近紅外單光子崩潰二極體 (Single Photon Avalanche Photodiode,
SPAD)的應用相當廣泛，包含生物螢光分析、電子產業的VLSI 電路、
軍事、商業上的量子加密和車用電子偵測系統等。其操作原理是利用
元件逆向偏壓於崩潰電壓之上，理論而言吸收單光子便能觸發衝擊游
離機制，產生無窮大之增益，因此能夠偵測極弱的光。
為了提高動態偵測範圍 (dynamic range)或實現成像相關之應用，
可將SPAD 元件製作成多像素陣列；陣列的設計目標是縮小SPAD 元
件之間的距離以提高偵測效率，減少光子損失。然而當元件間距微縮
時，因元件崩潰時產生的breakdown flash 將影響相鄰元件的操作，導
致鄰近元件發生不預期之崩潰，換言之，元件間距縮小將使光學串擾
的現象越趨嚴重；在此論文中，我們使用光學模擬軟體Rsoft 的
Fullwave 功能，將計算共振腔品質因子的方法延伸到模擬SPAD 元件
中的光學串擾，計算二維陣列中breakdown flash 傳遞至相鄰元件的能
量密度，並藉此方法計算在不同元件間距、金屬溝槽隔離、隔離深度
條件下，breakdown flash 對相鄰元件的影響，結果顯示能量密度與預
期趨勢相同，印證我們提出的方法可延伸模擬SPAD 陣列光學串擾之
現象。我們亦進一步討論共振腔結構對陣列中光學串擾的影響。

Near infrared single photon avalanche diodes (SPAD) have many
applications in various field, such as fluorescence lifetime imaging
microscopy in life sciences, VLSI circuits in electronics industries,
military and commercial quantum encryption, and automotive electronic
detection systems. A SPAD is reversely biased above the breakdown
voltage and the absorption of single photon can trigger impact ionization
process, resulting infinite number of carriers. Therefore, it is capable of
detecting faint light.
In order to improve the dynamic range as well as to perform the
imaging applications, a multi-pixel SPAD array is required. The array
size and density increases for improving photon detection efficiency and
reducing the losses of incoming photons. However, as the distance
between each pixel is reduced, the breakdown flash generated by the
avalanche carriers will couple to nearby SPADs in the array and induce
unwanted avalanche events. In other words, the optical crosstalk will
become more serious as shrinking the spacing between pixels. In this
thesis, we use the simulation tool of Fullwave in Rsoft to study the optical
crosstalk in SPADs by applying the method that is used to calculated the
quality factor of an optical cavity. Based on the above method, we can
calculate the energy density of breakdown flash propagation in a 2D array.
The optical crosstalk can be well predicted under different conditions of
pixel spacing, metal coated trench, and trench depth. We further discuss
the optical crosstalk in the resonant cavity-enhanced SPAD structure.

參考文獻
[1] H. Bruining, "Physics and Application of Secondary Electron
Emission," 1954.
[2] J.P.R. D vid nd .H. T n. ”M teri l nsider ti ns f r Av l nche
Ph t di des.” IEEE J. Sel. Top. Quant, vol.14,pp.998-1009, 2008.
[3] H. Yang, G. Luo, P. Karnchanaphanurach, T. M. Louie, I. Rech, S.
Cova, L. Xun, nd X. S. Xie, “Pr tein nf rm ti n l Dyn mics
Probed by Single-M lecule Electr n Tr nsfer,” Science 302,
262–266, 2003.
[4] F. Stell ri, A. T si, F. Z pp , nd S. v , “ MOS circuit testing vi
time-res lved luminescence me surements nd simul ti ns,” IEEE
Trans. Instrum. Meas. 53, 163–169, 2004.
[5] K. J. G rd n, . Fern ndez, P. D. T wnsend, nd G. S. Buller, “A
short wavelength GigaHertz clocked fiber-optic quantum key
distributi n system,” IEEE J. Quantum Electron. 40, 900–908, 2004.
[6] C.Mathas. ADAS takes greater control in 2015. Available:
http://ww.edu.com/design/automotive/4437761/ADAS-takes-greatercontrol-
in-2015.
[7] Andrea L. Lacaita, Member, IEEE, Franco Zappa, Stefan0 Bigliardi,
nd M nfred0 M nfredi, “On the bremsstrahlung origin of hot carrier
induced ph t ns in silic n devices,” IEEE Trans. Electron. Devices
40, 577–582, 1993.
[8] Roland H. Hail’Z, “Studies n ptic l c upling between silic n p-n
juncti ns,” Solid–State Electronics 8, 417–425, 1965.
[9] W. J. Kindt, H. W. v n Zeijl, nd S. Middelh ek, “Optic l r sst lk
42
in Geiger Mode Avalanche Photodiode Arrays: Modeling, Prevention
nd Me surement,” IEEE, 17 October 2005.
[10] Ivan Rech, Antonino Ingargiola, Roberto Spinelli, Ivan Labanca,
Stefano Marangoni, Massimo Ghioni and Sergio Cova, “Optic l
crosstalk in single photon avalanche diode arrays: a new complete
m del, ” OSA, June 2008.
[11] Niccolò Calandri, Mirko Sanzaro, Lorenzo Motta, Claudio Savoia,
and Alberto Tosi, Member, “Optic l r sst lk in InG As/InP SPAD
Array:Analysis and Reduction With FIB-Etched Trenches,” IEEE,
2016.
[12] K. S. Yee, "Numerical solution of initial boundary value problems
involoving Maxwell's equation in isotropic media," IEEE Trans.
Antennas and Propagat., vol. 14, no. 3, pp. 300-307, May 1966.
[13] Andreas C. Cangellaris, Member, "Numerical stability and numerical
dispersion of a compact 2-D/FDTD method used for the dispersion
analysis of waveguides", IEEE microwave and guided wave Letters,
vol. 3, no. 1, January 1993.
[14] J. P. Berenger, "A perfectly matched layer for free-space simulation
in finite-difference computer codes," Annals of Telecommunications,
1994.
[15] Gerrit Mur, " Absorbing Boundary Conditions for the Finite
Difference Approximation of the Time Domain Electromagnetic
Field Equations," IEEE, 1981.
[16] Zhiqiang Bi, Keli Wu, Chen Wu, and John Litva, "A dispersive
boundary condition for microstrip component analysis using the
FD-TD method," IEEE Trans. Antennas and Propagat., vol. MTT-40,
43
no. 4, pp. 774-777, Apr. 1992.
[17] O. M. Ramahi, "Complementary operators: A method to annihilate
artificial reflections arising from the truncation of the computational
domain in the solution of patial differential equations," IEEE Trans.
Antennas and Propagat., vol. 43, pp. 697-704, Jul. 1995.
[18] Zachary S. Sacks, David M. Kingsland, Robert Lee, and Jin-Fa Lee,
"A perfectly matched anisotropic absorber for use as an absorbing
boundary condition," IEEE Trans Antennas and Propagat., vol. 43,
pp. 1460-1463, Dec. 1995.
[19] J. P. Berenger, "A perfectly matched layer for the absorption of
electromagnetic waves," J. Computat. Phys., vol. 114, pp. 185-200,
1994.
[20] G. F. D ll Bett , “Av l nche ph t di des in submicr n MOS
technologies for high-sensitivity im ging”, Rijeka, InTech, 2011.
[21] Brian F. Aull, Andrew H. Loomis, Douglas J. Young, Richard M.
Heinrichs, Bradley J. Felton, Peter J. Daniels, and Deborah J.
Landers, “Geiger-Mode Avalanche Photodiodes for
ThreeDimensional Imaging, ”Lincoln Lab. Journal, vol. 13, 2002.
[22] S. Kasapa, J. A. Rowlands, S. D. Baranovskii, and K. Tanioka,
"Lucky drift impact ionization in amorphous semiconductors," J.
Appl. Phys., vol. 96, 2004.A. G. CHYNOWETH AND K. G.
MCKAY Bell Telephone Laboratories, Murray Hil/, Rem Jersey. "
Photon Emission from Avalanche Breakdown in Silicon, "
PHYSICAL REVIEW, 1956.
[23] A. G. CHYNOWETH AND K. G. MCKAY Bell Telephone
Laboratories, Murray Hil/, Rem Jersey. " Photon Emission from
44
Avalanche Breakdown in Silicon, " PHYSICAL REVIEW, 1956.
[24] YICHENG SHI, JANET ZHENG JIE LIM, HOU SHUN POH,
PENG KIAN TAN, PEIYU AMELIA TAN, ALEXANDER
LING, AND CHRISTIAN KURTSIEFER, "Breakdown flash at
telecom wavelengths in InGaAs avalanche photodiodes, "Journal,
2017.
[25] Richard D. Younger, K. Alex McIntosh, Joseph W. Chludzinski,
Douglas C. Oakley, Leonard J. Mahoney, Joseph E. Funk, Joseph P.
Donnelly, and S. Verghese Lincoln Laboratory, "Crosstalk Analysis
of Integrated Geiger-mode Avalanche Photodiode Focal Plane Arrays,
" Proc. of SPIE, Vol. 7320, 2010.
[26] Mahdi Zavvari, Kambiz Abedi and Mohammad Karimi. "Design of
resonant cavity structure for efficient high-temperature operation of
single-photon avalanche photodiodes, " OSA, 2014.
[27] M. Selim lhiiia and Samuel Strite, "Resonant cavity enhanced
photonic devices, "Journal of Applied Physics, 1995.