Open Access
Add to BibSonomyAbstract
We demonstrate vertical-incidence electroabsorption modulators for free-space optical interconnects. The devices operate via the quantum-confined Stark effect in Ge/SiGe quantum wells grown on silicon substrates by reduced pressure chemical vapor deposition. The strong electroabsorption contrast enables use of a moderate-Q asymmetric Fabry-Perot resonant cavity, formed using a film transfer process, which allows for operation over a wide optical bandwidth without thermal tuning. Extinction ratios of 3.4 dB and 2.5 dB are obtained for 3 V and 1.5 V drive swings, respectively, with insertion loss less than 4.5 dB. For 60 μm diameter devices, large signal modulation is demonstrated at 2 Gbps, and a 3 dB modulation bandwidth of 3.5 GHz is observed. These devices show promise for high-speed, low-energy operation given further miniaturization.
© 2012 Optical Society of America
1. Introduction
The substantial communication bandwidth required for short-distance interconnects in next-generation high-performance computing systems and large-scale data centers may soon exceed the capabilities of conventional electrical links, due to pin density constraints, power consumption, and signal integrity issues at high bit rates. Optical links, already the preferred solution at longer length scales, have the potential to replace electrical interconnects in short distance (cm-scale) inter-chip connections as well, provided they are sufficiently energy efficient [1]. Close integration of optical components with complementary metal oxide semiconductor (CMOS) circuitry will be required in order to decrease both the cost and the required energy per bit to levels competitive with electrical links.
There has been much recent work on silicon optical modulators for short-distance inter- and intra-chip optical interconnects [2], although the weak nature of electrooptic effects in silicon typically necessitates high-Q resonant devices that require thermal tuning. Electroabsorption modulators based on germanium represent another possible path towards CMOS-integrable photonic links. In addition to promising work on waveguide modulators based on the Franz-Keldysh effect in bulk SiGe [3, 4], there has been additional interest in utilizing the stronger electroabsorption contrast afforded by the quantum-confined Stark effect (QCSE) in Ge quantum well (QW) structures. Progress in the growth [5, 6] and modeling [7–9] of Ge QWs on Si substrates has enabled the fabrication of QCSE modulators using this CMOS-compatible material system [10–14].
Many of these recently demonstrated modulators are waveguide-integrated devices. However, there are significant challenges associated with coupling light efficiently into and out of silicon waveguides given their small dimensions. An alternative geometry that may be preferable for chip-to-chip links (such as between multiple processors or between a processor and DRAM) is the asymmetric Fabry-Perot modulator (AFPM), in which both the incident and modulated reflected beams are oriented perpendicular or near-perpendicular to the chip surface [15–17]. The challenge in using a vertical incidence geometry is that the optical interaction length is limited by the active region thickness (typically a few microns or less). Incorporating the active region inside an asymmetric Fabry-Perot (AFP) resonant cavity increases the effective interaction length, and thus enables a large change in the reflected power given only a modest change in the material absorption, yielding potentially high extinction ratios even for small voltage swings. Asymmetric Fabry-Perot modulators exhibit low insertion loss, polarization independence, and larger alignment tolerance compared to waveguide devices. They are suitable for dense 2-D array integration, which could enable spatially multiplexed free-space optical links with thousands of channels. This would provide continued scaling of inter-chip interconnect bandwidth without the complexity of wavelength division multiplexing schemes that would be required by waveguide approaches [1]. To date, there have been several experimental demonstrations of highly parallelized free-space optical links for short-distance optical interconnects [18–20]. Modeling of AFPMs based on the QCSE in Ge/SiGe QWs indicates that these structures can be made sufficiently small to have attractive switching energies and modulation rates while maintaining good extinction ratios and low insertion losses [21], and first demonstrations of Ge/SiGe AFPMs have shown low-speed (DC) reflectance modulation in devices based on both a double silicon-on-insulator (SOI) and film transfer approach [12].
