## The suitability of SiGe multiple quantum well modulators for short reach DWDM optical interconnects |

Optics Express, Vol. 21, Issue 5, pp. 5318-5331 (2013)

http://dx.doi.org/10.1364/OE.21.005318

Acrobat PDF (1120 KB)

### Abstract

We describe calculations that address the suitability at using silicon-germanium multiple quantum well (MQW) modulators in dense wavelength division multiplexed (DWDM) short reach optical interconnects that vary over a significant temperature range. Our calculations indicate that there is a tradeoff between the number of channels, the temperature range and laser power required. Twenty to forty DWDM channels at 100 GHz and 50 GHz channel spacing is possible in DWDM links with a ∼ 12° temperature range with less than a 1 dB laser power penalty compared to the optimum single channel, single temperature case. The same number of channels can be operated over a wider 37° temperature range with laser power penalties of 3 dB. It shows that, even for DWDM systems, silicon-germanium modulators might provide an alternative to ring and disk resonant modulators without the need for stringent (≪ 1°C) temperature control.

© 2013 OSA

## 1. Introduction

1. R. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. **23**(1), 123–129 (1987) [CrossRef] .

2. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature **435**(7040), 325–327 (2005) [CrossRef] [PubMed] .

4. M. R. Watts, W. A. Zortman, D. C. Trotter, R. W. Young, and A. L. Lentine, “Vertical junction silicon microdisk modulators and switches,” Opt. Express **19**(22), 21,989–22,003 (2011) [CrossRef] .

4. M. R. Watts, W. A. Zortman, D. C. Trotter, R. W. Young, and A. L. Lentine, “Vertical junction silicon microdisk modulators and switches,” Opt. Express **19**(22), 21,989–22,003 (2011) [CrossRef] .

5. A. Krishnamoorthy, “Focus Issue on Photonic Materials and Integration Architectures,” IEEE Photon. J. **3**(3), 564 –626 (2011) [CrossRef] .

6. W. A. Zortman, D. C. Trotter, and M. R. Watts, “Silicon photonics manufacturing,” Opt. Express **18**(23), 23598–23607 (2010) [CrossRef] [PubMed] .

5. A. Krishnamoorthy, “Focus Issue on Photonic Materials and Integration Architectures,” IEEE Photon. J. **3**(3), 564 –626 (2011) [CrossRef] .

10. B. Guha, K. Preston, and M. Lipson, “Athermal silicon microring electro-optic modulator,” Opt. Lett. **37**(12), 2253–2255 (2012) [CrossRef] [PubMed] .

11. 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] .

12. N.-N. Feng, D. Feng, S. Liao, X. Wang, P. Dong, H. Liang, C.-C. Kung, W. Qian, J. Fong, R. Shafiiha, Y. Luo, J. Cunningham, A. V. Krishnamoorthy, and M. Asghari, “30GHz Ge electro-absorption modulator integrated with 3*μ*m silicon-on-insulator waveguide,” Opt. Express **19**(8), 7062–7067 (2011) [CrossRef] [PubMed] .

13. 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**(7063), 1334–1336 (2005) [CrossRef] [PubMed] .

14. 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**(6), 461 –463 (2012) [CrossRef] .

14. 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**(6), 461 –463 (2012) [CrossRef] .

15. D. A. B. Miller, “Energy consumption in optical modulators for interconnects,” Opt. Express **20**(S2), A293–A308 (2012) [CrossRef] .

16. 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**(26), 5153–5171 (1993) [CrossRef] [PubMed] .

18. D. A. B. Miller, “Optics for low-energy communication inside digital processors: quantum detectors, sources, and modulators as efficient impedance converters,” Opt. Lett. **14**(2), 146–148 (1989) [CrossRef] [PubMed] .

13. 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**(7063), 1334–1336 (2005) [CrossRef] [PubMed] .

