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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 10 — May. 7, 2012
  • pp: 11031–11036
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310 GHz gain-bandwidth product Ge/Si avalanche photodetector for 1550 nm light detection

Ning Duan, Tsung-Yang Liow, Andy Eu-Jin Lim, Liang Ding, and G. Q. Lo  »View Author Affiliations


Optics Express, Vol. 20, Issue 10, pp. 11031-11036 (2012)
http://dx.doi.org/10.1364/OE.20.011031


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Abstract

We report a normal incidence Ge/Si avalanche photodiode with separate-absorption-charge-multiplication (SACM) structure by selective epitaxial growth. By proper design of charge and multiplication layers and by optimizing the electric field distribution in the depletion region to eliminate germanium impact-ionization at high gain, a high responsivity of 12 A/W and a large gain-bandwidth product of 310 GHz have been achieved at 1550 nm.

© 2012 OSA

1. Introduction

Avalanche photodiodes (APDs) are important components in optical communications due to the sensitivity margin provided by their internal gain. The separate absorption, charge, and multiplication (SACM) structure APD, which consists of an absorbing region and a multiplication region separated by a charge layer, has the advantage that the photon absorption process and the carrier multiplication process are independent and can be optimized individually to improve both the noise and the speed performance [1

1. H. Nie, K. Anselm, C. Hu, S. Murtaza, B. Streetman, and J. Campbell, “High-speed resonant-cavity separate absorption and multiplication avalanche photodiodes with 130 GHz gain-bandwidth product,” Appl. Phys. Lett. 70(2), 161–163 (1997). [CrossRef]

]. Furthermore, this structure effectively suppresses tunneling current in the narrow band-gap-absorbing layer.

Much of the research on these APDs has focused on achieving lower noise and higher gain-bandwidth products to accommodate the ever-increasing bit rates of fiber-optic systems. Conventional APD receivers that are typically made of III-V compound semiconductors were shown to have limited gain-bandwidth products (typically in the range of ~100 −160GHz), which makes them less attractive for high bit-rate applications [2

2. N. Yasuoka, H. Kuwatsuka, M. Makiuchi, T. Uchida, and A. Yasaki, “Large multiplication-bandwidth products in APDs with a thin InP multiplication layer,” in The 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2003. LEOS 2003 (IEEE/LEOS, 2003), Vol. 2, pp. 999–1000.

6

6. S. Demiguel, X. Zheng, N. Li, X. Li, J. Campbell, J. Decobert, N. Tscherptner, and A. Anselm, “High-responsivity and high-speed evanescently-coupled avalanche photodiodes,” Electron. Lett. 39(25), 1848–1849 (2003). [CrossRef]

]. Recent progress made in silicon photonics has shown Ge/Si SACM APDs to be promising for the realization of high performance APDs [7

7. Y. Kang, M. Zadka, S. Litski, G. Sarid, M. Morse, M. J. Paniccia, Y. H. Kuo, J. Bowers, A. Beling, H. D. Liu, D. C. McIntosh, J. Campbell, and A. Pauchard, “Epitaxially-grown Ge/Si avalanche photodiodes for 1.3 microm light detection,” Opt. Express 16(13), 9365–9371 (2008). [CrossRef] [PubMed]

,8

8. X. Wang, L. Chen, W. Chen, H. Cui, Y. Hu, P. Cai, R. Yang, C. Hong, D. Pan, K. Ang, M. B. Yu, Q. Fang, and G. Q. Lo, "80 GHz bandwidth-gain-product Ge/Si avalanche photodetector by selective Ge growth," in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OMR3.

] due to the intrinsic low k (ratio of the ionization coefficients of electrons and holes) value (~0.01−0.1) in silicon [9

9. R. Emmons, “Avalanche-photodiode frequency response,” J. Appl. Phys. 38(9), 3705–3714 (1967). [CrossRef]

,10

10. R. McIntyre, “The distribution of gains in uniformly multiplying avalanche photodiodes: theory,” IEEE Trans. Electron. Devices 19(6), 703–713 (1972). [CrossRef]

]. Using CMOS-compatible process technology, Kang et al [11

11. Y. Kang, H.-D. Liu, M. Morse, M. J. Paniccia, M. Zadka, S. Litski, G. Sarid, A. Pauchard, Y.-H. Kuo, H.-W. Chen, W. S. Zaoui, J. E. Bowers, A. Beling, D. C. McIntosh, X. Zheng, and J. C. Campbell, “Monolithic germanium/silicon avalanche photodiodes with 340 GHz gain–bandwidth product,” Nat. Photonics 3(1), 59–63 (2009). [CrossRef]

] reported the fabrication of Ge/Si APDs with a gain-bandwidth product of 340 GHz at wavelength of 1310 nm. The Ge and Si layers were grown non-selectively and circular mesas were formed by dry and wet etch.