In this paper, we present results from Ge/SiGe QCSE AFPMs fabricated using a film transfer process. The moderate-Q resonant cavity enables substantial reflectance contrast with low insertion loss over a large optical bandwidth. We obtain open eye diagrams at 2 Gbps and a 3 dB modulation bandwidth of 3.5 GHz on 60 μm diameter modulators, suggesting that smaller devices will be capable of low-power, high-speed operation at tens of gigahertz.
2. Design and fabrication
2.1. Epitaxy
The Ge/SiGe QW epitaxial structure from which the modulators were processed was grown directly on p-type Si wafers using an Applied Materials Centura Epi reduced pressure chemical vapor deposition (RPCVD) system, operated at a chamber pressure of 40 Torr and a growth temperature of 400°C. The layer structure is shown in Fig. 1(a).
Fig. 1 (a) Epitaxial layer structure consisting of fifteen Ge/SiGe quantum wells grown on a p-type silicon wafer with a fully relaxed SiGe buffer layer grown using a three-stage hydrogen annealing process. (b) Absorption spectrum of the epitaxial structure, deduced from photocurrent measurements. The effective absorption coefficient is calculated from the absorption per pass divided by the thickness of the epitaxial region.
The modulator uses a p-i-n structure, with the QW active region situated inside the intrinsic region of the reverse-biased diode. The structure is grown on top of a fully relaxed Si0.12Ge0.88 p-type buffer layer that reduces the propagation of crystal defects arising from the 4% lattice mismatch between Si and Ge. The boron-doped buffer is grown using several intermediate hydrogen annealing steps, as has been previously demonstrated for the growth of bulk Ge on Si [22]. In contrast to graded buffers grown via low-energy plasma-enhanced chemical vapor deposition [14], buffers grown using the multiple hydrogen anneal process can be made extremely thin while preserving strong QCSE [23].
The active region consists of fifteen 10 nm Ge QWs with 17 nm Si0.19Ge0.81 barriers. Thin undoped spacer regions above and below the active region prevent dopants from migrating into the QWs. At the top of the structure is an arsenic-doped n-type layer for making electrical contact. Following the epitaxial growth, a 15-second, 750°C post-growth rapid thermal anneal was performed.
Absorption spectra derived from photocurrent measurements are shown in Fig. 1(b). These spectra are taken from test structures fabricated on a second, nominally identically grown wafer. The built-in field in the p-i-n diodes ensures that even at small reverse bias voltages, nearly all of the photogenerated carriers are collected through the contacts. Thus, the photocurrent measurement can be directly correlated with the optical absorption. An absorption coefficient contrast approaching 5 dB is obtained for a 1 V drive swing across a broad range of wavelengths, given the proper choice of bias voltage.
2.2. Asymmetric Fabry-Perot cavity design
The asymmetric Fabry-Perot modulator, whose basic structure is shown in Fig. 2(a), consists of two mirrors surrounding a QW region, in which the absorption can be altered by application of an electric field. At normal incidence, the fraction of reflected optical power on resonance, RT, is
where Rf is the front mirror reflectance, and the effective back mirror reflectance Rb,eff is given by Rb,eff = Rb exp (−2αL) [16]. Here, Rb is the reflectance of the back mirror (ideally near unity), α is the effective power absorption coefficient inside the cavity, and L is the cavity length. Changing α and hence Rb,eff will alter RT. A critically coupled condition with zero reflectance is achieved when Rb,eff = Rf, or, equivalently, when the effective absorption is α = ln (Rb/Rf) / (2L).Fig. 2 (a) Schematic illustration of the asymmetric Fabry-Perot modulator. Light enters from the top. A voltage is applied across a p-i-n diode containing the quantum wells inside the intrinsic region. Field-dependent absorption in the QWs modulates the intensity of the reflected light. The asymmetric Fabry-Perot cavity is formed by DBR mirrors surrounding the SiGe. The device is bonded to a Pyrex handle wafer. (b) Microscope image of device showing the AFP modulator, electrically contacted by a high-speed probe.
