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Nanoscale resonant-cavity-enhanced germanium photodetectors with lithographically defined spectral response for improved performance at telecommunications wavelengths Krishna C. Balram, * Ross M. Audet, and David A. B. Miller Edward L. Ginzton Laboratory, Stanford University, CA 94305, USA * [email protected] Abstract: We demonstrate the use of a subwavelength planar metal- dielectric resonant cavity to enhance the absorption of germanium photodetectors at wavelengths beyond the material’s direct absorption edge, enabling high responsivity across the entire telecommunications C and L bands. The resonant wavelength of the detectors can be tuned linearly by varying the width of the Ge fin, allowing multiple detectors, each resonant at a different wavelength, to be fabricated in a single-step process. This approach is promising for the development of CMOS-compatible devices suitable for integrated, high-speed, and energy-efficient photodetection at telecommunications wavelengths. ©2013 Optical Society of America OCIS codes: (200.4650) Optical interconnects; (250.0250) Optoelectronics; (350.4238) Nanophotonics and photonic crystals; (070.5753) Resonators; (230.5160) Photodetectors. References and links 1. M. Hilbert and P. López, “The world’s technological capacity to store, communicate, and compute information,” Science 332(6025), 60–65 (2011). 2. D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE 97(7), 1166–1185 (2009). 3. R. Ding, T. Baehr-Jones, T. Pinguet, J. Li, N. C. Harris, M. Streshinsky, L. He, A. Novack, E.-J. Lim, T.-Y. Liow, H.-G. Teo, G.-Q. Lo, and M. Hochberg, “A silicon platform for high-speed photonics systems - OSA Technical Digest,” in Optical Fiber Communication Conference (Optical Society of America, 2012), OM2E.6. 4. J. Michel, J. Liu, and L. C. Kimerling, “High-performance Ge-on-Si photodetectors,” Nat. Photonics 4(8), 527– 534 (2010). 5. L. Chen and M. Lipson, “Ultra-low capacitance and high speed germanium photodetectors on silicon,” Opt. Express 17(10), 7901–7906 (2009). 6. G. Li, Y. Luo, X. Zheng, G. Masini, A. Mekis, S. Sahni, H. Thacker, J. Yao, I. Shubin, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, “Improving CMOS-compatible Germanium photodetectors,” Opt. Express 20(24), 26345–26350 (2012). 7. J. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, S. Jongthammanurak, D. T. Danielson, J. Michel, and L. C. Kimerling, “Tensile strained Ge p-i-n photodetectors on Si platform for C and L band telecommunications,” Appl. Phys. Lett. 87(1), 11110 (2005). 8. R. Roucka, J. Mathews, C. Weng, R. Beeler, J. Tolle, J. Menendez, and J. Kouvetakis, “High-performance near- IR photodiodes: a novel chemistry-based approach to Ge and Ge-Sn devices integrated on silicon,” IEEE J. Quantum Electron. 47(2), 213–222 (2011). 9. J. R. Jain, A. Hryciw, T. M. Baer, D. A. B. Miller, M. L. Brongersma, and R. T. Howe, “A micromachining- based technology for enhancing germanium light emission via tensile strain,” Nat. Photonics 6(6), 398–405 (2012). 10. D. Nam, D. Sukhdeo, A. Roy, K. Balram, S.-L. Cheng, K. C.-Y. Huang, Z. Yuan, M. Brongersma, Y. Nishi, D. Miller, and K. Saraswat, “Strained germanium thin film membrane on silicon substrate for optoelectronics,” Opt. Express 19(27), 25866–25872 (2011). 11. L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D.-S. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2(4), 226–229 (2008). #185716 - $15.00 USD Received 20 Feb 2013; revised 28 Mar 2013; accepted 31 Mar 2013; published 18 Apr 2013 (C) 2013 OSA 22 April 2013 | Vol. 21, No. 8 | DOI:10.1364/OE.21.010228 | OPTICS EXPRESS 10228

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Page 1: Nanoscale resonant-cavity-enhanced germanium photodetectors …dabm/431.pdf · 2013. 4. 22. · Nanoscale resonant-cavity-enhanced germanium photodetectors with lithographically defined

