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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 28 — Dec. 31, 2012
  • pp: 29338–29346
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A critically coupled Germanium photodetector under vertical illumination

Tsung-Ting Wu, Ching-Yang Chou, Ming-Chang M. Lee, and Neil Na  »View Author Affiliations


Optics Express, Vol. 20, Issue 28, pp. 29338-29346 (2012)
http://dx.doi.org/10.1364/OE.20.029338


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Abstract

We propose and study a practical design of a Germanium photodetector implemented on a Silicon-on-insulator substrate to reach the critical coupling regime under vertical illumination at 1310 nm wavelength. With appropriate optimization procedures, a high efficiency bandwidth product larger than 50 GHz and a large 3dB spectral full width around 30 nm can be obtained given realistic material parameters and fabrication constraints. Our device is fully compatible to the state-of-art CMOS process technology, and may serve as a high performance, low cost solution for the optical receiver in Silicon photonics based optical interconnects.

© 2012 OSA

1. Introduction

2. Device design considerations and calculations

In Fig. 1(a)
Fig. 1 (a) A vertically illuminated Ge on SOI photodetector. (b) The same as in (a) but with a dielectric DBR mirror deposited on top and a metallic V-groove mirror fabricated at bottom.
, we show the schematic plot of a Ge photodetector based on a commercially available SOI substrate with 250 nm thick crystalline Si (c-Si) and 3 μm thick buried oxide (BOX). Ge is assumed to be epitaxially grown on c-Si with high quality so that the defect induced leakage current arisen from Ge-Si interface lattice-mismatch can be minimized. Phosphorus and Boron are used for the n + and p + doped regions in Si and Ge, respectively. After Ge mesa etch, the Ge surface is passivated by a thin layer of amorphous Si (a-Si) [20

20. M. Morse, O. Dosunmu, G. Sarid, and Y. Chetrit, “Performance of Ge-on-Si p-i-n photodetectors for standard eeceiver modules,” IEEE Photon. Technol. Lett. 18(23), 2442–2444 (2006). [CrossRef]

] and NiSi contacts with Al electrodes are applied for backend process. The aperture accepting incoming light has a diameter equal to 14 μm, which is chosen to butt-couple a single-mode fiber with unity fill factor. The 5 μm and 1 μm design rules (from Ge mesa sidewall to n and p electrodes) as well as the 10 μm and 1 μm metal trace widths (for n and p electrodes) are limited by i-line lithography tool. In Fig. 1(b), we add a front side mirror by depositing Si and oxide to form a dielectric distributed-Bragg-reflector (DBR). A back side mirror is fabricated by first wet-etching the substrate Si to open up a V groove and then coat it with a thin Al layer.

The use of metal coating on BOX to form a back side mirror is based on three considerations. First, the BOX layer serves as a Si wet etch stop so that the cavity thickness can be precisely controlled. Second, we apply thin metal coating instead of thick DBR film on BOX to avoid stresses that can potential crack the wafer due to large V groove topography. Finally, a Si-oxide-Al layer offers ~98% reflectivity that is superior compared to a Si-Al layer with only ~89% reflectivity. The reflectivity of back side metallic mirror has a crucial impact on our device performance and will be discussed in detail in the following paragraphs.

To model our device, we construct an effective cavity structure shown in Fig. 2
Fig. 2 An effective cavity structure (RHS) to model the central portion of the Ge photodetector in Fig. 1 (LHS).
. The BOX and Al layers are considered as a part of back side metallic mirror, and the DBR layers above a-Si are considered as a part of front side dielectric mirror. The reflection between Ge and a-Si or c-Si interface is neglected because it’s only ~0.8%, given Ge refractive index nGe = 4.2 and Si refractive index nSi = 3.5. Such an approximation is valid in the critical coupling regime that we are interested in and will be confirmed numerically in Sec. 3. By applying the formalism of waveguide-ring resonator coupling [17