## 2. Figure of Merit

*P*

_{laser}is the power in the laser in Watts,

*T*

_{mod}is the transmission of the modulator,

*T*

_{optics}is the transmission of the optical path, both before the modulator and between the modulator and the detector, and

*R*

_{PD}is the responsivity of the photodiode in A/W.

*T*

_{H}and

*T*

_{L}. Typically a threshold is set in the receiver given by the average of the two states of (

*T*

_{H}+

*T*

_{L})/2 (with

*P*

_{laser}

*T*

_{optics}

*R*

_{PD}= 1). The useful photocurrent that drives the output of a receiver is given by the difference in the signal levels and a threshold. Assuming the threshold is set to the midpoint (average) of the two signal levels, the useful photocurrent for these two cases are given by

*T*

_{H}− (

*T*

_{H}+

*T*

_{L})/2 and

*T*

_{L}− (

*T*

_{H}+

*T*

_{L})/2. In either case, the useful photocurrent is (

*T*

_{H}−

*T*

_{L})/2.

19. G. P. Agarwal, *Fiber-Optic Communication Systems* Wiley series in Microwave and Optical Engineering, 4th ed. (Wiley, 2010) [CrossRef] .

*T*

_{H}+

*T*

_{L})/2]; it is the average power after the modulator as measured with a power meter, not the high-state loss. The power penalty from the finite extinction ratio is 10log[(

*E*+ 1)/(

*E*− 1)] where

*E*is the extinction ratio [19

19. G. P. Agarwal, *Fiber-Optic Communication Systems* Wiley series in Microwave and Optical Engineering, 4th ed. (Wiley, 2010) [CrossRef] .

*T*

_{H}/

*T*

_{L}for

*E*, gives a result of 10log[(

*T*

_{H}−

*T*

_{L})/2] as the figure of merit, and this is the same as the result derived from photocurrent arguments.

21. A. L. Lentine and F. A. P. Tooley, “Relationships between speed and tolerances for self-electro-optic-effect devices,” Appl. Opt. **33**(8), 1354–1367 (1994) [CrossRef] [PubMed] .

*T*

_{H}(1 −

*f*) and

*T*

_{L}(1 +

*f*) for the high and low modulator states respectively where

*f*is the fractional variation in the high and low state transmissivities.

## 3. Quantum well modeling

### 3.1. Fitting experimental room temperature electroabsorption

13. 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**(7063), 1334–1336 (2005) [CrossRef] [PubMed] .

_{0.15}Ge

_{0.85}barriers. The entire structure is capped by 100 nm of Si

_{0.1}Ge

_{0.9}spacer layers on top and bottom. Reference [13

**437**(7063), 1334–1336 (2005) [CrossRef] [PubMed] .

*ab initio*calculation to obtain quantum well absorption spectra at various bias voltages. Such a calculation requires precise knowledge of several parameters like transition matrix elements, band offsets, subband structure at desired electric fields, band dispersion (

*E*–

*K*relationship), and exciton binding energies and linewidths presence and absence of electric fields. Because of relative novelty of Ge/SiGe quantum wells, many of these parameters are either unknown or have to estimated with considerable uncertainty. Further, even

*ab initio*models of quantum well absorption require adjustable parameters to get numerical values for the absorption coefficient [22

22. 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**(2), 187–197 (2012) [CrossRef] .

**437**(7063), 1334–1336 (2005) [CrossRef] [PubMed] .

23. D. Chemla, D. Miller, P. Smith, A. Gossard, and W. Wiegmann, “Room temperature excitonic nonlinear absorption and refraction in GaAs/AlGaAs multiple quantum well structures,” IEEE J. Quantum Electron. **20**(3), 265 –275 (1984) [CrossRef] .

*E*is the energy at which the absorption coefficient

*α*is desired. The rest of the parameters in Eq. (2) are fitting parameters. The subscripts ‘hh’, ‘lh’ and ‘c’ stand, respectively for heavy hole, light hole, and the continuum. The parameters

*α*,

_{i}*E*and

_{i}*W*are the relative strength, the energy onset and the width of the of the transition

_{i}*i*(

*i*= hh, lh or c).