On the other hand, in order to fabricate optical receivers with Ge/Si APD and TIA (trans-impedance amplifier) integrated on the same silicon substrate, selective epitaxial growth (SEG) of both silicon multiplication layer and Ge absorption layer is preferred. In this work, we report a Ge/Si APD fabricated using the SEG approach. The device structure is designed for high gain operation in order to achieve high responsivity at 1550 nm.

2. Device design and fabrication

The Ge/Si APD design features a SACM configuration in which germanium and silicon are employed for light absorption and carrier multiplication, respectively. Unlike the approach reported by Kang et al [11

11. Y. Kang, H.-D. Liu, M. Morse, M. J. Paniccia, M. Zadka, S. Litski, G. Sarid, A. Pauchard, Y.-H. Kuo, H.-W. Chen, W. S. Zaoui, J. E. Bowers, A. Beling, D. C. McIntosh, X. Zheng, and J. C. Campbell, “Monolithic germanium/silicon avalanche photodiodes with 340 GHz gain–bandwidth product,” Nat. Photonics 3(1), 59–63 (2009). [CrossRef]

] with non-selective Ge grown on Si substrate, this work employs a low thermal budget (<640°C) selective epitaxial growth of Ge and Si to form the optical absorption region and the multiplication region. The adoption of SEG Ge growth not only eliminates process complexity associated with Ge etch-back, but also prevents early edge breakdown due to the formation of beveled sidewalls. The device fabrication started with 8-inch high resistivity (100) Si-oxide (SOI) substrates with a 220 nm-thick silicon top layer and a 2 μm-thick buried oxide. Ion implantation of arsenic dopants with a relatively high dose (1 × 1015 cm−2) was performed to form the bottom n-type contact layer with low series resistance. Oxide window was formed by dry etch followed by wet etch to preserve the quality of the top Si surface. Selective Si epitaxial layer with a thickness of 0.7 μm was grown at a temperature of 640°C using an ultra high vacuum chemical vapor deposition (UHVCVD) reactor. This was followed by the p-type charge layer formation by implanting boron with a dose of 2 × 1012 cm−2 into the epi-Si. Subsequently, another oxide window was opened and a 1 μm-thick SEG Ge was grown using the same UHVCVD epitaxy reactor. The SEG Ge growth started with ~50 nm SiGe graded buffer layer followed by a Ge seed layer with a thickness of ~50nm at 350°C. The temperature was then increased to ~550°C to complete the Ge growth using a cyclical deposition and etch-back approach. The top and sidewalls of the epi-Ge were then covered with 100 nm of amorphous Si (a-Si) for passivation. The a-Si layer was implanted with a high dose of boron ions. The dopants were activated at 750°C to form the top p-type ohmic contact. The fabrication process was completed after the formation of aluminum interconnects and an anti-reflective coating (ARC) layer. A cross-sectional TEM view of a device with a Ge mesa having a bottom diameter of 30 µm is shown in Fig. 1
Fig. 1 (a) TEM cross section of a 30-µm-diameter device. (b) Zoomed in image with layer thickness.
. The diameter of the Si mesa, the bottom and top diameters of the Ge mesa are 33 µm, 30 µm, and 28 µm, respectively.