Nanoscale resonant-cavity-enhanced germanium photodetectors with lithographically defined

spectral response for improved performance at telecommunications wavelengths Krishna C. Balram,* Ross M. Audet, and David A. B. Miller

Edward L. Ginzton Laboratory, Stanford University, CA 94305, USA *[email protected]

Abstract: We demonstrate the use of a subwavelength planar metal-dielectric resonant cavity to enhance the absorption of germanium photodetectors at wavelengths beyond the material’s direct absorption edge, enabling high responsivity across the entire telecommunications C and L bands. The resonant wavelength of the detectors can be tuned linearly by varying the width of the Ge fin, allowing multiple detectors, each resonant at a different wavelength, to be fabricated in a single-step process. This approach is promising for the development of CMOS-compatible devices suitable for integrated, high-speed, and energy-efficient photodetection at telecommunications wavelengths.

©2013 Optical Society of America

OCIS codes: (200.4650) Optical interconnects; (250.0250) Optoelectronics; (350.4238) Nanophotonics and photonic crystals; (070.5753) Resonators; (230.5160) Photodetectors.

References and links 1. M. Hilbert and P. López, “The world’s technological capacity to store, communicate, and compute information,”

Science 332(6025), 60–65 (2011). 2. D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE 97(7), 1166–1185

(2009). 3. R. Ding, T. Baehr-Jones, T. Pinguet, J. Li, N. C. Harris, M. Streshinsky, L. He, A. Novack, E.-J. Lim, T.-Y.

Liow, H.-G. Teo, G.-Q. Lo, and M. Hochberg, “A silicon platform for high-speed photonics systems - OSA Technical Digest,” in Optical Fiber Communication Conference (Optical Society of America, 2012), OM2E.6.

4. J. Michel, J. Liu, and L. C. Kimerling, “High-performance Ge-on-Si photodetectors,” Nat. Photonics 4(8), 527–534 (2010).

5. L. Chen and M. Lipson, “Ultra-low capacitance and high speed germanium photodetectors on silicon,” Opt. Express 17(10), 7901–7906 (2009).

6. G. Li, Y. Luo, X. Zheng, G. Masini, A. Mekis, S. Sahni, H. Thacker, J. Yao, I. Shubin, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, “Improving CMOS-compatible Germanium photodetectors,” Opt. Express 20(24), 26345–26350 (2012).

7. J. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, S. Jongthammanurak, D. T. Danielson, J. Michel, and L. C. Kimerling, “Tensile strained Ge p-i-n photodetectors on Si platform for C and L band telecommunications,” Appl. Phys. Lett. 87(1), 11110 (2005).

8. R. Roucka, J. Mathews, C. Weng, R. Beeler, J. Tolle, J. Menendez, and J. Kouvetakis, “High-performance near-IR photodiodes: a novel chemistry-based approach to Ge and Ge-Sn devices integrated on silicon,” IEEE J. Quantum Electron. 47(2), 213–222 (2011).

9. J. R. Jain, A. Hryciw, T. M. Baer, D. A. B. Miller, M. L. Brongersma, and R. T. Howe, “A micromachining-based technology for enhancing germanium light emission via tensile strain,” Nat. Photonics 6(6), 398–405 (2012).

10. D. Nam, D. Sukhdeo, A. Roy, K. Balram, S.-L. Cheng, K. C.-Y. Huang, Z. Yuan, M. Brongersma, Y. Nishi, D. Miller, and K. Saraswat, “Strained germanium thin film membrane on silicon substrate for optoelectronics,” Opt. Express 19(27), 25866–25872 (2011).

11. L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D.-S. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2(4), 226–229 (2008).

#185716 - $15.00 USD Received 20 Feb 2013; revised 28 Mar 2013; accepted 31 Mar 2013; published 18 Apr 2013(C) 2013 OSA 22 April 2013 | Vol. 21, No. 8 | DOI:10.1364/OE.21.010228 | OPTICS EXPRESS 10228

Page 2: Nanoscale resonant-cavity-enhanced germanium photodetectors …dabm/431.pdf · 2013. 4. 22. · Nanoscale resonant-cavity-enhanced germanium photodetectors with lithographically defined

12. O. I. Dosunmu, D. D. Cannon, M. K. Emsley, L. C. Kimerling, and M. S. Unlu, “High-speed resonant cavity enhanced Ge photodetectors on reflecting Si substrates for 1550-nm operation,” IEEE Photon. Technol. Lett. 17(1), 175–177 (2005).