17. A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14(4), 483–485 (2002). [CrossRef]

], we can show that when the structure is vertically illuminated,
R=|b|2|a|2=γ2+r22γrcosθ1+γ2r22γrcosθ
(1)
where R is the total reflectance of our structure. a and b are the incident and reflected fields. γ2 is the power decay ratio after a round trip, and r2 is the dielectric mirror reflectance when light is injected from air. θ is the round trip phase shift. Note that analogy between Eq. (4) in ref. 17

17. A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14(4), 483–485 (2002). [CrossRef]

and Eq. (1) here can be established if the waveguide input/output ports on chip are associated with the incident/reflected fields in free space. The condition of critical coupling occurs at
γ=ri.e.|rM|e4πλ0κGetGe=|rD|,
(2)
where rM and rD are the reflectivities of metallic and dielectric mirrors seen from the cavity, respectively. λ0 is the wavelength of interest. κGe is the imaginary part of Ge refractive index, and tGe is the Ge layer thickness. When the condition in Eq. (2) is met, the light reflected by the dielectric mirror to air and the light transmitted from the cavity to air destructively interfere. All incoming light is therefore locked completely inside the cavity and dissipated by Ge and metal absorptions. In Fig. 3
Fig. 3 The required Ge thickness to reach the critical coupling plotted as a function of metallic mirror reflectance and dielectric mirror reflectance.
, we plot the required tGe to reach the critical coupling as a function of |rM|2 and |rD|2 given λ0 and κGe equal to 1310 nm and 0.08. It is shown that for a given tGe, a critical coupling can happen as long as |rM|2 > |rD|2. Note that the white region in Fig. 3 fails to satisfy this requirement.

For our Ge photodetector, only the optical power absorbed by Ge may contribute to the electrical current so the actual quantum efficiency at a critical coupling is calculated by
η=1e8πλ0κGetGe(1|rM|2)+(1e8πλ0κGetGe)
(3)
to exclude the metal absorption. η is plotted as a function of |rM|2 and |rD|2 in Fig. 4(a)
Fig. 4 Ge photodetector (a) efficiency, (b) bandwidth, and (c) efficiency-bandwidth-product plotted as a function of metallic mirror reflectance and dielectric mirror reflectance at a critical coupling.
, and a near unity quantum efficiency can only be obtained when |rM|2 is sufficiently close to 1. Next, we calculate the bandwidth of our Ge photodetector, which is controlled by the carrier transit time in the depletion region of p-i-n junction and the circuit delay time. The total optical bandwidth can be expressed by
BW=12π(tGe2.4vs)2+(RC)2
(4)
where the first and second terms in the square root correspond to carrier drift time and device resistance-capacitance delay time, respectively. vs is the hole (slower carrier) saturation velocity in Ge and is taken as 6x106 cm/s; R is the series resistance and C is the total capacitance. To accurately determine the bandwidth, we calculate R usingR=ρ4πt+ρtδ2πrocothwδfor a circular geometry [21

21. S. M. Sze, Physics of Semiconductor Device, 2nd ed. (John Wiley & Sons, 1981).

], in which the first and second terms are caused by sheet resistance (thin doped regions in Ge and Si) and contact resistance (NiSi plus Al), respectively. ρ and t are the resistivity and thickness of the doping region. δ is the transfer length of a contact and is equal toρct/ρwhere ρc is the specific contact resistivity. ro is the distance between detector center and the middle of ring electrode trace. w is the width of ring electrode trace. The following parameters [22

22. C.-K. Tseng, J.-D. Tian, W.-C. Hung, K.-N. Ku, C.-W. Tseng, Y.-S. Liu, N. Na, and M.-C. M. Lee, “Self-aligned microbonded Ge/Si PIN waveguide photodetector,” post-deadline session, 9th IEEE International Conference on Group IV Photonics (GFP), 29–31 Aug. (2012).