Design considerations for AFPMs have been discussed in depth previously for III–V based devices. Many of these results also apply to Ge/SiGe devices, including investigations of design optimization [17, 24] and studies of sensitivity to cavity length variations across a wafer as well as temperature [25]. Additionally, simulation work has investigated the effects of beam diffraction as well as both lateral and angular misalignments for Ge/SiGe modulators similar to those presented here [21].
Based on the absorption properties of the Ge/SiGe QW epitaxy, as shown in Fig. 1(b), a resonator structure with 93% top mirror reflectance and 99.8% bottom mirror reflectance was chosen here, such that the AFP matching condition RT = 0 in Eq. (1) could be satisfied in the modulator’s ”off” state.
2.3. Device fabrication
In order to form the AFP resonant cavity with DBR mirrors surrounding the QW structure, a film transfer process is used. Fabrication begins by chemical mechanical polishing (CMP) of the top surface of the SiGe epitaxy to yield less than 1 nm root mean square (RMS) roughness, as determined by atomic force microscopy. A three-layer distributed Bragg reflector (DBR) consisting of alternating quarter-wavelength layers of amorphous silicon (a-Si) and silicon dioxide (SiO2) forms the high-reflectance back mirror of the device. The a-Si layers are approximately 98 nm thick and are deposited by electron beam evaporation, while the SiO2 layers are approximately 243 nm thick and are formed using plasma-enhanced chemical vapor deposition (PECVD).
The top surface of this DBR mirror is then bonded to a Pyrex 7740 carrier wafer using an anodic bonding process [26]. The majority of the silicon substrate is removed by wafer grinding, and the remaining 25–50 μm of material is removed using a potassium hydroxide wet etch that stops at the lower Si/SiGe interface. Most of the Si0.12Ge0.88 buffer layer, where the epitaxy’s crystal defects are concentrated, is then removed via an iterative CMP process until spectrophotometer measurements indicate the cavity resonance is positioned near the wavelength corresponding to maximum electroabsorption contrast in the quantum wells.
To provide electrical isolation, mesas are dry etched using an SF6 chemistry through the epitaxy into the n-doped layer (closest to the Pyrex carrier wafer). A two-layer a-Si/SiO2 DBR top mirror is then deposited, with the top a-Si layer thickness determined by transfer matrix simulations [27] such that the top mirror reflectance target of 93% is achieved. A full 2-period a-Si/SiO2 DBR, deposited on SiGe, has a reflectance of 98% in air. By depositing a 35 nm top a-Si layer instead of the full 98 nm quarter-wave a-Si layer, the reflectance is reduced to 93% at 1440 nm.
Following deposition of the mirror, vias are dry etched through the insulating top mirror layers to reach the p- and n- doped regions. Electrical contacts are formed by e-beam evaporation of Ti/Pt/Au followed by a liftoff step. The structures are electrically contacted using standard 100-um pitch ground-signal-ground high-speed probes.
3. Device characterization
3.1. DC measurements
The fabricated modulators exhibit good electrical performance, with IV curves of the p-i-n diodes showing a reverse breakdown voltage near 15 V. The dark current is 4 mA/cm2 at 1 V reverse bias and 17 mA/cm2 at 5 V reverse bias, indicating low defect density in the epitaxial layers, as well as good surface passivation [28]. These values compare favorably to a recently reported Ge/SiGe MQW photodetector fabricated using a similar growth method, which had 19 mA/cm2 dark current at 1 V reverse bias [29].
The basic experimental setup (used for both DC and high-speed measurements) is illustrated in Fig. 3. To perform DC photocurrent and reflection measurements, light from a 1369–1481 nm fiber-coupled tunable laser source is sent through a polarization controller then collimated using a pigtailed fiber collimator. The linearly polarized light then passes directly through a polarizing beam splitter and a quarter-wave plate. The beam is focused onto the surface of the device at normal incidence using a Mitutoyo 10x long working distance near-infrared microscope objective. The reflected light travels back through the microscope objective and quarter-wave plate. By passing through the quarter-wave plate twice, the reflected beam polarization is rotated 90 degrees relative to the incident polarization. The polarizing beam splitter thus deflects the reflected light, and it is focused onto a germanium detector.
