Abstract

One of the main issues of Single Photon Avalanche Diode arrays is optical crosstalk. Since its intensity increases with reducing the distance between devices, this phenomenon limits the density of integration within arrays. In the past optical crosstalk was ascribed essentially to the light propagating from one detector to another through direct optical paths. Accordingly, reflecting trenches between devices were proposed to prevent it, but they proved to be not completely effective. In this paper we will present experimental evidence that a significant contribution to optical crosstalk comes from light reflected internally off the bottom of the chip, thus being impossible to eliminate it completely by means of trenches. We will also propose an optical model to predict the dependence of crosstalk on the distance between devices.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
  2. F. Stellari, A. Tosi, F. Zappa, and S. Cova, "CMOS circuit testing via time-resolved luminescence measurements and simulations," IEEE Trans. Instrum. Meas. 53, 163-169 (2004).
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2006

F. Zappa, S. Tisa, S. Cova, P. Maccagnani, D. B. Calia, R. Saletti, R. Roncella, G. Bonanno, and M. Belluso, "Single-photon avalanche diode arrays for fast transients and adaptive optics," IEEE Trans. Instrum. Meas. 55, 365-374 (2006).
[CrossRef]

A. Restelli, I. Rech, P. Maccagnani, M. Ghioni, and S. Cova, "Monolithic silicon matrix detector with 50 ?m photon counting pixels," J. Mod. Opt. 54, 213-224 (2006).
[CrossRef]

2004

K. J. Gordon, V. Fernandez, P. D. Townsend, and G. S. Buller, "A short wavelength GigaHertz clocked fiber-optic quantum key distribution system," IEEE J. Quantum Electron. 40, 900-908 (2004).
[CrossRef]

F. Stellari, A. Tosi, F. Zappa, and S. Cova, "CMOS circuit testing via time-resolved luminescence measurements and simulations," IEEE Trans. Instrum. Meas. 53, 163-169 (2004).
[CrossRef]

2003

H. Yang, G. Luo, P. Karnchanaphanurach, T. M. Louie, I. Rech, S. Cova, L. Xun, and X. S. Xie, "Protein Conformational Dynamics Probed by Single-Molecule Electron Transfer," Science 302, 262-266 (2003).
[CrossRef] [PubMed]

1999

N. Akil, S. E. Kerns, D. V., Jr., A. Hoffmann, and J. Charles, "A multimechanism model for photon generation by silicon junctions in avalanche breakdown," IEEE Trans. Electron. Devices 46, 1022-1028 (1999).
[CrossRef]

1996

1993

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. Devices 40, 577-582 (1993).
[CrossRef]

1992

J. Bude, "Hot-carrier luminescence in Si," Phys. Rev. B 45, 5848-5856 (1992).
[CrossRef]

1989

A. L. Lacaita, M. Ghioni, and S. Cova, "Double epitaxy improves single-photon avalanche diode performance," Electron. Lett. 25, 841-843 (1989).
[CrossRef]

1984

G. Lubberts and B. C. Burkey, "Optical and electrical properties of heavily phosphorus-doped epitaxial silicon layers," J. Appl. Phys. 55, 760-763 (1984).
[CrossRef]

1981

P. E. Schmid, "Optical absorption in heavily doped silicon," Phys. Rev. B 23, 5531-5536 (1981).
[CrossRef]

1978

D. K. Schroeder, R. N. Thomas, and J. C. Swartz, "Free Carrier Absorption in Silicon," IEEE J. Solid-State Circuits 13, 180-187 (1978).
[CrossRef]

1974

W. Haecker, "Infrared Radiation from Breakdown Plasmas in Si, GaSb, and Ge: Evidence for Direct Free Hole Radiation," Phys. Status Solidi 25, 301-310 (1974).
[CrossRef]

1965

R. H. Haitz, "Studies on optical coupling between silicon p-n junctions," Solid-State Electronics 8, 417-425 (1965).
[CrossRef]

1957

W. Spitzer and H. Y. Fan, "Infrared Absorption in n-Type Silicon," Phys. Rev. 108, 268-271 (1957).
[CrossRef]

1956

A. G. Chynoweth and K. G. McKay, "Photon Emission from Avalanche Breakdown in Silicon," Phys. Rev. 102, 369-376 (1956).
[CrossRef]

Akil, N.

