Abstract

We report a spatial model of optical crosstalk in InGaAsP Geiger-mode APD focal plane arrays created via non-sequential ray tracing. Using twenty-four equivalent experimental data sets as a baseline, we show that experimental results can be reproduced to a high degree of accuracy by incorporating secondary crosstalk effects, with reasonable assumptions of material and emission source properties. We use this model to categorize crosstalk according to source and path, showing that the majority of crosstalk in the immediate neighborhood of avalanching pixels in the present devices can be attributed to direct line-of-sight emissions.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
  8. Y. Kang, H. Lu, Y.-H. Lo, D. Bethune, and W. Risk, “Dark count probability and quantum efficiency of avalanche photodiodes for single-photon detection,” Appl. Phys. Lett. 83(14), 2955–2957 (2003).
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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  20. B. F. Aull, D. R. Schuette, D. J. Young, D. M. Craig, B. J. Felton, and K. Warner, “A Study of Crosstalk in a 256 x 256 Photon Counting Imager Based on Silicon Geiger-Mode Avalanche Photodiodes,” IEEE Sens. J. 15, 2123–2132 (2015).
    [Crossref]
  21. M. A. Itzler, U. Krishnamachari, M. Entwistle, X. Jiang, M. Owens, and K. Slomkowski, “Dark Count Statistics in Geiger-Mode Avalanche Photodiode Cameras for 3-D Imaging LADAR,” IEEE J. Quantum Electron. 20, 3802111 (2014).

2015 (1)

B. F. Aull, D. R. Schuette, D. J. Young, D. M. Craig, B. J. Felton, and K. Warner, “A Study of Crosstalk in a 256 x 256 Photon Counting Imager Based on Silicon Geiger-Mode Avalanche Photodiodes,” IEEE Sens. J. 15, 2123–2132 (2015).
[Crossref]

2014 (1)

M. A. Itzler, U. Krishnamachari, M. Entwistle, X. Jiang, M. Owens, and K. Slomkowski, “Dark Count Statistics in Geiger-Mode Avalanche Photodiode Cameras for 3-D Imaging LADAR,” IEEE J. Quantum Electron. 20, 3802111 (2014).

2008 (3)

I. Rech, A. Ingargiola, R. Spinelli, I. Labanca, S. Marangoni, M. Ghioni, and S. Cova, “Optical crosstalk in single photon avalanche diode arrays: A new complete model,” Opt. Express 16(12), 8381–8394 (2008).
[Crossref] [PubMed]

E. Sciacca, G. Condorelli, S. Aurite, S. Lombardo, M. Mazzillo, D. Sanfilippo, G. Fallica, and E. Rimini, “Crosstalk characterization in Geiger-mode avalanche photodiode arrays,” IEEE Electron. Dev. Lett. 29(3), 218–220 (2008).
[Crossref]

I. Rech, A. Ingargiola, R. Spinelli, I. Labanca, S. Marangoni, M. Ghioni, and S. Cova, “A new approach to optical crosstalk modeling in single-photon avalanche diodes,” IEEE Photonics Technol. Lett. 20(5), 330–332 (2008).
[Crossref]

2006 (1)

D. Renker, “Geiger-mode avalanche photodiodes, history, properties and problems,” Nucl. Instrum. Methods Phys. Res. A 567(1), 48–56 (2006).
[Crossref]

2003 (1)

Y. Kang, H. Lu, Y.-H. Lo, D. Bethune, and W. Risk, “Dark count probability and quantum efficiency of avalanche photodiodes for single-photon detection,” Appl. Phys. Lett. 83(14), 2955–2957 (2003).
[Crossref]

2002 (2)

J. Jackson, P. Hurley, B. Lane, A. Mathewson, and A. Morrison, “Comparing leakage currents and dark count rates in Geiger-mode avalanche photodiodes,” Appl. Phys. Lett. 80(22), 4100–4102 (2002).
[Crossref]

B. F. Aull, A. H. Loomis, D. J. Young, R. M. Heinrichs, B. J. Felton, P. J. Daniels, and D. J. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Linc. Lab. J. 13, 335–349 (2002).