Fig. 3 Simplified diagram of the experimental setup. The instrumentation shown is for large-signal high-speed measurements. DC measurements and small-signal high-speed measurements use the same optical train but different measurement equipment, as described in Sec. 3.1 and 3.2, respectively.
To measure the DC behavior of the device, a voltage is applied across the modulator. The tunable laser’s internal modulation is used to generate an incident optical signal modulated at 1.5 kHz. Photocurrent corresponding to optical absorption in the modulator under test is collected using a current preamplifier then measured using a lock-in detection scheme. The reflected optical signal intensity is measured by attaching the output of the Ge photodetector to a second lock-in amplifier.
Figure 4(a) shows the collected photocurrent as a function of applied reverse bias voltage. Around the cavity resonance at 1430 nm, absorption in the QWs decreases as the applied reverse bias is increased, and thus the collected photocurrent decreases. The full width half maximum (FWHM) of the cavity resonance is 20 nm, corresponding to a Q ≈ 70.
Fig. 4 DC modulator performance. (a) Photocurrent spectra for different applied reverse bias voltages. (b) Corresponding reflection spectra for the same set of applied voltages. (c) Spectra showing the extinction ratio versus wavelength for 1, 2, and 3 V swings, with starting reverse bias of 0.5 V.
The measured reflectance of a 100 μm diameter device (referenced to a > 99.9% reflective broadband dielectric mirror) is shown in Fig. 4(b). As the absorption inside the AFP cavity (measured by photocurrent) decreases, the device reflectance increases. The minimum reflectance of approximately 19% at 1429 nm is achieved for a reverse bias of 0.5 V, where the collected photocurrent is maximized. The nonzero reflectance indicates that the AFP matching condition has not been achieved. This is because the front mirror reflectance is lower than optimal given the amount of electroabsorption at this wavelength. Nonetheless, a useful change in reflectance is still obtained.
Figure 4(c) shows the extinction ratio (ER) corresponding to modulation between different applied voltages. For a 3 V swing, between 0.5 and 3.5 V reverse bias, an ER of 3.4 dB is achieved. A 2V swing, between 0.5 and 2.5 V, yields an ER of 2.8 dB, while a 1.5 V swing between 1V and 2.5V results in an ER of 2.5 dB. There is no observable dependence of the contrast ratio on the incident optical power, up to a maximum tested power of approximately 3 mW (the maximum obtainable from the tunable laser), suggesting that these power levels are below the saturation point of the excitonic absorption. Furthermore, these values are unchanged for electrical modulation frequencies ranging from 10 Hz – 10 MHz, indicating that thermal effects do not substantially impact the modulation depth at these moderate incident power levels.
For practical devices, the absolute change in reflectance, ΔR, can be just as important as the extinction ratio. Due to the relatively low insertion loss of these modulators, a large absolute reflectance modulation on resonance ΔR = 22.9% (from 42.3% to 19.4%) is achieved for a 3 V swing, and ΔR = 15.4% is obtained for a 1.5 V swing. The insertion loss in the high reflectance state is 3.7 dB and 4.4 dB for the 3 V and 1.5 V swings, respectively.
Because the AFP cavity has Q ≈ 70, the optical bandwidth over which substantive modulation can be achieved is large. For a 3 V swing (between 0.5 and 3.5 V), a 2 dB extinction ratio is observed over an optical bandwidth of 1.6 THz (1423–1434 nm), as can be seen in Fig. 4(c). For a 1.5 V swing (between 1 V and 2.5 V), a 2 dB ER is maintained over 1.0 THz (1426–1433 nm).