N. Akil, S. E. Kerns, D. V., Jr., A. Hoffmann, and J. Charles, "A multimechanism model for photon generation by silicon junctions in avalanche breakdown," IEEE Trans. Electron. Devices 46, 1022-1028 (1999).
[CrossRef]

Belluso, M.

F. Zappa, S. Tisa, S. Cova, P. Maccagnani, D. B. Calia, R. Saletti, R. Roncella, G. Bonanno, and M. Belluso, "Single-photon avalanche diode arrays for fast transients and adaptive optics," IEEE Trans. Instrum. Meas. 55, 365-374 (2006).
[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. Devices 40, 577-582 (1993).
[CrossRef]

Bonanno, G.

F. Zappa, S. Tisa, S. Cova, P. Maccagnani, D. B. Calia, R. Saletti, R. Roncella, G. Bonanno, and M. Belluso, "Single-photon avalanche diode arrays for fast transients and adaptive optics," IEEE Trans. Instrum. Meas. 55, 365-374 (2006).
[CrossRef]

Bude, J.

J. Bude, "Hot-carrier luminescence in Si," Phys. Rev. B 45, 5848-5856 (1992).
[CrossRef]

Buller, G. S.

K. J. Gordon, V. Fernandez, P. D. Townsend, and G. S. Buller, "A short wavelength GigaHertz clocked fiber-optic quantum key distribution system," IEEE J. Quantum Electron. 40, 900-908 (2004).
[CrossRef]

Burkey, B. C.

G. Lubberts and B. C. Burkey, "Optical and electrical properties of heavily phosphorus-doped epitaxial silicon layers," J. Appl. Phys. 55, 760-763 (1984).
[CrossRef]

Calia, D. B.

F. Zappa, S. Tisa, S. Cova, P. Maccagnani, D. B. Calia, R. Saletti, R. Roncella, G. Bonanno, and M. Belluso, "Single-photon avalanche diode arrays for fast transients and adaptive optics," IEEE Trans. Instrum. Meas. 55, 365-374 (2006).
[CrossRef]

Chynoweth, A. G.

A. G. Chynoweth and K. G. McKay, "Photon Emission from Avalanche Breakdown in Silicon," Phys. Rev. 102, 369-376 (1956).
[CrossRef]

Cova, S.

A. Restelli, I. Rech, P. Maccagnani, M. Ghioni, and S. Cova, "Monolithic silicon matrix detector with 50 ?m photon counting pixels," J. Mod. Opt. 54, 213-224 (2006).
[CrossRef]

F. Zappa, S. Tisa, S. Cova, P. Maccagnani, D. B. Calia, R. Saletti, R. Roncella, G. Bonanno, and M. Belluso, "Single-photon avalanche diode arrays for fast transients and adaptive optics," IEEE Trans. Instrum. Meas. 55, 365-374 (2006).
[CrossRef]

F. Stellari, A. Tosi, F. Zappa, and S. Cova, "CMOS circuit testing via time-resolved luminescence measurements and simulations," IEEE Trans. Instrum. Meas. 53, 163-169 (2004).
[CrossRef]

H. Yang, G. Luo, P. Karnchanaphanurach, T. M. Louie, I. Rech, S. Cova, L. Xun, and X. S. Xie, "Protein Conformational Dynamics Probed by Single-Molecule Electron Transfer," Science 302, 262-266 (2003).
[CrossRef] [PubMed]

S. Cova, M. Ghioni, A. L. Lacaita, C. Samori, and F. Zappa, "Avalanche photodiodes and quenching circuits for single-photon detection," Appl. Opt. 35, 1956-1976 (1996).
[CrossRef] [PubMed]

A. L. Lacaita, M. Ghioni, and S. Cova, "Double epitaxy improves single-photon avalanche diode performance," Electron. Lett. 25, 841-843 (1989).
[CrossRef]

Fan, H. Y.

W. Spitzer and H. Y. Fan, "Infrared Absorption in n-Type Silicon," Phys. Rev. 108, 268-271 (1957).
[CrossRef]

Fernandez, V.

K. J. Gordon, V. Fernandez, P. D. Townsend, and G. S. Buller, "A short wavelength GigaHertz clocked fiber-optic quantum key distribution system," IEEE J. Quantum Electron. 40, 900-908 (2004).
[CrossRef]

Ghioni, M.