1994 (1)

J. A. McCaulley, V. M. Donnelly, M. Vernon, and I. Taha, “Temperature dependence of the near-infrared refractive index of silicon, gallium arsenide, and indium phosphide,” Phys. Rev. B Condens. Matter 49(11), 7408–7417 (1994).
[Crossref] [PubMed]

1993 (1)

A. L. Lacaita, F. Zappa, S. Bigliardi, and M. Manfredi, “On the bremsstrahlung origin of hot-carrier-induced photons in silicon devices,” IEEE Trans. Electron Dev. 40(3), 577–582 (1993).
[Crossref]

1990 (1)

Z. Hang, H. Shen, and F. H. Pollak, “Temperature dependence of the E0 and E0 + △0 gaps of InP up to 600°C,” Solid State Commun. 73(1), 15–18 (1990).
[Crossref]

1982 (1)

J. S. Blakemore, “Semiconducting and other major properties of gallium arsenide,” J. Appl. Phys. 53(10), R123–R181 (1982).
[Crossref]

Aull, B. F.

B. F. Aull, D. R. Schuette, D. J. Young, D. M. Craig, B. J. Felton, and K. Warner, “A Study of Crosstalk in a 256 x 256 Photon Counting Imager Based on Silicon Geiger-Mode Avalanche Photodiodes,” IEEE Sens. J. 15, 2123–2132 (2015).
[Crossref]

B. F. Aull, A. H. Loomis, D. J. Young, R. M. Heinrichs, B. J. Felton, P. J. Daniels, and D. J. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Linc. Lab. J. 13, 335–349 (2002).

Aurite, S.

E. Sciacca, G. Condorelli, S. Aurite, S. Lombardo, M. Mazzillo, D. Sanfilippo, G. Fallica, and E. Rimini, “Crosstalk characterization in Geiger-mode avalanche photodiode arrays,” IEEE Electron. Dev. Lett. 29(3), 218–220 (2008).
[Crossref]

Bethune, D.

Y. Kang, H. Lu, Y.-H. Lo, D. Bethune, and W. Risk, “Dark count probability and quantum efficiency of avalanche photodiodes for single-photon detection,” Appl. Phys. Lett. 83(14), 2955–2957 (2003).
[Crossref]

Bigliardi, S.

A. L. Lacaita, F. Zappa, S. Bigliardi, and M. Manfredi, “On the bremsstrahlung origin of hot-carrier-induced photons in silicon devices,” IEEE Trans. Electron Dev. 40(3), 577–582 (1993).
[Crossref]

Blakemore, J. S.

J. S. Blakemore, “Semiconducting and other major properties of gallium arsenide,” J. Appl. Phys. 53(10), R123–R181 (1982).
[Crossref]

Condorelli, G.

E. Sciacca, G. Condorelli, S. Aurite, S. Lombardo, M. Mazzillo, D. Sanfilippo, G. Fallica, and E. Rimini, “Crosstalk characterization in Geiger-mode avalanche photodiode arrays,” IEEE Electron. Dev. Lett. 29(3), 218–220 (2008).
[Crossref]

Cova, S.

I. Rech, A. Ingargiola, R. Spinelli, I. Labanca, S. Marangoni, M. Ghioni, and S. Cova, “A new approach to optical crosstalk modeling in single-photon avalanche diodes,” IEEE Photonics Technol. Lett. 20(5), 330–332 (2008).
[Crossref]

I. Rech, A. Ingargiola, R. Spinelli, I. Labanca, S. Marangoni, M. Ghioni, and S. Cova, “Optical crosstalk in single photon avalanche diode arrays: A new complete model,” Opt. Express 16(12), 8381–8394 (2008).
[Crossref] [PubMed]

Craig, D. M.

