153.167. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp
261102-2
Appl. Phys. Lett. 93, 261102 共2008兲
Saini et al. λ=850 nm
~500 m
θ=78.5° (Si) (i) (ii)
NA=0.2
θ=11.5° (SiO2)
n=1.45 fiber core
VCSEL n=3.46 Si subst.
fiber cladding
β
(a)
(b)
FIG. 2. 共Color online兲 共a兲 Schematic of device application using a partial confinement PC waveguide. A VCSEL light source with NA ⬇ 0.2 injects light with a finite angular emission 共and thus range of 兲 into an air via. The PC deposited in region 共i兲 inhibits transmission and reflects both TE and TM polarizations, resulting in an air defect layer that guides light along the via. At the end of the via, the finite angular emission is incident on the PC at complementary -values, resulting in transmission to low-dielectric states. 共b兲 Theoretical reflectivity plot for light incident at the limiting angle of VCSEL emission 共 = 78.46°兲 in region 共i兲 and—with a complementary angle 共 = 11.54°兲—in region 共ii兲.
that concentrate optical power within the air defect. However, at = 850 nm 关 ⬇ 0.35共2c / L兲兴, we observe partial optical confinement: for 0 ⱕ  ⬍ 0.2共2 / L兲, = 850 nm light will not be confined to the air defect. For this range of , the curvature of the photonic band edge results in the presence of low-dielectric state modes,19 concentrating optical power in the low refractive index layers of the PC. For lower frequencies of light, this range of  lies again within the photonic band gap. At = 850 nm, the range of  corresponds to incident angles 0 ⱕ ⱕ 35°, where is measured with respect to the normal axis. Figure 2共a兲 shows the schematic diagram for our proposed device application: an optoelectronic transceiver.
Gigahertz-linewidth laser diodes such as vertical cavity surface emitting laser 共VCSEL兲 may be bonded to the backside of a Si wafer containing microelectronic devices, provided the VCSEL signal can be guided along an air via 共through the wafer兲 that is optically isolated from field effect transistor 共FET兲 devices on the wafer front side. Optical isolation in this case is critical: evanescent absorption of the VCSEL signal in the Si wafer would result in generation of excess free electron-hole pairs, thereby adding noise to the FET gate current. A waveguide design is needed that simultaneously confines light to the air via in region 共i兲 while ensuring high transmission to the front side at region 共ii兲. Our proposed design20 takes advantage of PECVD conformal deposition in order to deposit a 1D PC of uniform film thickness over regions 共i兲 and 共ii兲. The numerical aperture of a typical = 850 nm VCSEL is specified as NA⯝ 0.2,21 corresponding to a range of angles 78.5° ⱕ ⱕ 90°. For our PC structure from Fig. 1, these angles lie within the photonic band gap. Hence, in region 共i兲, the VCSEL signal will be strongly reflected and propagate along the air via. A high index contrast PC such as SiO2 : SiNx predicts an evanescent decay length of x ⬃ 672 nm using the formula x = Lnav / ⌬n 关⌬n ⬅ n2 − n1, nav ⬅ 共n1 + n2兲 / 2兴 共Ref. 6兲. This assures strong optical isolation. At the end of the air via, VCSEL light will be incident at angles 0 ° ⱕ ⱕ 11.5°, thereby lying well within the photonic bands in Fig. 1. The signal will couple to low-dielectric PC states and transmit through to the wafer front side. Figure 2共b兲 shows the theoretical computation of TE reflectivity in region 共i兲 共the PC against a Si substrate兲 and region 共ii兲 共the PC against a SiO2 substrate兲. The dotted line helps identify = 850 nm; we observe that for a TE mode, there will be a high reflection in region 共i兲 and high transmission in region 共ii兲.
FIG. 3. 共Color online兲 共a兲 Apodized refractive index profile for region 共i兲. 共b兲 Apodized refractive index profile for region 共ii兲. 共c兲 Cross-section TEM of structure grown by PECVD on Si substrate for characterization of region 共i兲.
Downloaded 06 Jan 2009 to 117.32.153.167. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp
261102-3
Appl. Phys. Lett. 93, 261102 共2008兲
Saini et al.
TABLE I. Refractive index 共n兲 and film thickness 共t兲 values for apodized PC structure deposited on a Si substrate. The apodized pattern follows the profile shown in Fig. 3共a兲 and lists values for lower periodic layers and defect layer. Upper periodic layers are a mirror image of the lower periodic layers. n t 共nm兲
1.45 202
1.6 172
1.45 202
2.01 137
1.45 202
2.15 128
1.45 202
2.2 125
¯ ¯
For a finite PC, reflectivity sidelobes in the spectral regions around = 850 nm can inadvertently reduce transmission through region 共ii兲. The sidelobes were minimized by deposition of an apodized7 refractive index profile 关Figs. 3共a兲 and 3共b兲兴. TEM 关Fig. 3共c兲 shows the PC on Si substrate兴 confirmed the deposited structure thicknesses to be within the error bar of the nominal design. For the apodized profile, refractive index values intermediate to n = 1.453 and n = 2.2 were achieved by PECVD growth of silicon oxynitride 共SiON兲, i.e., a miscible mixture of SiO2 and Si3N4. Table I lists the nominal film thickness and refractive index values for Fig. 3共a兲, showing the lower periodic layers and defect layer values. The upper periodic layer is a mirror image of the lower periodic layers. Figures 4共a兲–4共d兲 overlay experimental versus theoretical reflectivity for the PC deposited on Si or quartz 共SiO2兲 substrates, thereby simulating light interaction with regions 共i兲 or 共ii兲, respectively. The plots show data for two angles of incidence 共 = 20°, 70° to the normal兲 in TE and TM polarizations. In all plots, we observe a ⬍10 nm discrepancy between theory and experiment attributable to calibration drift in deposited film thickness or SiON refractive index values.
