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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 1 — Jan. 14, 2013
  • pp: 867–876
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Low-voltage broad-band electroabsorption from thin Ge/SiGe quantum wells epitaxially grown on silicon

Elizabeth H. Edwards, Leon Lever, Edward T. Fei, Theodore I. Kamins, Zoran Ikonic, James S. Harris, Robert W. Kelsall, and David A. B. Miller  »View Author Affiliations


Optics Express, Vol. 21, Issue 1, pp. 867-876 (2013)
http://dx.doi.org/10.1364/OE.21.000867


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Abstract

We demonstrate electroabsorption contrast greater than 5 dB over the entire telecommunication S- and C-bands with only 1V drive using a new Ge/SiGe QW epitaxy design approach; further, this is demonstrated with the thinnest Ge/SiGe epitaxy to date, using a virtual substrate only 320-nm-thick. We use an eigenmode expansion method to model the optical coupling between SOI waveguides and both vertically and butt-coupled Ge/SiGe devices, and show that this reduction in thickness is expected to lead to a significant improvement in the insertion loss of waveguide-integrated devices.

© 2013 OSA

1. Introduction

Improving the efficiency of optical interconnects is critical to the economic and environmental sustainability of the projected growth of data transmission needed for the rapid expansion of communication, commerce, and computation. The adoption of Si photonics technology hinges on meeting power efficiency requirements [11

11. D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE 97, 1166–1185 (2009). [CrossRef]

], and a low drive voltage (1V or less) is particularly important for CMOS compatibility and minimizing energy dissipation [12

12. D. A. B. Miller, “Energy consumption in optical modulators for interconnects,” Opt. Express 20, A293–A308 (2012). [CrossRef] [PubMed]

]. In addition, C-band (1530–1565 nm) wavelength modulation is desired for telecommunication, and compatibility with integrated photonic platforms requires compact form factors. High-speed devices generally require small capacitive footprints to avoid resistance-capacitance limitations, and in-plane, e.g., waveguide and microdisk active devices, should be comparable in thickness to SOI device layers.

Strong electroabsorption modulation can be obtained using multiple quantum well (MQW) layers via the quantum-confined Stark effect (QCSE) [13

13. D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Band edge electro-absorption in quantum well structures: The quantum confined stark effect,” Phys. Rev. Lett. 53, 2173–2176 (1984). [CrossRef]

,14

14. D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Electric field dependence of optical absorption near the band gap of quantum well structures,” Phys. Rev. B 32, 1043–1060 (1985). [CrossRef]

], which is now the dominant technology for optical modulation in III–V semiconductor systems. The effect was first demonstrated in a silicon-based platform using Ge/SiGe QWs in 2005 [15

15. Y. H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris, “Strong quantum-confined stark effect in germanium quantum well structures on silicon,” Nature 437, 1334–1336 (2005). [CrossRef] [PubMed]

] and has since been explored in a range of structural configurations including surface-normal [1

1. 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]

], side-entry [2

2. J. Roth, O. Fidaner, E. Edwards, R. Schaevitz, Y.-H. Kuo, N. Herman, T. Kamins, J. Harris, and D. Miller, “C-band side-entry Ge quantum-well electroabsorption modulator on SOI operating at 1 V swing,” Electron. Lett. 44, 49 –50 (2008). [CrossRef]

], waveguide [6

6. O. Fidaner, A. Okyay, J. Roth, R. Schaevitz, Y.-H. Kuo, K. Saraswat, J. Harris, and D. Miller, “Ge\SiGe quantum well waveguide photodetectors on silicon for the near infrared,” IEEE Photon. Technol. Lett. 19, 1631 –1633 (2007). [CrossRef]

], and microdisk [3

3. E. H. Edwards, R. M. Audet, E. Fei, G. Shambat, R. Schaevitz, Y. Rong, S. Claussen, T. Kamins, J. Vuckovic, J. S. Harris, and D. A. B. Miller, “Ge quantum well resonator modulators,” in “2011 8th IEEE International Conf. on Group IV Photonics (GFP),” (2011), pp. 80–82.

]. However, the design and epitaxial growth of Ge/SiGe films on Si substrates are complicated by differences in lattice constants and thermal expansion coefficients.

The strain induced by the lattice mismatch between Ge and Si may be accommodated by inserting an epitaxially grown, relaxed buffer layer between the Si substrate and the QW layers. These buffer layers are necessary to facilitate the growth of mechanically stable Ge/SiGe MQW stacks by providing strain compensation, since the MQW layers would relax if epitaxially grown on a Si substrate. During crystal relaxation, misfit dislocations form, with some threading dislocations terminating at the surface. Therefore, as well as providing strain compensation, a critical function of the buffer layer is to provide a trap for misfit dislocations and reduce the threading dislocation defect density of the growth surface for the quantum well layers.

