Abstract

We present a design of monolithically integrated GeSi electro-absorption modulators and photodetectors for electronic-photonic integrated circuits on a silicon-on-insulator (SOI) platform. The GeSi electro-absorption modulator is based on the Franz-Keldysh effect, and the GeSi composition is chosen for optimal performance around 1550 nm. The designed modulator device is butt-coupled to Si(core)/SiO2(cladding) high index contrast waveguides, and has a predicted 3 dB bandwidth of >50 GHz and an extinction ratio of 10 dB. The same device structure can also be used for a waveguide-coupled photodetector with a predicted responsivity of > 1 A/W and a 3 dB bandwidth of > 35 GHz. Use of the same GeSi composition and device structure allows efficient monolithic process integration of the modulators and the photodetectors on an SOI platform.

© 2007 Optical Society of America

1. Introduction

The combined integration of electronic and photonic circuits has become an increasingly promising technology for high functionality extension of traditional technology shrink [1,2]. Among the key components of Si-based photonic technology are high performance photonic modulators and photodetectors. In recent years, significant progress has been made in Si modulators based on free carrier plasma dispersion, and the bandwidth has reached a few GHz [3,4]. High performance, waveguide-integrated Ge photodetectors on Si have also been demonstrated recently. A responsivity of ∼1.0 A/W and a 3 dB bandwidth greater than 4 GHz have been achieved [5].

Electro-absorption (EA) modulators are desirable for electronic-photonic integration due to their high speed and relatively low power consumption. Recently, we have demonstrated an enhanced Franz-Keldysh (FK) effect in tensile strained, epitaxial Ge-on-Si. [6]. The absorption contrast Δα/α∼3.0 at 1647 nm, where α is the absorption coefficient at an electric field of 14 kV/cm and Δα is the absolute change in the absorption coefficient due to the FK effect when the electric field increases to 70 kV/cm. Such an absorption contrast is comparable to the EA effect in Ge multiple quantum wells [7]. The optimal operation wavelength of our tensile strained Ge material is around 1647 nm due to the tensile strain induced direct band gap shrinkage [8,9]. To shift the optimal wavelength to 1550 nm, an effective way is to add a small amount of Si into Ge in order to increase its band gap.

In this paper we present a design of monolithically integrated, high performance Ge1-xSix EA modulators and photodetectors on a silicon-on-insulator (SOI) platform. Since the FK effect takes place in sub-ps time scale [10], the speed of the EA modulator based on the FK effect is only limited by the RC delay and can be designed to achieve a bandwidth of >50 GHz. With adequate design of butt-coupling to high index contrast Si(core)/SiO2(cladding) waveguides, a high extinction ratio of 10 dB can be achieved. The same device structure can also be used as a waveguide-coupled photodetector with a predicted responsivity of >1.0 A/W and a bandwidth of >35 GHz. Therefore, a monolithic integration of modulators, waveguides, and photodetectors with CMOS electronics can be achieved with our design.

2. Material design of the GeSi EA modulator

The EA property of the Ge1-xSix material is modeled using the generalized FK theory [11]. We only consider the FK effect of the direct band gap and neglect that of the indirect gap because the former is three orders of magnitude stronger than the latter [12]. This model agrees well with the experimental results of epitaxial Ge-on-Si [6]. The input material parameters required in this model are the direct band gap (E g Γ), the effective mass of electrons (me) and holes (mh), the optical transition matrix element (EP), and the real part of the refractive index (nr).

The band gap is affected by the composition and the strain of Ge1-xSix. The direct band gap of unstrained Ge1-xSix is E g Γ(Ge1-xSix)=(0.8+3.26x)eV [13,14]. For optimal operation around 1550 nm we need a direct band gap slightly larger than 0.80 eV, therefore the Si composition is <3% in a candidate composition for EA modulation at 1550 nm. Tensile strain can enhance the EA effect in Ge [6], and it is preferred for modulator devices. About 0.2% thermally induced tensile strain is introduced to our epitaxial Ge-on-Si [8,9]. When x<0.03 the thermal expansion coefficient of Ge1-xSix is very similar to Ge [14], so the tensile strain in epitaxial Ge1-xSix-on-Si is also around 0.2% for x<0.03. Since the required length of the Ge1-xSix EA modulators (tens of μm) is much larger than its cross-sectional dimensions (<1 μm), we have found that the strain in the transverse direction is almost fully relaxed and the structure is mainly strained along the longitudinal direction. Details about the experimental results of strain analysis will be reported elsewhere. Assuming the Ge1-xSix modulator is oriented along the [110] direction on the Si wafer, the most common crystallographic direction of patterned rectangular features on Si due to the alignment of lithography, the band gaps from the maxima of light hole, heavy hole and split-off bands to the minima of the Γ valley E g Γ(lh), E g Γ(hh) and E g Γ(so) are calculated by the deformation potential theory for the case of uniaxial strain along the [110] direction [15]. The deformation potential, elastic constants and split-off energy are linearly interpolated between Ge and Si [9,13,14]. With the approach described above, the band gap of the Ge1-xSix material can be obtained given the composition and the strain.

The effective mass of electrons and holes of Ge1-xSix is almost the same as Ge for x<0.03, and the difference is actually within the experimental error [13]. Therefore, we simply use the electron and hole effective mass of Ge in our simulation for Ge1-xSix with x<0.03, i.e., electron effective mass me=0.038m0 (note that this is the electron effective mass at Γ valley corresponding to the direct band gap), light hole effective mass mlh=0.043m0 and heavy hole effective mass mhh=033m0, where m0 is the mass of a free electron. From the k∙p theory, the optical transition matrix element is given by [16]

Ep=3(m0me+1)(1EgΓ(lh)+1EgΓ(hh)+1EgΓ(so)).

The value of EP can be easily calculated for Ge1-xSix since we have already determined me, and we can calculate the band gaps E g Γ(lh), E g Γ(hh) and E g Γ(so) with the methods described in the previous paragraph. Finally, the real part of the refractive index of Ge1-xSix at 1550 nm is nr(Ge1-xSix) =4.10–0.64x [13,14].

With the material parameters described above, we are able to calculate the absorption coefficient of uniaxially strained Ge1-xSix (x<0.03) in the presence of an electric field. In particular, we are most interested in the absorption contrast of Ge1-xSixα/α) at 1550 nm. The breakdown field of intrinsic Ge is 125 kV/cm [17] and Ge1-xSix with x<0.03 should have a similar breakdown behavior, so we adopt a maximum applied electric field of 100 kV/cm in our Ge1-xSix EA modulator design. Figure 1(a) plots Δα/α at 1550 nm as a function of Si content, assuming an applied electric field of 100 kV/cm at optical off-state and 10 kV/cm built-in electric field at optical on-state (0V bias) in the intrinsic Ge1-xSix layer of a p-i-n diode structure. The optimal composition is around x=0.75%, giving an absorption contrast (Δα/α) of ∼3.0. Figure 1(b) shows the absorption coefficient of Ge0.9925Si0.0075 at 1550 nm as a function of electric field. At 10 kV/cm and 100 kV/cm the absorption coefficients are 158 and 633/cm, respectively. Due to the relatively high absorption coefficient of Ge0.9925Si0.0075 at optical on-state (158/cm), the length of the EA modulator should be less than 70 μm for an insertion loss of less than 5 dB. For photodetectors, the high absorption state at a high electric field conveniently corresponds to the condition under reverse bias, resulting in an enhanced quantum efficiency together with a higher bandwidth. In the next section we will focus on the device design of monolithically integrated Ge0.9925Si0.0075 EA modulators and photodetectors.

 

Fig. 1. (a) The absorption constrast (Δα/α) at 1550nm as a function of Si composition, and (b) the absorption coefficient of Ge0.9925Si0.0075 vs. electric field at 1550 nm.

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3. Device design of Ge0.9925Si0.0075 EA modulators and photodetectors

 

Fig. 2. Schematic structure of a Ge0.9925Si0.0075 EA modulator and a photodetector monolithically integrated on an SOI platform. The p+ Si layers are formed in the single crystal SOI device layer.