B. F. Aull, D. R. Schuette, D. J. Young, D. M. Craig, B. J. Felton, and K. Warner, “A Study of Crosstalk in a 256 x 256 Photon Counting Imager Based on Silicon Geiger-Mode Avalanche Photodiodes,” IEEE Sens. J. 15, 2123–2132 (2015).
[Crossref]

Daniels, P. J.

B. F. Aull, A. H. Loomis, D. J. Young, R. M. Heinrichs, B. J. Felton, P. J. Daniels, and D. J. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Linc. Lab. J. 13, 335–349 (2002).

Donnelly, V. M.

J. A. McCaulley, V. M. Donnelly, M. Vernon, and I. Taha, “Temperature dependence of the near-infrared refractive index of silicon, gallium arsenide, and indium phosphide,” Phys. Rev. B Condens. Matter 49(11), 7408–7417 (1994).
[Crossref] [PubMed]

Entwistle, M.

M. A. Itzler, U. Krishnamachari, M. Entwistle, X. Jiang, M. Owens, and K. Slomkowski, “Dark Count Statistics in Geiger-Mode Avalanche Photodiode Cameras for 3-D Imaging LADAR,” IEEE J. Quantum Electron. 20, 3802111 (2014).

Fallica, G.

E. Sciacca, G. Condorelli, S. Aurite, S. Lombardo, M. Mazzillo, D. Sanfilippo, G. Fallica, and E. Rimini, “Crosstalk characterization in Geiger-mode avalanche photodiode arrays,” IEEE Electron. Dev. Lett. 29(3), 218–220 (2008).
[Crossref]

Felton, B. J.

B. F. Aull, D. R. Schuette, D. J. Young, D. M. Craig, B. J. Felton, and K. Warner, “A Study of Crosstalk in a 256 x 256 Photon Counting Imager Based on Silicon Geiger-Mode Avalanche Photodiodes,” IEEE Sens. J. 15, 2123–2132 (2015).
[Crossref]

B. F. Aull, A. H. Loomis, D. J. Young, R. M. Heinrichs, B. J. Felton, P. J. Daniels, and D. J. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Linc. Lab. J. 13, 335–349 (2002).

Ghioni, M.

I. Rech, A. Ingargiola, R. Spinelli, I. Labanca, S. Marangoni, M. Ghioni, and S. Cova, “Optical crosstalk in single photon avalanche diode arrays: A new complete model,” Opt. Express 16(12), 8381–8394 (2008).
[Crossref] [PubMed]

I. Rech, A. Ingargiola, R. Spinelli, I. Labanca, S. Marangoni, M. Ghioni, and S. Cova, “A new approach to optical crosstalk modeling in single-photon avalanche diodes,” IEEE Photonics Technol. Lett. 20(5), 330–332 (2008).
[Crossref]

Hang, Z.

Z. Hang, H. Shen, and F. H. Pollak, “Temperature dependence of the E0 and E0 + △0 gaps of InP up to 600°C,” Solid State Commun. 73(1), 15–18 (1990).
[Crossref]

Heinrichs, R. M.

B. F. Aull, A. H. Loomis, D. J. Young, R. M. Heinrichs, B. J. Felton, P. J. Daniels, and D. J. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Linc. Lab. J. 13, 335–349 (2002).

Hurley, P.

J. Jackson, P. Hurley, B. Lane, A. Mathewson, and A. Morrison, “Comparing leakage currents and dark count rates in Geiger-mode avalanche photodiodes,” Appl. Phys. Lett. 80(22), 4100–4102 (2002).
[Crossref]

Ingargiola, A.

I. Rech, A. Ingargiola, R. Spinelli, I. Labanca, S. Marangoni, M. Ghioni, and S. Cova, “Optical crosstalk in single photon avalanche diode arrays: A new complete model,” Opt. Express 16(12), 8381–8394 (2008).
[Crossref] [PubMed]

I. Rech, A. Ingargiola, R. Spinelli, I. Labanca, S. Marangoni, M. Ghioni, and S. Cova, “A new approach to optical crosstalk modeling in single-photon avalanche diodes,” IEEE Photonics Technol. Lett. 20(5), 330–332 (2008).
[Crossref]

Itzler, M. A.