A. Restelli, I. Rech, P. Maccagnani, M. Ghioni, and S. Cova, "Monolithic silicon matrix detector with 50 ?m photon counting pixels," J. Mod. Opt. 54, 213-224 (2006).
[CrossRef]

S. Cova, M. Ghioni, A. L. Lacaita, C. Samori, and F. Zappa, "Avalanche photodiodes and quenching circuits for single-photon detection," Appl. Opt. 35, 1956-1976 (1996).
[CrossRef] [PubMed]

A. L. Lacaita, M. Ghioni, and S. Cova, "Double epitaxy improves single-photon avalanche diode performance," Electron. Lett. 25, 841-843 (1989).
[CrossRef]

Gordon, K. J.

K. J. Gordon, V. Fernandez, P. D. Townsend, and G. S. Buller, "A short wavelength GigaHertz clocked fiber-optic quantum key distribution system," IEEE J. Quantum Electron. 40, 900-908 (2004).
[CrossRef]

Haecker, W.

W. Haecker, "Infrared Radiation from Breakdown Plasmas in Si, GaSb, and Ge: Evidence for Direct Free Hole Radiation," Phys. Status Solidi 25, 301-310 (1974).
[CrossRef]

Haitz, R. H.

R. H. Haitz, "Studies on optical coupling between silicon p-n junctions," Solid-State Electronics 8, 417-425 (1965).
[CrossRef]

Karnchanaphanurach, P.

H. Yang, G. Luo, P. Karnchanaphanurach, T. M. Louie, I. Rech, S. Cova, L. Xun, and X. S. Xie, "Protein Conformational Dynamics Probed by Single-Molecule Electron Transfer," Science 302, 262-266 (2003).
[CrossRef] [PubMed]

Kerns, S. E.

N. Akil, S. E. Kerns, D. V., Jr., A. Hoffmann, and J. Charles, "A multimechanism model for photon generation by silicon junctions in avalanche breakdown," IEEE Trans. Electron. Devices 46, 1022-1028 (1999).
[CrossRef]

Lacaita, A. L.

S. Cova, M. Ghioni, A. L. Lacaita, C. Samori, and F. Zappa, "Avalanche photodiodes and quenching circuits for single-photon detection," Appl. Opt. 35, 1956-1976 (1996).
[CrossRef] [PubMed]

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. Devices 40, 577-582 (1993).
[CrossRef]

A. L. Lacaita, M. Ghioni, and S. Cova, "Double epitaxy improves single-photon avalanche diode performance," Electron. Lett. 25, 841-843 (1989).
[CrossRef]

Louie, T. M.

H. Yang, G. Luo, P. Karnchanaphanurach, T. M. Louie, I. Rech, S. Cova, L. Xun, and X. S. Xie, "Protein Conformational Dynamics Probed by Single-Molecule Electron Transfer," Science 302, 262-266 (2003).
[CrossRef] [PubMed]

Lubberts, G.

G. Lubberts and B. C. Burkey, "Optical and electrical properties of heavily phosphorus-doped epitaxial silicon layers," J. Appl. Phys. 55, 760-763 (1984).
[CrossRef]

Luo, G.

H. Yang, G. Luo, P. Karnchanaphanurach, T. M. Louie, I. Rech, S. Cova, L. Xun, and X. S. Xie, "Protein Conformational Dynamics Probed by Single-Molecule Electron Transfer," Science 302, 262-266 (2003).
[CrossRef] [PubMed]

Maccagnani, P.

F. Zappa, S. Tisa, S. Cova, P. Maccagnani, D. B. Calia, R. Saletti, R. Roncella, G. Bonanno, and M. Belluso, "Single-photon avalanche diode arrays for fast transients and adaptive optics," IEEE Trans. Instrum. Meas. 55, 365-374 (2006).
[CrossRef]

A. Restelli, I. Rech, P. Maccagnani, M. Ghioni, and S. Cova, "Monolithic silicon matrix detector with 50 ?m photon counting pixels," J. Mod. Opt. 54, 213-224 (2006).
[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. Devices 40, 577-582 (1993).
[CrossRef]

McKay, K. G.

A. G. Chynoweth and K. G. McKay, "Photon Emission from Avalanche Breakdown in Silicon," Phys. Rev. 102, 369-376 (1956).
[CrossRef]

Rech, I.