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The structure of a Ge0.9925Si0.0075 EA modulator and a photodetector monolithically integrated on an SOI platform is schematically shown in Fig. 2. High index contrast Si(core)/SiO2(cladding) waveguides are butt-coupled to the modulator and the photodetector. The Si waveguide is 500 nm wide and 200 nm high for single mode operation at 1550 nm. Currently, a fiber-to-waveguide coupling loss of <1 dB [18] and a propagation loss of ∼0.35 dB/cm in the Si waveguide [19] can be achieved. Since this paper focuses on the modulator and detector design, we do not include the Si waveguide loss into the design parameters. The GeSi EA modulator and the photodetector are of the same vertical Si/Ge0.9925Si0.0075/Si p-i-n diode structure with a doping level of 2× 1019/cm3 in n + and p + Si, and their heights (H) and widths (W) can be designed for the optimal device performance. The only difference in the dimensions of the GeSi EA modulator and the photodetector is that the latter is longer than the former (L2>L1) to increase the absorption. Use of the same GeSi composition and device structure allows efficient monolithic process integration of the modulators and the photodetectors on an SOI platform.

For electronic-photonic integration the TE mode in Si waveguides is preferred because a small bending radius of ∼1 μm can be achieved with low loss. Therefore, we will focus our discussions on the coupling of TE modes in these devices. The modes of the Si waveguide and the GeSi EA modulator are calculated with Apollo Photonics Solution Suite 2.3 using the complex refractive indexes of the materials and the full vector method in the finite domain analysis. Both the mode profile and the complex effective indexes are obtained from the mode solver. Two factors should be considered in calculating the insertion loss and the extinction ratio of the GeSi EA modulator: the modal overlap Ω in the x-y plane (see Fig. 2) between the Si waveguide and the GeSi EA modulator, and the transmittance t through the modulator in the z direction. The modal overlap (Ω) is obtained by calculating the overlap integral between the TE modes of the Si waveguide and the GeSi EA modulator. The transmittance (t) in the z direction is calculated by the propagation matrix element method, using the complex effective indexes of the GeSi EA modulator and the Si waveguides. The transmittance (t) thus calculated takes into account both the impedance mismatch in the z direction and the absorption in the GeSi EA modulator. The insertion loss and extinction ratio are given by

InsertionLoss=101g10(t(0)Ω(0)2),
ExtinctionRatio=101g10(t(V)Ω(V)2)+101g10(t(0)Ω(0)2)101g10(t(V)t(0)),

where Ω(0), t(0), Ω(V) and t(V) are the modal overlap and transmittance at 0 bias and a reverse bias of V, respectively. The square terms of Ω in the equations take into account the coupling loss into and out of the GeSi EA modulator due to modal mismatch in the x-y plane. As the electric field has little effect on the real part of the refractive index of Ge0.9925Si0.0075 (|Δnr|≤10-3), the mode profile in the GeSi EA modulator is not affected by the electric field. Therefore Ω(0) ≈ Ω(V) to obtain the approximation for the extinction ratio in Eq. (2b).

 

Fig. 3. (a) Extinction ratio over insertion loss of 50 μm-long Ge0.9925Si0.0075 EA modulators with different cross-sectional dimensions, and (b) modulator performance vs. device length for Ge0.9925Si0.0075 EA modulators with H=400 nm and W=600nm.

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Figure 3(a) plots the extinction ratio over insertion loss of 50 μm-long GeSi EA modulators with different widths (W) and thicknesses (H) of the GeSi active layers. Since we want a high extinction ratio and a low insertion loss, the value on the vertical axis in Fig. 3(a) should be maximized with the optimal design. In this calculation, we specify that the reverse bias applied at the optical off-state of the modulator should not exceed 3.3 V to be compatible with 180 nm CMOS technology. Nor should the electric field exceed 100 kV/cm due to the limit of material breakdown. The optimal GeSi thickness is determined to be ∼400 nm. Below this thickness the optical confinement in the GeSi active layer decreases significantly and the extent of optical modulation is reduced. Above this thickness the modal overlap with the Si waveguide (Ω) and the electric field at 3.3 V reverse bias both decrease, leading to a higher coupling loss and a lower extinction ratio. The optimal width is ∼700 nm. However, for H=400 nm the values of extinction ratio over insertion loss are almost identical for W=600–800 nm. To reduce the capacitance, a narrower device is preferred. Therefore, we choose a dimension of H=400 nm and W=600 nm. Figure 3(b) plots the bandwidth, extinction ratio and insertion loss as a function of device length for a Ge0.9925Si0.0075 EA modulator with W=600 nm and H=400 nm. We assume 50 × 50 μm2 metal contact pads with a vertical distance of 4 μm from the substrate, so the pad capacitance is 21.6 fF. For a 50 μm-long GeSi modulator we predict a high extinction ratio of 10 dB and a 3 dB bandwidth of >50 GHz. The corresponding insertion loss is 5 dB, including 1 dB coupling loss budget and 4 dB material absorption loss. The coupling loss can be decreased to 0 with optimal coupling design. Depending on the applications, the extinction ratio can be traded off for lower material loss by decreasing the device length. The size of the metal contact pad can be decreased to further increase the RC-limited bandwidth. With 180 nm CMOS fabrication technology the misalignment between the waveguide and the modulator can be easily controlled below 50 nm, and our simulation results show that the insertion loss increases by <0.5 dB and the extinction ratio is not affected in that case. Therefore, the design can be well implemented with 180 nm CMOS technology.

The same p-i-n diode structure can also be used as a waveguide-integrated photodetector. The responsivity R at a reverse bias of V is given by

R(AW)=(λ(nm)1240)(1r)Ω(V)[1exp(αeff(V)L)],

where r is the reflectance at the input port of the photodetector, and α eff(V) is the effective absorption coefficient of Ge0.9925Si0.0075 in the detector at a reverse bias of V. Equation (3) is adapted from the responsivity of a normally incident photodetector [20] by considering the modal overlap and the effective absorption coefficient in the case of waveguide coupling. Note that α eff(V) is different from the material absorption coefficient of Ge0.9925Si0.0075 since not all the light is confined in GeSi. To obtain α eff(V) we set the imaginary indexes of the n + and the p + Si to 0 and calculate the imaginary effective index n i,eff(V) of the detector structure. The mode profile remains the same in this way, and n i,eff(V) is only due to the absorption of Ge0.9925Si0.0075. So we have α eff(V) =4πn i,eff(V)/λ. The 3 dB frequency of a photodetector is determined by the carrier transit time and the RC delay. Figure 4 plots the responsivity and 3 dB frequency of waveguide-coupled Ge0.9925Si0.0075 photodetectors as a function of device length. A high responsivity of ∼1.1 A/W and a 3 dB bandwidth of >35 GHz can be achieved with an 80 μm-long device. By shortening the device we can also trade off lower responsivity for higher speed, depending on the requirement of applications. High bandwidth driver circuits for the modulator and trans-impedance amplifiers (TIA) for the photodetector can be achieved with SiGe bipolar CMOS (BICMOS) technology and integrated with the modulator and the detector devices [21].

 

Fig. 4. The responsivity and bandwidth of Ge0.9925Si0.0075 photodetectors (W=600 nm, H=400 nm) as a function of device length.

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4. Conclusions

We have presented a design of monolithically integrated GeSi EA modulators and photodetectors on a SOI platform. The GeSi EA modulator is optimized for operation at 1550 nm, and has a predicted 3 dB bandwidth of >50 GHz and an extinction ratio of 10 dB. The photodetector has a predicted responsivity of ∼1.1 A/W and a 3 dB bandwidth of >35 GHz. Both devices utilize the same material composition and device structure, so they can be monolithically integrated on-chip.

Early portion of this work was partially supported by Pirelli Lab, S.p.A. This research was sponsored under the Defense Advanced Research Projects Agency’s (DARPA) EPIC program supervised by Dr. Jagdeep Shah in the Microsystems Technology Office (MTO) under Contract No. HR0011-05-C-0027. The authors would like to thank Dr. John Yasaitis for helpful discussions.

