R. J. Mcintyre, Multiplication noise in uniform avalanche diodes, IEEE Transactions on Electron Devices, vol.13, pp.164-168, 1966.

Y. Musienko, Advances in Avalanche Photodiodes, Workshop of Innovative detectors for Supercolliders, Italy Pansart J.P, 1997.

. Geiger-mode, Avalanche Photodiodes for three-dimensional imaging, pp.335-350

C. G. Bethea, B. F. Levine, S. Cova, and G. Ripamonti, High-resolution and high-sensitivity optical-time-domain reflectometer, Optics Letters, vol.13, issue.3, pp.233-235, 1988.
DOI : 10.1364/OL.13.000233

G. Collazuol, G. Ambrosi, M. Boscardin, F. Corsi, G. F. Betta et al., Single photon timing resolution and detection efficiency of the IRST silicon photo-multipliers, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol.581, issue.1-2, pp.461-464, 2007.
DOI : 10.1016/j.nima.2007.08.027

F. Corsi, C. Marzocca, A. Perrota, A. Dragone, M. Foresta et al., Electrical characterization of silicon photomultiplier detectors for optimal front-end design, IEEE Nuclear Science Symposium Conference Record, pp.30-222, 2006.

S. Cova, G. Ripamonti, and A. Lacaita, Avalanche semiconductor detector for single optical photons with a time resolution of 60ps; Nuclear Instruments and Methods in, Physics Research A, vol.253, pp.482-487, 1987.

S. Cova, . Lacaita, and G. Ripamonti, Trapping phenomena in avalanche photodiodes on nanosecond scale, IEEE Electron Device Letters, vol.12, issue.12, pp.685-687, 1991.
DOI : 10.1109/55.116955

S. Cova, M. Ghioni, A. Lacaita, C. Samori, and F. Zappa, Avalanche photodiodes and quenching circuits for single-photon detection, Applied Optics, vol.35, issue.12, pp.1956-1976, 1996.
DOI : 10.1364/AO.35.001956

J. Frenkel, On Pre-Breakdown Phenomena in Insulators and Electronic Semi-Conductors, Physical Review, vol.54, issue.8, pp.647-648, 1938.
DOI : 10.1103/PhysRev.54.647

S. D. Ganichev, I. N. Yassievich, W. Prettl, J. Diener, B. K. Meyer et al., Centers in Terahertz Fields, Physical Review Letters, vol.75, issue.8, p.1590, 1995.
DOI : 10.1103/PhysRevLett.75.1590

S. D. Ganichev, E. Ziemann, W. Prettl, I. N. Yassievich, A. A. Istratov et al., Distinction between the Poole-Frenkel and tunneling models of electric-field-stimulated carrier emission from deep levels in semiconductors, Physical Review B, vol.61, issue.15, pp.10361-10365, 2000.
DOI : 10.1103/PhysRevB.61.10361

V. M. Golovin, Russian patent, nr, p.1644708, 1999.

W. N. Grant, Electron and hole ionization rates in epitaxial silicon at high electric fields, Solid-State Electronics, vol.16, issue.10, pp.1189-1203, 1973.
DOI : 10.1016/0038-1101(73)90147-0

A. S. Grove, Physics and technology of semiconductor devices Model for the electrical behavior of the micro-plasma, Journal of Applied Physics, vol.35, issue.5, pp.1370-1376, 1964.

R. H. Haitz, Mechanisms Contributing to the Noise Pulse Rate of Avalanche Diodes, Journal of Applied Physics, vol.36, issue.10, pp.3123-3130, 1965.
DOI : 10.1063/1.1702936

G. Hungerford and D. J. Birch, Single-photon timing detectors for fluorescence lifetime spectroscopy, Measurement Science and Technology, vol.7, issue.2, pp.121-135, 1996.
DOI : 10.1088/0957-0233/7/2/002