M. A. Itzler, U. Krishnamachari, M. Entwistle, X. Jiang, M. Owens, and K. Slomkowski, “Dark Count Statistics in Geiger-Mode Avalanche Photodiode Cameras for 3-D Imaging LADAR,” IEEE J. Quantum Electron. 20, 3802111 (2014).

Jackson, J.

J. Jackson, P. Hurley, B. Lane, A. Mathewson, and A. Morrison, “Comparing leakage currents and dark count rates in Geiger-mode avalanche photodiodes,” Appl. Phys. Lett. 80(22), 4100–4102 (2002).
[Crossref]

Jiang, X.

M. A. Itzler, U. Krishnamachari, M. Entwistle, X. Jiang, M. Owens, and K. Slomkowski, “Dark Count Statistics in Geiger-Mode Avalanche Photodiode Cameras for 3-D Imaging LADAR,” IEEE J. Quantum Electron. 20, 3802111 (2014).

Kang, Y.

Y. Kang, H. Lu, Y.-H. Lo, D. Bethune, and W. Risk, “Dark count probability and quantum efficiency of avalanche photodiodes for single-photon detection,” Appl. Phys. Lett. 83(14), 2955–2957 (2003).
[Crossref]

Krishnamachari, U.

M. A. Itzler, U. Krishnamachari, M. Entwistle, X. Jiang, M. Owens, and K. Slomkowski, “Dark Count Statistics in Geiger-Mode Avalanche Photodiode Cameras for 3-D Imaging LADAR,” IEEE J. Quantum Electron. 20, 3802111 (2014).

Labanca, I.

I. Rech, A. Ingargiola, R. Spinelli, I. Labanca, S. Marangoni, M. Ghioni, and S. Cova, “A new approach to optical crosstalk modeling in single-photon avalanche diodes,” IEEE Photonics Technol. Lett. 20(5), 330–332 (2008).
[Crossref]

I. Rech, A. Ingargiola, R. Spinelli, I. Labanca, S. Marangoni, M. Ghioni, and S. Cova, “Optical crosstalk in single photon avalanche diode arrays: A new complete model,” Opt. Express 16(12), 8381–8394 (2008).
[Crossref] [PubMed]

Lacaita, A. L.

A. L. Lacaita, F. Zappa, S. Bigliardi, and M. Manfredi, “On the bremsstrahlung origin of hot-carrier-induced photons in silicon devices,” IEEE Trans. Electron Dev. 40(3), 577–582 (1993).
[Crossref]

Landers, D. J.

B. F. Aull, A. H. Loomis, D. J. Young, R. M. Heinrichs, B. J. Felton, P. J. Daniels, and D. J. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Linc. Lab. J. 13, 335–349 (2002).

Lane, B.

J. Jackson, P. Hurley, B. Lane, A. Mathewson, and A. Morrison, “Comparing leakage currents and dark count rates in Geiger-mode avalanche photodiodes,” Appl. Phys. Lett. 80(22), 4100–4102 (2002).
[Crossref]

Lo, Y.-H.

Y. Kang, H. Lu, Y.-H. Lo, D. Bethune, and W. Risk, “Dark count probability and quantum efficiency of avalanche photodiodes for single-photon detection,” Appl. Phys. Lett. 83(14), 2955–2957 (2003).
[Crossref]

Lombardo, S.

E. Sciacca, G. Condorelli, S. Aurite, S. Lombardo, M. Mazzillo, D. Sanfilippo, G. Fallica, and E. Rimini, “Crosstalk characterization in Geiger-mode avalanche photodiode arrays,” IEEE Electron. Dev. Lett. 29(3), 218–220 (2008).
[Crossref]

Loomis, A. H.

B. F. Aull, A. H. Loomis, D. J. Young, R. M. Heinrichs, B. J. Felton, P. J. Daniels, and D. J. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Linc. Lab. J. 13, 335–349 (2002).

Lu, H.