13. C. B. Li, R. W. Mao, Y. H. Zuo, L. Zhao, W. H. Shi, L. P. Luo, B. W. Cheng, J. Z. Yu, and Q. M. Wang, “1.55 µm Ge islands resonant-cavity-enhanced detector with high-reflectivity bottom mirror,” Appl. Phys. Lett. 85(14), 2697–2699 (2004).

14. S. Assefa, F. Xia, and Y. A. Vlasov, “Reinventing germanium avalanche photodetector for nanophotonic on-chip optical interconnects,” Nature 464(7285), 80–84 (2010).

15. R. Chen, H. Chin, D. A. B. Miller, Kai Ma, and J. S. Harris, “MSM-based integrated CMOS wavelength-tunable optical receiver,” IEEE Photon. Technol. Lett. 17(6), 1271–1273 (2005).

16. A. Nayfeh, C. O. Chui, K. C. Saraswat, and T. Yonehara, “Effects of hydrogen annealing on heteroepitaxial-Ge layers on Si: Surface roughness and electrical quality,” Appl. Phys. Lett. 85(14), 2815–2817 (2004).

17. J. R. Jain, D.-S. Ly-Gagnon, K. C. Balram, J. S. White, M. L. Brongersma, D. A. B. Miller, and R. T. Howe, “Tensile-strained germanium-on-insulator substrate fabrication for silicon-compatible optoelectronics,” Opt. Mater. Express 1(6), 1121–1126 (2011).

18. K. C. Balram and D. A. B. Miller, “Self-aligned silicon fins in metallic slits as a platform for planar wavelength-selective nanoscale resonant photodetectors,” Opt. Express 20(20), 22735–22742 (2012).

19. S. Y. Chou and M. Y. Liu, “Nanoscale tera-hertz metal-semiconductor-metal photodetectors,” IEEE J. Quantum Electron. 28(10), 2358–2368 (1992).

20. A. Dimoulas, P. Tsipas, A. Sotiropoulos, and E. K. Evangelou, “Fermi-level pinning and charge neutrality level in germanium,” Appl. Phys. Lett. 89(25), 252110 (2006).

Introduction

Germanium is a promising detector material for CMOS-compatible optoelectronic devices. However, the C (1530-1565 nm) and L (1565-1625 nm) bands commonly used in telecommunications include wavelengths beyond germanium’s direct bandgap absorption edge at 1550 nm; consequently, to achieve sufficiently high responsivity across the entire C and L bands, thick or long Ge regions are usually required, which can increase detector capacitance and/or response time. Here, we demonstrate the use of a subwavelength planar metal-dielectric resonant cavity to enhance the absorption of Ge detectors at telecommunications wavelengths, enabling compact, high-responsivity devices suitable for integrated, high-speed, energy-efficient photodetection. Furthermore, the resonant wavelength of the detectors can be tuned linearly by varying the width of the Ge fin, allowing multiple detectors, each resonant at a different wavelength, to be fabricated in a single-step process. This approach creates exciting possibilities for developing integrated demultiplexing and detection units for future coarse wavelength division multiplexing (CWDM) systems.

The worldwide demand for information bandwidth is expected to continue to grow rapidly, based on the steady rise in mobile and internet traffic in recent years [1]. High-bandwidth, inexpensive, power-efficient optical transceivers will thus be a necessity, particularly for applications such as fiber-to-the-home links and large-scale data centers. Integrating optics and electronics on the same CMOS platform could provide numerous benefits in terms of performance, cost, and energy efficiency [2]. While a wide variety of photonic devices such as grating couplers, waveguides, multiplexers/demultiplexers, and modulators can be realized in silicon [3], its weak absorption at telecommunications wavelengths necessitates incorporating other materials for photodetection. The InGaAs/InP materials system has dominated the telecommunications industry because the direct band gap allows one to engineer efficient light sources and detectors at telecommunications wavelengths. Unfortunately, integration of such materials with silicon remains challenging.