] are used: ρ = 9x10−4 Ω·cm and 5x10−4 Ω·cm for n + Si and p + Ge; t = 150 nm; ρc = 5x10−8 Ω·cm2 and 3.29x10−6 Ω·cm2 for n + NiSi-Si contact and p + NiSi-Ge contact. The final R is equal to 9.85 Ω (Ge related) plus 4.92 Ω (Si related) ~15 Ω. In addition, C=nGe2ε0A/tGeis used to calculate the junction capacitance but neglect the parasitic capacitance associated with electrode pads. A is the area of p-i-n junction. In Fig. 4(b), BW at a critical coupling is plotted as a function of |rM|2 and |rD|2. It can be seen that the maximum bandwidth can be obtained at tGe ~300 nm and its value is slightly larger than 50 GHz. We also plot the EBP at a critical coupling as a function of |rM|2 and |rD|2 in Fig. 4(c), and find that a > 50 GHz EBP can be readily reached if |rM|2 is sufficiently close to 1.

Since the proposed Ge photodetector is based on reaching the critical coupling regime in a one-sided resonant cavity coupled to free-space, it is natural to ask whether the cavity linewidth is too small so the efficiency degrades significantly when there is an incident laser wavelength fluctuation or thermally induced wavelength drift. In Fig. 5(c)
Fig. 5 (a) Cavity order, (b) a-Si thickness, and (c) FWHM of cavity resonance plotted as a function of metallic mirror reflectance and dielectric mirror reflectance at a critical coupling.
, we plot Δλ, the spectral full-width-half maximum (FHWM) of cavity resonance at a critical coupling, as a function of |rM|2 and |rD|2 using the formula
Δλ=λ0πm1|r|2|r|
(5)
derived from Eq. (1) assuming Δλ << λ0. m is the cavity order defined as the round rip phase shift at λ0 divided by 2π. Note that the a-Si thickness is adjusted for every given |rM|2 and |rD|2 so that λ0 is positioned at 1310 nm. In addition, a minimum a-Si thickness (see Fig. 5(b)) is chosen to have the lowest possible cavity order (see Fig. 5(a)), i.e., picking up the smallest possible cavity Q factor, to maximize the spectral FWHM. It is shown that at |rM|2 ~98% and |rD|2 ~61%, a ~51 GHz EBP can be reach accompanied with a Δλ ~51 nm (Q ~26). Such a broad spectral response suggests that our device is robust against the wavelength mismatch between incoming laser and photodetector.

3. Numerical simulations

Although the analysis discussed above has captured the main idea of an effective cavity structure shown in Fig. 2, it is necessary to perform numerical simulations to take into account the finer design details. In the following, we use a commercial finite-difference-time-domain (FDTD) simulation package [23

23. Lumerical Solutions, Inc., http://www.lumerical.com/.

] to investigate our critically coupled Ge photodetector. Here we target the point (|rM|2, |rD|2) = (61.5%, 98.1%) on Fig. 4(c) with an EBP = 51.4 GHz. The corresponding tGe is 304 nm. For the part of dielectric mirror, a three quarter-wave-plate structure, i.e., oxide-Si-oxide on top of a-Si, has a reflectance 65.6% and can be tweaked to 61.5% using DBR Si thickness ~93 nm and DBR oxide thickness ~226 nm. For the part of metallic mirror consisting of BOX and Al, we plot the simulated |rM|2 as a function of tBOX in Fig. 6(a)
Fig. 6 (a) The Al mirror reflectance plotted as a function of BOX thickness. (b) The total reflectance of our device plotted as a function of incoming laser wavelength. The imaginary part of refractive index of Ge and Al are “turned” on/off to illustrate the effect of critical coupling. The simulations are done via 2D FDTD method with Bloch boundary condition in the horizontal direction.
. The maximum reflectance is 98.4% if the BOX thickness tBOX is equal to quarter wavelength in oxide, and drops to 89.1% if tBOX is equal to half wavelength in oxide. Eventually tBOX ~2.922 μm (a number that is closest to 3 μm) is chosen to pick up 98.1% reflectance.