G. A. Hurkx, . Graaff, H. C. De, W. J. Kloosterman, and M. P. Knuvers, A new analytical diode model including tunneling and avalanche breakdown, IEEE Transactions on Electron Devices, vol.39, issue.9, pp.2090-2098, 1992.
DOI : 10.1109/16.155882

T. Isoshima, Y. Isojima, K. Hakomori, K. Kikuchi, and K. Nagai, Ultrahigh sensitivity single???photon detector using a Si avalanche photodiode for the measurement of ultraweak biochemiluminescence, Review of Scientific Instruments, vol.66, issue.4, pp.2922-2926, 1995.
DOI : 10.1063/1.1145578

P. G. Kwiat, A. M. Steinberg, P. H. Eberhard, R. Y. Chiao, and D. Petroff, High-efficiency single-photon detectors, High-efficiency single photon detectors, pp.867-870, 1993.
DOI : 10.1103/PhysRevA.48.R867

A. Lacaita, M. Mastrapasqua, M. Ghioni, and S. Vanoli, junctions, Applied Physics Letters, vol.57, issue.5, pp.489-491, 1990.
DOI : 10.1063/1.103629

A. Lacaita, S. Cova, A. Spinelli, and F. Zappa, Photon???assisted avalanche spreading in reach???through photodiodes, Applied Physics Letters, vol.62, issue.6, pp.606-608, 1993.
DOI : 10.1063/1.108870

A. Lacaita, F. Zappa, S. Bigliardi, and M. Manfredi, On the bremsstrahlung origin of hot-carrier-induced photons in silicon devices, IEEE Transactions on Electron Devices, vol.40, issue.3, pp.577-582, 1993.
DOI : 10.1109/16.199363

W. R. Leo, T. A. Verlag-berlin-heidelberg-louis, G. Ripamonti, and A. Lacaita, Techniques for nuclear and particle physics experiments, Second Edition Photoluminescence lifetime microscope spectrometer based on timecorrelated single-photon counting with an avalanche diode detector, Review of Scientific Instruments, vol.61, issue.1, pp.11-22, 1990.

R. J. Mcintyre, Theory of Microplasma Instability in Silicon, Journal of Applied Physics, vol.32, issue.6, pp.983-995, 1961.
DOI : 10.1063/1.1736199

R. J. Mcintyre, Multiplication noise in uniform avalanche diodes, IEEE Transactions on Electron Devices, vol.13, issue.1, pp.164-168, 1966.

N. S. Nightingale, A new silicon avalanche photodiode photon counting detector module for astronomy, Experimental Astronomy, vol.35, issue.6, pp.407-422, 1991.
DOI : 10.1007/BF00426721

W. G. Oldham, R. R. Samuelson, and P. Antognetti, Triggering phenomena in avalanche diodes, IEEE Transactions on Electron Devices, vol.19, issue.9, pp.1056-1060, 1972.
DOI : 10.1109/T-ED.1972.17544

V. R. Overstraten, . Man, and H. De, Measurement of the ionization rates in diffused silicon p-n junctions, Solid-State Electronics, vol.13, issue.5, pp.583-608, 1970.
DOI : 10.1016/0038-1101(70)90139-5

C. Piemonte, A new silicon photomultiplier structure for blue light detection, Nuclear Instruments and Methods in, Physics Research A, vol.568, pp.224-232, 2006.

C. Piemonte, R. Battiston, G. Collazuol, G. F. Betta, A. Guerra et al., New results on the characterization of FBK-irst silicon photomultipliers, IEEE Nuclear Science Symposium Conference Record, pp.42-46, 2006.

D. Renker, G. Ripamonti, and S. Cova, Silicon Photomultipliers; International Conference on New developments in photo-detection Carrier diffusion effects in the time-response of a fast photodiode, Solid state Electronics, vol.28, pp.925-931, 1985.

Z. Sadygov, Russian Patent, nr Silicon planar technology for single-photon optical detectors, IEEE Transaction on Electron Devices, vol.50, issue.4, pp.918-925, 1997.