Germanium, a group IV material, is possibly the most promising candidate for CMOS-compatible long-wavelength photodetection, and extensive research has been carried out to develop high-quality Ge / SiGe photodetectors on silicon substrates [4–6]. While the absorption of Ge at 1310 nm is comparable to that of InGaAs, its absorption drops significantly in the C and L bands because its direct absorption edge only extends to ~1550 nm. To circumvent this problem, researchers have investigated various methods to shift the direct absorption edge of Ge to longer wavelengths. Some of these include using high temperature growth of strained layers [7], novel alloys like GeSn [8] and post-growth

#185716 - $15.00 USD Received 20 Feb 2013; revised 28 Mar 2013; accepted 31 Mar 2013; published 18 Apr 2013(C) 2013 OSA 22 April 2013 | Vol. 21, No. 8 | DOI:10.1364/OE.21.010228 | OPTICS EXPRESS 10229

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application of tensile strain using techniques borrowed from MEMS [9,10]. While all of these approaches are promising, they involve either special processing conditions or novel materials, or result in non-planar structures that may be difficult to integrate with other optical components. Alternative approaches to enhancing absorption in Ge include integrating resonant structures like metallic dipole antennas [11] or Fabry-Perot cavities [12, 13] and using avalanche gain [14]. Creating Fabry-Perot cavities that are resonant at different wavelengths requires repeating the fabrication process for each additional wavelength to match the thickness of the cavity to the resonant wavelength. In contrast, the metal-dielectric cavities discussed here can be tuned by varying the width of the fin, which allows multiple resonant cavities to be fabricated in a single-step process. In addition, the MSM geometry allows one to link multiple cavities together and engineer the spectral response of the detector [15].

Device fabrication

Fig. 1. (a) Schematic of the resonant-cavity-enhanced photodetector. A submicron Ge fin is self-aligned to an Au slit. The Au slit serves to both enhance absorption inside the Ge fin and extract photocurrent from the structure. (b) SEM image of a fabricated device in top view and (c) SEM image with sample tilted at 40.

Figure 1(a) shows a schematic of our device showing a submicron Ge fin surrounded on two sides by metal. Figure 1(b) and 1(c) show SEM images of fabricated devices viewed in top view and at 40 tilt angle from the horizontal, respectively. Epitaxial Ge was grown by reduced pressure chemical vapor deposition on a Si substrate using the multiple-hydrogen-annealing-for-heteroepitaxy (MHAH) approach [16]. The Ge was then bonded to a Pyrex handle wafer using anodic bonding, and the silicon substrate was subsequently removed using an alkaline wet etch. The Ge layer was thinned to a thickness of approximately 280 nm using a controlled wet etch. A layer of SiO2 approximately 250 nm thick was then deposited on the sample using plasma-enhanced chemical vapor deposition (PECVD). Ge fins with thickness 230 nm and varying widths were patterned using electron beam lithography and dry etching (using CHF3/O2) with the oxide serving as a hard mask. Cr (5 nm)/Au (225 nm) contacts were then evaporated, and the oxide fin was lifted off in a 20:1 Buffered Oxide Etch (BOE) solution to leave the Ge fin self-aligned to the Au slit. The Pyrex substrate and gold contacts were chosen primarily to demonstrate a proof-of-principle device. This work can be extended, with minor modifications, to Ge-on-insulator substrates fabricated in a CMOS compatible process [17] or Ge heteroepitaxially grown on SOI substrates. In addition, CMOS-compatible metals like aluminium or copper can be substituted for gold, as the metal is employed here as a conventional mirror and not for its plasmonic properties.