In a SACM structure, optimization of the electric field distribution in absorption and multiplication layers is critical. Firstly, the electric field within the Ge absorption region should be sufficiently high (>10 kV/cm) to ensure maximum carrier drift saturation velocity (~6 × 106 cm/s). However, the applied electric field must be kept below 100kV/cm to avoid impact ionization in Ge. Carrier multiplication in the absorbing region, even a small amount, will generate long carrier feedback loops. These carrier feedback loops between absorbing and multiplication regions not only increase the APD dark current level, but also degrade its gain-bandwidth product [12

12. L. Tarof, J. Yu, R. Bruce, D. G. Knight, T. Baird, and B. Oosterbrink, “High-frequency performance of separate absorption grading, charge, and multiplication InP/InGaAs avalanche photodiodes,” IEEE Photon. Technol. Lett. 5(6), 672–674 (1993). [CrossRef]

,13

13. N. Duan, S. Wang, X. G. Zheng, X. Li, N. Li, J. C. Campbell, C. Wang, and L. A. Coldren, “Detrimental effect of impact ionization in the absorption region on the frequency response and excess noise performance of InGaAs/InAlAs SACM avalanche photodiodes,” IEEE J. Quantum Electron. 41(4), 568–572 (2005). [CrossRef]

]. Secondly, it is desirable to confine the high electric field within the Si multiplication region, which can be achieved by increasing the doping concentration in the charge layer. To enable carrier multiplication through the impact ionization process, an electric field of >300 kV/cm will be needed. By implanting boron with a dose of 2 × 1012 cm−2 into the charge layer, an electric field difference of close to 300 kV/cm is obtained between the multiplication layer and the absorption layer.

3. Device characteristics and discussion

Figure 2(a)
Fig. 2 (a) Measured total photocurrent (solid curve) under 1550 nm illumination, dark current (dash curve), and capacitance vs. bias voltage at room temperature of a 30-µm-diameter APD. (b) The measured multiplication gain and photoresponsivity versus bias voltage under 1550 nm illumination. The primary photoresponsivity is 0.3 A/W.
plots the current-voltage (I-V) characteristics of a 30-µm-diameter Ge/Si APD device measured under dark and 1550 nm illumination conditions against reverse bias. The detector was observed to exhibit a typical rectifying characteristic at room temperature. The breakdown voltage Vb is ~-29.4V, and is defined as the voltage at which the dark current is equal to 100 µA. Under a low applied bias of less than −5V, the photocurrent is relatively small since the optically generated electrons in Ge are blocked by the energy barrier at the Ge/Si heterointerface [14

14. C. Masini, L. Calace, G. Assanto, H.-C. Luan, and L. C. Kimerling, “High-performance p-i-n Ge on Si photodetectors for the near infrared: from model to demonstration,” IEEE Trans. Electron. Dev. 48(6), 1092–1096 (2001). [CrossRef]

]. The triangular barrier in the conduction band at the Ge/Si interface prevents the electrons from traveling to the electrodes. At −5V < V < −10 V, the electric field starts to penetrate into the charge region. When this occurs, the photo current begins to increase rapidly due to heterojuction barrier breakthrough. At −10V, nearly all photo-generated carriers can overcome the heterojunction barrier and be collected by the electrodes. The punch-through voltage is ~−28V, which is estimated from capacitance vs. voltage measurement plotted in Fig. 2(a). Above −28V, the Ge absorption region is fully depleted. The rise in the dark current after 28V is from both multiplication in silicon and trap-assisted tunneling at the Ge-Si interface. Below 28V, optically generated electrons and holes in Ge diffuse to electrodes with minimal recombination loss as the diffusion length is > 4µm [15

15. Y. S. Shin, D. Lee, H. S. Lee, Y. J. Cho, C. J. Kim, and M. H. Jo, “Determination of the photocarrier diffusion length in intrinsic Ge nanowires,” Opt. Express 19(7), 6119–6124 (2011). [CrossRef] [PubMed]

], which is also reported for APDs with undepleted absorbers [16

16. Y. Hirota, S. Ando, and T. Ishibashi, “High-speed avalanche photodiode with a neutral absorption layer for 1.55 µm wavelength,” Jpn. J. Appl. Phys. 43(No. 3A), L375–L377 (2004). [CrossRef]

,17

17. K. Shiba, T. Nakata, T. Takeuchi, K. Kasahara, and K. Makita, “Theoretical and experimental study on waveguide avalanche photodiodes with an undepleted absorption layer for 25-Gb/s operation,” IEEE J. Lightwave Technol. 29(2), 153–161 (2011). [CrossRef]

]. Holes diffuse upwards to top P + layer and electrons diffuse to the Si depletion region and are swept to the electrode.