B. Senitzky and J. L. Moll, Breakdown in Silicon, Physical Review, vol.110, issue.3, 1958.
DOI : 10.1103/PhysRev.110.612

W. Shockley and W. Read, Statistics of the Recombinations of Holes and Electrons, Physical Review, vol.87, issue.5, pp.835-842, 1952.
DOI : 10.1103/PhysRev.87.835

A. Spinelli and L. Lacaita, Physics and numerical simulation of single photon avalanche diodes, IEEE Transactions on Electron Devices, vol.44, issue.11, 1943.
DOI : 10.1109/16.641363

S. M. Sze, Physics of semiconductor devices, 2 nd edition Physics of semiconductor devices ? 3 rd edition, 1981.

X. Y. Zou, L. J. Wang, and L. Mandel, Induced coherence and indistinguishability in optical interference, Physical Review Letters, vol.67, issue.3, pp.318-321, 1991.
DOI : 10.1103/PhysRevLett.67.318

V. Chaumat, C. Bazin, N. Dinu, V. Puill, J. F. Vagnucci et al., Absolute photo-detection efficiency measurement of SiPM Single photon timing resolution and detection efficiency of the IRST silicon photo-multipliers, Proceedings of Science, in press Collazuol, pp.461-464, 2007.

G. Colazuol, M. G. Bisogni, S. Marcatili, C. Piemonte, and A. Guerra, Studies of silicon photomultipliers at cryogenic temperatures, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol.628, issue.1, pp.389-392, 2011.
DOI : 10.1016/j.nima.2010.07.008

F. Corsi, A. Dragone, C. Marzocca, A. Guerra, P. Delizia et al., Modeling a silicon photomultiplier (SiPM) as a signal source for optimum front-end design, Nuclear Instruments and Methods A, pp.416-418, 2007.

S. Cova, Temperature dependence of avalanche multiplication in semiconductors, NIST workshop on Single Photon Detectors Crowell, pp.242-244, 1966.

S. Marcatili, C. Marzocca, C. Piemonte, G. Pignatel, A. Pozza et al., Development of the first prototypes of silicon photomultiplier (SiPM) at FBK-irst, Nuclear Instruments and Methods A, pp.422-424, 2007.

N. Dinu, P. Barrillon, C. Bazin, N. Belcari, M. G. Bisogni et al., Characterization of a prototype matrix of SiPM, Physics Research A, vol.610, pp.101-104, 2009.

R. H. Haitz, Studies on optical coupling between silicon p???n junctions, Solid-State Electronics, vol.8, issue.4, pp.417-425, 1965.
DOI : 10.1016/0038-1101(65)90119-X

W. J. Kindt, V. H. Zeijl, and S. Middelhoek, Optical cross-talk in Geiger mode avalanche photodiodes arrays: modeling, prevention and measurement, Solid-State Device research Conference, Proceedings of the 28 th European, 1998.

A. Lacaita, M. Mastrapasqua, M. Ghioni, and S. Vanoli, junctions, Applied Physics Letters, vol.57, issue.5, pp.489-491, 1990.
DOI : 10.1063/1.103629

A. Lacaita, F. Zappa, S. Bigliradi, and M. Manfredi, On the bremsstrahlung origin of hot-carrier-induced photons in silicon devices, IEEE Transactions on Electron Devices, vol.40, issue.3, pp.577-582, 1993.
DOI : 10.1109/16.199363

A. Lacaita, S. Cova, A. Spinelli, and F. Zappa, Photon???assisted avalanche spreading in reach???through photodiodes, Applied Physics Letters, vol.62, issue.6, pp.606-608, 1993.
DOI : 10.1063/1.108870

A. Nagai, Temperature dependence of SiPM characteristics, Internship report supervised by N, 2013.

C. Piemonte, M. Boscardin, G. F. Betta, M. Melchiorri, N. Zorzi et al., Recent developments on silicon photomultipliers produced at FBK-irst, 2007 IEEE Nuclear Science Symposium Conference Record, pp.41-43, 2007.
DOI : 10.1109/NSSMIC.2007.4436565

I. Prochzka, K. Hamal, L. Kral, and J. Blazej, Silicon photon counting detector optical cross-talk effect, 5 th International Conference on Photonics, Devices and Systems, Optical crosstalk in single photon avalanche diode arrays: a new complete model, pp.8381-8394, 2005.

