基于InGaAs/InP单光子雪崩二极管的红外单光子探测研究
|
摘要
单光子探测是一种重要的技术,被广泛应用在量子保密通信、量子计算和测量灵敏度需要达到单光子水平的其他领域。对于1310nm和1550nm的通信波段,具有吸收、渐变、电荷、倍增分区结构(SAGCM)的In0.53Ga0.47As/InP雪崩光电二极管(APD)被广泛地研究,并认为是最具实用性的单光子探测器。因为APD工作在反偏压高于雪崩击穿电压条件下,即处于所谓的盖革模式下,所以它也被叫作盖革模式雪崩光电二极管或者单光子雪崩二极管(SPAD)。
本论文通过理论和实验研究了SAGCM In0.53Ga0.47As/InP SPAD的雪崩击穿特性,观察并解释了相对电流增益饱和的现象。据此提出了一种能够简单准确地测量SPAD的贯穿电压和雪崩击穿电压的方法。该方法不依赖于温度,具有很好的实用性。
采用了历史相关的碰撞电离模型,通过数值分析的方法,研究了具有SAGCM结构的In0.53Ga0.47As/InP SPAD击穿电压的影响因素。计算结果表明击穿电压会随着温度的升高,电荷层电荷密度的增大而升高。同时存在某一特征倍增区厚度,当SPAD倍增区厚度小于这一特征值时,雪崩击穿电压会随倍增区厚度增大而降低;而当倍增区厚度大于这一特征值时,击穿电压会随之缓慢升高。提高单光子探测性能有两种有效的途径,首先是设计单光子探测专用的SPAD,然后是改进器件的驱动和控制技术。本文给出了一种In0.53Ga0.47As/InP SPAD的结构和参数设计,通过控制倍增区、吸收区及电荷层的厚度和掺杂浓度,使其更适用于单光子探测。
为了尽可能地减少暗计数,提高单光子量子效率,优化器件的结构和驱动电路,有必要弄清产生暗计数的物理机制,以及单光子量子效率和暗计数概率对器件结构和工作条件的依赖关系。本文提出了一个比较严格的模型来计算SPAD的单光子量子效率和暗计数概率,在此模型中考虑了电荷层和吸收区的碰撞电离对倍增区雪崩击穿的贡献,假设雪崩击穿只能发生在倍增区。计算雪崩击穿概率与电场的关系时,采用了历史相关的碰撞电离模型。在较宽的温度范围内,计算了不同结构、不同偏置电压下的SPAD的单光子量子效率和暗计数概率。结果表明,如果忽略了电荷层和吸收区的碰撞电离,将会导致对暗计数的低估,低估率随着温度的升高而升高。增大倍增区会提高SPAD的峰值单光子量子效率,但是如果倍增区厚度超过1μm,峰值单光子量子效率随着Wm的升高会变得非常缓慢,并最终达到饱和而接近器件的内量子效率。决定SPAD暗计数的物理机制取决于器件的结构和工作条件。当SPAD倍增区较薄时,暗计数的最主要来源是倍增区的隧穿;当SPAD倍增区较厚时,暗计数的决定性机制为吸收区的产生-复合效应。对于倍增区为1μm左右的SPAD,当温度较低时,倍增区的隧穿是暗计数的最主要来源,随着温度的升高,吸收区的产生-复合作用变得重要起来,当温度达到某一特定值时,吸收区的产生-复合成为暗计数的最主要来源。
改进了SPAD的驱动和控制技术,提出了积分门控模式单光子探测器方案,并给出了实验验证。与通常门控模式不同,在这个方案中,通过检测雪崩脉冲的电荷量,使电尖峰问题得到了很好的解决,进而有效地提高了单光子探测器的性能。对于1550nm波长,单光子量子效率达到了29.9%,同时每门暗计数降到了5.57×10~(-6),即达到1.11×10~(-7)/ns。
Single photon detectors are increasingly needed in the emerging fields of quantum computation and quantum cryptography as well as in some more traditional fields that requiring single photon sensitivity. As in the telecom wavelengths of 1310 and 1550nm, a separate absorption, grading, charge and multiplication (SAGCM) In0.53Ga0.47As/InP avalanche photodiode (APD) that reverse biased beyond breakdown voltage (VB) and operated in so-called Geiger mode is regarded as one of the most practical single photon detectors. These APDs are also known as Geiger mode avalanche photodiodes or single photon avalanche diodes (SPADs).
In this thesis, characteristics of the avalanche breakdown in SAGCM In0.53Ga0.47As/InP SPADs are analyzed numerically and experimentally. In the experiment, saturation of the relative current gain is observed and interpreted. According to this, the punch-through voltage and breakdown voltage of single photon avalanche diodes can be measured in a simple and accurate way. The analysis method is temperature independent and more practical.
The structure and operation dependence of breakdown voltage is also calculated. The results indicate that the breakdown voltage increases with the temperature and charge density in the charge layer. And there is a critical value of the multiplication layer width Wm0. When the multiplicition layer width (Wm) is smaller than Wm0, VB decreases with Wm. While VB increases slowly with when Wm is above Wm0. An improved structure of In0.53Ga0.47As/InP SPAD is proposed in which the width and doping concentration of the multiplication, absorption and charge layer is carefully designed specially for single photon detection.
In order to optimize the structure design and operation of SPADs, it is necessary to clarify the mechanisms that give rise to dark counts, as well as the dependence of SPQE and Pd on the structure, voltage and temperature. In the thesis, a more rigorous model is developed to determine the SPQE and Pb, in which impact ionization in charge and absorption layers have been taken into account to have contribution to the avalanche breakdown which can take place only in the multiplication region. In the temperature range of 200-300K, dark count rate of SPADs with 0.2-3μm multiplication layer was calculated. Results show that, ignoring the impact ionization of charge and absorption layer will cause an underestimate of dark counts. The ratio of underestimate increases with temperature. The results also show that the primary mechanism of dark counts depends on both device structure and operating conditions. The thickness of charge layer greatly affects the dark counts and peak SPQE. The peak SPQE rises with the increase of multiplication layer width. But when Wm > 1μm, the peak SPQE increases slowly and it finally saturates at the quantum efficiency of the SPAD. The primary origin of dark counts depends on both device structure and operating conditions. For SPADs with thinner multiplication layer, band to band tunneling in multiplication layer is the dominative mechanism of dark counts, while for thicker SPADs, generation-recombination in the absorber dominates the dark counts. Dark counts from generation-recombination increase importance with temperature. As for a SPAD with multiplication layer arround 1μm, there is a critical temperature, when the operating temperature below the critical temperature, tunneling is the primary origin of dark counts, while when the operating temperature exceed the critical temperature, generation-recombination in the absorption layer begins to dominate.
An integral gated mode single photon detector is demonstrated at telecom wavelengths. The charge number of an avalanche pulse rather than the peak current is monitored for single photon detection. The transient spikes in conventional gate mode operation are cancelled completely by integrating, which effectively improves the performance of the single photon detector. This method may achieve a detection efficiency of 29.9% at the dark count probability per gate equals to 5.57×10-6/gate (1.11×10-7/ns) at 1550nm.