As discussed previously, the actual quantum efficiency at a critcal coupling depends on the portion of optical power absorbed by Ge and is not unity when there is metal absorption. To simulate this quantity, we enclose the Ge region by Poynting vector moniters and calculate the the power difference between the output and input directions. This corresponds exactly to the actual quantum efficiency and is plotted in Fig. 7
Fig. 7 The quantum efficiency plotted as a function of incoming laser wavelength with adjustment in (a) a-Si layer thickness and (b) BOX layer thickness. The solid lines are simulated via 2D FDTD method with Bloch boundary condition in the horizontal direction, and the dashed lines are simulated via full-structure 3D FDTD method.
(red-solid curve). At 1310 nm, η is ~95% and matches very nicely with analytical prediction with < 1% difference. On the other hand, Δλ is ~30 nm (Q ~44) and is smaller than the analytical prediction. It can be understood as the thicknesses of dielectric and metal mirrors are neglected previously, which underestimates the cavity Q factor. Note that the above simulations are all done via 2D FDTD method with Bloch boundary condition in the horizontal direction. We have also performed a full-structure 3D FDTD simulation, and the resultant η is plotted in Fig. 7 (yellow-dashed curve) in which the peak value is reduced to ~90% at 1310 nm. This is due to a small portion of light diffracting horizontally out of the mirror coverage during cavity photon lifetime. In Fig. 7(a) and 7(b), we adjust ta-Si and tBOX respectively to investigate the impact of layer stack uniformities. It is observed that the peak wavelength shift is quite sensitive to both ta-Si and tBOX variations (though the case of a-Si is stronger as expected), which suggests a precise control over layer stack thicknesses is crucial to having a high device yield over the whole wafer.

4. Summary

A critically coupled Ge photodetector fabricated on SOI substrate under vertical illumination is proposed and studied. The analytical calculations are verified with numerical simulations, and it is shown that a > 90% quantum efficiency and > 50 GHz optical bandwidth operation at 1310 nm wavelength is accessible. Consequently, the corresponding EBP is enhanced by an order of magnitude compared to conventional Ge-on-Si photodetectors. The spectral FWHM of an optimum design is ~30 nm, and further improvement on the spectral response to feature a “flat-top” shape may be obtained by designing a dielectric mirror with anomalous dispersion [24

24. C.-H. Chen, K. Tetz, and Y. Fainman, “Resonant-cavity-enhanced p-i-n photodiode with a broad quantum-efficiency spectrum by use of an anomalous-dispersion mirror,” Appl. Opt. 44(29), 6131–6140 (2005). [CrossRef] [PubMed]

]. This can be an attractive solution not only as a robust, stand-alone photodetector but also for application of wavelength-division multiplexing (WDM) in vertical illumination configuration.

Acknowledgments

The work is partially supported by Ministry of Education and National Tsing-Hua University (#100N7080E1) in Taiwan. T.T.W. and C.Y.C. thank Chih-Kuo Tseng for useful discussions on device fabrication.

References and links

1.

J. Michel, J. Liu, and L. C. Kimerling, “High-performance Ge-on-Si photodetectors,” Nat. Photonics 4(8), 527–534 (2010). [CrossRef]

2.

H. Yu, S. Ren, W. S. Jung, A. K. Okyay, D. A. B. Miller, and K. C. Saraswat, “High-efficiency p-i-n photodetectors on selective-area-grown Ge for monolithic integration,” IEEE Electron Device Lett. 30(11), 1161–1163 (2009). [CrossRef]

3.

J. Joo, S. Kim, I. G. Kim, K.-S. Jang, and G. Kim, “High-sensitivity 10 Gbps Ge-on-Si photoreceiver operating at λ~1.55 μm,” Opt. Express 18(16), 16474–16479 (2010). [CrossRef] [PubMed]

4.

J. Osmond, L. Vivien, J.-M. Fédéli, D. Marris-Morini, P. Crozat, J.-F. Damlencourt, E. Cassan, and Y. Lecunff, “40 Gb/s surface-illuminated Ge-on-Si photodetectors,” Appl. Phys. Lett. 95(15), 151116 (2009). [CrossRef]

5.

S. Klinger, M. Berroth, M. Kaschel, M. Oehme, and E. Kasper, “Ge-on-Si p-i-n photodiodes with a 3-dB bandwidth of 49 GHz,” IEEE Photon. Technol. Lett. 21(13), 920–922 (2009). [CrossRef]

6.