Z. Sadygov, Russian Patent, nr, Simulation of silicon photomultiplier signals, pp.3726-3733, 1997.

N. Serra, G. Giacomini, A. Piazza, C. Piemonte, A. Taroli et al., Experimental and TCAD Study of Breakdown Voltage Temperature Behavior in <formula formulatype="inline"><tex Notation="TeX">$n^{+}/p$</tex> </formula> SiPMs, IEEE Transactions on Nuclear Science, vol.58, issue.3, pp.1233-1240, 2011.
DOI : 10.1109/TNS.2011.2123919

A. Spinelli and L. Lacaita, Physics and numerical simulation of single photon avalanche diodes, IEEE Transactions on Electron Devices, vol.44, issue.11, 1943.
DOI : 10.1109/16.641363

T. H. Wilmshurst, Signal recovery from noise in electronic instrumentation, A. Hilger Publ. References on SiPM arrays and medical applications: ATLAS collaboration; (2007); ATLAS forward detectors for measurement of elastic scattering and luminosity determination, pp.2007-2011, 1985.

K. Chien, Genes and physiology: molecular physiology in genetically engineered animals., Journal of Clinical Investigation, vol.97, issue.4, pp.901-909, 1996.
DOI : 10.1172/JCI118512

L. Eriksson, D. Townsend, M. Eriksson, C. Melcher, M. Schmand et al., Experience with scintillators for PET: towards the fifth generation of PET scanners, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol.525, issue.1-2, pp.242-248, 2004.
DOI : 10.1016/j.nima.2004.03.067

D. Guerra, A. Bartoli, A. Belcari, N. Herbert, D. Motta et al., Performance evaluation of the fully engineered YAP-(S)PET scanner for small animal imaging, IEEE Transactions on Nuclear Science, vol.53, issue.3, pp.1078-1083, 2006.
DOI : 10.1109/TNS.2006.871900

E. Hoffman, M. Tornai, M. Janecek, B. Patt, and J. Iwanczyk, Intraoperative probes and imaging probes, European Journal of Nuclear Medicine and Molecular Imaging, vol.26, issue.8, pp.913-935, 1999.
DOI : 10.1007/s002590050468

J. S. Huber, W. W. Moses, S. E. Derenzo, M. H. Ho, M. S. Andreaco et al., Characterization of a 64 channel PET detector using photodiodes for crystal identification, IEEE Transactions on Nuclear Science, vol.44, issue.3, pp.1197-1201, 1997.
DOI : 10.1109/23.596987

L. J. Humm, A. Rosenfeld, and A. Del-guerra, From PET detectors to PET scanners, European Journal of Nuclear Medicine and Molecular Imaging, vol.30, issue.11, pp.1574-1597, 2003.
DOI : 10.1007/s00259-003-1266-2

URL : http://doi.org/10.1007/s00259-003-1266-2

G. Llosá, R. Battiston, N. Belcari, M. Boscardin, G. Collazuol et al., Novel Silicon Photomultipliers for PET Applications, IEEE Transactions on Nuclear Science, vol.55, issue.3, pp.877-881, 2008.
DOI : 10.1109/TNS.2008.922812

G. Llosá, N. Belcari, M. G. Bisogni, A. Guerra, S. Marcatili et al., Evaluation of the first Silicon Photomultiplier matrices for a small animal PET scanner, 2008 IEEE Nuclear Science Symposium Conference Record, pp.3574-3580, 2008.
DOI : 10.1109/NSSMIC.2008.4774094