Figure 2(b) plots the dependence of multiplication gain against the applied reverse bias at room temperature. Using a conventional 30-µm-diameter Ge p-i-i-n detector as a reference, the primary responsivity was measured to be ~0.3 A/W, which agrees well with the predicted value calculated using an absorption coefficient of 0.3 µm−1 and a reflection loss of 10% at the incident surface. By normalizing the measured APD’s responsivity (right y-axis) to the primary responsivity of the reference detector, the multiplication gain factor can be calculated (left y-axis). Gain value below punch-through may not be very accurate as electrons generated in Ge experience recombination loss while diffusing to silicon multiplication region. The recombination loss is estimated to be less than 20%. The gain value should be accurate beyond −28V as Ge absorption region is fully depleted. Impact ionization in silicon occurs before punch-through, which is inevitable as the electric field difference between the Si multiplication layer and the Ge absorption layer is designed to be ~300 kV/cm. This is not an issue as the APD device is designed for high gain operation with bias above punch-through. The gain increases sharply to reach ~40 near the breakdown voltage with a responsivity as high as 12 A/W at 1550 nm due to the carrier multiplication process within the Si layer. This Ge/Si APD device can work at a gain value of about ~30 with a relatively low dark current of ~5 μA as the tunneling current in the low band-gap Ge region is suppressed by designing a charge layer with an optimum doping concentration.

Figure 3
Fig. 3 Simulated electric field profile in the APD at different bias voltages.
shows the simulated electric field distribution in Ge and Si layers at different reverse bias voltages of 10 V, 15 V, 20 V, 25 V and 28 V. For bias voltages less than 25V, the electric field in the Ge absorption layer is close to zero, indicating that Ge is not depleted. With increasing reverse bias, the electric field in the Ge absorption layer and the Si multiplication layer increases simultaneously. The bulk of the electric potential is dropped across the Si multiplication region. For bias voltages higher than punch-through (28 V), the 1 μm-thick Ge layer is fully depleted. However, the electric field in Ge is still maintained at a moderate value (<30kV/cm), which is high enough for electrons and holes to achieve saturation velocity without Ge impact ionization. The electric field in the Si multiplication layer is nearly 380kV/cm, above which Si breakdown will take place for this type of junction.

The RF response of the device shown in Fig. 4
Fig. 4 RF response of a 30-µm-diameter APD at different gains under 1550 nm illumination. The −3 dB bandwidth is 8 GHz from gain of 32 to 39. The inset shows −3 dB bandwidth of a 30-µm-diameter PIN to be around 12 GHz.
was measured using an Agilent Lightwave Component Analyzer with its internal laser and modulator at operating at 1550 nm. The −3 dB bandwidth of a 30-μm-diameter p-i-i-n device fabricated on the same wafer with the APDs is ~12 GHz (inset of Fig. 4), which is limited by both RC and transit-time effects. Impedance was measured by the same analyzer. Both the p-i-i-n device and the APD had a series resistance of ~60 Ω and a capacitance of ~80 fF after punch-through. The calculated RC-limited bandwidth is 16.5 GHz. The carrier saturation velocities are 107 cm/S and 6 x 106 cm/S for Ge and Si, respectively [18

18. S. Sze, Physics of Semiconductor Devices (Wiley, 1981), Chap. 1.

]. Thereafter, total transit time in Ge and Si for the p-i-i-n device is 24 ps, giving rise to a transit-time limited bandwidth of 18.6 GHz. The total −3 dB bandwidth is calculated to be 13 GHz, which is close to the measured value of 12 GHz. For the APD, the −3 dB bandwidths at low bias voltages are less than 5 GHz as the Ge absorption layer is not fully depleted, which results in a long transit time as a result of slow carrier diffusion. When Ge is fully depleted, with an electric field of more than 10 kV/cm, the maximum measured bandwidth is 8 GHz for a gain of ~30. This bandwidth at high gain is likely to be dominated by avalanche build-up time. Bandwidth remains at 8 GHz when gain reaches to 39 before breakdown. This gives rise to a resulting gain-bandwidth product of 310 GHz as shown in Fig. 5
Fig. 5 Measured −3 dB bandwidth versus multiplication gain. The gain-bandwidth product is 310 GHz.
. No bandwidth degradation is observed when gain increases from ~30 to 39 because of the intrinsic low k value in silicon material [9

9. R. Emmons, “Avalanche-photodiode frequency response,” J. Appl. Phys. 38(9), 3705–3714 (1967). [CrossRef]

]. No impact ionization occurs in Ge absorption layer close to breakdown. Otherwise the bandwidth would drop significantly because germanium has a much higher k value. The −3 dB bandwidth at high gain can be increased further to ~10 GHz by reducing the silicon multiplication layer thickness.