A. Restelli, I. Rech, P. Maccagnani, M. Ghioni, and S. Cova, "Monolithic silicon matrix detector with 50 ?m photon counting pixels," J. Mod. Opt. 54, 213-224 (2006).
[CrossRef]

H. Yang, G. Luo, P. Karnchanaphanurach, T. M. Louie, I. Rech, S. Cova, L. Xun, and X. S. Xie, "Protein Conformational Dynamics Probed by Single-Molecule Electron Transfer," Science 302, 262-266 (2003).
[CrossRef] [PubMed]

Restelli, A.

A. Restelli, I. Rech, P. Maccagnani, M. Ghioni, and S. Cova, "Monolithic silicon matrix detector with 50 ?m photon counting pixels," J. Mod. Opt. 54, 213-224 (2006).
[CrossRef]

Roncella, R.

F. Zappa, S. Tisa, S. Cova, P. Maccagnani, D. B. Calia, R. Saletti, R. Roncella, G. Bonanno, and M. Belluso, "Single-photon avalanche diode arrays for fast transients and adaptive optics," IEEE Trans. Instrum. Meas. 55, 365-374 (2006).
[CrossRef]

Saletti, R.

F. Zappa, S. Tisa, S. Cova, P. Maccagnani, D. B. Calia, R. Saletti, R. Roncella, G. Bonanno, and M. Belluso, "Single-photon avalanche diode arrays for fast transients and adaptive optics," IEEE Trans. Instrum. Meas. 55, 365-374 (2006).
[CrossRef]

Samori, C.

Schmid, P. E.

P. E. Schmid, "Optical absorption in heavily doped silicon," Phys. Rev. B 23, 5531-5536 (1981).
[CrossRef]

Schroeder, D. K.

D. K. Schroeder, R. N. Thomas, and J. C. Swartz, "Free Carrier Absorption in Silicon," IEEE J. Solid-State Circuits 13, 180-187 (1978).
[CrossRef]

Spitzer, W.

W. Spitzer and H. Y. Fan, "Infrared Absorption in n-Type Silicon," Phys. Rev. 108, 268-271 (1957).
[CrossRef]

Stellari, F.

F. Stellari, A. Tosi, F. Zappa, and S. Cova, "CMOS circuit testing via time-resolved luminescence measurements and simulations," IEEE Trans. Instrum. Meas. 53, 163-169 (2004).
[CrossRef]

Swartz, J. C.

D. K. Schroeder, R. N. Thomas, and J. C. Swartz, "Free Carrier Absorption in Silicon," IEEE J. Solid-State Circuits 13, 180-187 (1978).
[CrossRef]

Thomas, R. N.

D. K. Schroeder, R. N. Thomas, and J. C. Swartz, "Free Carrier Absorption in Silicon," IEEE J. Solid-State Circuits 13, 180-187 (1978).
[CrossRef]

Tisa, S.

F. Zappa, S. Tisa, S. Cova, P. Maccagnani, D. B. Calia, R. Saletti, R. Roncella, G. Bonanno, and M. Belluso, "Single-photon avalanche diode arrays for fast transients and adaptive optics," IEEE Trans. Instrum. Meas. 55, 365-374 (2006).
[CrossRef]

Tosi, A.

F. Stellari, A. Tosi, F. Zappa, and S. Cova, "CMOS circuit testing via time-resolved luminescence measurements and simulations," IEEE Trans. Instrum. Meas. 53, 163-169 (2004).
[CrossRef]

Townsend, P. D.

K. J. Gordon, V. Fernandez, P. D. Townsend, and G. S. Buller, "A short wavelength GigaHertz clocked fiber-optic quantum key distribution system," IEEE J. Quantum Electron. 40, 900-908 (2004).
[CrossRef]

Xie, X. S.

H. Yang, G. Luo, P. Karnchanaphanurach, T. M. Louie, I. Rech, S. Cova, L. Xun, and X. S. Xie, "Protein Conformational Dynamics Probed by Single-Molecule Electron Transfer," Science 302, 262-266 (2003).
[CrossRef] [PubMed]

Xun, L.

H. Yang, G. Luo, P. Karnchanaphanurach, T. M. Louie, I. Rech, S. Cova, L. Xun, and X. S. Xie, "Protein Conformational Dynamics Probed by Single-Molecule Electron Transfer," Science 302, 262-266 (2003).
[CrossRef] [PubMed]

Yang, H.