G. Llosá, N. Belcari, M. G. Bisogni, G. Collazuol, S. Marcatili et al., Energy, Timing and Position Resolution Studies With 16-Pixel Silicon Photomultiplier Matrices for Small Animal PET, IEEE Transactions on Nuclear Science, vol.56, issue.5, pp.2586-2593, 2009.
DOI : 10.1109/TNS.2009.2030191

R. Lecomte, Technology challenges in small animal PET imaging, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol.527, issue.1-2, pp.157-165, 2004.
DOI : 10.1016/j.nima.2004.03.113

C. Mathelin, I. Piqueras, and J. L. Guyonnet, Performances of a new prototype handheld scintillating probe for the search of sentinel lymph nodes in breast cancer, European Journal of Surgical Oncology (EJSO), vol.32, issue.1, pp.24-28, 2006.
DOI : 10.1016/j.ejso.2005.09.017

URL : https://hal.archives-ouvertes.fr/in2p3-00025435

D. P. Mcelroy, W. Pimpl, B. J. Pichler, M. Rafecas, T. Schuler et al., Characterization and readout of MADPET-II detector modules: validation of a unique design concept for high resolution small animal PET, IEEE Transactions on Nuclear Science, vol.52, issue.1, pp.199-204, 2005.
DOI : 10.1109/TNS.2004.843114

W. W. Moses, S. Derenzo, and T. Budinger, PET detector modules based on novel detector technologies, Nuclear Instruments and methods A, pp.1-3, 1994.

W. W. Moses, Time of flight in pet revisited, IEEE Transactions on Nuclear Science, vol.50, issue.5, pp.1325-1330, 2003.
DOI : 10.1109/TNS.2003.817319

K. Paigen, A miracle enough: the power of mice, Nature Medicine, vol.4, issue.3, pp.215-220, 1995.
DOI : 10.1038/372425a0

M. Phelps, PET: the merging of biology and imaging into molecular imaging, The Journal of Nuclear Medicine, vol.41, issue.4, pp.661-681, 2000.

L. Pidol, A. Kahr-harari, B. Viana, E. Virey, B. Ferrand et al., High efficiency of lutetium silicate scintillators, Ce-doped LPS, and LYSO crystals, IEEE Transactions on Nuclear Science, vol.51, issue.3, pp.1084-1087, 2004.
DOI : 10.1109/TNS.2004.829542

C. Piemonte, M. Boscardin, G. F. Betta, M. Melchiorri, N. Zorzi et al., Recent developments on silicon photomultipliers produced at FBK-irst, 2007 IEEE Nuclear Science Symposium Conference Record, pp.41-43, 2007.
DOI : 10.1109/NSSMIC.2007.4436565

R. R. Raylman and R. Wahl, Evaluation of ion-implanted-silicon detectors for use in intraoperative positron-sensitive probes, Medical Physics, vol.23, issue.11, pp.1889-1895, 1996.
DOI : 10.1118/1.597751

R. R. Raylman, A solid-state intraoperative beta probe system, IEEE Transactions on Nuclear Science, vol.47, issue.4, pp.1696-1703, 2000.
DOI : 10.1109/23.870863

I. Sarikaya, A. Sarikaya, and R. Reba, Gamma probes and their use in tumor detection in colorectal cancer, International Seminars in Surgical Oncology, vol.5, issue.1, pp.25-26, 2008.
DOI : 10.1186/1477-7800-5-25

Y. Shao, S. Cherry, and A. Chatziioannou, Design and development of 1mm resolution PET detectors with position sensitive PMT's, Nuclear Instruments and Methods A, pp.486-490, 2005.