References and links

1. R. A. Soref, “Silicon-based optoelectronics,” Proc. IEEE. 81,1687–1706 (1993). [CrossRef]  

2. L. C. Kimerling, D. Aim, A. B. Apsel, M. Beals, D. Carothers, Y-K. Chen, T. Conway, D. M. Gill, M. Grove, C-Y Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125,612502 (2006). [CrossRef]  

3. A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on metal-oxide-semiconductor capacitor,” Nature 427,615–618 (2004). [CrossRef]   [PubMed]  

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

5. J. F. Liu, D. Ahn, C. Y. Hong, S. Jongthanmmanurak, D. Pan, M. Beals, L. C. Kimerling, J. Michel, A. T. Pomerene, C. Hill, M. Jaso, K. Y. Tu, Y. K. Chen, S. Patel, M. Rasras, A. White, and D. M. Gill, “Waveguide-integrated Ge p-i-n photodetectors on Si,” 3rd IEEE International Conference on Group IV Photonics (IEEE Cat. No. 06EX1276C), Ottawa, ON, Canada, 13-15 Sept. 2006, pp.173–175.

6. S. Jongthanmmanurak, J. F. Liu, K. Wada, D. D. Cannon, D. T. Danielson, D. Pan, L. C. Kimeriling, and J. Michel, “Large electro-optic effect in tensile strained Ge-on-Si films,” Appl. Phys. Lett. 89,161115 (2006). [CrossRef]  

7. 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]  

8. Y. Ishikawa, K. Wada, D. D. Cannon, J. F. Liu, H. C. Luan, and L. C. Kimerling, “Strain-induced direct band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett. 82,2044–2046 (2003). [CrossRef]  

9. J. F. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, and L C. Kimerling, “Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si (100),” Phys. Rev B 70,155309 (2004). [CrossRef]  

10. J. F. Lampin, L. Desplanque, and F. Mollot, “Detection of picosecond electrical pulses using the intrinsic Franz-Keldysh effect,” Appl. Phys. Lett. 78,4103–4105 (2001). [CrossRef]  

11. H. Shen and F. H. Pollak, “Generalized Franz-Keldysh theory of electromodulation,” Phys. Rev. B 42,7097–7102 (1990). [CrossRef]  

12. A. Frova, P. Handler, F. A. Germano, and D. E. Aspnes, “Electro-absorption effect at the band edges of silicon and germanium,” Phys. Rev. 145,575–583 (1966). [CrossRef]  

13. Physics of Group IV Elements and III-V Compounds, edited by O. Madelung, Landolt-Börnstein:Numerical Data and Functional Relationships in Science and Technology (Springer, Berlin, 1982), vol. 17a, pp.449–454.

14. Properties of Advanced Semiconductor Materials: GaN, AlN, InN, BN, SiC, SiGe, edited by M. E. Levinshtein, S. L. Rumyantsev, and M. S. Shur, (Wiley, New York, 2001), Chap. 6.

15. F. H. Pollak and M. Cardona, “Piezo-electroreflectance in Ge, GaAs and Si,” Phys. Rev. 172,816–837 (1968). [CrossRef]  

16. P. Lawaetz, “Valence-band parameters in cubic semiconductors,” Phy. Rev. B 4,3460–3467 (1971). [CrossRef]  

17. A. S. Kyuregyan and S. N. Yurkov, “Room-temperature avalanche breakdown voltages of Si, Ge, SiC, GaAs, GaP and InP,” Sov. Phys. Semicond 23,1126–1132 (1989).

18. V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28,1302–1304(2003). [CrossRef]   [PubMed]  

19. D. K. Sparacin, Process and Design Techniques for Low Loss Integrated Silicon Photonics, Ph.D. thesis, (Massachusetts Institute of Technology, 2006), Chap. 7.

20. S. M. Sze, Physics of Semiconductor Devices (Wiley, New York, 1981), Chap. 13.

21. G. Freeman, M. Meghelli, Y. Kwark, S. Zier, A. Rylyakov, J. S. Soma, T. Tanji, O. M. Schreiber, K. Walder, J. S. Rieh, B. Jaganathan, A. Joseph, and S. Subbannas, “40-Gb/s circuits built from a 120-GHzfT SiGe technology,” IEEE. J. Solid-St. Circ. 37,1106–1114(2002). [CrossRef]  

References

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  1. R. A. Soref, “Silicon-based optoelectronics,” Proc. IEEE. 81,1687–1706 (1993).
    [Crossref]
  2. L. C. Kimerling, D. Aim, A. B. Apsel, M. Beals, D. Carothers, Y-K. Chen, T. Conway, D. M. Gill, M. Grove, C-Y Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125,612502 (2006).
    [Crossref]
  3. A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on metal-oxide-semiconductor capacitor,” Nature 427,615–618 (2004).
    [Crossref] [PubMed]
  4. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435,325–327 (2005).
    [Crossref] [PubMed]
  5. J. F. Liu, D. Ahn, C. Y. Hong, S. Jongthanmmanurak, D. Pan, M. Beals, L. C. Kimerling, J. Michel, A. T. Pomerene, C. Hill, M. Jaso, K. Y. Tu, Y. K. Chen, S. Patel, M. Rasras, A. White, and D. M. Gill, “Waveguide-integrated Ge p-i-n photodetectors on Si,” 3rd IEEE International Conference on Group IV Photonics (IEEE Cat. No. 06EX1276C), Ottawa, ON, Canada, 13-15 Sept. 2006, pp.173–175.
  6. S. Jongthanmmanurak, J. F. Liu, K. Wada, D. D. Cannon, D. T. Danielson, D. Pan, L. C. Kimeriling, and J. Michel, “Large electro-optic effect in tensile strained Ge-on-Si films,” Appl. Phys. Lett. 89,161115 (2006).
    [Crossref]
  7. 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]
  8. Y. Ishikawa, K. Wada, D. D. Cannon, J. F. Liu, H. C. Luan, and L. C. Kimerling, “Strain-induced direct band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett. 82,2044–2046 (2003).
    [Crossref]
  9. J. F. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, and L C. Kimerling, “Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si (100),” Phys. Rev B 70,155309 (2004).
    [Crossref]
  10. J. F. Lampin, L. Desplanque, and F. Mollot, “Detection of picosecond electrical pulses using the intrinsic Franz-Keldysh effect,” Appl. Phys. Lett. 78,4103–4105 (2001).
    [Crossref]
  11. H. Shen and F. H. Pollak, “Generalized Franz-Keldysh theory of electromodulation,” Phys. Rev. B 42,7097–7102 (1990).
    [Crossref]
  12. A. Frova, P. Handler, F. A. Germano, and D. E. Aspnes, “Electro-absorption effect at the band edges of silicon and germanium,” Phys. Rev. 145,575–583 (1966).
    [Crossref]
  13. Physics of Group IV Elements and III-V Compounds, edited by O. Madelung, Landolt-Börnstein:Numerical Data and Functional Relationships in Science and Technology (Springer, Berlin, 1982), vol. 17a, pp.449–454.
  14. Properties of Advanced Semiconductor Materials: GaN, AlN, InN, BN, SiC, SiGe, edited by M. E. Levinshtein, S. L. Rumyantsev, and M. S. Shur, (Wiley, New York, 2001), Chap. 6.
  15. F. H. Pollak and M. Cardona, “Piezo-electroreflectance in Ge, GaAs and Si,” Phys. Rev. 172,816–837 (1968).
    [Crossref]
  16. P. Lawaetz, “Valence-band parameters in cubic semiconductors,” Phy. Rev. B 4,3460–3467 (1971).
    [Crossref]
  17. A. S. Kyuregyan and S. N. Yurkov, “Room-temperature avalanche breakdown voltages of Si, Ge, SiC, GaAs, GaP and InP,” Sov. Phys. Semicond 23,1126–1132 (1989).
  18. V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28,1302–1304(2003).
    [Crossref] [PubMed]
  19. D. K. Sparacin, Process and Design Techniques for Low Loss Integrated Silicon Photonics, Ph.D. thesis, (Massachusetts Institute of Technology, 2006), Chap. 7.
  20. S. M. Sze, Physics of Semiconductor Devices (Wiley, New York, 1981), Chap. 13.
  21. G. Freeman, M. Meghelli, Y. Kwark, S. Zier, A. Rylyakov, J. S. Soma, T. Tanji, O. M. Schreiber, K. Walder, J. S. Rieh, B. Jaganathan, A. Joseph, and S. Subbannas, “40-Gb/s circuits built from a 120-GHzfT SiGe technology,” IEEE. J. Solid-St. Circ. 37,1106–1114(2002).
    [Crossref]