3.2. High-speed operation
To characterize the high-speed performance of the modulators, measurements were made using the setup depicted in Fig. 3. Large signal modulation was demonstrated using an HP 8133A 3.5 GHz pulse generator producing a non-return to zero (NRZ) 223 – 1 pseudo-random binary sequence (PRBS). Both the pulse generator and a DC power supply (to provide a bias voltage) were connected to the device using a bias-T. An Agilent 86100A Infiniium Digital Communications Analyzer (DCA), connected via a 20 dB pickoff-T, was used to monitor the voltage applied at the modulator. The laser was operated in continuous wave, set to a fixed wavelength, with an optical power of approximately 2 mW incident upon the modulator. The reflected light was focused onto a New Focus 1 GHz photoreceiver, which was connected to one of the electrical input channels of the DCA.
For this measurement, 60 μm diameter devices were tested. An open eye diagram at 2 Gbps data rate with 2.2 V reverse bias and 1 V peak-to-peak swing is shown in Fig. 5(a). The slow rise and fall times are partly due to the limited bandwidth of the photoreceiver used in this measurement.
Fig. 5 High-speed measurement results for a 60 μm diameter device, with 2.2 V DC reverse bias, at a wavelength of 1436 nm. (a) Open eye diagram at 2 Gbps, 1 V swing. (b) Small signal measurement of the optical modulation showing a 3 dB modulation bandwidth of 3.5 GHz, and measurable response beyond 10 GHz.
The small-signal response of the devices was also characterized. The electrical output of an HP 8703A 20 GHz Lightwave Component Analyzer (LCA) provided the modulating signal. The reflected beam was coupled into a single mode fiber, and was fed into the optical input of the LCA. The response curve is shown in Fig. 5(b), for a 2.2 V DC reverse bias. A 3 dB bandwidth of 3.5 GHz is measured, with observable modulation extending beyond 10 GHz.
In AFPMs based on the QCSE, the device speed is determined primarily by the RC delay rather than the carrier transit time [30]. From the forward bias portion of the IV curve for the 60 μm device, the series resistance was determined to be less than 200 Ω. The capacitance of the p-i-n device can be estimated using a parallel plate approximation, C = εA/xd, where ε is the dielectric constant of the SiGe intrinsic region, A is the surface area of the modulator pillar, and xd is the depletion width, which for low bias voltages is approximately 500 nm. This yields an expected capacitance of C ≈ 750 fF and hence a characteristic RC time in the range of 150 ps. The switching energy per bit of 1/4 C(Von − Voff)2[31] is approximately 190 fJ/bit for a 1 V swing.
It is expected that the modulation bandwidth and switching energy can be improved by decreasing the device diameter, which will lower the capacitance. For a 10 μm diameter device using the same epitaxial layer structure, the capacitance would be approximately 20 fF and the switching energy per bit for a 1 V swing would be 5 fJ. It should be noted, however, that the energy consumption due to dissipated photocurrent may also become significant in these small devices [8, 31].
The modulation bandwidth of the AFPMs can also be further improved by decreasing the resistance. In particular, the n-contact may be a significant contributor to the series resistance. It is been shown elsewhere that contact resistance to n-doped germanium can be substantially reduced by an ALD TiO2 layer which depins the Fermi level at the interface [32]. Additionally, by reducing the device size, the distributed RC (ie., the diffusive conduction time) will also be reduced [33].
Implementing the improvements described above, it should be possible to achieve modulation rates in the tens of gigahertz. A 3 dB modulation bandwidth of 37 GHz has been previously demonstrated in 16 x 20 μm AFPMs operating at 864 nm using a GaAs/AlGaAs material system [30].
4. Conclusion
We have demonstrated asymmetric Fabry-Perot electroabsorption modulators using Ge/SiGe quantum wells grown on silicon substrates. The surface-normal configuration makes dense 2-D array integration possible, which could enable a system architecture suitable for high-bandwidth, low-power free-space optical interconnects between silicon chips. The high-speed measurements of the 60 μm diameter devices indicate substantial promise for modulation at tens of GHz in smaller devices, with energy per bit in the tens of fJ.
The relatively moderate extinction ratios (< 4 dB) reported here can be further improved by better matching the top mirror reflectance to the absorption provided by the QW epitaxy at the operation wavelength. The insertion loss of the device can also be improved by changing the resonant cavity thickness to move the resonance to longer wavelengths, such that the absorption from the Ge indirect bandgap is decreased [34]. For interconnect applications, an extinction ratio of at least 7 dB is desirable, although 4 – 5 dB may be sufficient [2].