W. H. Sweet, The Uses of Nuclear Disintegration in the Diagnosis and Treatment of Brain Tumor, New England Journal of Medicine, vol.245, issue.23, pp.875-887, 1951.
DOI : 10.1056/NEJM195112062452301

S. Tavernier, P. Bruyndonckx, S. Leonard, and O. Devroede, A high-resolution PET detector based on continuous scintillators, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol.537, issue.1-2, pp.1-2, 2005.
DOI : 10.1016/j.nima.2004.08.035

C. J. Thompson, S. James, . St, and N. Tomic, Under-sampling in PET scanners as a source of image blurring, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol.545, issue.1-2, pp.436-445, 2005.
DOI : 10.1016/j.nima.2005.01.329

P. Zanzonico and S. Heller, The intraoperative gamma probe: Basic principles and choices available, Seminars in Nuclear Medicine, vol.30, issue.1, pp.33-48, 2000.
DOI : 10.1016/S0001-2998(00)80060-4

S. Yamamoto, K. Matsumoto, S. Sakamoto, K. Tarutani, K. Minato et al., An intra-operative positron probe with background rejection capability for FDG-guided surgery, Annals of Nuclear Medicine, vol.18, issue.3, pp.23-28, 2005.
DOI : 10.1007/BF02986331

S. Yamamoto, T. Higashi, K. Matsumoto, and M. Senda, Development of a positron-imaging detector with background rejection capability, Annals of Nuclear Medicine, vol.48, issue.(1), pp.655-662, 2006.
DOI : 10.1007/BF02984676

S. Yamamoto, M. Imaizumi, T. Warabe, H. Watabe, Y. Kanai et al., Development of a Si-PM-based high-resolution PET system for small animals, Physics in Medicine and Biology, vol.55, issue.19, pp.5817-5831, 2010.
DOI : 10.1088/0031-9155/55/19/013

P. Allport, B. Di-girolamo, B. Heinemann, E. Torrence, and P. Wells, Expected pileup values at the HL-LHC, ATLAS-Communication- UPGRADE-2013-036 ATLAS Collaboration The ATLAS experiment at the CERN Large Hadron Collider S08003 ATLAS Collaboration; (2008, b); ATLAS pixel detector electronics and sensors, Prototype ATLAS IBL modules using the FE-I4A front-end readout chip, p.11010, 2008.

M. Benoit, . Lounis, and N. Dinu, Simulation of guard ring influence on the performance of ATLAS pixel detectors for inner layer replacement, Journal of Instrumentation, vol.4, issue.03, 2008.
DOI : 10.1088/1748-0221/4/03/P03025

URL : https://hal.archives-ouvertes.fr/in2p3-00389827

M. Benoit, . Lounis, and N. Dinu, Simulation of Radiation Damage Effects on Planar Pixel Guard Ring Structure for ATLAS Inner Detector Upgrade, IEEE Transactions on Nuclear Science, vol.56, issue.6, pp.3236-3243, 2009.
DOI : 10.1109/TNS.2009.2034002

URL : https://hal.archives-ouvertes.fr/in2p3-00448947

M. Benoit, . Lounis, and N. Dinu, Simulation of charge multiplication and trap-assisted tunneling in irradiated planar pixel sensors, IEEE Nuclear Science Symposuim & Medical Imaging Conference, pp.612-616, 2010.
DOI : 10.1109/NSSMIC.2010.5873832

URL : https://hal.archives-ouvertes.fr/in2p3-00577158

R. Brennan, An introduction to spreading resistance analysis and its application in the semiconductor industry; A Solecon Labs Seminar, www.solecon.com Da Via, C. & al.; (2012); 3D silicon sensors: Design, large area production and quality assurance for the ATLAS IBL pixel det ector upgrade, Nuclear Instruments and Methods in, Physics Research A, vol.694, pp.321-330

N. Dinu, A. Lounis, M. Benoit, G. Calderinu, J. Idarraga et al., Dopant profiles of planar pixel sensors for the upgrade of the ATLAS inner detector, IEEE Nuclear Science Symposium Conference, 2011.

N. Dinu, on behalf of ATLAS upgrade PPS collaboration; (2011, b); Recent progress of the ATLAS upgrade planar pixel sensors R&D project; Presented at IEEE Nuclear Science Symposium Conference

C. Goessling and D. Muenstermann, R&D on planar pixel sensor technology for the ATLAS inner detector upgrade (PPS proposal), CERN, https, p.966140, 2008.