*R*

_{y}is the Rydberg constant of the materials and depends on its relative permittivity and the electron and hole effective masses.

### 3.2. Electroabsorption spectra at elevated temperatures

27. D. Wolpert and P. Ampadu, *Managing Temperature Effects in Nanoscale Adaptive Systems*, 1st ed. (Springer, 2012) [CrossRef] .

*E*

_{g}is the bandgap at temperature

*T*and

*α*and

*β*are the Varshney parameters with values of

*α*= 4.77 × 10

^{−4}eV/K and

*β*= 235 K for Ge [26

26. Y. P. Varshni, “Temperature dependence of the energy gap in semiconductors,” Physica **34**, 149–154 (1967) [CrossRef] .

*W*, is proportional to the phonon population whose distribution is controlled by the Bose-Einstein function. The broadening of the exciton resonance peak is therefore expressed as [23

23. D. Chemla, D. Miller, P. Smith, A. Gossard, and W. Wiegmann, “Room temperature excitonic nonlinear absorption and refraction in GaAs/AlGaAs multiple quantum well structures,” IEEE J. Quantum Electron. **20**(3), 265 –275 (1984) [CrossRef] .

*W*is the width of the exciton resonance,

*T*is the temperature,

*k*is the Boltzmann constant, and

*E*

_{LO}= 36 meV is the LO phonon energy in Ge. The parameter

*γ*quantifies the strength of the exciton-phonon coupling. The subscript

*i*indicates that phonons can impact each of the three transitions in Eq. (2)(

*i*= hh, lh, and c) in Eq. (2) with potentially different strengths

*γ*for each transition. Our literature search, however, did not yield any experimentally measured values of

_{i}*γ*for these transitions in bulk Ge or SiGe quantum wells. We have therefore used the value of

_{i}*γ*for AlGaAs quantum wells reported in [23

_{i}23. D. Chemla, D. Miller, P. Smith, A. Gossard, and W. Wiegmann, “Room temperature excitonic nonlinear absorption and refraction in GaAs/AlGaAs multiple quantum well structures,” IEEE J. Quantum Electron. **20**(3), 265 –275 (1984) [CrossRef] .

*γ*in our calculations using the following reasons. First, quantum well absorption spectra are relatively insensitive to precise values of

*γ*as seen from our variation study in the appendix. Second,

_{i}*γ*seems to have a very weak dependence on the well width and the degree of confinement (bulk vs quantum well) [28

_{i}28. D. Gammon, S. Rudin, T. L. Reinecke, D. S. Katzer, and C. S. Kyono, “Phonon broadening of excitons in GaAs/Al* _{x}*Ga

_{1−x}As quantum wells,” Phys. Rev. B

**51**, 16785–16789 (1995) [CrossRef] .

**20**(3), 265 –275 (1984) [CrossRef] .

28. D. Gammon, S. Rudin, T. L. Reinecke, D. S. Katzer, and C. S. Kyono, “Phonon broadening of excitons in GaAs/Al* _{x}*Ga

_{1−x}As quantum wells,” Phys. Rev. B

**51**, 16785–16789 (1995) [CrossRef] .

29. Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris Jr., “Quantum-Confined Stark Effect in Ge/SiGe Quantum Wells on Si for Optical Modulators,” IEEE J. Sel. Topics Quantum Electron. **12**(6), 1503 –1513 (2006) [CrossRef] .

## 4. Modulator performance at elevated temperatures

*λ*, if

*α*(

*λ*,

*T*,

*V*

_{ON}) >

*α*(

*λ*,

*T*,

*V*

_{OFF}) then FOM is negative. Otherwise, it is positive. The sign of the FOM is not of any particular concern since it can always be inverted electronically. Often this variation in the sign is described as “normally on” or “normally off” depending on whether the modulator has its highest output at 0V or under positive bias. The operating points and the maximum values discussed below have therefore been derived on the basis of the absolute values of the FOM.