H. Yang, G. Luo, P. Karnchanaphanurach, T. M. Louie, I. Rech, S. Cova, L. Xun, and X. S. Xie, "Protein Conformational Dynamics Probed by Single-Molecule Electron Transfer," Science 302, 262-266 (2003).
[CrossRef] [PubMed]

Zappa, F.

F. Zappa, S. Tisa, S. Cova, P. Maccagnani, D. B. Calia, R. Saletti, R. Roncella, G. Bonanno, and M. Belluso, "Single-photon avalanche diode arrays for fast transients and adaptive optics," IEEE Trans. Instrum. Meas. 55, 365-374 (2006).
[CrossRef]

F. Stellari, A. Tosi, F. Zappa, and S. Cova, "CMOS circuit testing via time-resolved luminescence measurements and simulations," IEEE Trans. Instrum. Meas. 53, 163-169 (2004).
[CrossRef]

S. Cova, M. Ghioni, A. L. Lacaita, C. Samori, and F. Zappa, "Avalanche photodiodes and quenching circuits for single-photon detection," Appl. Opt. 35, 1956-1976 (1996).
[CrossRef] [PubMed]

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. Devices 40, 577-582 (1993).
[CrossRef]

Appl. Opt.

Electron. Lett.

A. L. Lacaita, M. Ghioni, and S. Cova, "Double epitaxy improves single-photon avalanche diode performance," Electron. Lett. 25, 841-843 (1989).
[CrossRef]

IEEE J. Quantum Electron.

K. J. Gordon, V. Fernandez, P. D. Townsend, and G. S. Buller, "A short wavelength GigaHertz clocked fiber-optic quantum key distribution system," IEEE J. Quantum Electron. 40, 900-908 (2004).
[CrossRef]

IEEE J. Solid-State Circuits

D. K. Schroeder, R. N. Thomas, and J. C. Swartz, "Free Carrier Absorption in Silicon," IEEE J. Solid-State Circuits 13, 180-187 (1978).
[CrossRef]

IEEE Trans. Electron. Devices

N. Akil, S. E. Kerns, D. V., Jr., A. Hoffmann, and J. Charles, "A multimechanism model for photon generation by silicon junctions in avalanche breakdown," IEEE Trans. Electron. Devices 46, 1022-1028 (1999).
[CrossRef]

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. Devices 40, 577-582 (1993).
[CrossRef]

IEEE Trans. Instrum. Meas.

F. Stellari, A. Tosi, F. Zappa, and S. Cova, "CMOS circuit testing via time-resolved luminescence measurements and simulations," IEEE Trans. Instrum. Meas. 53, 163-169 (2004).
[CrossRef]

F. Zappa, S. Tisa, S. Cova, P. Maccagnani, D. B. Calia, R. Saletti, R. Roncella, G. Bonanno, and M. Belluso, "Single-photon avalanche diode arrays for fast transients and adaptive optics," IEEE Trans. Instrum. Meas. 55, 365-374 (2006).
[CrossRef]

J. Appl. Phys.

G. Lubberts and B. C. Burkey, "Optical and electrical properties of heavily phosphorus-doped epitaxial silicon layers," J. Appl. Phys. 55, 760-763 (1984).
[CrossRef]

J. Mod. Opt.

A. Restelli, I. Rech, P. Maccagnani, M. Ghioni, and S. Cova, "Monolithic silicon matrix detector with 50 ?m photon counting pixels," J. Mod. Opt. 54, 213-224 (2006).
[CrossRef]

Phys. Rev.

W. Spitzer and H. Y. Fan, "Infrared Absorption in n-Type Silicon," Phys. Rev. 108, 268-271 (1957).
[CrossRef]

A. G. Chynoweth and K. G. McKay, "Photon Emission from Avalanche Breakdown in Silicon," Phys. Rev. 102, 369-376 (1956).
[CrossRef]

Phys. Rev. B

P. E. Schmid, "Optical absorption in heavily doped silicon," Phys. Rev. B 23, 5531-5536 (1981).
[CrossRef]

J. Bude, "Hot-carrier luminescence in Si," Phys. Rev. B 45, 5848-5856 (1992).
[CrossRef]

Phys. Status Solidi

W. Haecker, "Infrared Radiation from Breakdown Plasmas in Si, GaSb, and Ge: Evidence for Direct Free Hole Radiation," Phys. Status Solidi 25, 301-310 (1974).
[CrossRef]

Science

H. Yang, G. Luo, P. Karnchanaphanurach, T. M. Louie, I. Rech, S. Cova, L. Xun, and X. S. Xie, "Protein Conformational Dynamics Probed by Single-Molecule Electron Transfer," Science 302, 262-266 (2003).
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Solid-State Electronics

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Figures (15)

Fig. 1.
Fig. 1.