P. Grenier, Test beam results of 3D silicon pixel sensors for the ATLAS upgrade, Nuclear Instruments and Methods in, Physics Research A, vol.638, pp.33-40, 2011.

R. Hull, Properties of crystalline silicon, 1999.

A. Lounis, D. Martinot, . Calderini, G. Marchiori, M. Benoit et al., TCAD simulation of ATLAS pixel guard-ring and edge structure for Super-LHC upgrade, ATLAS Note, 2009.

A. Lounis, M. Benoit, and N. Dinu, ) ; TCAD simulations of planar pixel sensors, Proceedings of Science, p.30, 2011.

R. G. Mazur and P. H. Dickey, A Spreading Resistance Technique for Resistivity Measurements on Silicon, Journal of The Electrochemical Society, vol.113, issue.3, pp.255-259, 1966.
DOI : 10.1149/1.2423927

M. Moll, S. I. Parker, C. J. Kenney, and J. Segal, Radiation damage in silicon particle detectors 3D ? A proposed new architecture for solid-state radiation detectors, Nuclear Instruments and Methods in, Physics Research A, vol.395, pp.328-343, 1997.

L. Rossi, P. Fischer, T. Rohe, and N. Wermes, Pixel detectors: from fundamentals to applications, High Luminosity Large Hadron Collider ? A description for the European Strategy Preparatory Group, 2006.

S. Inc, http://www.silvaco.fr/products/tcad/index ATLAS User's Manual, Device Simulation Software, html Silvaco Inc, p.139, 2008.

S. Technology, C. Home-page, and S. University, aspx well defined shape (i.e. quadratic dependence with the overvoltage ?V), as it can be seen in the experimental results in the Section 4.2.1. The I post-BD is essentially given by the bulk generation current before breakdown (since surface charges cannot generate avalanches in the depletion region), multiplied by the multiplication factor G. Knowing the gain G, the value of the diode leakage current I post-BD of a GM-APD gives us information on DCR. Since the value of DCR is desired to be as low as possible, the number of carriers traversing the depletion region in dark conditions should be as low as possible (i.e reducing the number of generation-recombination centers in the depletion region)

W. N. Grant, Electron and hole ionization rates in epitaxial silicon at high electric fields, Solid-State Electronics, vol.16, issue.10, pp.1189-1203, 1973.
DOI : 10.1016/0038-1101(73)90147-0

C. A. Lee, R. A. Logan, R. L. Batdorf, J. J. Kleimack, and W. Wiegmann, Ionization Rates of Holes and Electrons in Silicon, Physical Review, vol.134, issue.3A, pp.761-774, 1964.
DOI : 10.1103/PhysRev.134.A761

V. R. Overstraten, . Man, and H. De, Measurement of the ionization rates in diffused silicon p-n junctions, Solid-State Electronics, vol.13, issue.5, pp.583-608, 1970.
DOI : 10.1016/0038-1101(70)90139-5

K. K. Thornber, Applications of scaling to problems in high???field electronic transport, Journal of Applied Physics, vol.52, issue.1, pp.279-290, 1981.
DOI : 10.1063/1.328490

R. B. Adler, A. C. Smith, and R. L. Longini, Introduction to semiconductor physics Distribution functions and ionization rates for hot electrons in semiconductors, Physical review, vol.1, issue.6, pp.2507-2517, 1962.

C. Y. Chang, S. S. Chiu, and L. P. Hsu, Temperature dependence of breakdown voltage in silicon abrupt p-n junctions, IEEE Transactions on Electron Devices, vol.18, issue.6, pp.391-393, 1971.
DOI : 10.1109/T-ED.1971.17210

C. R. Crowell and S. M. Sze, TEMPERATURE DEPENDENCE OF AVALANCHE MULTIPLICATION IN SEMICONDUCTORS, Applied Physics Letters, vol.9, issue.6, pp.242-244, 1966.
DOI : 10.1063/1.1754731