Previously demonstrated buffer layers have ranged in thickness from 500 nm to 13 μm [1

1. 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]

, 2

2. J. Roth, O. Fidaner, E. Edwards, R. Schaevitz, Y.-H. Kuo, N. Herman, T. Kamins, J. Harris, and D. Miller, “C-band side-entry Ge quantum-well electroabsorption modulator on SOI operating at 1 V swing,” Electron. Lett. 44, 49 –50 (2008). [CrossRef]

, 4

4. P. Chaisakul, D. Marris-Morini, M.-S. Rouifed, G. Isella, D. Chrastina, J. Frigerio, X. L. 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]

6

6. O. Fidaner, A. Okyay, J. Roth, R. Schaevitz, Y.-H. Kuo, K. Saraswat, J. Harris, and D. Miller, “Ge\SiGe quantum well waveguide photodetectors on silicon for the near infrared,” IEEE Photon. Technol. Lett. 19, 1631 –1633 (2007). [CrossRef]

, 15

15. Y. H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris, “Strong quantum-confined stark effect in germanium quantum well structures on silicon,” Nature 437, 1334–1336 (2005). [CrossRef] [PubMed]

, 17

17. P. Chaisakul, D. Marris-Morini, G. Isella, D. Chrastina, X. L. Roux, E. Gatti, S. Edmond, J. Osmond, E. Cassan, and L. Vivien, “Quantum-confined Stark effect measurements in Ge/SiGe quantum-well structures,” Opt. Lett. 35, 2913–2915 (2010). [CrossRef] [PubMed]

]. However, thick buffers are not desirable due to the time and expense required to grow them and because non-planar surfaces pose difficulty for integration with CMOS. Furthermore, SOI waveguide layers employed in silicon photonic chips are typically either 220 or 400-nm-thick, and the resulting difference in thickness between the device and the access waveguide complicates the design of optical modulators. A similar problem occurs in hybrid III–V/silicon laser structures, in which the thickness difference has been circumvented by vertical coupling, rather than butt-coupling, of the active device and waveguide [18

18. A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bowers, “Electrically pumped hybrid AlGaInAs-silicon evanescent laser,” Opt. Express 14, 9203–9210 (2006). [CrossRef] [PubMed]

]. However, as discussed in Section 5, thin buffer layers are still preferred in the vertical coupling geometry, in order to achieve high coupling efficiencies.

In order to reduce the required epitaxy layer thickness without compromising epitaxy quality, we propose a new design for Ge/SiGe MQWs grown on Si substrates to reduce strain accumulation, preventing the formation of crystal dislocations. This is important to device performance and efficiency because such defects in the crystal structure correlate with leakage current [16

16. L. M. Giovane, H. 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]

]. In addition to affecting power efficiency, such conductive paths can lead to uneven electric field distribution over the QWs. This causes exciton peak broadening resulting in lower electroabsorption contrast ratios. Using this design, we show that electroabsorption contrast greater than 5 dB is possible over the entire telecommunication S- and C-bands with only 1V drive; further, this is demonstrated with the thinnest Ge/SiGe epitaxy to date, using a virtual substrate only 320-nm-thick. We have carried out simulations of the optical mode propagation in Ge/SiGe epitaxial systems on silicon, and show that this reduction in the thickness of the epitaxial layers significantly improves the optical properties of waveguide-integrated devices. Our results demonstrate the potential for room-temperature waveguide-integrated electroabsorption devices operating across all of the S-band and C-band with a 1V swing.

2. Thin epitaxy design

However, during cooling, x-ray diffraction (XRD) measurement showed that the SiGe film becomes 0.18% tensile-strained, due to the larger thermal expansion coefficient of Ge and incomplete relaxation during annealing. The XRD measurement was performed on a test sample containing only epitaxial buffer layers grown according to the process described in Section 3. The XRD measurement showed that the parallel lattice constant mismatch in the SiGe buffer was found to be uniformly 38986 ppm (3.8986%) of Si, and the perpendicular lattice constant mismatch was 3.5699%. Because the ratio of in- to out-of-plane lattice constant is greater than one, the crystal is deformed by tensile strain. The percentage tensile strain (0.18%) was calculated by comparing the measured strained SiGe in-plane lattice parameter with the theoretical relaxed lattice constant (which is the same in both perpendicular and parallel directions). SiGe does not quite follow Vegard’s law, so the theoretical relaxed lattice constant is calculated using aSiGe_relaxed = aSi(1 + ε) where ε = (aSi1−xGexaSi)/aSi = 0.00501x2 + 0.03675x. The in-plane strain is therefore 1 − aSiGe_measured/aSiGe_relaxed = −0.18%, with the negative value indicating tensile strain. Additionally, a reciprocal space map (RSM) was taken of a similar test epitaxial structure, which indicated that the growth above the buffer maintained the same lattice constant as the buffer after cooling to room temperature.