While the devices presented here operate in the wavelength range of 1400–1450 nm, the addition of silicon to the quantum wells [8] or application of strain via high silicon content barriers [35] can enable modulation at 1300 nm. Likewise, modulation in the telecommunications ”C” band around 1550 nm can be achieved by application of a DC bias, as can be seen in Fig. 1(b), or by operation at higher temperatures, since the absorption band edge redshifts by approximately 0.8nm/°C [5].
The film transfer process, which involves anodic bonding to a Pyrex carrier wafer, produces chips suitable for flip-chip bonding to silicon circuits, but an alternative process is necessary for monolithic integration with CMOS circuitry. Possible approaches include the use of a double SOI wafer [36] to serve as one of the DBR reflectors [12], or performing a backside etch followed by deposition of a bottom DBR mirror [37].
Acknowledgments
The authors thank Kelley Rivoire for her assistance with low-temperature measurements to determine background absorption mechanisms in the SiGe epitaxy. This work is supported by DARPA under Agreement No. HR0011-08-09-0001 between Oracle and the Government, the Semiconductor Research Corporation Interconnect Focus Center, and the Stanford Graduate Fellowship program. 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, its lab members, and the industrial members of the Stanford Center for Integrated Systems. This research was funded in part by the US Government. The views and conclusions contained in this document are those of the authors and should not be interpreted to represent the official policies, either expressed or implied, of the US Government.
References and links
1. D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE 97, 1166–1185 (2009). [CrossRef]
2. G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4, 518–526 (2010). [CrossRef]
3. J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators,” Nat. Photonics 2, 433–437 (2008). [CrossRef]
4. D. Feng, S. Liao, H. Liang, J. Fong, B. Bijlani, R. Shafiiha, B. J. Luff, Y. Luo, J. Cunningham, A. V. Krishnamoorthy, and M. Asghari, “High speed GeSi electro-absorption modulator at 1550 nm wavelength on SOI waveguide,” Opt. Express 20, 22224–22232 (2012). [CrossRef] [PubMed]
5. Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris, “Quantum-confined Stark effect in Ge/SiGe quantum wells on Si for optical modulators,” IEEE J. Sel. Top. Quantum Electron. 12, 1503–1513 (2006). [CrossRef]
6. S. Ren, Y. Rong, T. I. Kamins, J. S. Harris, and D. A. B. Miller, “Selective epitaxial growth of Ge/Si0.15Ge0.85 quantum wells on Si substrate using reduced pressure chemical vapor deposition,” Appl. Phys. Lett. 98, 151108 (2011). [CrossRef]
7. R. K. Schaevitz, J. E. Roth, S. Ren, O. Fidaner, and D. A. B. Miller, “Material properties of Si-Ge/Ge quantum wells,” IEEE J. Sel. Top. Quantum Electron. 14, 1082–1089 (2008). [CrossRef]
8. R. Schaevitz, E. Edwards, J. Roth, E. Fei, Y. Rong, P. Wahl, T. Kamins, J. Harris, and D. Miller, “Simple electroabsorption calculator for designing 1310 nm and 1550 nm modulators using germanium quantum wells,” IEEE J. Quantum Electron. 48, 187–197 (2012). [CrossRef]
9. L. Lever, Z. Ikonic, A. Valavanis, J. Cooper, and R. Kelsall, “Design of Ge/SiGe quantum-confined Stark effect electroabsorption heterostructures for CMOS compatible photonics,” J. Lightwave Technol. 28, 3273–3281 (2010).