Cross-section of the planar SPAD structure used in our tests.

Fig. 2.
Fig. 2.

Layout of the tested SPAD arrays. The numbers from 1 to 7 and from 8 to 14 are used to identify the position of the single devices within the array.

Fig. 3.
Fig. 3.

Schematic representation of optical crosstalk between two devices A and B. When a primary signal photon triggers an avalanche in the SPAD A, secondary photons are emitted by the SPAD itself. These photons propagate through the bulk of the array and finally they are detected by the SPAD B.

Fig. 4.
Fig. 4.

Measured pseudo-crosstalk as a function of the position of the emitter and the detector. The two plots refer to the two rows of the array; the abscissas indicate the numbering of the SPAD as reported Fig. 2; the detector (in this case SPAD 1) is indicated by an arrow.

Fig. 5.
Fig. 5.

Dependence of the pseudo-crosstalk on the distance R between the emitter and the detector. The values shown represent the mean pseudo-crosstalk over all the couples at the same distance on the array. For comparison 1/R 2 curves are reported (dashed lines). Since crosstalk does not follow this law and it does not even decrease monotonically, also optical paths different from the direct ones have to be considered to describe this phenomenon.

Fig. 6.
Fig. 6.

Measurement of the light escaping from the bottom of the chip. The light is collected by a Hamamatsu C4880 Silicon CCD. Also the light escaping from the top surface was measured, in order to perform a comparison of the two contributions.

Fig. 7.
Fig. 7.

Increase in the total optical intensity reaching the detector due to a metal sheet manually placed under the chip.

Fig. 8.
Fig. 8.

Absorption coefficient of silicon as a function of the wavelength for different doping levels. The absorption coefficient for intrinsic silicon is taken from [13]. Coefficients (a)1.7·1017 cm-3, (b) 3.2·1017 cm-3, and (c)1019 cm-3 were reported by Spitzer and Fan in [14]. Coefficients (d) 2.4·1019 cm-3 and (e) 4·1019 cm-3 were reported by Schmid in [15].

Fig. 9.
Fig. 9.

Direct (Fig. (a)) and indirect (Fig. (b)) optical paths between SPAD A and SPAD B.

Fig. 10.
Fig. 10.

Measured SPAD emission spectrum for the devices shown in Fig. 1. The spectrum extends up to 1100 nm and beyond, thus indicating that even these spectral components can contribute to crosstalk.

Fig. 11.
Fig. 11.

Measured Photon Detection Efficiency for the tested planar SPADs.

Fig. 12.
Fig. 12.

Model developed to perform numerical simulations of optical crosstalk. The red dots correspond to the active regions of the SPADs and represent the possible emitting devices (as an example, the light emitted by one SPAD and reflecting off the bottom of the chip is shown in yellow). The black absorbing rings keep the effect of the isolation into account, whereas the bulk is modeled as a piece of uniform material (n-type silicon).

Fig. 13.
Fig. 13.

Simulated 2D intensity profile at the top surface of the chip with one emitter (at the top right of the image) turned on. The black dots represents the SPADs position on the array.

Fig. 14.
Fig. 14.

Overcoming of the critical angle for a single (a) and a double (b) reflection off the bottom of the chip. When this condition is reached (at a distance d 1 and d 2 from the emitter, respectively) all the optical power is reflected at the bottom silicon–air interface, therefore two variations of the intensity at the top surface of the chip can be seen in Fig. 13.

Fig. 15.
Fig. 15.

Simulated (solid line) and measured (dashed line) pseudo-crosstalk for the situation of Fig. 4. As before, the two plots refer to the two rows of the array; the abscissas indicate the numbering of the SPAD as reported Fig. 2; the detector (in this case SPAD 1) is indicated by an arrow. The numerical data are in very good agreement with the experimental results, thus indicating the developedmodel represents a helpful tool for the prediction of the dependence of crosstalk on the position of the devices within the array.

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