T. Yin, R. Cohen, M. M. Morse, G. Sarid, Y. Chetrit, D. Rubin, and M. J. Paniccia, “31 GHz Ge n-i-p waveguide photodetectors on Silicon-on-Insulator substrate,” Opt. Express 15(21), 13965–13971 (2007). [CrossRef] [PubMed]

7.

L. Colace, V. Sorianello, M. Balbi, and G. Assanto, “Germanium near infrared detector in Silicon on insulator,” Appl. Phys. Lett. 91(2), 021107 (2007). [CrossRef]

8.

D. Feng, S. Liao, P. Dong, N.-N. Feng, H. Liang, D. Zheng, C.-C. Kung, J. Fong, R. Shafiiha, J. Cunningham, A. V. Krishnamoorthy, and M. Asghari, “High-speed Ge photodetector monolithically integrated with large cross-section Silicon-on-insulator waveguide,” Appl. Phys. Lett. 95(26), 261105 (2009). [CrossRef]

9.

C. T. DeRose, D. C. Trotter, W. A. Zortman, A. L. Starbuck, M. Fisher, M. R. Watts, and P. S. Davids, “Ultra compact 45 GHz CMOS compatible Germanium waveguide photodiode with low dark current,” Opt. Express 19(25), 24897–24904 (2011). [CrossRef] [PubMed]

10.

A. Barkai, A. Liu, D. Kim, R. Cohen, N. Elek, H.-H. Chang, B. H. Malik, R. Gabay, R. Jones, M. Paniccia, and N. Izhaky, “Double-stage taper for coupling between SOI waveguides and single-mode fiber,” J. Lightwave Technol. 26(24), 3860–3865 (2008). [CrossRef]

11.

N. Na and T. Yin, “Misalignment-tolerant spot-size converter for efficient coupling between single-mode fibers and integrated optical receivers,” IEEE Photon. J. 4(1), 187–193 (2012). [CrossRef]

12.

D. Vermeulen, S. Selvaraja, P. Verheyen, G. Lepage, W. Bogaerts, P. Absil, D. Van Thourhout, and G. Roelkens, “High-efficiency fiber-to-chip grating couplers realized using an advanced CMOS-compatible Silicon-on-insulator platform,” Opt. Express 18(17), 18278–18283 (2010). [CrossRef] [PubMed]

13.

N. Na, H. Frish, I.-W. Hsieh, O. Harel, R. George, A. Barkai, and H. Rong, “Efficient broadband Silicon-on-insulator grating coupler with low backreflection,” Opt. Lett. 36(11), 2101–2103 (2011). [CrossRef] [PubMed]

14.

K. Kishino, M. S. Ünlü, J.-I. Chyi, J. Reed, L. Arsenault, and H. Morkoc, “Resonant cavity-enhanced (RCE) photodetectors,” IEEE J. Quantum Electron. 27(8), 2025–2034 (1991). [CrossRef]

15.

M. S. Ünlü and S. Strite, “Resonant cavity enhanced photonic devices,” Appl. Phys. Rev. 78(2), 607–639 (1995). [CrossRef]

16.

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85(1), 74–77 (2000). [CrossRef] [PubMed]

17.

A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14(4), 483–485 (2002). [CrossRef]

18.

M. K. Emsley, O. Dosunmu, and M. S. Ünlü, “High-speed resonant-cavity-enhanced Silicon photodetectors on reflecting Silicon-on-insulator substrates,” IEEE Photon. Technol. Lett. 14(4), 519–521 (2002). [CrossRef]

19.

O. I. Dosunmu, D. D. Cannon, M. K. Emsley, L. C. Kimerling, and M. S. Ünlü, “High-speed resonant cavity enhanced Ge photodetectors on reflecting Si substrates for 1550-nm operation,” IEEE Photon. Technol. Lett. 17(1), 175–177 (2005). [CrossRef]

20.