*μ*m and 8

*μ*m) and the high bias voltage (1V to 4V). The low voltage is always assumed to equal 0V. From these maps of the FOM, it is possible to obtain a number of quantities that help us evaluate the suitability of quantum well modulators for interconnects.

*T*

_{H}and

*T*

_{L}and plug them into the definitions of insertion loss and extinction ratio. We can generate the maps of these quantities similar to that of the FOM shown in Fig. 4. Figure 5 shows as an example the maps of insertion loss and extinction ratio generated for a 5

*μ*m long modulator for on and off voltages of 4V and 0V respectively.

*V*≤ 4), modulator length (

*L*= 5

*μ*m), and threshold FOM (Th. FOM = 0.125, 0.15, 0.175, and 0.20).

4. M. R. Watts, W. A. Zortman, D. C. Trotter, R. W. Young, and A. L. Lentine, “Vertical junction silicon microdisk modulators and switches,” Opt. Express **19**(22), 21,989–22,003 (2011) [CrossRef] .

*μ*m, which is near the optimum. The maximum figure of merit at a single wavelength and temperature was ∼0.25 at 4V. By choosing an allowed figure of merit, operating voltage, and temperature, we can directly read the optical bandwidth from the graph. By further choosing the channel spacing, we can easily determine the number of channels from the channel bandwidth. Fairly obvious tradeoffs are evident. If we constrain the temperature variation to a greater extent, we can have more optical bandwidth and hence more channels. If we reduce the voltage, reducing the energy of the modulator itself, we reduce the number of channels or the allowed temperature variation. Several data points are summarized below:

- The MQW modulator cannot effectively be used in DWDM systems without temperature control over very large (> 60° C) temperature ranges.
- If we constrain the temperature variation to a rather large 37° C, we can potentially have ∼2 THz of optical bandwidth, meaning 20 to 40 channels at 100 or 50 GHz channels spacing respectively with a power penalty of 3 dB compared to the optimum single wavelength and temperature case.
- If we constrain the temperature further to about ∼ 12° C, we can then have the 20–40 channels for a figure of merit of 0.2; that figure of merit is about equal to what can be done with silicon photonics resonant ring or disk modulators with active temperature control to ±0.2° C.

15. D. A. B. Miller, “Energy consumption in optical modulators for interconnects,” Opt. Express **20**(S2), A293–A308 (2012) [CrossRef] .

*α*with the confinement factor Γ (Γ < 100%). The confinement factor can be tailored by choice of waveguide dimensions, and sub-micron single mode silicon waveguides with Γ approaching 80% are routinely fabricated [30–32]. While there are clearly some differences in the electro-absorption characteristics of waveguide versus surface normal devices, it is likely that the conclusions drawn here are still relevant, independent of device geometry. Also, in a waveguide geometry, one can tradeoff the length, applied field, and applied voltage across the device. Indeed [14

14. 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**(6), 461 –463 (2012) [CrossRef] .

## 5. Conclusion

## Appendix 1: Sensitivity of thermal model to exciton-phonon coupling parameter *γ*

*γ*in Eq. (4) on the predicted high-temperature absorption of quantum wells. As noted in section 3.2, because of the relative difficulty in finding reported measured values of

*γ*, we have used

*γ*= 5.5 meV for all transitions (

_{i}*i*= e-hh, e-lh, and continuum). Our choice was motivated by the observation that 5 meV ≤

*γ*≤ 10 meV for most common semiconductors. It is important, however, to check the relative sensitivity of our thermal model to this parameter. To that end, we have calculated the predicted zero-bias absorption spectrum of SiGe MQW studied in this paper by varying

*γ*from 2 meV to 10 meV. The spectra are plotted in Fig. 7.

*γ*are used. However, even for a 5× variation in

*γ*, the predicted high temperature absorption spectra are relatively insensitive to its precise value. Therefore, while we recognize the potential limitation to our model due to the lack of precise knowledge of

*γ*, we do not anticipate any significant change to our findings when the precise values of gamma are input to the model as long as they are in the 1–10 meV range.