4. Conclusion

A mesa-type normal incidence SACM Ge/Si APD designed for high gain operation (~30) and fabricated using selective Ge and Si growth was demonstrated using a CMOS-compatible process. The device achieved a responsivity of ~0.3 A/W at unity gain under 1550 nm illumination. The −3 dB bandwidth for a 30 µm-diameter APD is 8 GHz for gains from 30 to 39, resulting in a large gain-bandwidth product of 310 GHz for a C-band communication wavelength of 1550 nm.

References and links

1.

H. Nie, K. Anselm, C. Hu, S. Murtaza, B. Streetman, and J. Campbell, “High-speed resonant-cavity separate absorption and multiplication avalanche photodiodes with 130 GHz gain-bandwidth product,” Appl. Phys. Lett. 70(2), 161–163 (1997). [CrossRef]

2.

N. Yasuoka, H. Kuwatsuka, M. Makiuchi, T. Uchida, and A. Yasaki, “Large multiplication-bandwidth products in APDs with a thin InP multiplication layer,” in The 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2003. LEOS 2003 (IEEE/LEOS, 2003), Vol. 2, pp. 999–1000.

3.

J. Campbell, W. Tsang, G. Qua, and B. Johnson, “High-speed InP/InGaAsP/InGaAs avalanche photodiodes grown by chemical beam epitaxy,” IEEE J. Quantum Electron. 24(3), 496–500 (1988). [CrossRef]

4.

A. Rouvie, D. Carpentier, N. Lagay, J. Decobert, F. Pommereau, and M. Achouche, “High gain bandwidth product over 140 GHz planar junction AlInAs avalanche photodiodes,” IEEE Photon. Technol. Lett. 20(6), 455–457 (2008). [CrossRef]

5.

E. Yagyu, E. Ishimura, M. Nakaji, H. Itamoto, T. Aoyagi, K. Yoshiara, and Y. Tokuda, “Recent advances in AlInAs avalanche photodiodes,” Proc. OFC, 145–147 (2007).

6.

S. Demiguel, X. Zheng, N. Li, X. Li, J. Campbell, J. Decobert, N. Tscherptner, and A. Anselm, “High-responsivity and high-speed evanescently-coupled avalanche photodiodes,” Electron. Lett. 39(25), 1848–1849 (2003). [CrossRef]

7.

Y. Kang, M. Zadka, S. Litski, G. Sarid, M. Morse, M. J. Paniccia, Y. H. Kuo, J. Bowers, A. Beling, H. D. Liu, D. C. McIntosh, J. Campbell, and A. Pauchard, “Epitaxially-grown Ge/Si avalanche photodiodes for 1.3 microm light detection,” Opt. Express 16(13), 9365–9371 (2008). [CrossRef] [PubMed]

8.

X. Wang, L. Chen, W. Chen, H. Cui, Y. Hu, P. Cai, R. Yang, C. Hong, D. Pan, K. Ang, M. B. Yu, Q. Fang, and G. Q. Lo, "80 GHz bandwidth-gain-product Ge/Si avalanche photodetector by selective Ge growth," in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OMR3.

9.

R. Emmons, “Avalanche-photodiode frequency response,” J. Appl. Phys. 38(9), 3705–3714 (1967). [CrossRef]

10.

R. McIntyre, “The distribution of gains in uniformly multiplying avalanche photodiodes: theory,” IEEE Trans. Electron. Devices 19(6), 703–713 (1972). [CrossRef]

11.