Table 1. Epitaxy design for the Ge/SiGe QW structure grown on silicon.

table-icon
View This Table

3. Device fabrication

This epitaxial structure of Table 1 was grown on lightly p-doped <100> Si wafers using RP-CVD at a chamber pressure of 40 mTorr. The boron-doped buffer was grown in three stages. After each third of the total buffer thickness was grown at 400°C the whole structure was hydrogen annealed in-situ for 30 minutes at 800°C. The rest of the structure was grown at 400°C. Thin undoped spacers were grown before and after the QW regions to reduce dopant diffusion from the p- and n-doped regions into the active region, which consists of five nominally 12 nm Ge QWs separated by 17nm Si0.19Ge0.81 barriers.

An atomic force microscope (AFM) image taken of the finished epitaxy revealed surface roughness <0.2 nm RMS (Fig. 1(a)). A cross-sectional bright-field transmission electron microscope (TEM) image of the finished structure is shown in Fig. 1(b) clearly showing the five QWs along with some crystal dislocation defects. An accurate exact threading dislocation defect count could not be obtained from the AFM or TEM, but given that they are visible within small TEM cross sections, we estimate the count to be between 3x107 cm−2 and 1x1010 cm−2. The apparent discrepancies between design and TEM thicknesses are noted in Table 1, and could be explained by variation in machine condition between the time of calibration and final growth run or layer thickness variation across the wafer, which can be seen even over small ranges in the TEM.

Fig. 1 (a) Surface AFM showing 0.162 nm RMS roughness. To emphasize the majority of the behavior, the color bar shows variations from −0.5 to +0.3 nm. White regions indicate positive variations beyond 0.3 nm. The minimum and maximum were −0.485 nm and 2.078 nm. (b) Cross-sectional TEM image of the epitaxial structure.

To facilitate photocurrent collection, test p-i-n diodes were fabricated by vertically dry etching square structures through the Ge/SiGe QW epitaxy down to the p-doped SiGe region to form electrically isolated devices. Ti/Pt ring contacts were deposited by electron-beam evaporation.

4. Experimental results

The devices were illuminated using a tunable laser with a lensed fiber, and photocurrent resulting from absorption was measured using a lock-in current amplifier. Photocurrent absorption spectra are shown in Fig. 2(a) for a range of DC biases. Photocurrent absorption contrast ratios with a 1-V-swing are shown in Fig. 2(b); contrast greater than 5dB (3dB) was achieved for a 1V (0.4V) swing throughout the range 1449 – 1580 nm, demonstrating for the first time that useful modulation contrast [27

27. G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4, 518–526 (2010). [CrossRef]

] is obtainable over the entire telecom S-band (1460 – 1530 nm) and C-band (1530 – 1565 nm) at room temperature using the QCSE with Ge/SiGe QWs.

Fig. 2 (a) Absorption-per-pass spectra deduced from vertical photocurrent measurements from a 5QW Ge/SiGe QW epitaxy embedded in a diode with a 220nm intrinsic region. (b) Photocurrent absorption contrast ratios at 1V swing with biases between 0.1V forward and 2.3V reverse.

The thin epitaxy improves the potential of integration with CMOS and photonic silicon-on-insulator (SOI) platforms. This reduction in the thickness of the epitaxial layers will enable significantly improved optical coupling to SOI waveguides by reducing the mismatch between the optical modes of the SOI waveguide and the Ge/SiGe epitaxial device layer. The epitaxy design was <560 nm, including the virtual substrate. The TEM taken from a wafer section (Table 1) estimates an as-grown thickness of 614nm. However, some of the n-doped cap could be removed by polishing using a technique similar to [5

5. E. H. Edwards, R. M. Audet, E. T. Fei, S. A. Claussen, R. K. Schaevitz, E. Tasurek, Y. Rong, T. I. Kamins, J. S. Harris, and D. A. B. Miller, “Ge/SiGe asymmetric Fabry-Perot quantum well electroabsorption modulators,” Opt. Express 20, 29164–29173 (2012). [CrossRef]

] to render the structure thickness commensurate with, or even thinner than, the design thickness.