10. J. E. Roth, O. Fidaner, R. K. Schaevitz, Y. Kuo, T. I. Kamins, J. S. Harris, and D. A. B. Miller, “Optical modulator on silicon employing germanium quantum wells,” Opt. Express 15, 5851–5859 (2007). [CrossRef] [PubMed]
11. Y. Rong, Y. Ge, Y. Huo, M. Fiorentino, M. Tan, T. Kamins, T. Ochalski, G. Huyet, and J. Harris, “Quantum-confined Stark effect in Ge/SiGe quantum wells on Si,” IEEE J. Sel. Top. Quantum Electron. 16, 85–92 (2010). [CrossRef]
12. E. H. Edwards, R. M. Audet, S. A. Claussen, R. K. Schaevitz, E. Tasyurek, S. Ren, O. I. Dosunmu, M. S. Ünlü, and D. A. B. Miller, “Si-Ge surface-normal asymmetric Fabry-Perot quantum-confined Stark effect electroabsorption modulator,” in “Proc. IEEE Photonics Society Summer Topical Meetings, Playa del Carmen, Mexico,” 211–212 (2010).
13. S. Ren, Y. Rong, S. Claussen, R. Schaevitz, T. Kamins, J. Harris, and D. Miller, “A Ge/SiGe quantum well waveguide modulator monolithically integrated with SOI waveguides,” in “2011 8th IEEE International Conference on Group IV Photonics (GFP),” 11–13 (2011). [CrossRef]
14. P. Chaisakul, D. Marris-Morini, M.-S. Rouifed, G. Isella, D. Chrastina, J. Frigerio, X. Le Roux, S. Edmond, J.-R. Coudevylle, and L. Vivien, “23 GHz Ge/SiGe multiple quantum well electro-absorption modulator,” Opt. Express 20, 3219–3224 (2012). [CrossRef] [PubMed]
15. M. Whitehead and G. Parry, “High-contrast reflection modulation at normal incidence in asymmetric multiple quantum well Fabry-Perot structure,” Electron. Lett. 25, 566–568 (1989). [CrossRef]
16. R. H. Yan, R. J. Simes, and L. A. Coldren, “Surface-normal electroabsorption reflection modulators using asymmetric Fabry-Perot structures,” IEEE J. Quantum Electron. 27, 1922–1931 (1991). [CrossRef]
17. C. C. Barron, C. J. Mahon, B. J. Thibeault, and L. A. Coldren, “Design, fabrication and characterization of high-speed asymmetric Fabry-Perot modulators for optical interconnect applications,” Opt. Quantum Electron. 25, S885–S898 (1993). [CrossRef]
18. F. B. McCormick, T. J. Cloonan, F. A. P. Tooley, A. L. Lentine, J. M. Sasian, J. L. Brubaker, R. L. Morrison, S. L. Walker, R. J. Crisci, R. A. Novotny, S. J. Hinterlong, H. S. Hinton, and E. Kerbis, “Six-stage digital free-space optical switching network using symmetric self-electro-optic-effect devices,” Appl. Opt. 32, 5153–5171 (1993). [CrossRef] [PubMed]
19. A. G. Kirk, D. V. Plant, T. H. Szymanski, Z. G. Vranesic, F. A. P. Tooley, D. R. Rolston, M. H. Ayliffe, F. K. Lacroix, B. Robertson, E. Bernier, and D. F. Brosseau, “Design and implementation of a modulator-based free-space optical backplane for multiprocessor applications,” Appl. Opt. 42, 2465–2481 (2003). [CrossRef] [PubMed]
20. M. Haney, M. Christensen, P. Milojkovic, G. Fokken, M. Vickberg, B. Gilbert, J. Rieve, J. Ekman, P. Chandramani, and F. Kiamilev, “Description and evaluation of the FAST-Net smart pixel-based optical interconnection prototype,” Proc. IEEE 88, 819–828 (2000). [CrossRef]
21. R. M. Audet, E. H. Edwards, P. Wahl, and D. A. B. Miller, “Investigation of limits to the optical performance of asymmetric Fabry-Perot electroabsorption modulators,” IEEE J. Quantum Electron. 48, 198–209 (2012). [CrossRef]
22. 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, 2815–2817 (2004). [CrossRef]
23. S. Ren, “Ge/SiGe quantum well waveguide modulator for optical interconnect systems,” Ph.D. thesis, Stanford University (2011).