Y. Kang, H. Lu, Y.-H. Lo, D. Bethune, and W. Risk, “Dark count probability and quantum efficiency of avalanche photodiodes for single-photon detection,” Appl. Phys. Lett. 83(14), 2955–2957 (2003).
[Crossref]

Manfredi, M.

A. L. Lacaita, F. Zappa, S. Bigliardi, and M. Manfredi, “On the bremsstrahlung origin of hot-carrier-induced photons in silicon devices,” IEEE Trans. Electron Dev. 40(3), 577–582 (1993).
[Crossref]

Marangoni, S.

I. Rech, A. Ingargiola, R. Spinelli, I. Labanca, S. Marangoni, M. Ghioni, and S. Cova, “Optical crosstalk in single photon avalanche diode arrays: A new complete model,” Opt. Express 16(12), 8381–8394 (2008).
[Crossref] [PubMed]

I. Rech, A. Ingargiola, R. Spinelli, I. Labanca, S. Marangoni, M. Ghioni, and S. Cova, “A new approach to optical crosstalk modeling in single-photon avalanche diodes,” IEEE Photonics Technol. Lett. 20(5), 330–332 (2008).
[Crossref]

Mathewson, A.

J. Jackson, P. Hurley, B. Lane, A. Mathewson, and A. Morrison, “Comparing leakage currents and dark count rates in Geiger-mode avalanche photodiodes,” Appl. Phys. Lett. 80(22), 4100–4102 (2002).
[Crossref]

Mazzillo, M.

E. Sciacca, G. Condorelli, S. Aurite, S. Lombardo, M. Mazzillo, D. Sanfilippo, G. Fallica, and E. Rimini, “Crosstalk characterization in Geiger-mode avalanche photodiode arrays,” IEEE Electron. Dev. Lett. 29(3), 218–220 (2008).
[Crossref]

McCaulley, J. A.

J. A. McCaulley, V. M. Donnelly, M. Vernon, and I. Taha, “Temperature dependence of the near-infrared refractive index of silicon, gallium arsenide, and indium phosphide,” Phys. Rev. B Condens. Matter 49(11), 7408–7417 (1994).
[Crossref] [PubMed]

Morrison, A.

J. Jackson, P. Hurley, B. Lane, A. Mathewson, and A. Morrison, “Comparing leakage currents and dark count rates in Geiger-mode avalanche photodiodes,” Appl. Phys. Lett. 80(22), 4100–4102 (2002).
[Crossref]

Owens, M.

M. A. Itzler, U. Krishnamachari, M. Entwistle, X. Jiang, M. Owens, and K. Slomkowski, “Dark Count Statistics in Geiger-Mode Avalanche Photodiode Cameras for 3-D Imaging LADAR,” IEEE J. Quantum Electron. 20, 3802111 (2014).

Pollak, F. H.

Z. Hang, H. Shen, and F. H. Pollak, “Temperature dependence of the E0 and E0 + △0 gaps of InP up to 600°C,” Solid State Commun. 73(1), 15–18 (1990).
[Crossref]

Rech, I.

I. Rech, A. Ingargiola, R. Spinelli, I. Labanca, S. Marangoni, M. Ghioni, and S. Cova, “A new approach to optical crosstalk modeling in single-photon avalanche diodes,” IEEE Photonics Technol. Lett. 20(5), 330–332 (2008).
[Crossref]

I. Rech, A. Ingargiola, R. Spinelli, I. Labanca, S. Marangoni, M. Ghioni, and S. Cova, “Optical crosstalk in single photon avalanche diode arrays: A new complete model,” Opt. Express 16(12), 8381–8394 (2008).
[Crossref] [PubMed]

Renker, D.

D. Renker, “Geiger-mode avalanche photodiodes, history, properties and problems,” Nucl. Instrum. Methods Phys. Res. A 567(1), 48–56 (2006).
[Crossref]

Rimini, E.

E. Sciacca, G. Condorelli, S. Aurite, S. Lombardo, M. Mazzillo, D. Sanfilippo, G. Fallica, and E. Rimini, “Crosstalk characterization in Geiger-mode avalanche photodiode arrays,” IEEE Electron. Dev. Lett. 29(3), 218–220 (2008).
[Crossref]

Risk, W.

Y. Kang, H. Lu, Y.-H. Lo, D. Bethune, and W. Risk, “Dark count probability and quantum efficiency of avalanche photodiodes for single-photon detection,” Appl. Phys. Lett. 83(14), 2955–2957 (2003).
[Crossref]

Sanfilippo, D.

E. Sciacca, G. Condorelli, S. Aurite, S. Lombardo, M. Mazzillo, D. Sanfilippo, G. Fallica, and E. Rimini, “Crosstalk characterization in Geiger-mode avalanche photodiode arrays,” IEEE Electron. Dev. Lett. 29(3), 218–220 (2008).
[Crossref]

Schuette, D. R.

B. F. Aull, D. R. Schuette, D. J. Young, D. M. Craig, B. J. Felton, and K. Warner, “A Study of Crosstalk in a 256 x 256 Photon Counting Imager Based on Silicon Geiger-Mode Avalanche Photodiodes,” IEEE Sens. J. 15, 2123–2132 (2015).
[Crossref]

Sciacca, E.

E. Sciacca, G. Condorelli, S. Aurite, S. Lombardo, M. Mazzillo, D. Sanfilippo, G. Fallica, and E. Rimini, “Crosstalk characterization in Geiger-mode avalanche photodiode arrays,” IEEE Electron. Dev. Lett. 29(3), 218–220 (2008).
[Crossref]

Shen, H.

Z. Hang, H. Shen, and F. H. Pollak, “Temperature dependence of the E0 and E0 + △0 gaps of InP up to 600°C,” Solid State Commun. 73(1), 15–18 (1990).
[Crossref]

Slomkowski, K.

M. A. Itzler, U. Krishnamachari, M. Entwistle, X. Jiang, M. Owens, and K. Slomkowski, “Dark Count Statistics in Geiger-Mode Avalanche Photodiode Cameras for 3-D Imaging LADAR,” IEEE J. Quantum Electron. 20, 3802111 (2014).

Spinelli, R.

I. Rech, A. Ingargiola, R. Spinelli, I. Labanca, S. Marangoni, M. Ghioni, and S. Cova, “A new approach to optical crosstalk modeling in single-photon avalanche diodes,” IEEE Photonics Technol. Lett. 20(5), 330–332 (2008).
[Crossref]

I. Rech, A. Ingargiola, R. Spinelli, I. Labanca, S. Marangoni, M. Ghioni, and S. Cova, “Optical crosstalk in single photon avalanche diode arrays: A new complete model,” Opt. Express 16(12), 8381–8394 (2008).
[Crossref] [PubMed]

Taha, I.

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Figures (8)

Fig. 1
Fig. 1 (a) Pixel-level overview of typical GmAPD device layer structure, including a microlens array used in increasing optical fill factor. (b) Array-level overview of optical crosstalk, illustrating an array of pixels optically isolated by etched trench structures. Light emitted from the multiplication region of pixel 0 (with spectral properties given in [10]) can reach neighboring active regions through three distinct vectors: back side metal reflection (A), back side SiNx reflection (B), and direct “line-of-sight” transmission (C). θ denotes the angle between back side reflections and the back side surface normal, used in defining the InP/SiNx/air interface critical angle of 17.7° beyond which all photons approaching the interface undergo total internal reflection. Though the total crosstalk seen by each pixel is frequently a combination of both back- and front-side contributions, in the interest of simplified categorization, all pixels will henceforth be referred to as “Type A” or “Type B” if their primary backside contribution involves a metal or SiNx reflection, respectively.
Fig. 2
Fig. 2 (a) Schematic of basic model geometry, shown in cross-section. The emission source is modeled as a cylinder in the center of the multiplication layer, with thickness equal to the multiplication layer thickness and diameter equal to the lithographically-defined active area size (16 µm in this case). Individual detectors at each pixel are modeled as cylinders in the center of the absorption layer, again with diameters equal to 16 µm. Inset: Detailed view of the epitaxial layer structure, as modeled. (b) Interior view of three-dimensional 5 × 5 pixel model geometry, showing emission from pixel in far corner, where rays are grouped by color according to number of surface interactions. Front side trenches outline all pixels in a square grid, with sidewalls etched normal to the front-side wafer surface. All epitaxial layers detailed in Fig. 1(a) have been modeled but are left transparent for illustrative purposes.
Fig. 3
Fig. 3 (a) Experimental and (b) simulated spatial maps of optical crosstalk magnitude with active pixels at (0,0) (denoted with an “A”), normalized to first-nearest-neighbor crosstalk. Experimental results show cumulative crosstalk (including 2nd- and higher-order crosstalk events), while the simulation shows 1st order crosstalk events only. Type B pixels are shown with black borders, and only photons with energy above the absorber band gap are counted. Color map scale is common to both (a) and (b). (c) Data from (a) and (b) plotted as a function of distance on a logarithmic scale, with reflections further separated according to source of backside reflection.
Fig. 4
Fig. 4 Illustration of method for adding 2nd-order crosstalk events to 1st-order effects. a) The 1st-order model results from Fig. 3(b) are presented as a full, symmetric quadrant of data, with the 12 nearest neighbors to the active pixel delimited with a thick border. b) 2nd-order effects are simulated by first re-centering the map from a) so that the active pixel is now at (0,1). After this, all numbers in a given 2nd-order map are multiplied by the nearest-neighbor crosstalk probability per avalanche (3.5% in this illustration), and then multiplied by the number of secondary avalanches the new active pixel represents (1 for pixel (0,1), as determined by its normalized value in a)). c) The map from a) is added to 2nd-order maps which have been generated for all 12 pixels outlined in a), and then re-normalized. This produces a simulated cumulative crosstalk map.
Fig. 5
Fig. 5 Normalized crosstalk power as a function of distance, showing the same cumulative experimental crosstalk and simulated 1st-order crosstalk from Fig. 3(c), now plotted alongside the results from the cumulative crosstalk simulation obtained via the methodology shown in Fig. 4.
Fig. 6
Fig. 6 Absolute cumulative crosstalk probabilities per primary avalanche event (primary avalanche located at pixel (0,0), denoted with an “A”). a) Experimental averages obtained from three cameras at 3V overbiases corresponding to a PDE of 30%, and b) simulated results obtained by scaling the cumulative model results shown in Fig. 5 by the factors obtained from Eq. (1).
Fig. 7
Fig. 7 Detailed spatial maps of transmitted power through the upper (a) and lower (b) monitor layers first illustrated in Fig. 2(a), for light emitted from the primary avalanche in pixel (0,0). Only light with energy above the absorber bandgap is registered.
Fig. 8
Fig. 8 Simulated cumulative line-of-sight fraction versus distance plot for all Type B pixels, grouped by angular deviation from normal incidence to the trench walls (e.g. the 0° line includes pixels (4, 0) and (2,0)). This grouping illustrates the dominance of the line-of-sight crosstalk vector for pixels in the same column or row of the active pixel.

Tables (2)

Tables Icon

Table 1 Percentage contribution of all physical crosstalk paths to cumulative crosstalk probability total for 9 × 9 sub-array.

Tables Icon

Table 2 Line-of-sight contributions for the 16 nearest neighbors surrounding the active pixel, alongside their magnitude contribution to the 9 × 9 and 128 × 32 cumulative totals. Percentages are sums of the total crosstalk percentages for all pixels equivalent by symmetry, i.e. the percentages for (0,1) represent the sum of crosstalk counts for (0,1), (1,0), (0,-1), and (−1,0). Pixels denoted with an asterisk lie in the same column as the active pixel.

Equations (1)

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0.035 photons collected at NN 1 Avalanche × 1 0 7 photons generated 53,700 photons collected at NN = 6.5 photons generated 1 Avalanche

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