5. Discussion

5.1. Effect of epitaxy thickness on coupling losses

In order to assess the effect of the total thickness of the epitaxy on the optical coupling losses between the SOI waveguide core and the Ge/SiGe device waveguide, we performed eigenmode expansion method [28

28. “www.photond.com,” (2012).

] simulations for both vertically- and butt-coupled approaches. The proposed vertically-coupled structure is illustrated in Fig. 3(a). We modeled a 600-nm-wide strip waveguide in 400-nm SOI, and used a linear taper to couple the input mode shown in Fig. 3(b) into the mode of the device section, shown in Fig. 3(c). These simulations were carried out for various device thicknesses and as a function of the length of the taper. In order to assess the coupling efficiency between the modes of the SOI waveguide core and of the device, we neglected the losses in the layers due to free carrier absorption and interband absorption. The results are shown in Fig 4. The taper length required to provide efficient mode conversion is strongly dependent on the total thickness of the epitaxial layers. Ge/SiGe MQW devices reported to date have total thicknesses of 900 nm or more [1

1. 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]

10

10. E. Gatti, E. Grilli, M. Guzzi, D. Chrastina, G. Isella, and H. von Kanel, “Room temperature photoluminescence of Ge multiple quantum wells with Ge-rich barriers,” Appl. Phys. Lett. 98, 031106 (2011). [CrossRef]

, 15

15. Y. H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris, “Strong quantum-confined stark effect in germanium quantum well structures on silicon,” Nature 437, 1334–1336 (2005). [CrossRef] [PubMed]

, 17

17. P. Chaisakul, D. Marris-Morini, G. Isella, D. Chrastina, X. L. Roux, E. Gatti, S. Edmond, J. Osmond, E. Cassan, and L. Vivien, “Quantum-confined Stark effect measurements in Ge/SiGe quantum-well structures,” Opt. Lett. 35, 2913–2915 (2010). [CrossRef] [PubMed]

, 23

23. S. Ren, Y. Rong, S. Claussen, R. Schaevitz, T. Kamins, J. Harris, and D. Miller, “Ge/SiGe quantum well waveguide modulator monolithically integrated with SOI waveguides,” IEEE Photon. Technol. Lett. 24, 461–463 (2012). [CrossRef]

, 24

24. P. Chaisakul, D. Marris-Morini, M. Rouifed, G. Isella, D. Chrastina, J. Frigerio, X. Le Roux, S. Edmond, J. Coudevylle, and L. Vivien, “23 GHz Ge/SiGe multiple quantum well electro-absorption modulator,” Opt. Express 20, 3219–3224 (2012). [CrossRef] [PubMed]

], requiring a waveguide taper length of more than 100 μm to provide efficient mode coupling. However, if this total thickness can be reduced to 600 nm, we can see that the required taper length is reduced by a factor of more than two.

Fig. 3 (a) Schematic of the vertically-coupled lateral taper device geometry. The strip waveguide is 600-nm-wide and is etched into 400-nm-thick SOI. (b) The incoming optical mode in the SOI waveguide core is transformed into the mode in the SiGe device section (c) using the tapered mode adapters.
Fig. 4 (a) The coupling efficiency of the vertically-coupled lateral tapers as a function of the taper length for various total thicknesses of the Ge/SiGe epitaxial layers. (b) The taper length when the coupling loss is −0.05 dB, with a power-law fit giving an exponent of 2.28.

Alternatively, waveguide integration can be achieved using a butt-coupled geometry, whereby a recess is etched into the 400-nm-wide, 400-nm-thick Si waveguide core layer, and epitaxial growth proceeds in this recess. This scheme is similar to that described in [23

23. S. Ren, Y. Rong, S. Claussen, R. Schaevitz, T. Kamins, J. Harris, and D. Miller, “Ge/SiGe quantum well waveguide modulator monolithically integrated with SOI waveguides,” IEEE Photon. Technol. Lett. 24, 461–463 (2012). [CrossRef]

], except that the recess should not be completely etched through the top Si layer: rather, a 10-nm-thick Si layer should be left on which the epitaxial growth can proceed. The resulting structure will have a discontinuity in the thickness, and the device section will be able to support multiple vertical modes, which may be excited by the fundamental mode of the incoming SOI waveguide. This leads to multi-mode interference and coherent reimaging at the output SOI waveguide, and an oscillation in the coupling loss as a function of the device length. Figure 5(a) shows the calculated coupling loss as a function of the device length for 900-nm-thick epitaxial layers, and Fig. 5(b) shows the coupling loss for 560-nm-thick epitaxial layers. Because the 560-nm-thick epitaxial layers support fewer vertical optical modes, the magnitude of the oscillations in the coupling loss is markedly reduced.