本论文通过理论和实验研究了SAGCM In0.53Ga0.47As/InP SPAD的雪崩击穿特性,观察并解释了相对电流增益饱和的现象。据此提出了一种能够简单准确地测量SPAD的贯穿电压和雪崩击穿电压的方法。该方法不依赖于温度,具有很好的实用性。
采用了历史相关的碰撞电离模型,通过数值分析的方法,研究了具有SAGCM结构的In0.53Ga0.47As/InP SPAD击穿电压的影响因素。计算结果表明击穿电压会随着温度的升高,电荷层电荷密度的增大而升高。同时存在某一特征倍增区厚度,当SPAD倍增区厚度小于这一特征值时,雪崩击穿电压会随倍增区厚度增大而降低;而当倍增区厚度大于这一特征值时,击穿电压会随之缓慢升高。提高单光子探测性能有两种有效的途径,首先是设计单光子探测专用的SPAD,然后是改进器件的驱动和控制技术。本文给出了一种In0.53Ga0.47As/InP SPAD的结构和参数设计,通过控制倍增区、吸收区及电荷层的厚度和掺杂浓度,使其更适用于单光子探测。
为了尽可能地减少暗计数,提高单光子量子效率,优化器件的结构和驱动电路,有必要弄清产生暗计数的物理机制,以及单光子量子效率和暗计数概率对器件结构和工作条件的依赖关系。本文提出了一个比较严格的模型来计算SPAD的单光子量子效率和暗计数概率,在此模型中考虑了电荷层和吸收区的碰撞电离对倍增区雪崩击穿的贡献,假设雪崩击穿只能发生在倍增区。计算雪崩击穿概率与电场的关系时,采用了历史相关的碰撞电离模型。在较宽的温度范围内,计算了不同结构、不同偏置电压下的SPAD的单光子量子效率和暗计数概率。结果表明,如果忽略了电荷层和吸收区的碰撞电离,将会导致对暗计数的低估,低估率随着温度的升高而升高。增大倍增区会提高SPAD的峰值单光子量子效率,但是如果倍增区厚度超过1μm,峰值单光子量子效率随着Wm的升高会变得非常缓慢,并最终达到饱和而接近器件的内量子效率。决定SPAD暗计数的物理机制取决于器件的结构和工作条件。当SPAD倍增区较薄时,暗计数的最主要来源是倍增区的隧穿;当SPAD倍增区较厚时,暗计数的决定性机制为吸收区的产生-复合效应。对于倍增区为1μm左右的SPAD,当温度较低时,倍增区的隧穿是暗计数的最主要来源,随着温度的升高,吸收区的产生-复合作用变得重要起来,当温度达到某一特定值时,吸收区的产生-复合成为暗计数的最主要来源。
改进了SPAD的驱动和控制技术,提出了积分门控模式单光子探测器方案,并给出了实验验证。与通常门控模式不同,在这个方案中,通过检测雪崩脉冲的电荷量,使电尖峰问题得到了很好的解决,进而有效地提高了单光子探测器的性能。对于1550nm波长,单光子量子效率达到了29.9%,同时每门暗计数降到了5.57×10~(-6),即达到1.11×10~(-7)/ns。
Single photon detectors are increasingly needed in the emerging fields of quantum computation and quantum cryptography as well as in some more traditional fields that requiring single photon sensitivity. As in the telecom wavelengths of 1310 and 1550nm, a separate absorption, grading, charge and multiplication (SAGCM) In0.53Ga0.47As/InP avalanche photodiode (APD) that reverse biased beyond breakdown voltage (VB) and operated in so-called Geiger mode is regarded as one of the most practical single photon detectors. These APDs are also known as Geiger mode avalanche photodiodes or single photon avalanche diodes (SPADs).
In this thesis, characteristics of the avalanche breakdown in SAGCM In0.53Ga0.47As/InP SPADs are analyzed numerically and experimentally. In the experiment, saturation of the relative current gain is observed and interpreted. According to this, the punch-through voltage and breakdown voltage of single photon avalanche diodes can be measured in a simple and accurate way. The analysis method is temperature independent and more practical.
The structure and operation dependence of breakdown voltage is also calculated. The results indicate that the breakdown voltage increases with the temperature and charge density in the charge layer. And there is a critical value of the multiplication layer width Wm0. When the multiplicition layer width (Wm) is smaller than Wm0, VB decreases with Wm. While VB increases slowly with when Wm is above Wm0. An improved structure of In0.53Ga0.47As/InP SPAD is proposed in which the width and doping concentration of the multiplication, absorption and charge layer is carefully designed specially for single photon detection.
In order to optimize the structure design and operation of SPADs, it is necessary to clarify the mechanisms that give rise to dark counts, as well as the dependence of SPQE and Pd on the structure, voltage and temperature. In the thesis, a more rigorous model is developed to determine the SPQE and Pb, in which impact ionization in charge and absorption layers have been taken into account to have contribution to the avalanche breakdown which can take place only in the multiplication region. In the temperature range of 200-300K, dark count rate of SPADs with 0.2-3μm multiplication layer was calculated. Results show that, ignoring the impact ionization of charge and absorption layer will cause an underestimate of dark counts. The ratio of underestimate increases with temperature. The results also show that the primary mechanism of dark counts depends on both device structure and operating conditions. The thickness of charge layer greatly affects the dark counts and peak SPQE. The peak SPQE rises with the increase of multiplication layer width. But when Wm > 1μm, the peak SPQE increases slowly and it finally saturates at the quantum efficiency of the SPAD. The primary origin of dark counts depends on both device structure and operating conditions. For SPADs with thinner multiplication layer, band to band tunneling in multiplication layer is the dominative mechanism of dark counts, while for thicker SPADs, generation-recombination in the absorber dominates the dark counts. Dark counts from generation-recombination increase importance with temperature. As for a SPAD with multiplication layer arround 1μm, there is a critical temperature, when the operating temperature below the critical temperature, tunneling is the primary origin of dark counts, while when the operating temperature exceed the critical temperature, generation-recombination in the absorption layer begins to dominate.
An integral gated mode single photon detector is demonstrated at telecom wavelengths. The charge number of an avalanche pulse rather than the peak current is monitored for single photon detection. The transient spikes in conventional gate mode operation are cancelled completely by integrating, which effectively improves the performance of the single photon detector. This method may achieve a detection efficiency of 29.9% at the dark count probability per gate equals to 5.57×10-6/gate (1.11×10-7/ns) at 1550nm.
引文
[1] Siegmund O H W. Advances in Microchannel Plate Detectors for UV/visible Astronomy[C], Proc. SPIE, 2003, 4854: 181-190.
[2] Felekyan S, Kühnemuth R, Kudryavtsev V, et al. Full Correlation from Picoseconds to Seconds by Time-resolved and Time-correlated Single Photon Detection[J], Rev. Sci. Instrum., 2005, 76(8): 083104.
[3] Cova S, Ghioni M, Rech I, Photon Counting and Timing Detector Modules for Single-molecule Spectroscopy and DNA Analysis[C]. Proceedings of IEEE LEOS Annual Conference, 2004, 1: 70-71.
[4] Rech I, Cova S, Restelli A, et al. Microchips and Single-Photon Avalanche Diodes for DNA Separation with High Sensitivity[J], Electrophoresis, 2006, 27(19): 3797-3804.
[5] Li L Q, Davis L M. Single Photon Avalanche Diode for Single Molecule Detection[J], Review Sci. Intrum., 1993, 64(6): 1524-1529.
[6] Gisin N, Ribordy G, Tittel W, et al. Quantum Cryptography[J], Rev. Mod. Phys., 2002, 74(1): 145-195.