24. P. Zouganeli, P. J. Stevens, D. Atkinson, and G. Parry, “Design trade-offs and evaluation of the performance attainable by GaAs – Al0.3Ga0.7As asymmetric Fabry-Perot modulators,” IEEE J. Quantum Electron. 31, 927–943 (1995). [CrossRef]
25. P. Zouganeli and G. Parry, “Evaluation of the tolerance of asymmetric Fabry-Perot modulators with respect to realistic operating conditions,” IEEE J. Quantum Electron. 31, 1140–1151 (1995). [CrossRef]
26. M. Schmidt, “Wafer-to-wafer bonding for microstructure formation,” Proc. IEEE 86, 1575–1585 (1998). [CrossRef]
27. C. L. Mitsas and D. I. Siapkas, “Generalized matrix method for analysis of coherent and incoherent reflectance and transmittance of multilayer structures with rough surfaces, interfaces, and finite substrates,” Appl. Opt. 34, 1678–1683 (1995). [CrossRef] [PubMed]
28. L. M. Giovane, H.-C. Luan, A. M. Agarwal, and L. C. Kimerling, “Correlation between leakage current density and threading dislocation density in SiGe p-i-n diodes grown on relaxed graded buffer layers,” Appl. Phys. Lett. 78, 541–543 (2001). [CrossRef]
29. E. Onaran, M. C. Onbasli, A. Yesilyurt, H. Y. Yu, A. M. Nayfeh, and A. K. Okyay, “Silicon-germanium multi-quantum well photodetectors in the near infrared,” Opt. Express 20, 7608 (2012). [CrossRef] [PubMed]
30. C. Barron, C. Mahon, B. Thibeault, G. Wang, W. Jiang, L. Coldren, and J. Bowers, “Millimeter-wave asymmetric Fabry-Perot modulators,” IEEE J. Quantum Electron. 31, 1484–1493 (1995). [CrossRef]
31. D. A. B. Miller, “Energy consumption in optical modulators for interconnects,” Opt. Express 20, A293–A308 (2012). [CrossRef] [PubMed]
32. J. J. Lin, A. M. Roy, A. Nainani, Y. Sun, and K. C. Saraswat, “Increase in current density for metal contacts to n-germanium by inserting TiO2 interfacial layer to reduce Schottky barrier height,” Appl. Phys. Lett. 98, 092113 (2011). [CrossRef]
33. S. A. Claussen, E. Tasyurek, J. E. Roth, and D. A. B. Miller, “Measurement and modeling of ultrafast carrier dynamics and transport in germanium/silicon-germanium quantum wells,” Opt. Express 18, 25596–25607 (2010). [CrossRef] [PubMed]
34. R. K. Schaevitz, D. S. Ly-Gagnon, J. E. Roth, E. H. Edwards, and D. A. B. Miller, “Indirect absorption in germanium quantum wells,” AIP Advances 1, 032164 (2011). [CrossRef]
35. M. S. Rouifed, P. Chaisakul, D. Marris-Morini, J. Frigerio, G. Isella, D. Chrastina, S. Edmond, X. L. Roux, J.-R. Coudevylle, and L. Vivien, “Quantum-confined Stark effect at 1.3 μm in Ge/Si0.35Ge0.65 quantum-well structure,” Opt. Lett. 37, 3960–3962 (2012). [CrossRef] [PubMed]
36. O. Dosunmu, D. Cannon, M. Emsley, L. Kimerling, and M. Unlu, “High-speed resonant cavity enhanced Ge photodetectors on reflecting Si substrates for 1550-nm operation,” IEEE Photon. Technol. Lett. 17, 175–177 (2005). [CrossRef]
37. J. Potfajova, B. Schmidt, M. Helm, T. Gemming, M. Benyoucef, A. Rastelli, and O. G. Schmidt, “Microcavity enhanced silicon light emitting pn-diode,” Appl. Phys. Lett. 96, 151113 (2010). [CrossRef]