Y. Kang, H.-D. Liu, M. Morse, M. J. Paniccia, M. Zadka, S. Litski, G. Sarid, A. Pauchard, Y.-H. Kuo, H.-W. Chen, W. S. Zaoui, J. E. Bowers, A. Beling, D. C. McIntosh, X. Zheng, and J. C. Campbell, “Monolithic germanium/silicon avalanche photodiodes with 340 GHz gain–bandwidth product,” Nat. Photonics 3(1), 59–63 (2009). [CrossRef]

12.

L. Tarof, J. Yu, R. Bruce, D. G. Knight, T. Baird, and B. Oosterbrink, “High-frequency performance of separate absorption grading, charge, and multiplication InP/InGaAs avalanche photodiodes,” IEEE Photon. Technol. Lett. 5(6), 672–674 (1993). [CrossRef]

13.

N. Duan, S. Wang, X. G. Zheng, X. Li, N. Li, J. C. Campbell, C. Wang, and L. A. Coldren, “Detrimental effect of impact ionization in the absorption region on the frequency response and excess noise performance of InGaAs/InAlAs SACM avalanche photodiodes,” IEEE J. Quantum Electron. 41(4), 568–572 (2005). [CrossRef]

14.

C. Masini, L. Calace, G. Assanto, H.-C. Luan, and L. C. Kimerling, “High-performance p-i-n Ge on Si photodetectors for the near infrared: from model to demonstration,” IEEE Trans. Electron. Dev. 48(6), 1092–1096 (2001). [CrossRef]

15.

Y. S. Shin, D. Lee, H. S. Lee, Y. J. Cho, C. J. Kim, and M. H. Jo, “Determination of the photocarrier diffusion length in intrinsic Ge nanowires,” Opt. Express 19(7), 6119–6124 (2011). [CrossRef] [PubMed]

16.

Y. Hirota, S. Ando, and T. Ishibashi, “High-speed avalanche photodiode with a neutral absorption layer for 1.55 µm wavelength,” Jpn. J. Appl. Phys. 43(No. 3A), L375–L377 (2004). [CrossRef]

17.

K. Shiba, T. Nakata, T. Takeuchi, K. Kasahara, and K. Makita, “Theoretical and experimental study on waveguide avalanche photodiodes with an undepleted absorption layer for 25-Gb/s operation,” IEEE J. Lightwave Technol. 29(2), 153–161 (2011). [CrossRef]

18.

S. Sze, Physics of Semiconductor Devices (Wiley, 1981), Chap. 1.

OCIS Codes
(040.5160) Detectors : Photodetectors
(060.2330) Fiber optics and optical communications : Fiber optics communications
(040.1345) Detectors : Avalanche photodiodes (APDs)

ToC Category:
Detectors

History
Original Manuscript: January 10, 2012
Revised Manuscript: February 17, 2012
Manuscript Accepted: March 9, 2012
Published: April 27, 2012

Virtual Issues
Vol. 7, Iss. 7 Virtual Journal for Biomedical Optics

Citation
Ning Duan, Tsung-Yang Liow, Andy Eu-Jin Lim, Liang Ding, and G. Q. Lo, "310 GHz gain-bandwidth product Ge/Si avalanche photodetector for 1550 nm light detection," Opt. Express 20, 11031-11036 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-10-11031