Simulation

When excited with electric field polarized along the fin (Ez), the structure supports strong absorption resonances that can be tuned linearly by varying the width of the fin [18]. The electric field (Ez) profile of the resonant mode is shown in Fig. 2(a). There is strong diffraction of incident radiation at the germanium-metal interfaces, especially at the top two edges. This edge diffraction excites a quasi-guided mode in the Ge fin (with electric field Ez)

#185716 - $15.00 USD Received 20 Feb 2013; revised 28 Mar 2013; accepted 31 Mar 2013; published 18 Apr 2013(C) 2013 OSA 22 April 2013 | Vol. 21, No. 8 | DOI:10.1364/OE.21.010228 | OPTICS EXPRESS 10230

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that can propagate along x. Reflection at the Ge/metal interfaces sets up a lateral standing wave resonance in the Ge fin that gives rise to strong resonant absorption and yields an approximately linear tuning of the resonance with fin width. The devices use the fifth-order resonance (as can be easily identified by the four nodes in the electric field profile in Fig. 2(a)) and the fin width (w) and wavelength (λ) are related by w ~5λ/2nGe, where nGe is the refractive index of Ge. The fifth-order resonance is chosen as it provides the highest Q-factor while still remaining sub-wavelength in width, which is desirable for dense integration. The metal-semiconductor-metal (MSM) geometry is used for both light confinement and photocurrent extraction, which is ideal for designing high-speed photodetectors for future on-chip optical interconnect systems [19]. Though the device here is designed for, and operated with, light incident from the top, the device can also respond to z-polarized light propagating in the x direction in a waveguide mode in the thin Ge layer, but we will not investigate this operation further here.

Fig. 2. (a) Plot of the electric field (Ez) profile inside a representative device (fin width of 975 nm) at resonance (λ = 1567 nm). (b) Simulated absorption cross-sections of devices with varying fin width (in nm) when excited with electric field polarization along the fin (Ez).

Figure 2(b) plots the simulated absorption cross-section spectra for Ge fin devices with widths varying from 925 nm to 1025 nm. The simulated structures are excited by a plane wave with polarization along the fin (Ez), and the absorbed power is measured in the simulation in a region defined by the Ge fin and a 1.5 µm wide Ge base region of thickness 60 nm. The refractive index values for Ge and Au were obtained from ellipsometric measurements of our films. The absorption cross-section is defined as the ratio of the power absorbed to the power incident on the fin. The incident power is calculated from a background simulation of a plane wave propagating in vacuum wherein the Poynting vector is integrated over a width equal to that of the Ge fin.

As shown in Fig. 2(b), the resonance redshifts with increasing width. The Q-factor of the resonance is approximately 130 for the 975 nm wide device (red curve). The 925 nm-wide device (blue curve) shows reduced Q because of the substantial direct gap absorption at shorter wavelengths. The absorption spectrum for the 1025 nm (magenta) device shows that one can use these resonances to enhance the effective indirect absorption in Ge at long wavelength (λ = 1614 nm) to a level greater than the direct-gap absorption. The 1025 nm device has a calculated absorption cross section of 0.45 (at resonance, λ = 1614 nm), which means that an amount equal to 45% of the power incident on the fin is absorbed in the device. This absorption takes place in a device with a device thickness around 280 nm. In contrast, the absorption length in Ge at 1614 nm is approximately 40 µm. Devices with resonances at shorter wavelengths perform even better, as expected, with simulations for both the 950 and 975 nm devices indicating more than 70% of the light incident on the Ge fin is absorbed.

#185716 - $15.00 USD Received 20 Feb 2013; revised 28 Mar 2013; accepted 31 Mar 2013; published 18 Apr 2013(C) 2013 OSA 22 April 2013 | Vol. 21, No. 8 | DOI:10.1364/OE.21.010228 | OPTICS EXPRESS 10231

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Experimental results

Figure 3(a) shows the experimentally measured absorption spectra for devices with widths varying from 925 nm to 975 nm, in two orthogonal polarizations. Light from a tunable laser (Agilent 8164A) was focused (beam waist diameter 2w0 = 4.6 µm) on the sample using a 20x NIR Mitutoyo Achromat objective. The polarization was controlled using a polarizing beam splitter and half-wave plate. For the spectra shown in Fig. 3(a), the sample is biased at 500 mV using a low noise current preamplifier (Stanford Research Systems 570), and the amplified photocurrent signal is detected by a lock-in amplifier, which is phase-locked to the reference signal (frequency ~2 kHz) from the internally modulated laser. The incident power is measured at the sample using a Ge detector and power meter (Thor Labs PM 700).