M. Morse, O. Dosunmu, G. Sarid, and Y. Chetrit, “Performance of Ge-on-Si p-i-n photodetectors for standard eeceiver modules,” IEEE Photon. Technol. Lett. 18(23), 2442–2444 (2006). [CrossRef]

21.

S. M. Sze, Physics of Semiconductor Device, 2nd ed. (John Wiley & Sons, 1981).

22.

C.-K. Tseng, J.-D. Tian, W.-C. Hung, K.-N. Ku, C.-W. Tseng, Y.-S. Liu, N. Na, and M.-C. M. Lee, “Self-aligned microbonded Ge/Si PIN waveguide photodetector,” post-deadline session, 9th IEEE International Conference on Group IV Photonics (GFP), 29–31 Aug. (2012).

23.

Lumerical Solutions, Inc., http://www.lumerical.com/.

24.

C.-H. Chen, K. Tetz, and Y. Fainman, “Resonant-cavity-enhanced p-i-n photodiode with a broad quantum-efficiency spectrum by use of an anomalous-dispersion mirror,” Appl. Opt. 44(29), 6131–6140 (2005). [CrossRef] [PubMed]

OCIS Codes
(040.5160) Detectors : Photodetectors
(250.0250) Optoelectronics : Optoelectronics

ToC Category:
Detectors

History
Original Manuscript: November 5, 2012
Revised Manuscript: December 10, 2012
Manuscript Accepted: December 10, 2012
Published: December 18, 2012

Citation
Tsung-Ting Wu, Ching-Yang Chou, Ming-Chang M. Lee, and Neil Na, "A critically coupled Germanium photodetector under vertical illumination," Opt. Express 20, 29338-29346 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-28-29338