Fig. 5 (a) The optical coupling losses from a butt-coupled geometry with epitaxial layers and a total thickness of 900 nm. (b) The optical coupling losses for a butt coupled geometry with a 560-nm-thick epitaxial structure.

If we include the absorption in the different layers that arise from interband absorption in the MQW layers at the on and off bias states, as well as free-carrier absorption in the doped layers, we may determine the expected insertion loss and extinction ratio of a device based on this butt-coupled geometry. This is shown in Fig. 6(a) at 1550 nm and Fig. 6(b) at 1490 nm as a function of the length of the device, both with a 1V swing. The periodic fluctuations in the insertion loss arise from the coherent reimaging of multiple modes, and the smaller periodic fluctuation in the extinction ratio occurs because of the perturbation to the mode indices that results from the change in the absorption coefficient of MQW layers, and because the losses of the different modes may be affected differently when the loss of the MQW layer is varied. We find that, at 1550 nm, a 200-μm-long device is expected to have an extinction ratio of 6.5 dB and an insertion loss of 3.5 – 4.5 dB, depending on the exact device length. This same device is expected to have an extinction ratio of 15 dB at 1490 nm with an insertion loss of 6.5 – 8 dB.

Fig. 6 The insertion loss (green) and extinction ratio (red) of the butt-coupled geometry device as a function of its length. (a) At 1550 nm and (b) at 1490 nm.

5.2. Effect of epitaxy thickness on modulator energy efficiency

6. Conclusion

Acknowledgments

This work is supported by DARPA under Agreement No. HR0011-08-09-0001 between Oracle and the Government, the SRC FCRP Interconnect Focus Center, and the National Science Foundation Graduate Research Fellowship. Work was performed in part at the Stanford Nanofabrication Facility (a member of the National Nanotechnology Infrastructure Network). 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.

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26.

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 Tech . 28, 3273–3281 (2010).

27.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4, 518–526 (2010). [CrossRef]

28.

www.photond.com,” (2012).

29.

R. Schaevitz, E. H. Edwards, J. E. Roth, E. Fei, Y. Rong, P. Wahl, T. I. Kamins, J. S. 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]

OCIS Codes
(160.2100) Materials : Electro-optical materials
(230.2090) Optical devices : Electro-optical devices
(230.4110) Optical devices : Modulators
(250.3140) Optoelectronics : Integrated optoelectronic circuits

ToC Category:
Optoelectronics

History
Original Manuscript: October 25, 2012
Revised Manuscript: December 19, 2012
Manuscript Accepted: December 19, 2012
Published: January 8, 2013

Citation
Elizabeth H. Edwards, Leon Lever, Edward T. Fei, Theodore I. Kamins, Zoran Ikonic, James S. Harris, Robert W. Kelsall, and David A. B. Miller, "Low-voltage broad-band electroabsorption from thin Ge/SiGe quantum wells epitaxially grown on silicon," Opt. Express 21, 867-876 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-1-867


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References

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  23. S. Ren, Y. Rong, S. Claussen, R. Schaevitz, T. Kamins, J. Harris, and D. Miller, “Ge/SiGe quantum well waveguide modulator monolithically integrated with SOI waveguides,” IEEE Photon. Technol. Lett.24, 461–463 (2012). [CrossRef]
  24. P. Chaisakul, D. Marris-Morini, M. Rouifed, G. Isella, D. Chrastina, J. Frigerio, X. Le Roux, S. Edmond, J. Coudevylle, and L. Vivien, “23 GHz Ge/SiGe multiple quantum well electro-absorption modulator,” Opt. Express20, 3219–3224 (2012). [CrossRef] [PubMed]
  25. P. Harrison, Quantum Wells, Wires and Dots: Theoretical and Computational Physics of Semiconductor Nanostructures, 3rd ed. (Wiley, Chichester, U.K., 2009).
  26. 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 Tech. 28, 3273–3281 (2010).
  27. G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010). [CrossRef]
  28. “ www.photond.com ,” (2012).
  29. R. Schaevitz, E. H. Edwards, J. E. Roth, E. Fei, Y. Rong, P. Wahl, T. I. Kamins, J. S. 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]

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