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References

  1. H. Nie, K. Anselm, C. Hu, S. Murtaza, B. Streetman, and J. Campbell, “High-speed resonant-cavity separate absorption and multiplication avalanche photodiodes with 130 GHz gain-bandwidth product,” Appl. Phys. Lett.70(2), 161–163 (1997). [CrossRef]
  2. N. Yasuoka, H. Kuwatsuka, M. Makiuchi, T. Uchida, and A. Yasaki, “Large multiplication-bandwidth products in APDs with a thin InP multiplication layer,” in The 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2003. LEOS 2003 (IEEE/LEOS, 2003), Vol. 2, pp. 999–1000.
  3. J. Campbell, W. Tsang, G. Qua, and B. Johnson, “High-speed InP/InGaAsP/InGaAs avalanche photodiodes grown by chemical beam epitaxy,” IEEE J. Quantum Electron.24(3), 496–500 (1988). [CrossRef]
  4. A. Rouvie, D. Carpentier, N. Lagay, J. Decobert, F. Pommereau, and M. Achouche, “High gain bandwidth product over 140 GHz planar junction AlInAs avalanche photodiodes,” IEEE Photon. Technol. Lett.20(6), 455–457 (2008). [CrossRef]
  5. E. Yagyu, E. Ishimura, M. Nakaji, H. Itamoto, T. Aoyagi, K. Yoshiara, and Y. Tokuda, “Recent advances in AlInAs avalanche photodiodes,” Proc. OFC, 145–147 (2007).
  6. S. Demiguel, X. Zheng, N. Li, X. Li, J. Campbell, J. Decobert, N. Tscherptner, and A. Anselm, “High-responsivity and high-speed evanescently-coupled avalanche photodiodes,” Electron. Lett.39(25), 1848–1849 (2003). [CrossRef]
  7. Y. Kang, M. Zadka, S. Litski, G. Sarid, M. Morse, M. J. Paniccia, Y. H. Kuo, J. Bowers, A. Beling, H. D. Liu, D. C. McIntosh, J. Campbell, and A. Pauchard, “Epitaxially-grown Ge/Si avalanche photodiodes for 1.3 microm light detection,” Opt. Express16(13), 9365–9371 (2008). [CrossRef] [PubMed]
  8. X. Wang, L. Chen, W. Chen, H. Cui, Y. Hu, P. Cai, R. Yang, C. Hong, D. Pan, K. Ang, M. B. Yu, Q. Fang, and G. Q. Lo, "80 GHz bandwidth-gain-product Ge/Si avalanche photodetector by selective Ge growth," in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OMR3.
  9. R. Emmons, “Avalanche-photodiode frequency response,” J. Appl. Phys.38(9), 3705–3714 (1967). [CrossRef]
  10. R. McIntyre, “The distribution of gains in uniformly multiplying avalanche photodiodes: theory,” IEEE Trans. Electron. Devices19(6), 703–713 (1972). [CrossRef]
  11. Y. Kang, H.-D. Liu, M. Morse, M. J. Paniccia, M. Zadka, S. Litski, G. Sarid, A. Pauchard, Y.-H. Kuo, H.-W. Chen, W. S. Zaoui, J. E. Bowers, A. Beling, D. C. McIntosh, X. Zheng, and J. C. Campbell, “Monolithic germanium/silicon avalanche photodiodes with 340 GHz gain–bandwidth product,” Nat. Photonics3(1), 59–63 (2009). [CrossRef]
  12. L. Tarof, J. Yu, R. Bruce, D. G. Knight, T. Baird, and B. Oosterbrink, “High-frequency performance of separate absorption grading, charge, and multiplication InP/InGaAs avalanche photodiodes,” IEEE Photon. Technol. Lett.5(6), 672–674 (1993). [CrossRef]
  13. N. Duan, S. Wang, X. G. Zheng, X. Li, N. Li, J. C. Campbell, C. Wang, and L. A. Coldren, “Detrimental effect of impact ionization in the absorption region on the frequency response and excess noise performance of InGaAs/InAlAs SACM avalanche photodiodes,” IEEE J. Quantum Electron.41(4), 568–572 (2005). [CrossRef]
  14. C. Masini, L. Calace, G. Assanto, H.-C. Luan, and L. C. Kimerling, “High-performance p-i-n Ge on Si photodetectors for the near infrared: from model to demonstration,” IEEE Trans. Electron. Dev.48(6), 1092–1096 (2001). [CrossRef]
  15. Y. S. Shin, D. Lee, H. S. Lee, Y. J. Cho, C. J. Kim, and M. H. Jo, “Determination of the photocarrier diffusion length in intrinsic Ge nanowires,” Opt. Express19(7), 6119–6124 (2011). [CrossRef] [PubMed]
  16. Y. Hirota, S. Ando, and T. Ishibashi, “High-speed avalanche photodiode with a neutral absorption layer for 1.55 µm wavelength,” Jpn. J. Appl. Phys.43(No. 3A), L375–L377 (2004). [CrossRef]
  17. K. Shiba, T. Nakata, T. Takeuchi, K. Kasahara, and K. Makita, “Theoretical and experimental study on waveguide avalanche photodiodes with an undepleted absorption layer for 25-Gb/s operation,” IEEE J. Lightwave Technol.29(2), 153–161 (2011). [CrossRef]
  18. S. Sze, Physics of Semiconductor Devices (Wiley, 1981), Chap. 1.

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