## Appendix 2: Implementation note

33. “IGOR Pro technical graphing and analysis,” (2010). URL www.wavemetrics.com.

34. “Python programming language - Official website,” URL www.python.org.

## Acknowledgments

## References and links

1. | R. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. |

2. | Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature |

3. | P. Dong, S. Liao, H. Liang, W. Qian, X. Wang, R. Shafiiha, D. Feng, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “High-speed and compact silicon modulator based on a racetrack resonator with a 1 V drive voltage,” Opt. Lett. |

4. | M. R. Watts, W. A. Zortman, D. C. Trotter, R. W. Young, and A. L. Lentine, “Vertical junction silicon microdisk modulators and switches,” Opt. Express |

5. | A. Krishnamoorthy, “Focus Issue on Photonic Materials and Integration Architectures,” IEEE Photon. J. |

6. | W. A. Zortman, D. C. Trotter, and M. R. Watts, “Silicon photonics manufacturing,” Opt. Express |

7. | C. T. DeRose, M. R. Watts, D. C. Trotter, D. L. Luck, G. N. Nielson, and R. W. Young, “Silicon Microring Modulator with Integrated Heater and Temperature Sensor for Thermal Control,” in Conference on Lasers and Electro-Optics CThJ3 (2010). |

8. | E. Timurdogan, A. Biberman, D. C. Trotter, C. Sun, M. Moresco, V. Stojanovic, and M. R. Watts, “Automated Wavelength Recovery for Microring Resonators,” in CLEO: Science and Innovations CM2M.1 (2012). |

9. | K. Padmaraju, J. Chan, L. Chen, M. Lipson, and K. Bergman, “Dynamic Stabilization of a Microring Modulator Under Thermal Perturbation,” in Optical Fiber Communication Conference OW4F.2 (2012). |

10. | B. Guha, K. Preston, and M. Lipson, “Athermal silicon microring electro-optic modulator,” Opt. Lett. |

11. | 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 |

12. | N.-N. Feng, D. Feng, S. Liao, X. Wang, P. Dong, H. Liang, C.-C. Kung, W. Qian, J. Fong, R. Shafiiha, Y. Luo, J. Cunningham, A. V. Krishnamoorthy, and M. Asghari, “30GHz Ge electro-absorption modulator integrated with 3 |

13. | 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 |

14. | 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. |

15. | D. A. B. Miller, “Energy consumption in optical modulators for interconnects,” Opt. Express |

16. | 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. |

17. | M. Haney, R. Nair, and T. Gu, “Chip-scale integrated optical interconnects: a key enabler for future high-performance computing,” in |

18. | D. A. B. Miller, “Optics for low-energy communication inside digital processors: quantum detectors, sources, and modulators as efficient impedance converters,” Opt. Lett. |

19. | G. P. Agarwal, |

20. | A. Emami-Neyestanak, “Design of CMOS receivers for parallel optical interconnects,” Ph.D. thesis, Stanford University (2004). |

21. | A. L. Lentine and F. A. P. Tooley, “Relationships between speed and tolerances for self-electro-optic-effect devices,” Appl. Opt. |

22. | 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. |

23. | D. Chemla, D. Miller, P. Smith, A. Gossard, and W. Wiegmann, “Room temperature excitonic nonlinear absorption and refraction in GaAs/AlGaAs multiple quantum well structures,” IEEE J. Quantum Electron. |

24. | W. H. Press, S. A. Teukolsky, W. J. Vetterling, and B. P. Flannery, |

25. | S. M. Sze, |

26. | Y. P. Varshni, “Temperature dependence of the energy gap in semiconductors,” Physica |

27. | D. Wolpert and P. Ampadu, |

28. | D. Gammon, S. Rudin, T. L. Reinecke, D. S. Katzer, and C. S. Kyono, “Phonon broadening of excitons in GaAs/Al _{1−x}As quantum wells,” Phys. Rev. B 51, 16785–16789 (1995) [CrossRef] . |

29. | Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris Jr., “Quantum-Confined Stark Effect in Ge/SiGe Quantum Wells on Si for Optical Modulators,” IEEE J. Sel. Topics Quantum Electron. |

30. | S. Schonenberger, N. Moll, T. Stoferle, T. Wahlbrink, J. Bolten, S. Gotzinger, T. Mollenhauer, C. Moormann, R. Mahrt, and B. Offrein, “Circular grating resonators as candidates for ultra-small photonic devices,” in Proc. SPIE , vol. |

31. | S. Xiao, M. H. Khan, H. Shen, and M. Qi, “Compact silicon microring resonators with ultra-low propagation loss in the C band,” Opt. Express |

32. | A. W.-L. Fang, “Silicon evanascent lasers,” Ph.D. thesis, University of California Santa Barbara (2008). |

33. | “IGOR Pro technical graphing and analysis,” (2010). URL www.wavemetrics.com. |

34. | “Python programming language - Official website,” URL www.python.org. |

**OCIS Codes**

(200.4650) Optics in computing : Optical interconnects

(250.3140) Optoelectronics : Integrated optoelectronic circuits

(130.4110) Integrated optics : Modulators

**ToC Category:**

Optics in Computing

**History**

Original Manuscript: January 3, 2013

Revised Manuscript: February 8, 2013

Manuscript Accepted: February 19, 2013

Published: February 25, 2013

**Citation**

Rohan D. Kekatpure and Anthony Lentine, "The suitability of SiGe multiple quantum well modulators for short reach DWDM optical interconnects," Opt. Express **21**, 5318-5331 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-5-5318

Sort: Year | Journal | Reset

### References

- R. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron.23(1), 123–129 (1987). [CrossRef]
- Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature435(7040), 325–327 (2005). [CrossRef] [PubMed]
- P. Dong, S. Liao, H. Liang, W. Qian, X. Wang, R. Shafiiha, D. Feng, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “High-speed and compact silicon modulator based on a racetrack resonator with a 1 V drive voltage,” Opt. Lett.35(19), 3246–3248 (2010). [CrossRef] [PubMed]
- M. R. Watts, W. A. Zortman, D. C. Trotter, R. W. Young, and A. L. Lentine, “Vertical junction silicon microdisk modulators and switches,” Opt. Express19(22), 21,989–22,003 (2011). [CrossRef]
- A. Krishnamoorthy, “Focus Issue on Photonic Materials and Integration Architectures,” IEEE Photon. J.3(3), 564 –626 (2011). [CrossRef]
- W. A. Zortman, D. C. Trotter, and M. R. Watts, “Silicon photonics manufacturing,” Opt. Express18(23), 23598–23607 (2010). [CrossRef] [PubMed]
- C. T. DeRose, M. R. Watts, D. C. Trotter, D. L. Luck, G. N. Nielson, and R. W. Young, “Silicon Microring Modulator with Integrated Heater and Temperature Sensor for Thermal Control,” in Conference on Lasers and Electro-Optics CThJ3 (2010).
- E. Timurdogan, A. Biberman, D. C. Trotter, C. Sun, M. Moresco, V. Stojanovic, and M. R. Watts, “Automated Wavelength Recovery for Microring Resonators,” in CLEO: Science and Innovations CM2M.1 (2012).
- K. Padmaraju, J. Chan, L. Chen, M. Lipson, and K. Bergman, “Dynamic Stabilization of a Microring Modulator Under Thermal Perturbation,” in Optical Fiber Communication Conference OW4F.2 (2012).
- B. Guha, K. Preston, and M. Lipson, “Athermal silicon microring electro-optic modulator,” Opt. Lett.37(12), 2253–2255 (2012). [CrossRef] [PubMed]
- 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. Photonics2, 433–437 (2008). [CrossRef]
- N.-N. Feng, D. Feng, S. Liao, X. Wang, P. Dong, H. Liang, C.-C. Kung, W. Qian, J. Fong, R. Shafiiha, Y. Luo, J. Cunningham, A. V. Krishnamoorthy, and M. Asghari, “30GHz Ge electro-absorption modulator integrated with 3μm silicon-on-insulator waveguide,” Opt. Express19(8), 7062–7067 (2011). [CrossRef] [PubMed]
- 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,” Nature437(7063), 1334–1336 (2005). [CrossRef] [PubMed]
- 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(6), 461 –463 (2012). [CrossRef]
- D. A. B. Miller, “Energy consumption in optical modulators for interconnects,” Opt. Express20(S2), A293–A308 (2012). [CrossRef]
- 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(26), 5153–5171 (1993). [CrossRef] [PubMed]
- M. Haney, R. Nair, and T. Gu, “Chip-scale integrated optical interconnects: a key enabler for future high-performance computing,” in Proc. SPIE, L. Glebov, Alexei, and R. T. Chen, eds., 82670X, 8267 (2012).
- D. A. B. Miller, “Optics for low-energy communication inside digital processors: quantum detectors, sources, and modulators as efficient impedance converters,” Opt. Lett.14(2), 146–148 (1989). [CrossRef] [PubMed]
- G. P. Agarwal, Fiber-Optic Communication Systems Wiley series in Microwave and Optical Engineering, 4th ed. (Wiley, 2010). [CrossRef]
- A. Emami-Neyestanak, “Design of CMOS receivers for parallel optical interconnects,” Ph.D. thesis, Stanford University (2004).
- A. L. Lentine and F. A. P. Tooley, “Relationships between speed and tolerances for self-electro-optic-effect devices,” Appl. Opt.33(8), 1354–1367 (1994). [CrossRef] [PubMed]
- 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(2), 187–197 (2012). [CrossRef]
- D. Chemla, D. Miller, P. Smith, A. Gossard, and W. Wiegmann, “Room temperature excitonic nonlinear absorption and refraction in GaAs/AlGaAs multiple quantum well structures,” IEEE J. Quantum Electron.20(3), 265 –275 (1984). [CrossRef]
- W. H. Press, S. A. Teukolsky, W. J. Vetterling, and B. P. Flannery, Numerical recipes in C++, The art of scientific computing, 2nd ed. (Cambridge University Press, 2002).
- S. M. Sze, The Physics of Semiconductor Devices (Wiley, New York, 1969).
- Y. P. Varshni, “Temperature dependence of the energy gap in semiconductors,” Physica34, 149–154 (1967). [CrossRef]
- D. Wolpert and P. Ampadu, Managing Temperature Effects in Nanoscale Adaptive Systems, 1st ed. (Springer, 2012). [CrossRef]
- D. Gammon, S. Rudin, T. L. Reinecke, D. S. Katzer, and C. S. Kyono, “Phonon broadening of excitons in GaAs/AlxGa1−xAs quantum wells,” Phys. Rev. B51, 16785–16789 (1995). [CrossRef]
- 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. Topics Quantum Electron.12(6), 1503 –1513 (2006). [CrossRef]
- S. Schonenberger, N. Moll, T. Stoferle, T. Wahlbrink, J. Bolten, S. Gotzinger, T. Mollenhauer, C. Moormann, R. Mahrt, and B. Offrein, “Circular grating resonators as candidates for ultra-small photonic devices,” in Proc. SPIE, vol. 6996, p. 69906A1 (2008).
- S. Xiao, M. H. Khan, H. Shen, and M. Qi, “Compact silicon microring resonators with ultra-low propagation loss in the C band,” Opt. Express15(22), 14,467–14,475 (2007). [CrossRef]
- A. W.-L. Fang, “Silicon evanascent lasers,” Ph.D. thesis, University of California Santa Barbara (2008).
- “IGOR Pro technical graphing and analysis,” (2010). URL www.wavemetrics.com .
- “Python programming language - Official website,” URL www.python.org .

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.