2006 (2)

L. C. Kimerling, D. Aim, A. B. Apsel, M. Beals, D. Carothers, Y-K. Chen, T. Conway, D. M. Gill, M. Grove, C-Y Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125,612502 (2006).
[Crossref]

S. Jongthanmmanurak, J. F. Liu, K. Wada, D. D. Cannon, D. T. Danielson, D. Pan, L. C. Kimeriling, and J. Michel, “Large electro-optic effect in tensile strained Ge-on-Si films,” Appl. Phys. Lett. 89,161115 (2006).
[Crossref]

2005 (2)

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]

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

2004 (2)

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on metal-oxide-semiconductor capacitor,” Nature 427,615–618 (2004).
[Crossref] [PubMed]

J. F. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, and L C. Kimerling, “Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si (100),” Phys. Rev B 70,155309 (2004).
[Crossref]

2003 (2)

Y. Ishikawa, K. Wada, D. D. Cannon, J. F. Liu, H. C. Luan, and L. C. Kimerling, “Strain-induced direct band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett. 82,2044–2046 (2003).
[Crossref]

V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28,1302–1304(2003).
[Crossref] [PubMed]

2002 (1)

G. Freeman, M. Meghelli, Y. Kwark, S. Zier, A. Rylyakov, J. S. Soma, T. Tanji, O. M. Schreiber, K. Walder, J. S. Rieh, B. Jaganathan, A. Joseph, and S. Subbannas, “40-Gb/s circuits built from a 120-GHzfT SiGe technology,” IEEE. J. Solid-St. Circ. 37,1106–1114(2002).
[Crossref]

2001 (1)

J. F. Lampin, L. Desplanque, and F. Mollot, “Detection of picosecond electrical pulses using the intrinsic Franz-Keldysh effect,” Appl. Phys. Lett. 78,4103–4105 (2001).
[Crossref]

1993 (1)

R. A. Soref, “Silicon-based optoelectronics,” Proc. IEEE. 81,1687–1706 (1993).
[Crossref]

1990 (1)

H. Shen and F. H. Pollak, “Generalized Franz-Keldysh theory of electromodulation,” Phys. Rev. B 42,7097–7102 (1990).
[Crossref]

1989 (1)

A. S. Kyuregyan and S. N. Yurkov, “Room-temperature avalanche breakdown voltages of Si, Ge, SiC, GaAs, GaP and InP,” Sov. Phys. Semicond 23,1126–1132 (1989).

1971 (1)

P. Lawaetz, “Valence-band parameters in cubic semiconductors,” Phy. Rev. B 4,3460–3467 (1971).
[Crossref]

1968 (1)

F. H. Pollak and M. Cardona, “Piezo-electroreflectance in Ge, GaAs and Si,” Phys. Rev. 172,816–837 (1968).
[Crossref]

1966 (1)

A. Frova, P. Handler, F. A. Germano, and D. E. Aspnes, “Electro-absorption effect at the band edges of silicon and germanium,” Phys. Rev. 145,575–583 (1966).
[Crossref]

Ahn, D.

J. F. Liu, D. Ahn, C. Y. Hong, S. Jongthanmmanurak, D. Pan, M. Beals, L. C. Kimerling, J. Michel, A. T. Pomerene, C. Hill, M. Jaso, K. Y. Tu, Y. K. Chen, S. Patel, M. Rasras, A. White, and D. M. Gill, “Waveguide-integrated Ge p-i-n photodetectors on Si,” 3rd IEEE International Conference on Group IV Photonics (IEEE Cat. No. 06EX1276C), Ottawa, ON, Canada, 13-15 Sept. 2006, pp.173–175.

Aim, D.

L. C. Kimerling, D. Aim, A. B. Apsel, M. Beals, D. Carothers, Y-K. Chen, T. Conway, D. M. Gill, M. Grove, C-Y Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125,612502 (2006).
[Crossref]

Almeida, V. R.

Apsel, A. B.

L. C. Kimerling, D. Aim, A. B. Apsel, M. Beals, D. Carothers, Y-K. Chen, T. Conway, D. M. Gill, M. Grove, C-Y Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125,612502 (2006).
[Crossref]

Aspnes, D. E.

A. Frova, P. Handler, F. A. Germano, and D. E. Aspnes, “Electro-absorption effect at the band edges of silicon and germanium,” Phys. Rev. 145,575–583 (1966).
[Crossref]

Beals, M.

L. C. Kimerling, D. Aim, A. B. Apsel, M. Beals, D. Carothers, Y-K. Chen, T. Conway, D. M. Gill, M. Grove, C-Y Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125,612502 (2006).
[Crossref]

J. F. Liu, D. Ahn, C. Y. Hong, S. Jongthanmmanurak, D. Pan, M. Beals, L. C. Kimerling, J. Michel, A. T. Pomerene, C. Hill, M. Jaso, K. Y. Tu, Y. K. Chen, S. Patel, M. Rasras, A. White, and D. M. Gill, “Waveguide-integrated Ge p-i-n photodetectors on Si,” 3rd IEEE International Conference on Group IV Photonics (IEEE Cat. No. 06EX1276C), Ottawa, ON, Canada, 13-15 Sept. 2006, pp.173–175.

Cannon, D. D.

S. Jongthanmmanurak, J. F. Liu, K. Wada, D. D. Cannon, D. T. Danielson, D. Pan, L. C. Kimeriling, and J. Michel, “Large electro-optic effect in tensile strained Ge-on-Si films,” Appl. Phys. Lett. 89,161115 (2006).
[Crossref]

J. F. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, and L C. Kimerling, “Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si (100),” Phys. Rev B 70,155309 (2004).
[Crossref]

Y. Ishikawa, K. Wada, D. D. Cannon, J. F. Liu, H. C. Luan, and L. C. Kimerling, “Strain-induced direct band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett. 82,2044–2046 (2003).
[Crossref]

Cardona, M.

F. H. Pollak and M. Cardona, “Piezo-electroreflectance in Ge, GaAs and Si,” Phys. Rev. 172,816–837 (1968).
[Crossref]

Carothers, D.

L. C. Kimerling, D. Aim, A. B. Apsel, M. Beals, D. Carothers, Y-K. Chen, T. Conway, D. M. Gill, M. Grove, C-Y Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125,612502 (2006).
[Crossref]

Chen, Y. K.

J. F. Liu, D. Ahn, C. Y. Hong, S. Jongthanmmanurak, D. Pan, M. Beals, L. C. Kimerling, J. Michel, A. T. Pomerene, C. Hill, M. Jaso, K. Y. Tu, Y. K. Chen, S. Patel, M. Rasras, A. White, and D. M. Gill, “Waveguide-integrated Ge p-i-n photodetectors on Si,” 3rd IEEE International Conference on Group IV Photonics (IEEE Cat. No. 06EX1276C), Ottawa, ON, Canada, 13-15 Sept. 2006, pp.173–175.

Chen, Y-K.

L. C. Kimerling, D. Aim, A. B. Apsel, M. Beals, D. Carothers, Y-K. Chen, T. Conway, D. M. Gill, M. Grove, C-Y Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125,612502 (2006).
[Crossref]

Cohen, O.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on metal-oxide-semiconductor capacitor,” Nature 427,615–618 (2004).
[Crossref] [PubMed]

Conway, T.

L. C. Kimerling, D. Aim, A. B. Apsel, M. Beals, D. Carothers, Y-K. Chen, T. Conway, D. M. Gill, M. Grove, C-Y Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125,612502 (2006).
[Crossref]

Danielson, D. T.

S. Jongthanmmanurak, J. F. Liu, K. Wada, D. D. Cannon, D. T. Danielson, D. Pan, L. C. Kimeriling, and J. Michel, “Large electro-optic effect in tensile strained Ge-on-Si films,” Appl. Phys. Lett. 89,161115 (2006).
[Crossref]

J. F. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, and L C. Kimerling, “Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si (100),” Phys. Rev B 70,155309 (2004).
[Crossref]

Desplanque, L.

J. F. Lampin, L. Desplanque, and F. Mollot, “Detection of picosecond electrical pulses using the intrinsic Franz-Keldysh effect,” Appl. Phys. Lett. 78,4103–4105 (2001).
[Crossref]

Freeman, G.

G. Freeman, M. Meghelli, Y. Kwark, S. Zier, A. Rylyakov, J. S. Soma, T. Tanji, O. M. Schreiber, K. Walder, J. S. Rieh, B. Jaganathan, A. Joseph, and S. Subbannas, “40-Gb/s circuits built from a 120-GHzfT SiGe technology,” IEEE. J. Solid-St. Circ. 37,1106–1114(2002).
[Crossref]

Frova, A.

A. Frova, P. Handler, F. A. Germano, and D. E. Aspnes, “Electro-absorption effect at the band edges of silicon and germanium,” Phys. Rev. 145,575–583 (1966).
[Crossref]

Ge, Y.

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]

Germano, F. A.

A. Frova, P. Handler, F. A. Germano, and D. E. Aspnes, “Electro-absorption effect at the band edges of silicon and germanium,” Phys. Rev. 145,575–583 (1966).
[Crossref]

Gill, D. M.

L. C. Kimerling, D. Aim, A. B. Apsel, M. Beals, D. Carothers, Y-K. Chen, T. Conway, D. M. Gill, M. Grove, C-Y Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125,612502 (2006).
[Crossref]

J. F. Liu, D. Ahn, C. Y. Hong, S. Jongthanmmanurak, D. Pan, M. Beals, L. C. Kimerling, J. Michel, A. T. Pomerene, C. Hill, M. Jaso, K. Y. Tu, Y. K. Chen, S. Patel, M. Rasras, A. White, and D. M. Gill, “Waveguide-integrated Ge p-i-n photodetectors on Si,” 3rd IEEE International Conference on Group IV Photonics (IEEE Cat. No. 06EX1276C), Ottawa, ON, Canada, 13-15 Sept. 2006, pp.173–175.

Grove, M.

L. C. Kimerling, D. Aim, A. B. Apsel, M. Beals, D. Carothers, Y-K. Chen, T. Conway, D. M. Gill, M. Grove, C-Y Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125,612502 (2006).
[Crossref]

Handler, P.

A. Frova, P. Handler, F. A. Germano, and D. E. Aspnes, “Electro-absorption effect at the band edges of silicon and germanium,” Phys. Rev. 145,575–583 (1966).
[Crossref]

Harris, J. S.

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]

Hill, C.

J. F. Liu, D. Ahn, C. Y. Hong, S. Jongthanmmanurak, D. Pan, M. Beals, L. C. Kimerling, J. Michel, A. T. Pomerene, C. Hill, M. Jaso, K. Y. Tu, Y. K. Chen, S. Patel, M. Rasras, A. White, and D. M. Gill, “Waveguide-integrated Ge p-i-n photodetectors on Si,” 3rd IEEE International Conference on Group IV Photonics (IEEE Cat. No. 06EX1276C), Ottawa, ON, Canada, 13-15 Sept. 2006, pp.173–175.

Hong, C. Y.

J. F. Liu, D. Ahn, C. Y. Hong, S. Jongthanmmanurak, D. Pan, M. Beals, L. C. Kimerling, J. Michel, A. T. Pomerene, C. Hill, M. Jaso, K. Y. Tu, Y. K. Chen, S. Patel, M. Rasras, A. White, and D. M. Gill, “Waveguide-integrated Ge p-i-n photodetectors on Si,” 3rd IEEE International Conference on Group IV Photonics (IEEE Cat. No. 06EX1276C), Ottawa, ON, Canada, 13-15 Sept. 2006, pp.173–175.

Hong, C-Y

L. C. Kimerling, D. Aim, A. B. Apsel, M. Beals, D. Carothers, Y-K. Chen, T. Conway, D. M. Gill, M. Grove, C-Y Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125,612502 (2006).
[Crossref]

Ishikawa, Y.

J. F. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, and L C. Kimerling, “Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si (100),” Phys. Rev B 70,155309 (2004).
[Crossref]

Y. Ishikawa, K. Wada, D. D. Cannon, J. F. Liu, H. C. Luan, and L. C. Kimerling, “Strain-induced direct band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett. 82,2044–2046 (2003).
[Crossref]

Jaganathan, B.

G. Freeman, M. Meghelli, Y. Kwark, S. Zier, A. Rylyakov, J. S. Soma, T. Tanji, O. M. Schreiber, K. Walder, J. S. Rieh, B. Jaganathan, A. Joseph, and S. Subbannas, “40-Gb/s circuits built from a 120-GHzfT SiGe technology,” IEEE. J. Solid-St. Circ. 37,1106–1114(2002).
[Crossref]

Jaso, M.

J. F. Liu, D. Ahn, C. Y. Hong, S. Jongthanmmanurak, D. Pan, M. Beals, L. C. Kimerling, J. Michel, A. T. Pomerene, C. Hill, M. Jaso, K. Y. Tu, Y. K. Chen, S. Patel, M. Rasras, A. White, and D. M. Gill, “Waveguide-integrated Ge p-i-n photodetectors on Si,” 3rd IEEE International Conference on Group IV Photonics (IEEE Cat. No. 06EX1276C), Ottawa, ON, Canada, 13-15 Sept. 2006, pp.173–175.

Jones, R.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on metal-oxide-semiconductor capacitor,” Nature 427,615–618 (2004).
[Crossref] [PubMed]

Jongthammanurak, S.

J. F. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, and L C. Kimerling, “Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si (100),” Phys. Rev B 70,155309 (2004).
[Crossref]

Jongthanmmanurak, S.

S. Jongthanmmanurak, J. F. Liu, K. Wada, D. D. Cannon, D. T. Danielson, D. Pan, L. C. Kimeriling, and J. Michel, “Large electro-optic effect in tensile strained Ge-on-Si films,” Appl. Phys. Lett. 89,161115 (2006).
[Crossref]

J. F. Liu, D. Ahn, C. Y. Hong, S. Jongthanmmanurak, D. Pan, M. Beals, L. C. Kimerling, J. Michel, A. T. Pomerene, C. Hill, M. Jaso, K. Y. Tu, Y. K. Chen, S. Patel, M. Rasras, A. White, and D. M. Gill, “Waveguide-integrated Ge p-i-n photodetectors on Si,” 3rd IEEE International Conference on Group IV Photonics (IEEE Cat. No. 06EX1276C), Ottawa, ON, Canada, 13-15 Sept. 2006, pp.173–175.

Joseph, A.

G. Freeman, M. Meghelli, Y. Kwark, S. Zier, A. Rylyakov, J. S. Soma, T. Tanji, O. M. Schreiber, K. Walder, J. S. Rieh, B. Jaganathan, A. Joseph, and S. Subbannas, “40-Gb/s circuits built from a 120-GHzfT SiGe technology,” IEEE. J. Solid-St. Circ. 37,1106–1114(2002).
[Crossref]

Kamins, T. I.

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]

Kimeriling, L. C.

S. Jongthanmmanurak, J. F. Liu, K. Wada, D. D. Cannon, D. T. Danielson, D. Pan, L. C. Kimeriling, and J. Michel, “Large electro-optic effect in tensile strained Ge-on-Si films,” Appl. Phys. Lett. 89,161115 (2006).
[Crossref]

Kimerling, L C.

J. F. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, and L C. Kimerling, “Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si (100),” Phys. Rev B 70,155309 (2004).
[Crossref]

Kimerling, L. C.

L. C. Kimerling, D. Aim, A. B. Apsel, M. Beals, D. Carothers, Y-K. Chen, T. Conway, D. M. Gill, M. Grove, C-Y Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125,612502 (2006).
[Crossref]

Y. Ishikawa, K. Wada, D. D. Cannon, J. F. Liu, H. C. Luan, and L. C. Kimerling, “Strain-induced direct band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett. 82,2044–2046 (2003).
[Crossref]

J. F. Liu, D. Ahn, C. Y. Hong, S. Jongthanmmanurak, D. Pan, M. Beals, L. C. Kimerling, J. Michel, A. T. Pomerene, C. Hill, M. Jaso, K. Y. Tu, Y. K. Chen, S. Patel, M. Rasras, A. White, and D. M. Gill, “Waveguide-integrated Ge p-i-n photodetectors on Si,” 3rd IEEE International Conference on Group IV Photonics (IEEE Cat. No. 06EX1276C), Ottawa, ON, Canada, 13-15 Sept. 2006, pp.173–175.

Kuo, Y.-H.

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]

Kwark, Y.

G. Freeman, M. Meghelli, Y. Kwark, S. Zier, A. Rylyakov, J. S. Soma, T. Tanji, O. M. Schreiber, K. Walder, J. S. Rieh, B. Jaganathan, A. Joseph, and S. Subbannas, “40-Gb/s circuits built from a 120-GHzfT SiGe technology,” IEEE. J. Solid-St. Circ. 37,1106–1114(2002).
[Crossref]

Kyuregyan, A. S.

A. S. Kyuregyan and S. N. Yurkov, “Room-temperature avalanche breakdown voltages of Si, Ge, SiC, GaAs, GaP and InP,” Sov. Phys. Semicond 23,1126–1132 (1989).

Lampin, J. F.

J. F. Lampin, L. Desplanque, and F. Mollot, “Detection of picosecond electrical pulses using the intrinsic Franz-Keldysh effect,” Appl. Phys. Lett. 78,4103–4105 (2001).
[Crossref]

Lawaetz, P.

P. Lawaetz, “Valence-band parameters in cubic semiconductors,” Phy. Rev. B 4,3460–3467 (1971).
[Crossref]

Lee, Y. K.

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]

Liao, L.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on metal-oxide-semiconductor capacitor,” Nature 427,615–618 (2004).
[Crossref] [PubMed]

Lipson, M.

L. C. Kimerling, D. Aim, A. B. Apsel, M. Beals, D. Carothers, Y-K. Chen, T. Conway, D. M. Gill, M. Grove, C-Y Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125,612502 (2006).
[Crossref]

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

V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28,1302–1304(2003).
[Crossref] [PubMed]

Liu, A.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on metal-oxide-semiconductor capacitor,” Nature 427,615–618 (2004).
[Crossref] [PubMed]

Liu, J.

L. C. Kimerling, D. Aim, A. B. Apsel, M. Beals, D. Carothers, Y-K. Chen, T. Conway, D. M. Gill, M. Grove, C-Y Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125,612502 (2006).
[Crossref]

Liu, J. F.

S. Jongthanmmanurak, J. F. Liu, K. Wada, D. D. Cannon, D. T. Danielson, D. Pan, L. C. Kimeriling, and J. Michel, “Large electro-optic effect in tensile strained Ge-on-Si films,” Appl. Phys. Lett. 89,161115 (2006).
[Crossref]

J. F. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, and L C. Kimerling, “Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si (100),” Phys. Rev B 70,155309 (2004).
[Crossref]

Y. Ishikawa, K. Wada, D. D. Cannon, J. F. Liu, H. C. Luan, and L. C. Kimerling, “Strain-induced direct band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett. 82,2044–2046 (2003).
[Crossref]

J. F. Liu, D. Ahn, C. Y. Hong, S. Jongthanmmanurak, D. Pan, M. Beals, L. C. Kimerling, J. Michel, A. T. Pomerene, C. Hill, M. Jaso, K. Y. Tu, Y. K. Chen, S. Patel, M. Rasras, A. White, and D. M. Gill, “Waveguide-integrated Ge p-i-n photodetectors on Si,” 3rd IEEE International Conference on Group IV Photonics (IEEE Cat. No. 06EX1276C), Ottawa, ON, Canada, 13-15 Sept. 2006, pp.173–175.

Luan, H. C.

Y. Ishikawa, K. Wada, D. D. Cannon, J. F. Liu, H. C. Luan, and L. C. Kimerling, “Strain-induced direct band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett. 82,2044–2046 (2003).
[Crossref]

Meghelli, M.

G. Freeman, M. Meghelli, Y. Kwark, S. Zier, A. Rylyakov, J. S. Soma, T. Tanji, O. M. Schreiber, K. Walder, J. S. Rieh, B. Jaganathan, A. Joseph, and S. Subbannas, “40-Gb/s circuits built from a 120-GHzfT SiGe technology,” IEEE. J. Solid-St. Circ. 37,1106–1114(2002).
[Crossref]

Michel, J.

S. Jongthanmmanurak, J. F. Liu, K. Wada, D. D. Cannon, D. T. Danielson, D. Pan, L. C. Kimeriling, and J. Michel, “Large electro-optic effect in tensile strained Ge-on-Si films,” Appl. Phys. Lett. 89,161115 (2006).
[Crossref]

L. C. Kimerling, D. Aim, A. B. Apsel, M. Beals, D. Carothers, Y-K. Chen, T. Conway, D. M. Gill, M. Grove, C-Y Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125,612502 (2006).
[Crossref]

J. F. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, and L C. Kimerling, “Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si (100),” Phys. Rev B 70,155309 (2004).
[Crossref]

J. F. Liu, D. Ahn, C. Y. Hong, S. Jongthanmmanurak, D. Pan, M. Beals, L. C. Kimerling, J. Michel, A. T. Pomerene, C. Hill, M. Jaso, K. Y. Tu, Y. K. Chen, S. Patel, M. Rasras, A. White, and D. M. Gill, “Waveguide-integrated Ge p-i-n photodetectors on Si,” 3rd IEEE International Conference on Group IV Photonics (IEEE Cat. No. 06EX1276C), Ottawa, ON, Canada, 13-15 Sept. 2006, pp.173–175.

Miller, D. A. B.

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]

Mollot, F.

J. F. Lampin, L. Desplanque, and F. Mollot, “Detection of picosecond electrical pulses using the intrinsic Franz-Keldysh effect,” Appl. Phys. Lett. 78,4103–4105 (2001).
[Crossref]

Nicolaescu, R.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on metal-oxide-semiconductor capacitor,” Nature 427,615–618 (2004).
[Crossref] [PubMed]

Pan, D.

L. C. Kimerling, D. Aim, A. B. Apsel, M. Beals, D. Carothers, Y-K. Chen, T. Conway, D. M. Gill, M. Grove, C-Y Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125,612502 (2006).
[Crossref]

S. Jongthanmmanurak, J. F. Liu, K. Wada, D. D. Cannon, D. T. Danielson, D. Pan, L. C. Kimeriling, and J. Michel, “Large electro-optic effect in tensile strained Ge-on-Si films,” Appl. Phys. Lett. 89,161115 (2006).
[Crossref]

J. F. Liu, D. Ahn, C. Y. Hong, S. Jongthanmmanurak, D. Pan, M. Beals, L. C. Kimerling, J. Michel, A. T. Pomerene, C. Hill, M. Jaso, K. Y. Tu, Y. K. Chen, S. Patel, M. Rasras, A. White, and D. M. Gill, “Waveguide-integrated Ge p-i-n photodetectors on Si,” 3rd IEEE International Conference on Group IV Photonics (IEEE Cat. No. 06EX1276C), Ottawa, ON, Canada, 13-15 Sept. 2006, pp.173–175.

Panepucci, R. R.

Paniccia, M.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on metal-oxide-semiconductor capacitor,” Nature 427,615–618 (2004).
[Crossref] [PubMed]

Patel, S.

J. F. Liu, D. Ahn, C. Y. Hong, S. Jongthanmmanurak, D. Pan, M. Beals, L. C. Kimerling, J. Michel, A. T. Pomerene, C. Hill, M. Jaso, K. Y. Tu, Y. K. Chen, S. Patel, M. Rasras, A. White, and D. M. Gill, “Waveguide-integrated Ge p-i-n photodetectors on Si,” 3rd IEEE International Conference on Group IV Photonics (IEEE Cat. No. 06EX1276C), Ottawa, ON, Canada, 13-15 Sept. 2006, pp.173–175.

Patel, S. S.

L. C. Kimerling, D. Aim, A. B. Apsel, M. Beals, D. Carothers, Y-K. Chen, T. Conway, D. M. Gill, M. Grove, C-Y Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125,612502 (2006).
[Crossref]

Pollak, F. H.

H. Shen and F. H. Pollak, “Generalized Franz-Keldysh theory of electromodulation,” Phys. Rev. B 42,7097–7102 (1990).
[Crossref]

F. H. Pollak and M. Cardona, “Piezo-electroreflectance in Ge, GaAs and Si,” Phys. Rev. 172,816–837 (1968).
[Crossref]

Pomerene, A. T.

L. C. Kimerling, D. Aim, A. B. Apsel, M. Beals, D. Carothers, Y-K. Chen, T. Conway, D. M. Gill, M. Grove, C-Y Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125,612502 (2006).
[Crossref]

J. F. Liu, D. Ahn, C. Y. Hong, S. Jongthanmmanurak, D. Pan, M. Beals, L. C. Kimerling, J. Michel, A. T. Pomerene, C. Hill, M. Jaso, K. Y. Tu, Y. K. Chen, S. Patel, M. Rasras, A. White, and D. M. Gill, “Waveguide-integrated Ge p-i-n photodetectors on Si,” 3rd IEEE International Conference on Group IV Photonics (IEEE Cat. No. 06EX1276C), Ottawa, ON, Canada, 13-15 Sept. 2006, pp.173–175.

Pradhan, S.

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

Rasras, M.

L. C. Kimerling, D. Aim, A. B. Apsel, M. Beals, D. Carothers, Y-K. Chen, T. Conway, D. M. Gill, M. Grove, C-Y Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125,612502 (2006).
[Crossref]

J. F. Liu, D. Ahn, C. Y. Hong, S. Jongthanmmanurak, D. Pan, M. Beals, L. C. Kimerling, J. Michel, A. T. Pomerene, C. Hill, M. Jaso, K. Y. Tu, Y. K. Chen, S. Patel, M. Rasras, A. White, and D. M. Gill, “Waveguide-integrated Ge p-i-n photodetectors on Si,” 3rd IEEE International Conference on Group IV Photonics (IEEE Cat. No. 06EX1276C), Ottawa, ON, Canada, 13-15 Sept. 2006, pp.173–175.

Ren, S.

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]

Rieh, J. S.

G. Freeman, M. Meghelli, Y. Kwark, S. Zier, A. Rylyakov, J. S. Soma, T. Tanji, O. M. Schreiber, K. Walder, J. S. Rieh, B. Jaganathan, A. Joseph, and S. Subbannas, “40-Gb/s circuits built from a 120-GHzfT SiGe technology,” IEEE. J. Solid-St. Circ. 37,1106–1114(2002).
[Crossref]

Roth, J. E.

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]

Rubin, D.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on metal-oxide-semiconductor capacitor,” Nature 427,615–618 (2004).
[Crossref] [PubMed]

Rylyakov, A.

G. Freeman, M. Meghelli, Y. Kwark, S. Zier, A. Rylyakov, J. S. Soma, T. Tanji, O. M. Schreiber, K. Walder, J. S. Rieh, B. Jaganathan, A. Joseph, and S. Subbannas, “40-Gb/s circuits built from a 120-GHzfT SiGe technology,” IEEE. J. Solid-St. Circ. 37,1106–1114(2002).
[Crossref]

Samara-Rubio, D.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on metal-oxide-semiconductor capacitor,” Nature 427,615–618 (2004).
[Crossref] [PubMed]

Schmidt, B.

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

Schreiber, O. M.

G. Freeman, M. Meghelli, Y. Kwark, S. Zier, A. Rylyakov, J. S. Soma, T. Tanji, O. M. Schreiber, K. Walder, J. S. Rieh, B. Jaganathan, A. Joseph, and S. Subbannas, “40-Gb/s circuits built from a 120-GHzfT SiGe technology,” IEEE. J. Solid-St. Circ. 37,1106–1114(2002).
[Crossref]

Shen, H.

H. Shen and F. H. Pollak, “Generalized Franz-Keldysh theory of electromodulation,” Phys. Rev. B 42,7097–7102 (1990).
[Crossref]

Soma, J. S.

G. Freeman, M. Meghelli, Y. Kwark, S. Zier, A. Rylyakov, J. S. Soma, T. Tanji, O. M. Schreiber, K. Walder, J. S. Rieh, B. Jaganathan, A. Joseph, and S. Subbannas, “40-Gb/s circuits built from a 120-GHzfT SiGe technology,” IEEE. J. Solid-St. Circ. 37,1106–1114(2002).
[Crossref]

Soref, R. A.

R. A. Soref, “Silicon-based optoelectronics,” Proc. IEEE. 81,1687–1706 (1993).
[Crossref]

Sparacin, D. K.

L. C. Kimerling, D. Aim, A. B. Apsel, M. Beals, D. Carothers, Y-K. Chen, T. Conway, D. M. Gill, M. Grove, C-Y Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125,612502 (2006).
[Crossref]

D. K. Sparacin, Process and Design Techniques for Low Loss Integrated Silicon Photonics, Ph.D. thesis, (Massachusetts Institute of Technology, 2006), Chap. 7.

Subbannas, S.

G. Freeman, M. Meghelli, Y. Kwark, S. Zier, A. Rylyakov, J. S. Soma, T. Tanji, O. M. Schreiber, K. Walder, J. S. Rieh, B. Jaganathan, A. Joseph, and S. Subbannas, “40-Gb/s circuits built from a 120-GHzfT SiGe technology,” IEEE. J. Solid-St. Circ. 37,1106–1114(2002).
[Crossref]

Sze, S. M.

S. M. Sze, Physics of Semiconductor Devices (Wiley, New York, 1981), Chap. 13.

Tanji, T.

G. Freeman, M. Meghelli, Y. Kwark, S. Zier, A. Rylyakov, J. S. Soma, T. Tanji, O. M. Schreiber, K. Walder, J. S. Rieh, B. Jaganathan, A. Joseph, and S. Subbannas, “40-Gb/s circuits built from a 120-GHzfT SiGe technology,” IEEE. J. Solid-St. Circ. 37,1106–1114(2002).
[Crossref]

Tu, K. Y.

J. F. Liu, D. Ahn, C. Y. Hong, S. Jongthanmmanurak, D. Pan, M. Beals, L. C. Kimerling, J. Michel, A. T. Pomerene, C. Hill, M. Jaso, K. Y. Tu, Y. K. Chen, S. Patel, M. Rasras, A. White, and D. M. Gill, “Waveguide-integrated Ge p-i-n photodetectors on Si,” 3rd IEEE International Conference on Group IV Photonics (IEEE Cat. No. 06EX1276C), Ottawa, ON, Canada, 13-15 Sept. 2006, pp.173–175.

Tu, K-Y.

L. C. Kimerling, D. Aim, A. B. Apsel, M. Beals, D. Carothers, Y-K. Chen, T. Conway, D. M. Gill, M. Grove, C-Y Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125,612502 (2006).
[Crossref]

Wada, K.

S. Jongthanmmanurak, J. F. Liu, K. Wada, D. D. Cannon, D. T. Danielson, D. Pan, L. C. Kimeriling, and J. Michel, “Large electro-optic effect in tensile strained Ge-on-Si films,” Appl. Phys. Lett. 89,161115 (2006).
[Crossref]

J. F. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, and L C. Kimerling, “Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si (100),” Phys. Rev B 70,155309 (2004).
[Crossref]

Y. Ishikawa, K. Wada, D. D. Cannon, J. F. Liu, H. C. Luan, and L. C. Kimerling, “Strain-induced direct band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett. 82,2044–2046 (2003).
[Crossref]

Walder, K.

G. Freeman, M. Meghelli, Y. Kwark, S. Zier, A. Rylyakov, J. S. Soma, T. Tanji, O. M. Schreiber, K. Walder, J. S. Rieh, B. Jaganathan, A. Joseph, and S. Subbannas, “40-Gb/s circuits built from a 120-GHzfT SiGe technology,” IEEE. J. Solid-St. Circ. 37,1106–1114(2002).
[Crossref]

White, A.

J. F. Liu, D. Ahn, C. Y. Hong, S. Jongthanmmanurak, D. Pan, M. Beals, L. C. Kimerling, J. Michel, A. T. Pomerene, C. Hill, M. Jaso, K. Y. Tu, Y. K. Chen, S. Patel, M. Rasras, A. White, and D. M. Gill, “Waveguide-integrated Ge p-i-n photodetectors on Si,” 3rd IEEE International Conference on Group IV Photonics (IEEE Cat. No. 06EX1276C), Ottawa, ON, Canada, 13-15 Sept. 2006, pp.173–175.

White, A. E.

L. C. Kimerling, D. Aim, A. B. Apsel, M. Beals, D. Carothers, Y-K. Chen, T. Conway, D. M. Gill, M. Grove, C-Y Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125,612502 (2006).
[Crossref]

Wong, C. W.

L. C. Kimerling, D. Aim, A. B. Apsel, M. Beals, D. Carothers, Y-K. Chen, T. Conway, D. M. Gill, M. Grove, C-Y Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125,612502 (2006).
[Crossref]

Xu, Q.

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

Yurkov, S. N.

A. S. Kyuregyan and S. N. Yurkov, “Room-temperature avalanche breakdown voltages of Si, Ge, SiC, GaAs, GaP and InP,” Sov. Phys. Semicond 23,1126–1132 (1989).

Zier, S.

G. Freeman, M. Meghelli, Y. Kwark, S. Zier, A. Rylyakov, J. S. Soma, T. Tanji, O. M. Schreiber, K. Walder, J. S. Rieh, B. Jaganathan, A. Joseph, and S. Subbannas, “40-Gb/s circuits built from a 120-GHzfT SiGe technology,” IEEE. J. Solid-St. Circ. 37,1106–1114(2002).
[Crossref]

Appl. Phys. Lett. (3)

S. Jongthanmmanurak, J. F. Liu, K. Wada, D. D. Cannon, D. T. Danielson, D. Pan, L. C. Kimeriling, and J. Michel, “Large electro-optic effect in tensile strained Ge-on-Si films,” Appl. Phys. Lett. 89,161115 (2006).
[Crossref]

Y. Ishikawa, K. Wada, D. D. Cannon, J. F. Liu, H. C. Luan, and L. C. Kimerling, “Strain-induced direct band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett. 82,2044–2046 (2003).
[Crossref]

J. F. Lampin, L. Desplanque, and F. Mollot, “Detection of picosecond electrical pulses using the intrinsic Franz-Keldysh effect,” Appl. Phys. Lett. 78,4103–4105 (2001).
[Crossref]

IEEE. J. Solid-St. Circ. (1)

G. Freeman, M. Meghelli, Y. Kwark, S. Zier, A. Rylyakov, J. S. Soma, T. Tanji, O. M. Schreiber, K. Walder, J. S. Rieh, B. Jaganathan, A. Joseph, and S. Subbannas, “40-Gb/s circuits built from a 120-GHzfT SiGe technology,” IEEE. J. Solid-St. Circ. 37,1106–1114(2002).
[Crossref]

Nature (3)

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]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on metal-oxide-semiconductor capacitor,” Nature 427,615–618 (2004).
[Crossref] [PubMed]

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

Opt. Lett. (1)

Phy. Rev. B (1)

P. Lawaetz, “Valence-band parameters in cubic semiconductors,” Phy. Rev. B 4,3460–3467 (1971).
[Crossref]

Phys. Rev B (1)

J. F. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, and L C. Kimerling, “Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si (100),” Phys. Rev B 70,155309 (2004).
[Crossref]

Phys. Rev. (2)

A. Frova, P. Handler, F. A. Germano, and D. E. Aspnes, “Electro-absorption effect at the band edges of silicon and germanium,” Phys. Rev. 145,575–583 (1966).
[Crossref]

F. H. Pollak and M. Cardona, “Piezo-electroreflectance in Ge, GaAs and Si,” Phys. Rev. 172,816–837 (1968).
[Crossref]

Phys. Rev. B (1)

H. Shen and F. H. Pollak, “Generalized Franz-Keldysh theory of electromodulation,” Phys. Rev. B 42,7097–7102 (1990).
[Crossref]

Proc. IEEE. (1)

R. A. Soref, “Silicon-based optoelectronics,” Proc. IEEE. 81,1687–1706 (1993).
[Crossref]

Proc. SPIE (1)

L. C. Kimerling, D. Aim, A. B. Apsel, M. Beals, D. Carothers, Y-K. Chen, T. Conway, D. M. Gill, M. Grove, C-Y Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125,612502 (2006).
[Crossref]

Sov. Phys. Semicond (1)

A. S. Kyuregyan and S. N. Yurkov, “Room-temperature avalanche breakdown voltages of Si, Ge, SiC, GaAs, GaP and InP,” Sov. Phys. Semicond 23,1126–1132 (1989).

Other (5)

D. K. Sparacin, Process and Design Techniques for Low Loss Integrated Silicon Photonics, Ph.D. thesis, (Massachusetts Institute of Technology, 2006), Chap. 7.

S. M. Sze, Physics of Semiconductor Devices (Wiley, New York, 1981), Chap. 13.

Physics of Group IV Elements and III-V Compounds, edited by O. Madelung, Landolt-Börnstein:Numerical Data and Functional Relationships in Science and Technology (Springer, Berlin, 1982), vol. 17a, pp.449–454.

Properties of Advanced Semiconductor Materials: GaN, AlN, InN, BN, SiC, SiGe, edited by M. E. Levinshtein, S. L. Rumyantsev, and M. S. Shur, (Wiley, New York, 2001), Chap. 6.

J. F. Liu, D. Ahn, C. Y. Hong, S. Jongthanmmanurak, D. Pan, M. Beals, L. C. Kimerling, J. Michel, A. T. Pomerene, C. Hill, M. Jaso, K. Y. Tu, Y. K. Chen, S. Patel, M. Rasras, A. White, and D. M. Gill, “Waveguide-integrated Ge p-i-n photodetectors on Si,” 3rd IEEE International Conference on Group IV Photonics (IEEE Cat. No. 06EX1276C), Ottawa, ON, Canada, 13-15 Sept. 2006, pp.173–175.

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Figures (4)

Fig. 1.
Fig. 1.

(a) The absorption constrast (Δα/α) at 1550nm as a function of Si composition, and (b) the absorption coefficient of Ge0.9925Si0.0075 vs. electric field at 1550 nm.

Fig. 2.
Fig. 2.

Schematic structure of a Ge0.9925Si0.0075 EA modulator and a photodetector monolithically integrated on an SOI platform. The p+ Si layers are formed in the single crystal SOI device layer.

Fig. 3.
Fig. 3.

(a) Extinction ratio over insertion loss of 50 μm-long Ge0.9925Si0.0075 EA modulators with different cross-sectional dimensions, and (b) modulator performance vs. device length for Ge0.9925Si0.0075 EA modulators with H=400 nm and W=600nm.

Fig. 4.
Fig. 4.

The responsivity and bandwidth of Ge0.9925Si0.0075 photodetectors (W=600 nm, H=400 nm) as a function of device length.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

E p = 3 ( m 0 m e + 1 ) ( 1 E g Γ ( lh ) + 1 E g Γ ( hh ) + 1 E g Γ ( so ) ) .
Insertion Loss = 101 g 10 ( t ( 0 ) Ω ( 0 ) 2 ) ,
Extinction Ratio = 101 g 10 ( t ( V ) Ω ( V ) 2 ) + 101 g 10 ( t ( 0 ) Ω ( 0 ) 2 ) 101 g 10 ( t ( V ) t ( 0 ) ) ,
R ( A W ) = ( λ ( nm ) 1240 ) ( 1 r ) Ω ( V ) [ 1 exp ( α eff ( V ) L ) ] ,

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