[7] Bethune D S, Risk W P. An Autocompensating Fiber Optic Quantum Cryptography System Based on Polarization Splitting of Light[J]. IEEE J. Quantum Electron, 2004, 36(3): 340-347.
[8] Bethune D S, Risk W P. Autocompensating Quantum Cryptography[J]. New J. Phys., 2002, 4(3):42.1-42.15.
[9] Risk W P, Bethune D S. Quantum Cryptography[J]. Optics and Photonics news, 2002, 13(7): 26-32.
[10] Levine B F, Bethea C G, Campbell J C. 1.52μm Room Temperature Photon Counting Optical Time Domain Reflectometer[J]. Electron. Lett., 1985, 21(5): 194-196.
[11] Lacaita A, Zappa F, Cova S, et al. Single-photon Detection beyond 1μm: Performance of Commercially Available InGaAs/InP Detectors[J]. Appl. Optics,1996, 35(16): 2986-2996.
[12] Smith J M, Hiskett P A, Gontijo I, et al. A Picosecond Time-resolved Photoluminescence Microscope with Detection at Wavelength Greater than 1500nm[J]. Review Sci. Intrum., 2001, 72(5): 2325-2329.
[13] Karve G V. Avalanche Photodiodes as Single Photon Detectors[D]. Austin: PH. D. Thesis of the University of Texas at Austin, 2005.
[14] Niclass C, Rochas A, Besse P A. Design and Characterization of a CMOS 3-D Image Sensor Based on Single Photon Avalanche Diodes[J]. IEEE J. Solid-St. Circ., 2005, 40(9): 1847-1854.
[15] Fujiwara M, Sasaki M. Multiphoton Discrimination at Telecom Wavelength with Charge Integration Photon Detector[J]. Appl. Phys. Lett., 2005, 86(11): 111119.
[16] Fujiwara M, Sasaki M. Photon-number-resolving Detection at a Telecommunica- tions Wavelength With a Charge-integration Photon Detector[J]. Optics Lett., 2006, 31(6): 691-693.
[17]张忠祥,韩正甫,刘云,等.超导单光子探测技术[J].物理学进展,2007,27(1):3-10.
[18]张裕恒.超导物理[M].合肥:中国科学技术大学出版社, 1997: 347-379.
[19] Miller A J, Nam S W, Martinis J M, et al. Demonstration of a Low-noise Near-infrared Photon Counter with Multiphoton Discrimination[J]. Appl. Phys. Lett., 2003, 83(4): 791-793.
[20] Verekin A, Pearlman A, Slysz W, et al. Ultrafast Superconducting Single-photon Detectors for Near-infrared-wavelength Quantum Communications[J]. J. Mod. Opt., 2004, 51(9): 1447-1458.
[21] Skocpol W J, Beasley M R, Tinkham M. SQUID Techniques I Obtaining Reliability in Point-contact SQUID's[J]. J. Appl. Phys. 1974. 45(9): 4054-4066.
[22] Robinson B S, Kerman A J, Dauler E A, et al. 781 Mbit/s Photon-counting Optical Communications Using a Superconducting Nanowire Detector[J]. Opt. Lett. 2006, 31(4): 444-446.
[23] Gol’tsman G N, Okunev O, Chulkova G, et al. Picosecond Superconducting Single-photon Optical Detector[J]. Appl. Phys. Lett., 2001. 79(6): 705-707.
[24] Korneev A, Kouminov P, Matvienko V. Sensitivity and Gigahertz Counting Performance of NbN Superconducting Single-photon Detectors[J]. Appl. Phys. Lett., 2004, 84(26): 5338-5340.
[25] Cova S, Ghioni M, Lacaita A, et al. Avalanche Photodiodes and Quenching Circuits for Single-photon Detection[J]. Appl. Opt. 1996, 35(12): 1956-1976.
[26] Cova S, Ghioni M, Lacaita A, et al. Avalanche Photodiodes and Quenching Circuits for Single-photon Detection[J]. Appl. Opt. 1996, 35(12): 1956-1976.
[27] Rarity J G, Wall T E, Ridley K D, et al. Single-photon Counting for the 1300-1600 nm Range by Use of Peltier-cooled and Passively Quenched InGaAs Avalanche Photodiodes[J]. Appl. Opt., 2000, 39(36): 6746-6753.
[28] Grayson T P, Wang L J. 400-ps Time Resolution with a Passively Quenched Avalanche Photodiode[J]. Appl. Opt., 1993, 32(16): 2907-2910.
[29] Brown R G. W, Jones R, Rarity J G., et al. Characterization of Silican Avalanche Photodiodes for Photon Correlation Measurements. 2: Active Quenching[J]. Appl. Opt., 1987, 16(12): 2383-2389.
[30] Gallivanoni A, Rech I, Resnati D, et al. Monolithic Active Quenching and Picosecond Timing Circuit Suitable for Large-area Single-photon Avalanche Diodes[J]. Opt. Express, 2006, 14(12): 5021-5030.
[31] Ribordy G, Gautier J D, Zbinden H, et al. Performance of InGaAs/InP Avalanche Photodiodes as Gated-mode Photon Counters[J]. Appl. Opt., 1998, 37(12): 2272-2277.
[32] Viterbini M, Nozzoli S, Poli M, et al. Voltage Breakdown Follower Avoids Hard Thermal Constrains in a Geiger Mode Avalanche Photodiode[J]. Appl. Opt., 1996, 35(27): 5345-5347.
[33] Gulinatti A, Maccagnani P, Rech I, et al. 35 ps Time Resolution at Room Temperature with Large Area Single Photon Avalanche Diodes[J]. Electron. Lett., 2005, 41: 272-274.
[34] Ghioni M, Gulinatti A, Rech I, et al. Progress in Silicon Single-photon Avalanche Diodes[J]. IEEE J. of Sel. Top. Quant. Electron., 2007, 13(4): 852-862.
[35] Owens P C M, Rarity J G, Tapster P R, et al. Photon Counting with PassivelyQuenched Germanium Avalanche[J]. Appl. Opt. 1994, 33(30): 6895-6901.
[36] Lacaita A, Francese P A, Zappa F, et al. Single-photon Detection beyond 1μm: Performances of Commercially Available Germanium Photodiodes[J]. Appl. Opt. 1994, 33(30): 6902-6918.
[37] Townsend P D. Quantum Cryptography on Multiuser Optical Fibre Networks[J]. Nature, 1997, 385: 47-49.
[38] Buller G S, Francey S J, Massa J S, et al. Time-resolved Photoluminescence Measurements of InGaAs/InP Multiple-quantum-well Structures at 1.3-μm Wavelengths by Use of Germanium Single-photon Avalanche Photodiode[J]. Appl.Opt., 1996, 35(6): 916-921.
[39] Townsend P D. Simultaneous Quantum Cryptographic Key Distribution and Conventional Data Transmission over Installed Fibre Using Wavelength-division Multiplexing[J]. IEEE Electron.Lett., 1997, 33(3): 188-189.
[40] Francey S. Single-photon Avalanche Diodes for Time-resolved Photoluminescence Measurements in the Near Infra-red[D]. Edinburgh: Ph. D. dissertation of Heriot-Watt University, 1996.
[41] Lacaita A, Francese P A, Zappa F, et al. Single-photon Detection beyond 1μm: Performances of Commercially Available InGaAs/InP Detectors[J]. Appl. Opt. 1996, 35(16): 2986-2996.
[42] Levine B F, Bethea C G, Campbell J C. Room-temperature 1.3-μm Optical Time Domain Reflectometer Using a Photon Counting InGaAs/InP Avalanche Detector[J]. Appl. Phys. Lett., 1985, 46(4): 333-335.
[43] Yuan Z L, Kardynal B E, Sharpe A W, et al. High Speed Single Photon Detection in the Near Infrared[J]. Appl. Phys. Lett., 2007, 91(4): 041114.
[44] Itzler M A, Ben-Michael R, Hsu C F, et al. Single Photon Avalanche Diodes (SPADs) for 1.5μm Photon Counting Applications[J]. J. Mod. Opt., 2007, 54(2-3): 283-304.
[45] Cova S, Lacaita A, Ripamonti G. Trapping Phenomena in Avalanche Photodiodes on Nanosecond Scale[J]. IEEE Electron. Devices Lett. 1991, 12(12): 685–687.
[46] Zappa F, Gulinatti A, Maccagnani P, et al. SPADA: Single-photon Avalanche DiodeArrays[J]. IEEE Photon. Tech. Lett., 2005, 17(3): 657-659.
[47] Niclass C, Sergio M, Charbon E. A Single Photon Avalanche Diode Array Fabricated in Deep-submicron CMOS Technology[C]. Proceedings of the conference on Design, automation and test in Europe, 2006, 81-86.
[48] Zappa F, Tisa S, Tosi A et al. Principles and Features of Single-photon Avalanche Diode Arrays[J]. Sensor Actuat. A: Phys., 2007, 140(1): 103-112.
[49] Tarof L E, Knight D G, Fox K E, et al. Planar InP/InGaAs Avalanche Photodetectors with Partial Charge Sheet in Device Periphery[J]. Appl. Phys. Lett., 1990, 57(7): 670-672.
[50] Liu M, Bai X, Hu C, et al. Low Dark Count Rate and High Single-Photon Detection Efficiency Avalanche Photodiode in Geiger-Mode Operation[J]. IEEE Photonic Technology Letters, 2007, 19(6): 378-380.
[51] Namekata N, Makino Y, Inoue S. Single-photon Detector for Long-distance Fiber-Optic Quantum Key Distribution[J]. Opt. Lett., 2002, 21(11): 954-956.
[52] Bethune D S, Risk W P, Pabst G W. A high-performance Integrated Single-photon Detector for Telecom Wavelengths[J]. J. Mod. Opt., 2004, 51(9-10): 1359-1368.
[53] Voss P L, K?prülüK G, Choi S K, et al. 14MHz Rate Photon Counting with Room Temperature InGaAs/InP Avalanche Photodiodes[J]. J. Mod. Opt., 2004, 51(9-10): 1369 -1379.
[54] Ribordy G, Gisin N, Guinnard O, et al. Photon Counting at Telecom Wavelengths with Commercial InGaAs/InP Avalanche Photodiodes: Current Performance[J]. J. Mod. Opt., 2004, 51(9-10): 1381-1398.
[55] Trifonov A, Subacius D, Berzanskis A, et al. Single Photon Counting at Telecom Wavelength and Quantum Key Distribution[J]. J. Mod. Opt., 2004, 51(9-10): 1399-1415.
[56] Namekata N, Makino Y, Inoue S. Single-photon Detector for Long-distance Quantum Cryptography[J]. Electronics and Communications in Japan (Part II: Electronics), 2003, 86(5): 10-15.
[57] Pellegrini S, Warburton R E, Tan L J J, et al. Design and Performance of an InGaAs–InP Single-Photon Avalanche Diode Detector[J]. IEEE J. Quant. Electron,2006, 42(4): 397-402.
[58] Niclass C, Gersbach M, Henderson R, et al. A Single Photon Avalanche Diode Implemented in 130-nm CMOS Technology[J]. IEEE J. of Sel. Top. Quant. Electron., 2007, 13(4): 863-869.
[59] Yoshizawa A, Kaji R. Tsuchida H. After-pulse-discarding in Single-photon Detection to Reduce Bit Errors in Quantum Key Distribution[J] Opt. Express, 2003, 11(11): 1303- 1309.
[60] Tomita A, Nakamura K. Balanced, Gated-mode Photon Detector for Quantum-bit Discrimination at 1550 nm[J]. Opt. Lett., 2002, 27(20): 1827-1829.
[61] Yoshizawa A, Kaji R, Teushida H. Gated-mode Single-photon Detection at 1550 nm by Discharge Pulse Counting[J]. Appl. Phys. Lett., 2004, 84(18): 3606-3608.
[62]刘云.红外单光子探测器的研制[D].合肥:中国科学技术大学博士学位论文, 2007.
[63]魏政军.红外单光子探测器的研究[D].广州:华南师范大学博士学位论文, 2008.
[64] Nesheim T. Single Photon Detection Using Avalanche Photodiode[D]. Trondheim: Master thesis of Norwegian University of Science and Technology, 1999.
[65] Wu G, Zhou C, Li H, et al. Balanced Single-photon Detectors Using InGaAs/InP Avalanche Photodiodes with Transformer Based Spikes Cancellation[J]. Chin. Phys. Lett., 2005, 22(3): 525-528.
[66] Namekata N, Sasamori S, Inoue S. 800 MHz Single-photon Detection at 1550-nm Using an InGaAs-InP Avalanche Photodiode Operated with a Sine Wave Gating[J]. Opt. Express 2006, 14(21): 10043.
[67] Yuan Z L, Kardynal B E, Sharpe A W, et al. High Speed Single Photon Detection in the Near Infrared[J]. Appl. Phy. Lett., 2007, 91(4): 041114.
[68] Tsang W T主编,半导体光检测器[M].杜宝勋,等译.北京:电子工业出版社,清华大学出版社, 1992.
[69] Pearsall T P. Threshold Energies for Impact Ionization by Electrons and Holes in InP[J]. Appl. Phys. Lett., 1979, 35(2): 168-170.
[70] Chelikowsky J R, Cohen M L. Nonlocal Pseudopotential Calculations for the Electronic Structure of Eleven Diamond and Zinc-blende Semiconductors[J]. Phys.Rev. B, 1976, 14(2): 556-582.
[71] Shockley W. Problems Related to p-n Junctions in Silicon[J]. Solid-State Electron., 1961, 2(1): 35-60.
[72] Wolff P A. Theory of Electron Multiplication in Silicon and Germanium[J]. Phys. Rev., 1954, 95(6): 1415-1420.
[73] Baraff G A. Distribution Functions and Ionization Rates for Hot Electrons in Semiconductors[J]. Phys. Rev., 1962, 128(6): 2507-2517.
[74] Crowell C R, Sze S M. Temperature Dependence of Avalanche Mulitiplication in Semiconductors[J]. Appl. Phys. Lett., 1966, 9(6): 242-244.
[75] Mcintyre R J. Multiplication Noise Uniform Avalanche Diodes[J]. IEEE Trans. Electron Devices, 1966, 13(1): 164-169.
[76] Mcintyre R J. The Distribution of Gains in Uniformly Multiplying Avalanche Photodiodes: Theory[J]. IEEE Trans. Electron Devices, 1972, 19(6): 703-713.
[77] Mcintyre R J. A New Look at Impact Ionization-PartⅠ: A Theory of Gain, Noise, Breakdown Probability, and Frequency Response[J]. IEEE Trans. Electron Devices, 1999, 46(8): 1623-1631.
[78] Yuan P, Anselm K A, Hu C, et al. A New Look at Impact Ionization-PartⅡ: Gain and Noise in Short Avalanche Photodiodes[J]. IEEE Trans. Electron Devices, 1999, 46: 1632-1639.
[79] Wang S, Ma F, Li X, et al. Analysis of Breakdown Probabilities in Avalanche Using a History-dependent Analytical Model[J]. Appl. Phys. Lett., 2003, 82(12): 1971-1973.
[80]马声全,陈贻汉.光电子理论与技术[M].北京:电子工业出版社, 2005.
[81] Okuto Y, Crowell C R. Energy-conservation Considerations in the Characterization of Impact Ionization in Semiconductors[J]. Phys. Rev. B, 1972, 6(8): 3076–3081.
[82] Okuto Y, Crowell C R. Ionization Coefficients in Semiconductors: A Nonlocal Property[J]. Phys. Rev. B, 1974, 10(10): 4284–4296.
[83] Okuto Y, Crowell C R. Threshold Energy Effect on Avalanche Breakdown Voltage in Semiconductor Junctions[J]. Solid-State Electron., 1975, 18(2): 161–168.
[84] Sze S M. Physics of Semiconductor Device[M]. 2nd Edition. New York: Wiley,1981: 96-108.
[85] Maruyama T, Narusawa F, Kudo M, et al. Development of a Near-infrared Photon-counting System Using an InGaAs Avalanche Photodiode[J]. Opt. Eng., 2002, 41(2): 395-402.
[86] Park C Y, Hyun KS, Kang S G, et al. Effect of Multiplication Layer Width on Breakdown Voltage in InP/InGaAs Avalanche Photodiode[J]. Appl. Phys. Lett., 1995, 67(25): 3789-3791.
[87] Hyun Y S, Park C Y. Breakdown Characteristics in InP/InGaAs Avalanche Photodiode with p-i-n Multiplication Layer Structure[J]. J. Appl. Phys., 1996, 81(2): 974-984.
[88] Hayat M M, Sako?luü, Kwon O, et al. Breakdown Probabilities for Thin Heterostructure Avalanche Photodiodes[J]. IEEE J. Quantum Electron., 2003, 39(1): 179-185.
[89] Lacaita A, Spinelli A, Longhi S. Avalanche Transients in Shallow p-n Junctions Biased Above Breakdown[J]. Appl. Phys. Lett., 1995, 67(18): 2627-2629.
[90] Lacaita A, Cova S, Spinelli A, et al. Photon-assisted Avalanche Spreading in Reach-though Photodiodes[J]. Appl. Phys. Lett., 1992, 62(6): 606-608.
[91] Ramirez D A, Hayat M M, Karve G, et al. Detection Efficiencies and Generalized Breakdown Probabilities for Nanosecond-gated Near Infrared Single-photon Avalanche Photodiodes[J]. IEEE J. Quantum Electron., 2006, 42(2): 137-145.
[92] Sugihara K, Yagyu E, Tokuda Y. Numerical Analysis of Single Photon Detection Avalanche Photodiodes Operated in the Geiger Mode[J]. J. Appl. Phys. 2006, 99(12): 124502.
[93] Osaka F, Mikawa T, Kaneda T. Low-temperature Characteristics of Electron and Hole Ionization Coefficients in (100) Oriented Ga1?xInxAsyP1?y[J]. Appl. Phys. Lett., 1985, 46(12): 1138.
[94] Forrest S R, Smith R G, Kim O K. Performance of In0.53Ga0.47As/InP Avalanche Photodiodes[J]. IEEE J. Quantum Electron., 1982, 18(12): 2040-2048.
[95] Huntington A S. Development of Long-wavelength Avalanche Photodiodes and Vertical-cavity Lasers for Epitaxial Integration as a Vertical-cavity Photon NumberAmplifier[D]. Santa barbara, CA: PH. D. Thesis of University of California, Santa Barbara, 2003.
[96] Kang Y, Lu H X, Lo Y H, et al. Dark Count Probability and Quantum Efficiency of avalanche Photodiodes for Single-photon Detection[J]. Appl. Phys. Lett., 2003, 83(14): 2955-2957.
[97] Karve G, Wang S, Ma F, et al. Origin of Dark Counts in In0.53Ga0.47As/ In0.52Al0.48As Avalanche Photodiodes Operated in Geiger Mode[J]. Appl. Phys. Lett., 2005, 86(6): 063505.
[98] Tan C H, Rees G J, Houston P A, et al. Temperature Dependence of Electron Impact Ionization in In0.53Ga0.47As[J]. Appl. Phys. Lett. 2004, 84(13): 2322-2324.
[99] Humphreys D A, King R J, Jenkins D, et al. Measurement of Absorption Coefficients of Ga0.47In0.53As over the Wavelength Range 1.0-1.7μm[J]. IEEE Electron. Lett., 1985, 21(25): 1187-1188.
[100] Moll J L. Physics of Semiconductor[M]. New York: McGraw-Hill, 1964.
[101] Forrest S R, Leheny R F, Nahory R E, et al. In0.53Ga0.47As Photodiodes with Dark Current Limited by Generation-recombination and Tunneling[J]. Appl. Phys. Lett., 1980, 37(3): 322-324.
[102] Hang Z, Shen H, Pollak F H. Temperature Dependence of the EO and EO+ΔO Gaps of InP up to 600°C [J]. Solid State Commun., 1990, 73(1): 15-18.
[103] Yu P W, Kuphal E. Photoluminescence of Mn- and Un-doped Ga0.47In0.53As on InP[J]. Solid State Commun., 1984, 49(9): 907-910.
[104] Yee A, Ng W K, David J P R, et al. Negative Temperature Dependence of Electron Multiplication in In0.53Ga0.47As[J]. Appl. Phys. Lett., 2003, 82(8): 1224-1246.
[105] Jiang X, Itzler M A, Ben-Michael R, et al. InGaAsP-InP Avalanche Photodiodes for Single Photon Detection[J]. IEEE J. Sel. Top. Quant., 2007, 13(4): 895-905.
[106] Jiang X, Itzler M A, Ben-Michael R. Afterpulsing Effects in Free-running InGaAsP Single-photon Avalanche Diodes[J]. IEEE J. Quantum Electron, 2008, 44(1): 3-11.
[107] Levine B F, Bethea C G. Single Photon Detection at 1.3um Using a Gated Avalanche Photodiode[J]. Appl. Phys. Lett. 1984, 44(5): 553-555.
[108] Wei Z, Zhou P, Wang J, et al. An Integral Gated Mode Single Photon Detector atTelecom Wavelengths[J]. J. of Phys. D: Appl. Phys., 2007, 40(22): 6922-6928.
[109] Liu Y, Wu Q L, Han Z F. Single Photon Detector at Telecom Wavelengths for Quantum Key Distribution[J]. Chin. Phys. Lett., 2006, 23(1): 252-255.
[2] Felekyan S, Kühnemuth R, Kudryavtsev V, et al. Full Correlation from Picoseconds to Seconds by Time-resolved and Time-correlated Single Photon Detection[J], Rev. Sci. Instrum., 2005, 76(8): 083104.
[3] Cova S, Ghioni M, Rech I, Photon Counting and Timing Detector Modules for Single-molecule Spectroscopy and DNA Analysis[C]. Proceedings of IEEE LEOS Annual Conference, 2004, 1: 70-71.
[4] Rech I, Cova S, Restelli A, et al. Microchips and Single-Photon Avalanche Diodes for DNA Separation with High Sensitivity[J], Electrophoresis, 2006, 27(19): 3797-3804.
[5] Li L Q, Davis L M. Single Photon Avalanche Diode for Single Molecule Detection[J], Review Sci. Intrum., 1993, 64(6): 1524-1529.
[6] Gisin N, Ribordy G, Tittel W, et al. Quantum Cryptography[J], Rev. Mod. Phys., 2002, 74(1): 145-195.
[7] Bethune D S, Risk W P. An Autocompensating Fiber Optic Quantum Cryptography System Based on Polarization Splitting of Light[J]. IEEE J. Quantum Electron, 2004, 36(3): 340-347.
[8] Bethune D S, Risk W P. Autocompensating Quantum Cryptography[J]. New J. Phys., 2002, 4(3):42.1-42.15.
[9] Risk W P, Bethune D S. Quantum Cryptography[J]. Optics and Photonics news, 2002, 13(7): 26-32.
[10] Levine B F, Bethea C G, Campbell J C. 1.52μm Room Temperature Photon Counting Optical Time Domain Reflectometer[J]. Electron. Lett., 1985, 21(5): 194-196.
[11] Lacaita A, Zappa F, Cova S, et al. Single-photon Detection beyond 1μm: Performance of Commercially Available InGaAs/InP Detectors[J]. Appl. Optics,1996, 35(16): 2986-2996.
[12] Smith J M, Hiskett P A, Gontijo I, et al. A Picosecond Time-resolved Photoluminescence Microscope with Detection at Wavelength Greater than 1500nm[J]. Review Sci. Intrum., 2001, 72(5): 2325-2329.
[13] Karve G V. Avalanche Photodiodes as Single Photon Detectors[D]. Austin: PH. D. Thesis of the University of Texas at Austin, 2005.
[14] Niclass C, Rochas A, Besse P A. Design and Characterization of a CMOS 3-D Image Sensor Based on Single Photon Avalanche Diodes[J]. IEEE J. Solid-St. Circ., 2005, 40(9): 1847-1854.
[15] Fujiwara M, Sasaki M. Multiphoton Discrimination at Telecom Wavelength with Charge Integration Photon Detector[J]. Appl. Phys. Lett., 2005, 86(11): 111119.
[16] Fujiwara M, Sasaki M. Photon-number-resolving Detection at a Telecommunica- tions Wavelength With a Charge-integration Photon Detector[J]. Optics Lett., 2006, 31(6): 691-693.
[17]张忠祥,韩正甫,刘云,等.超导单光子探测技术[J].物理学进展,2007,27(1):3-10.
[18]张裕恒.超导物理[M].合肥:中国科学技术大学出版社, 1997: 347-379.
[19] Miller A J, Nam S W, Martinis J M, et al. Demonstration of a Low-noise Near-infrared Photon Counter with Multiphoton Discrimination[J]. Appl. Phys. Lett., 2003, 83(4): 791-793.
[20] Verekin A, Pearlman A, Slysz W, et al. Ultrafast Superconducting Single-photon Detectors for Near-infrared-wavelength Quantum Communications[J]. J. Mod. Opt., 2004, 51(9): 1447-1458.
[21] Skocpol W J, Beasley M R, Tinkham M. SQUID Techniques I Obtaining Reliability in Point-contact SQUID's[J]. J. Appl. Phys. 1974. 45(9): 4054-4066.
[22] Robinson B S, Kerman A J, Dauler E A, et al. 781 Mbit/s Photon-counting Optical Communications Using a Superconducting Nanowire Detector[J]. Opt. Lett. 2006, 31(4): 444-446.
[23] Gol’tsman G N, Okunev O, Chulkova G, et al. Picosecond Superconducting Single-photon Optical Detector[J]. Appl. Phys. Lett., 2001. 79(6): 705-707.
[24] Korneev A, Kouminov P, Matvienko V. Sensitivity and Gigahertz Counting Performance of NbN Superconducting Single-photon Detectors[J]. Appl. Phys. Lett., 2004, 84(26): 5338-5340.
[25] Cova S, Ghioni M, Lacaita A, et al. Avalanche Photodiodes and Quenching Circuits for Single-photon Detection[J]. Appl. Opt. 1996, 35(12): 1956-1976.
[26] Cova S, Ghioni M, Lacaita A, et al. Avalanche Photodiodes and Quenching Circuits for Single-photon Detection[J]. Appl. Opt. 1996, 35(12): 1956-1976.
[27] Rarity J G, Wall T E, Ridley K D, et al. Single-photon Counting for the 1300-1600 nm Range by Use of Peltier-cooled and Passively Quenched InGaAs Avalanche Photodiodes[J]. Appl. Opt., 2000, 39(36): 6746-6753.
[28] Grayson T P, Wang L J. 400-ps Time Resolution with a Passively Quenched Avalanche Photodiode[J]. Appl. Opt., 1993, 32(16): 2907-2910.
[29] Brown R G. W, Jones R, Rarity J G., et al. Characterization of Silican Avalanche Photodiodes for Photon Correlation Measurements. 2: Active Quenching[J]. Appl. Opt., 1987, 16(12): 2383-2389.
[30] Gallivanoni A, Rech I, Resnati D, et al. Monolithic Active Quenching and Picosecond Timing Circuit Suitable for Large-area Single-photon Avalanche Diodes[J]. Opt. Express, 2006, 14(12): 5021-5030.
[31] Ribordy G, Gautier J D, Zbinden H, et al. Performance of InGaAs/InP Avalanche Photodiodes as Gated-mode Photon Counters[J]. Appl. Opt., 1998, 37(12): 2272-2277.
[32] Viterbini M, Nozzoli S, Poli M, et al. Voltage Breakdown Follower Avoids Hard Thermal Constrains in a Geiger Mode Avalanche Photodiode[J]. Appl. Opt., 1996, 35(27): 5345-5347.
[33] Gulinatti A, Maccagnani P, Rech I, et al. 35 ps Time Resolution at Room Temperature with Large Area Single Photon Avalanche Diodes[J]. Electron. Lett., 2005, 41: 272-274.
[34] Ghioni M, Gulinatti A, Rech I, et al. Progress in Silicon Single-photon Avalanche Diodes[J]. IEEE J. of Sel. Top. Quant. Electron., 2007, 13(4): 852-862.
[35] Owens P C M, Rarity J G, Tapster P R, et al. Photon Counting with PassivelyQuenched Germanium Avalanche[J]. Appl. Opt. 1994, 33(30): 6895-6901.
[36] Lacaita A, Francese P A, Zappa F, et al. Single-photon Detection beyond 1μm: Performances of Commercially Available Germanium Photodiodes[J]. Appl. Opt. 1994, 33(30): 6902-6918.
[37] Townsend P D. Quantum Cryptography on Multiuser Optical Fibre Networks[J]. Nature, 1997, 385: 47-49.
[38] Buller G S, Francey S J, Massa J S, et al. Time-resolved Photoluminescence Measurements of InGaAs/InP Multiple-quantum-well Structures at 1.3-μm Wavelengths by Use of Germanium Single-photon Avalanche Photodiode[J]. Appl.Opt., 1996, 35(6): 916-921.
[39] Townsend P D. Simultaneous Quantum Cryptographic Key Distribution and Conventional Data Transmission over Installed Fibre Using Wavelength-division Multiplexing[J]. IEEE Electron.Lett., 1997, 33(3): 188-189.
[40] Francey S. Single-photon Avalanche Diodes for Time-resolved Photoluminescence Measurements in the Near Infra-red[D]. Edinburgh: Ph. D. dissertation of Heriot-Watt University, 1996.
[41] Lacaita A, Francese P A, Zappa F, et al. Single-photon Detection beyond 1μm: Performances of Commercially Available InGaAs/InP Detectors[J]. Appl. Opt. 1996, 35(16): 2986-2996.
[42] Levine B F, Bethea C G, Campbell J C. Room-temperature 1.3-μm Optical Time Domain Reflectometer Using a Photon Counting InGaAs/InP Avalanche Detector[J]. Appl. Phys. Lett., 1985, 46(4): 333-335.
[43] Yuan Z L, Kardynal B E, Sharpe A W, et al. High Speed Single Photon Detection in the Near Infrared[J]. Appl. Phys. Lett., 2007, 91(4): 041114.
[44] Itzler M A, Ben-Michael R, Hsu C F, et al. Single Photon Avalanche Diodes (SPADs) for 1.5μm Photon Counting Applications[J]. J. Mod. Opt., 2007, 54(2-3): 283-304.
[45] Cova S, Lacaita A, Ripamonti G. Trapping Phenomena in Avalanche Photodiodes on Nanosecond Scale[J]. IEEE Electron. Devices Lett. 1991, 12(12): 685–687.
[46] Zappa F, Gulinatti A, Maccagnani P, et al. SPADA: Single-photon Avalanche DiodeArrays[J]. IEEE Photon. Tech. Lett., 2005, 17(3): 657-659.
[47] Niclass C, Sergio M, Charbon E. A Single Photon Avalanche Diode Array Fabricated in Deep-submicron CMOS Technology[C]. Proceedings of the conference on Design, automation and test in Europe, 2006, 81-86.
[48] Zappa F, Tisa S, Tosi A et al. Principles and Features of Single-photon Avalanche Diode Arrays[J]. Sensor Actuat. A: Phys., 2007, 140(1): 103-112.
[49] Tarof L E, Knight D G, Fox K E, et al. Planar InP/InGaAs Avalanche Photodetectors with Partial Charge Sheet in Device Periphery[J]. Appl. Phys. Lett., 1990, 57(7): 670-672.
[50] Liu M, Bai X, Hu C, et al. Low Dark Count Rate and High Single-Photon Detection Efficiency Avalanche Photodiode in Geiger-Mode Operation[J]. IEEE Photonic Technology Letters, 2007, 19(6): 378-380.
[51] Namekata N, Makino Y, Inoue S. Single-photon Detector for Long-distance Fiber-Optic Quantum Key Distribution[J]. Opt. Lett., 2002, 21(11): 954-956.
[52] Bethune D S, Risk W P, Pabst G W. A high-performance Integrated Single-photon Detector for Telecom Wavelengths[J]. J. Mod. Opt., 2004, 51(9-10): 1359-1368.
[53] Voss P L, K?prülüK G, Choi S K, et al. 14MHz Rate Photon Counting with Room Temperature InGaAs/InP Avalanche Photodiodes[J]. J. Mod. Opt., 2004, 51(9-10): 1369 -1379.
[54] Ribordy G, Gisin N, Guinnard O, et al. Photon Counting at Telecom Wavelengths with Commercial InGaAs/InP Avalanche Photodiodes: Current Performance[J]. J. Mod. Opt., 2004, 51(9-10): 1381-1398.
[55] Trifonov A, Subacius D, Berzanskis A, et al. Single Photon Counting at Telecom Wavelength and Quantum Key Distribution[J]. J. Mod. Opt., 2004, 51(9-10): 1399-1415.
[56] Namekata N, Makino Y, Inoue S. Single-photon Detector for Long-distance Quantum Cryptography[J]. Electronics and Communications in Japan (Part II: Electronics), 2003, 86(5): 10-15.
[57] Pellegrini S, Warburton R E, Tan L J J, et al. Design and Performance of an InGaAs–InP Single-Photon Avalanche Diode Detector[J]. IEEE J. Quant. Electron,2006, 42(4): 397-402.
[58] Niclass C, Gersbach M, Henderson R, et al. A Single Photon Avalanche Diode Implemented in 130-nm CMOS Technology[J]. IEEE J. of Sel. Top. Quant. Electron., 2007, 13(4): 863-869.
[59] Yoshizawa A, Kaji R. Tsuchida H. After-pulse-discarding in Single-photon Detection to Reduce Bit Errors in Quantum Key Distribution[J] Opt. Express, 2003, 11(11): 1303- 1309.
[60] Tomita A, Nakamura K. Balanced, Gated-mode Photon Detector for Quantum-bit Discrimination at 1550 nm[J]. Opt. Lett., 2002, 27(20): 1827-1829.
[61] Yoshizawa A, Kaji R, Teushida H. Gated-mode Single-photon Detection at 1550 nm by Discharge Pulse Counting[J]. Appl. Phys. Lett., 2004, 84(18): 3606-3608.
[62]刘云.红外单光子探测器的研制[D].合肥:中国科学技术大学博士学位论文, 2007.
[63]魏政军.红外单光子探测器的研究[D].广州:华南师范大学博士学位论文, 2008.
[64] Nesheim T. Single Photon Detection Using Avalanche Photodiode[D]. Trondheim: Master thesis of Norwegian University of Science and Technology, 1999.
[65] Wu G, Zhou C, Li H, et al. Balanced Single-photon Detectors Using InGaAs/InP Avalanche Photodiodes with Transformer Based Spikes Cancellation[J]. Chin. Phys. Lett., 2005, 22(3): 525-528.
[66] Namekata N, Sasamori S, Inoue S. 800 MHz Single-photon Detection at 1550-nm Using an InGaAs-InP Avalanche Photodiode Operated with a Sine Wave Gating[J]. Opt. Express 2006, 14(21): 10043.
[67] Yuan Z L, Kardynal B E, Sharpe A W, et al. High Speed Single Photon Detection in the Near Infrared[J]. Appl. Phy. Lett., 2007, 91(4): 041114.
[68] Tsang W T主编,半导体光检测器[M].杜宝勋,等译.北京:电子工业出版社,清华大学出版社, 1992.
[69] Pearsall T P. Threshold Energies for Impact Ionization by Electrons and Holes in InP[J]. Appl. Phys. Lett., 1979, 35(2): 168-170.
[70] Chelikowsky J R, Cohen M L. Nonlocal Pseudopotential Calculations for the Electronic Structure of Eleven Diamond and Zinc-blende Semiconductors[J]. Phys.Rev. B, 1976, 14(2): 556-582.
[71] Shockley W. Problems Related to p-n Junctions in Silicon[J]. Solid-State Electron., 1961, 2(1): 35-60.
[72] Wolff P A. Theory of Electron Multiplication in Silicon and Germanium[J]. Phys. Rev., 1954, 95(6): 1415-1420.
[73] Baraff G A. Distribution Functions and Ionization Rates for Hot Electrons in Semiconductors[J]. Phys. Rev., 1962, 128(6): 2507-2517.
[74] Crowell C R, Sze S M. Temperature Dependence of Avalanche Mulitiplication in Semiconductors[J]. Appl. Phys. Lett., 1966, 9(6): 242-244.
[75] Mcintyre R J. Multiplication Noise Uniform Avalanche Diodes[J]. IEEE Trans. Electron Devices, 1966, 13(1): 164-169.
[76] Mcintyre R J. The Distribution of Gains in Uniformly Multiplying Avalanche Photodiodes: Theory[J]. IEEE Trans. Electron Devices, 1972, 19(6): 703-713.
[77] Mcintyre R J. A New Look at Impact Ionization-PartⅠ: A Theory of Gain, Noise, Breakdown Probability, and Frequency Response[J]. IEEE Trans. Electron Devices, 1999, 46(8): 1623-1631.
[78] Yuan P, Anselm K A, Hu C, et al. A New Look at Impact Ionization-PartⅡ: Gain and Noise in Short Avalanche Photodiodes[J]. IEEE Trans. Electron Devices, 1999, 46: 1632-1639.
[79] Wang S, Ma F, Li X, et al. Analysis of Breakdown Probabilities in Avalanche Using a History-dependent Analytical Model[J]. Appl. Phys. Lett., 2003, 82(12): 1971-1973.
[80]马声全,陈贻汉.光电子理论与技术[M].北京:电子工业出版社, 2005.
[81] Okuto Y, Crowell C R. Energy-conservation Considerations in the Characterization of Impact Ionization in Semiconductors[J]. Phys. Rev. B, 1972, 6(8): 3076–3081.
[82] Okuto Y, Crowell C R. Ionization Coefficients in Semiconductors: A Nonlocal Property[J]. Phys. Rev. B, 1974, 10(10): 4284–4296.
[83] Okuto Y, Crowell C R. Threshold Energy Effect on Avalanche Breakdown Voltage in Semiconductor Junctions[J]. Solid-State Electron., 1975, 18(2): 161–168.
[84] Sze S M. Physics of Semiconductor Device[M]. 2nd Edition. New York: Wiley,1981: 96-108.
[85] Maruyama T, Narusawa F, Kudo M, et al. Development of a Near-infrared Photon-counting System Using an InGaAs Avalanche Photodiode[J]. Opt. Eng., 2002, 41(2): 395-402.
[86] Park C Y, Hyun KS, Kang S G, et al. Effect of Multiplication Layer Width on Breakdown Voltage in InP/InGaAs Avalanche Photodiode[J]. Appl. Phys. Lett., 1995, 67(25): 3789-3791.
[87] Hyun Y S, Park C Y. Breakdown Characteristics in InP/InGaAs Avalanche Photodiode with p-i-n Multiplication Layer Structure[J]. J. Appl. Phys., 1996, 81(2): 974-984.
[88] Hayat M M, Sako?luü, Kwon O, et al. Breakdown Probabilities for Thin Heterostructure Avalanche Photodiodes[J]. IEEE J. Quantum Electron., 2003, 39(1): 179-185.
[89] Lacaita A, Spinelli A, Longhi S. Avalanche Transients in Shallow p-n Junctions Biased Above Breakdown[J]. Appl. Phys. Lett., 1995, 67(18): 2627-2629.
[90] Lacaita A, Cova S, Spinelli A, et al. Photon-assisted Avalanche Spreading in Reach-though Photodiodes[J]. Appl. Phys. Lett., 1992, 62(6): 606-608.
[91] Ramirez D A, Hayat M M, Karve G, et al. Detection Efficiencies and Generalized Breakdown Probabilities for Nanosecond-gated Near Infrared Single-photon Avalanche Photodiodes[J]. IEEE J. Quantum Electron., 2006, 42(2): 137-145.
[92] Sugihara K, Yagyu E, Tokuda Y. Numerical Analysis of Single Photon Detection Avalanche Photodiodes Operated in the Geiger Mode[J]. J. Appl. Phys. 2006, 99(12): 124502.
[93] Osaka F, Mikawa T, Kaneda T. Low-temperature Characteristics of Electron and Hole Ionization Coefficients in (100) Oriented Ga1?xInxAsyP1?y[J]. Appl. Phys. Lett., 1985, 46(12): 1138.
[94] Forrest S R, Smith R G, Kim O K. Performance of In0.53Ga0.47As/InP Avalanche Photodiodes[J]. IEEE J. Quantum Electron., 1982, 18(12): 2040-2048.
[95] Huntington A S. Development of Long-wavelength Avalanche Photodiodes and Vertical-cavity Lasers for Epitaxial Integration as a Vertical-cavity Photon NumberAmplifier[D]. Santa barbara, CA: PH. D. Thesis of University of California, Santa Barbara, 2003.
[96] Kang Y, Lu H X, Lo Y H, et al. Dark Count Probability and Quantum Efficiency of avalanche Photodiodes for Single-photon Detection[J]. Appl. Phys. Lett., 2003, 83(14): 2955-2957.
[97] Karve G, Wang S, Ma F, et al. Origin of Dark Counts in In0.53Ga0.47As/ In0.52Al0.48As Avalanche Photodiodes Operated in Geiger Mode[J]. Appl. Phys. Lett., 2005, 86(6): 063505.
[98] Tan C H, Rees G J, Houston P A, et al. Temperature Dependence of Electron Impact Ionization in In0.53Ga0.47As[J]. Appl. Phys. Lett. 2004, 84(13): 2322-2324.
[99] Humphreys D A, King R J, Jenkins D, et al. Measurement of Absorption Coefficients of Ga0.47In0.53As over the Wavelength Range 1.0-1.7μm[J]. IEEE Electron. Lett., 1985, 21(25): 1187-1188.
[100] Moll J L. Physics of Semiconductor[M]. New York: McGraw-Hill, 1964.
[101] Forrest S R, Leheny R F, Nahory R E, et al. In0.53Ga0.47As Photodiodes with Dark Current Limited by Generation-recombination and Tunneling[J]. Appl. Phys. Lett., 1980, 37(3): 322-324.
[102] Hang Z, Shen H, Pollak F H. Temperature Dependence of the EO and EO+ΔO Gaps of InP up to 600°C [J]. Solid State Commun., 1990, 73(1): 15-18.
[103] Yu P W, Kuphal E. Photoluminescence of Mn- and Un-doped Ga0.47In0.53As on InP[J]. Solid State Commun., 1984, 49(9): 907-910.
[104] Yee A, Ng W K, David J P R, et al. Negative Temperature Dependence of Electron Multiplication in In0.53Ga0.47As[J]. Appl. Phys. Lett., 2003, 82(8): 1224-1246.
[105] Jiang X, Itzler M A, Ben-Michael R, et al. InGaAsP-InP Avalanche Photodiodes for Single Photon Detection[J]. IEEE J. Sel. Top. Quant., 2007, 13(4): 895-905.
[106] Jiang X, Itzler M A, Ben-Michael R. Afterpulsing Effects in Free-running InGaAsP Single-photon Avalanche Diodes[J]. IEEE J. Quantum Electron, 2008, 44(1): 3-11.
[107] Levine B F, Bethea C G. Single Photon Detection at 1.3um Using a Gated Avalanche Photodiode[J]. Appl. Phys. Lett. 1984, 44(5): 553-555.
[108] Wei Z, Zhou P, Wang J, et al. An Integral Gated Mode Single Photon Detector atTelecom Wavelengths[J]. J. of Phys. D: Appl. Phys., 2007, 40(22): 6922-6928.
[109] Liu Y, Wu Q L, Han Z F. Single Photon Detector at Telecom Wavelengths for Quantum Key Distribution[J]. Chin. Phys. Lett., 2006, 23(1): 252-255.