Fig. 3. (a) Measured absorption spectra of devices with varying widths in two orthogonal polarizations Ez (continuous curves) and Ex (dashed curves). (b) Variation of the resonant wavelength with fin width for both simulations and experiment. (c) Measured responsivity of two devices with different widths (nm) at their resonant wavelengths (nm) (d) I-V characteristics of the 925 nm width device under dark and illuminated conditions.

When excited with a focused laser beam with polarization along the fin (Ez), the devices show sharp resonances in the spectrum that shift to longer wavelengths with increasing fin width, as predicted by simulation. The orthogonal polarization (Ex) shows no resonances and corresponds to the absorption spectrum of bulk Ge. The qualitative features of the measured spectrum agree well with the simulated spectra in Fig. 2(b). The devices show significant polarization contrast (a factor of 15 at 1617 nm), which could have potential applications in polarization sensitive detectors.

Figure 3(b) plots the wavelength corresponding to the peak of the resonance as a function of fin width for both the simulation in Fig. 2(b) and the experimental measurements in Fig. 3(a). Both simulations and experiment show a linear increase in the resonant wavelength with increasing width, but there is a 40 nm discrepancy between the predicted and observed

#185716 - $15.00 USD Received 20 Feb 2013; revised 28 Mar 2013; accepted 31 Mar 2013; published 18 Apr 2013(C) 2013 OSA 22 April 2013 | Vol. 21, No. 8 | DOI:10.1364/OE.21.010228 | OPTICS EXPRESS 10232

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resonances. We believe this is primarily due to the presence of an air gap between the Ge fin and gold at the fin sidewalls after lift-off (seen in Figs. 1(b) and 1(c)), which leads to additional phase shifts on reflection.

Figure 3(c) shows the measured responsivity for two devices (widths 925 and 975 nm) at wavelengths corresponding to the peak of their spectral response (1572 nm and 1617 nm respectively) when they are illuminated with light with polarization along the fin (Ez). The I-V curves (obtained using an HP 4145B parameter analyzer.) for the 925 nm width device, under both dark and light conditions, are included in Fig. 3(d). The devices operate as photoconductors, as p-Ge forms a nearly ohmic contact with the metal because of Fermi level pinning at the valence band [20]. Both devices show good responsivity, with peak responsivities of 1.2 A/W for w = 925 nm and 0.3 A/W for w = 975 nm at −3V bias. The absorption lengths for Ge at these wavelengths are 22 µm and 45 µm, respectively, whereas the fin thickness is around 280 nm. While the responsivity numbers are quite high, this could be partially due to the presence of significant photoconductive gain due to trapping of minority charge carriers, which can lead to more than one electron of current through the external circuit for each electron-hole pair generated.

Conclusions

We have demonstrated planar metal dielectric cavity photodetectors based on Ge fins self-aligned to metallic slits, with strong absorption resonances that can be tuned by varying the width of the fins. These structures show high responsivity of 1.2 A/W at λ = 1572 nm and 0.3 A/W at λ = 1617 nm, due both to high simulated absorption cross-section as well as the likely presence of photoconductive gain, and strong polarization selectivity of 15:1 at wavelengths beyond the Ge direct band edge. We believe these structures hold promise for the development of high-speed, energy-efficient Ge photodetectors and modulators for future C and L band CWDM telecommunications and on-chip optical interconnects.

Acknowledgments

The authors would like to thank Dr. Raja Jain and members of Prof. Krishna Saraswat’s research group for help with Ge growth. KCB and RMA acknowledge the support of the Stanford Graduate Fellowship. This work was supported by a Multidisciplinary University Research Initiative grant (Air Force Office of Scientific Research, FA9550-10-1-0264) and the Semiconductor Research Corporation’s Interconnect Focus Center. Work was performed in part at the Stanford Nanofabrication Facility (a member of the National Nanotechnology Infrastructure Network), which is supported by the National Science Foundation under Grant ECS-9731293.

#185716 - $15.00 USD Received 20 Feb 2013; revised 28 Mar 2013; accepted 31 Mar 2013; published 18 Apr 2013(C) 2013 OSA 22 April 2013 | Vol. 21, No. 8 | DOI:10.1364/OE.21.010228 | OPTICS EXPRESS 10233