FIG. 4. 共Color online兲 Reflectivity theory 共blue dashed-dot lines兲 and experimental data 共red solid lines兲 on Si substrate at incident angles = 20° and 70° for 共a兲 TE polarization and 共b兲 TM polarization. Reflectivity theory 共blue dashed-dot lines兲 and experimental data 共red solid lines兲 on quartz 共SiO2兲 substrate at incident angles = 20° and 70° for 共c兲 TE polarization and 共d兲 TM polarization.
In Figs. 4共a兲 and 4共b兲, we observe for = 70° 关representative of emission from the VCSEL incident on region 共i兲兴, = 850 nm lies within the stop band and ensures confined propagation. In Figs. 4共c兲 and 4共d兲, we observe for = 20° 关representative of emission from the VCSEL incident on region 共ii兲兴, = 850 nm lies outside the stop band, as expected, ensuring transmission. In conclusion, we have modeled, fabricated, and measured PC structures that prove it possible to design partial confinement PC waveguides simultaneously in both TE and TM polarizations, based on a 1D PC theory. Partial confinement PC waveguides can solve unique integration requirements with performance characteristics specifically attuned to the interplay between device topology 共e.g., the air via兲 and the angular emission of a light source. This work was supported by the Fujifilm Corporation. The authors acknowledge Dr. X. Duan and National Semiconductor for TEM sample preparation and imaging. One of the authors 共S.S.兲 acknowledges Mrs. M. Aglietti 共MIT Materials Processing Center兲 for assistance in preparing Fig. 1. E. Yablonovitch, J. Mod. Opt. 41, 173 共1994兲. E. Yablonovitch, J. Opt. Soc. Am. B 10, 283 共1993兲. 3 S. John, Quantum Electronics and Laser Science Conference. Technical Digest Series, 2002 共unpublished兲, Vol. 74, p. 73. 4 J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature 共London兲 386, 143 共1997兲. 5 E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, Phys. Rev. Lett. 67, 3380 共1991兲. 6 P. Yeh, Waves in Layered Media, 2nd ed. 共Wiley, New York, 2005兲. 7 H. A. MacLeod, Thin-Film Optical Filters, 3rd ed. 共Taylor and Francis, London, 2001兲. 8 D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, and B. Miao, IEEE J. Sel. Top. Quantum Electron. 12, 1416 共2006兲. 9 P. Russell, Science 299, 358 共2003兲. 10 J. C. Knight, J. Opt. Soc. Am. B 24, 1661 共2007兲. 11 A. B. Fedotov, S. O. Konorov, O. A. Kolevatova, V. I. Beloglazov, N. B. Skibina, L. A. Melnikov, A. V. Shcherbakov, and A. M. Zheltikov, Quantum Electron. 33, 271 共2003兲. 12 F. Couny, H. Sabert, P. J. Roberts, D. P. Williams, A. Tomlinson, B. J. Mangan, L. Farr, J. C. Knight, T. A. Birks, and P. Russell, Opt. Express 13, 558 共2005兲. 13 K. K. Lee, A. Farjadpour, Y. Avniel, J. D. Joannopoulos, and S. G. Johnson, Proc. SPIE 6901, 69010K 共2008兲. 14 Y. Fink, J. N. Winn, S. Fan, J. Michel, C. Chen, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 共1998兲. 15 M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, Science 289, 415 共2000兲. 16 J. P. Barber, D. B. Conkey, M. M. Smith, J. R. Lee, B. A. Peeni, Z. A. George, A. R. Hawkins, D. Yin, and H. Schmidt, Conference on Lasers and Electro-Optics, 2005 共unpublished兲, Vol. 1, p. 695. 17 Y. Yi, S. Akiyama, P. Bermel, X. Duan, and L. C. Kimerling, Opt. Express 12, 4775 共2004兲. 18 Y. Yi, S. Akiyama, P. Bermel, X. Duan, and L. C. Kimerling, IEEE J. Sel. Top. Quantum Electron. 12, 1345 共2006兲. 19 J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light 共Princeton University Press, Princeton, NJ, 1995兲. 20 J. Michel, S. Saini, D. Pan, W. Giziewicz, and L. C. Kimerling, U.S. Patent No. 20070181915 共9 August 2007兲. 21 http://www.fujifilm.com/news/n060118.html 共2006兲. 1 2
Downloaded 06 Jan 2009 to 117.32.153.167. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp
