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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 2 — Jan. 22, 2007
  • pp: 623–628
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Design of monolithically integrated GeSi electro-absorption modulators and photodetectors on an SOI platform

Jifeng Liu, Dong Pan, Samerkhae Jongthammanurak, Kazumi Wada, Lionel C. Kimerling, and Jurgen Michel  »View Author Affiliations


Optics Express, Vol. 15, Issue 2, pp. 623-628 (2007)
http://dx.doi.org/10.1364/OE.15.000623


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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

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

,2

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]

]. 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

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

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

]. 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

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.

].

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

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]

]. 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

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]

]. 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

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

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]

]. 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

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]

], 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

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

]. 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

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]

]. This model agrees well with the experimental results of epitaxial Ge-on-Si [6

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]

]. 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

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

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.

]. 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

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]

], and it is preferred for modulator devices. About 0.2% thermally induced tensile strain is introduced to our epitaxial Ge-on-Si [8

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

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]

]. When x<0.03 the thermal expansion coefficient of Ge1-xSix is very similar to Ge [14

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.

], 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

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

]. The deformation potential, elastic constants and split-off energy are linearly interpolated between Ge and Si [9

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]

,13

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

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.

]. 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

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.

]. 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

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

]

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

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.

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

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

] and a propagation loss of ∼0.35 dB/cm in the Si waveguide [19

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

] 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.

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

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)],
(3)

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

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.

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]

OCIS Codes
(160.1890) Materials : Detector materials
(160.2100) Materials : Electro-optical materials
(230.4110) Optical devices : Modulators
(230.5160) Optical devices : Photodetectors
(230.7370) Optical devices : Waveguides
(250.3140) Optoelectronics : Integrated optoelectronic circuits

ToC Category:
Optical Devices

History
Original Manuscript: October 24, 2006
Revised Manuscript: December 22, 2006
Manuscript Accepted: January 10, 2007
Published: January 22, 2007

Citation
Jifeng Liu, Dong Pan, Samerkhae Jongthammanurak, Kazumi Wada, Lionel C. Kimerling, and Jurgen Michel, "Design of monolithically integrated GeSi electro-absorption modulators and photodetectors on a SOI platform," Opt. Express 15, 623-628 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-2-623


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References

  1. R. A. Soref, "Silicon-based optoelectronics," Proc. IEEE. 81, 1687-1706 (1993). [CrossRef]
  2. L. C. Kimerling, D. Ahn, 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. O. Madelung, ed., Physics of Group IV Elements and III-V Compounds, Landolt-Börnstein: Numerical Data and Functional Relationships in Science and Technology (Springer, Berlin, 1982), Vol. 17(a), pp. 449-454.
  14. M. E. Levinshtein, S. L. Rumyantsev, and M. S. Shur, eds.,Properties of Advanced Semiconductor Materials: GaN, AlN, InN, BN, SiC, SiGe, (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.
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