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References

  1. J. Michel, J. Liu, and L. C. Kimerling, “High-performance Ge-on-Si photodetectors,” Nat. Photonics4(8), 527–534 (2010). [CrossRef]
  2. H. Yu, S. Ren, W. S. Jung, A. K. Okyay, D. A. B. Miller, and K. C. Saraswat, “High-efficiency p-i-n photodetectors on selective-area-grown Ge for monolithic integration,” IEEE Electron Device Lett.30(11), 1161–1163 (2009). [CrossRef]
  3. J. Joo, S. Kim, I. G. Kim, K.-S. Jang, and G. Kim, “High-sensitivity 10 Gbps Ge-on-Si photoreceiver operating at λ~1.55 μm,” Opt. Express18(16), 16474–16479 (2010). [CrossRef] [PubMed]
  4. J. Osmond, L. Vivien, J.-M. Fédéli, D. Marris-Morini, P. Crozat, J.-F. Damlencourt, E. Cassan, and Y. Lecunff, “40 Gb/s surface-illuminated Ge-on-Si photodetectors,” Appl. Phys. Lett.95(15), 151116 (2009). [CrossRef]
  5. S. Klinger, M. Berroth, M. Kaschel, M. Oehme, and E. Kasper, “Ge-on-Si p-i-n photodiodes with a 3-dB bandwidth of 49 GHz,” IEEE Photon. Technol. Lett.21(13), 920–922 (2009). [CrossRef]
  6. T. Yin, R. Cohen, M. M. Morse, G. Sarid, Y. Chetrit, D. Rubin, and M. J. Paniccia, “31 GHz Ge n-i-p waveguide photodetectors on Silicon-on-Insulator substrate,” Opt. Express15(21), 13965–13971 (2007). [CrossRef] [PubMed]
  7. L. Colace, V. Sorianello, M. Balbi, and G. Assanto, “Germanium near infrared detector in Silicon on insulator,” Appl. Phys. Lett.91(2), 021107 (2007). [CrossRef]
  8. D. Feng, S. Liao, P. Dong, N.-N. Feng, H. Liang, D. Zheng, C.-C. Kung, J. Fong, R. Shafiiha, J. Cunningham, A. V. Krishnamoorthy, and M. Asghari, “High-speed Ge photodetector monolithically integrated with large cross-section Silicon-on-insulator waveguide,” Appl. Phys. Lett.95(26), 261105 (2009). [CrossRef]
  9. C. T. DeRose, D. C. Trotter, W. A. Zortman, A. L. Starbuck, M. Fisher, M. R. Watts, and P. S. Davids, “Ultra compact 45 GHz CMOS compatible Germanium waveguide photodiode with low dark current,” Opt. Express19(25), 24897–24904 (2011). [CrossRef] [PubMed]
  10. A. Barkai, A. Liu, D. Kim, R. Cohen, N. Elek, H.-H. Chang, B. H. Malik, R. Gabay, R. Jones, M. Paniccia, and N. Izhaky, “Double-stage taper for coupling between SOI waveguides and single-mode fiber,” J. Lightwave Technol.26(24), 3860–3865 (2008). [CrossRef]
  11. N. Na and T. Yin, “Misalignment-tolerant spot-size converter for efficient coupling between single-mode fibers and integrated optical receivers,” IEEE Photon. J.4(1), 187–193 (2012). [CrossRef]
  12. D. Vermeulen, S. Selvaraja, P. Verheyen, G. Lepage, W. Bogaerts, P. Absil, D. Van Thourhout, and G. Roelkens, “High-efficiency fiber-to-chip grating couplers realized using an advanced CMOS-compatible Silicon-on-insulator platform,” Opt. Express18(17), 18278–18283 (2010). [CrossRef] [PubMed]
  13. N. Na, H. Frish, I.-W. Hsieh, O. Harel, R. George, A. Barkai, and H. Rong, “Efficient broadband Silicon-on-insulator grating coupler with low backreflection,” Opt. Lett.36(11), 2101–2103 (2011). [CrossRef] [PubMed]
  14. K. Kishino, M. S. Ünlü, J.-I. Chyi, J. Reed, L. Arsenault, and H. Morkoc, “Resonant cavity-enhanced (RCE) photodetectors,” IEEE J. Quantum Electron.27(8), 2025–2034 (1991). [CrossRef]
  15. M. S. Ünlü and S. Strite, “Resonant cavity enhanced photonic devices,” Appl. Phys. Rev.78(2), 607–639 (1995). [CrossRef]
  16. M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett.85(1), 74–77 (2000). [CrossRef] [PubMed]
  17. A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett.14(4), 483–485 (2002). [CrossRef]
  18. M. K. Emsley, O. Dosunmu, and M. S. Ünlü, “High-speed resonant-cavity-enhanced Silicon photodetectors on reflecting Silicon-on-insulator substrates,” IEEE Photon. Technol. Lett.14(4), 519–521 (2002). [CrossRef]
  19. O. I. Dosunmu, D. D. Cannon, M. K. Emsley, L. C. Kimerling, and M. S. Ünlü, “High-speed resonant cavity enhanced Ge photodetectors on reflecting Si substrates for 1550-nm operation,” IEEE Photon. Technol. Lett.17(1), 175–177 (2005). [CrossRef]
  20. M. Morse, O. Dosunmu, G. Sarid, and Y. Chetrit, “Performance of Ge-on-Si p-i-n photodetectors for standard eeceiver modules,” IEEE Photon. Technol. Lett.18(23), 2442–2444 (2006). [CrossRef]
  21. S. M. Sze, Physics of Semiconductor Device, 2nd ed. (John Wiley & Sons, 1981).
  22. C.-K. Tseng, J.-D. Tian, W.-C. Hung, K.-N. Ku, C.-W. Tseng, Y.-S. Liu, N. Na, and M.-C. M. Lee, “Self-aligned microbonded Ge/Si PIN waveguide photodetector,” post-deadline session, 9th IEEE International Conference on Group IV Photonics (GFP), 29–31 Aug. (2012).
  23. Lumerical Solutions, Inc., http://www.lumerical.com/ .
  24. C.-H. Chen, K. Tetz, and Y. Fainman, “Resonant-cavity-enhanced p-i-n photodiode with a broad quantum-efficiency spectrum by use of an anomalous-dispersion mirror,” Appl. Opt.44(29), 6131–6140 (2005). [CrossRef] [PubMed]

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