Photon-Counting Image Sensors Eric R. Fossum, Nobukazu Teranishi, Albert Theuwissen, www.mdpi.com/journal/sensors Edited by Da vid Stoppa and Edoardo Charbon Printed Edition of the Special Issue Published in Sensors sensors Photon-Counting Image Sensors Special Issue Editors Eric R. Fossum Nobukazu Teranishi Albert Theuwissen David Stoppa Edoardo Charbon Nobukazu Teranishi University of Hyogo and Shizuoka University, Japan David Stoppa Fondazione Bruno Kessler (FBK) , Italy Guest Editors Eric R. Fossum Dartmouth College , USA Albert Theuwissen Harvest Imaging , Belgium and Delft University of Technology , The Netherlands Edoardo Charbon Delft University of Technology , The Netherlands Editorial Office MDPI AG St. Alban-Anlage 66 Basel, Switzerland This edition is a reprint of the Special Issue published online in the open access journal Sensors (ISSN 1424-8220) in 2016 (available at: http://www.mdpi.com/journal/sensors/special_issues/PCIS). For citation purposes, cite each article independently as indicated on the article page online and as indicated below: Author 1; Author 2; Author 3 etc. Article title. Journal Name Year . Article number/page range. ISBN 978-3-03842-374-4 (Pbk) ISBN 978-3-03842-375-1 (PDF) Articles in this volume are Open Access and distributed under the Creative Commons Attribution license (CC BY), which allows users to download, copy and build upon published articles even for commercial purposes, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. The book taken as a whole is © 2017 MDPI, Basel, Switzerland, distributed under the terms and conditions of the Creative Commons by Attribution (CC BY-NC-ND) license (http://creativecommons.org/licenses/by-nc- nd/4.0/). iii Table of Contents About the Guest Editors ............................................................................................................................ vii Preface to “ Photon-Counting Image Sensors ” ........................................................................................ xi Chapter 1: Photon Counting with CMOS Image Sensors Assim Boukhayma, Arnaud Peizerat and Christian Enz Noise Reduction Techniques and Scaling Effects towards Photon Counting CMOS Image Sensors Reprinted from: Sensors 2016 , 16 (4), 514; doi: 10.3390/s16040514 http://www.mdpi.com/1424-8220/16/4/514 ............................................................................................. 3 Michael Guidash, Jiaju Ma, Thomas Vogelsang and Jay Endsley Reduction of CMOS Image Sensor Read Noise to Enable Photon Counting Reprinted from: Sensors 2016 , 16 (4), 517; doi: 10.3390/s16040517 http://www.mdpi.com/1424-8220/16/4/517 ............................................................................................. 22 Nobukazu Teranishi Analysis of Subthreshold Current Reset Noise in Image Sensors Reprinted from: Sensors 2016 , 16 (5), 663; doi: 10.3390/s16050663 http://www.mdpi.com/1424-8220/16/5/663 ............................................................................................. 38 James Janesick and John Tower Particle and Photon Detection: Counting and Energy Measurement Reprinted from: Sensors 2016 , 16 (5), 688; doi: 10.3390/s16050688 http://www.mdpi.com/1424-8220/16/5/688 ............................................................................................. 55 Eric R. Fossum, Jiaju Ma, Saleh Masoodian, Leo Anzagira and Rachel Zizza The Quanta Image Sensor: Every Photon Counts Reprinted from: Sensors 2016 , 16 (8), 1260; doi: 10.3390/s16081260 http://www.mdpi.com/1424-8220/16/8/1260 ........................................................................................... 72 Shoji Kawahito and Min-Woong Seo Noise Reduction Effect of Multiple-Sampling-Based Signal-Readout Circuits for Ultra-Low Noise CMOS Image Sensors Reprinted from: Sensors 2016 , 16 (11), 1867; doi: 10.3390/s16111867 http://www.mdpi.com/1424-8220/16/11/1867 ......................................................................................... 97 Chapter 2: Photon Counting with Avalanche-Based Devices Isamu Takai, Hiroyuki Matsubara, Mineki Soga, Mitsuhiko Ohta, Masaru Ogawa and Tatsuya Yamashita Single-Photon Avalanche Diode with Enhanced NIR-Sensitivity for Automotive LIDAR Systems Reprinted from: Sensors 2016 , 16 (4), 459; doi: 10.3390/s16040459 http://www.mdpi.com/1424-8220/16/4/459 ............................................................................................. 119 Brian Aull Geiger-Mode Avalanche Photodiode Arrays Integrated to All-Digital CMOS Circuits Reprinted from: Sensors 2016 , 16 (4), 495; doi: 10.3390/s16040495 http://www.mdpi.com/1424-8220/16/4/495 ............................................................................................. 128 iv Matteo Perenzoni, Lucio Pancheri and David Stoppa Compact SPAD-Based Pixel Architectures for Time-Resolved Image Sensors Reprinted from: Sensors 2016 , 16 (5), 745; doi: 10.3390/s16050745 http://www.mdpi.com/1424-8220/16/5/745 ............................................................................................. 142 I. Michel Antolovic, Samuel Burri, Ron A. Hoebe, Yuki Maruyama, Claudio Bruschini and Edoardo Charbon Photon-Counting Arrays for Time-Resolved Imaging Reprinted from: Sensors 2016 , 16 (7), 1005; doi: 10.3390/s16071005 http://www.mdpi.com/1424-8220/16/7/1005 ........................................................................................... 154 Neale A. W. Dutton, Istvan Gyongy, Luca Parmesan and Robert K. Henderson Single Photon Counting Performance and Noise Analysis of CMOS SPAD-Based Image Sensors Reprinted from: Sensors 2016 , 16 (7), 1122; doi: 10.3390/s16071122 http://www.mdpi.com/1424-8220/16/7/1122 ........................................................................................... 169 Tomislav Resetar, Koen De Munck, Luc Haspeslagh, Maarten Rosmeulen, Andreas Süss, Robert Puers and Chris Van Hoof Development of Gated Pinned Avalanche Photodiode Pixels for High-Speed Low-Light Imaging Reprinted from: Sensors 2016 , 16 (8), 1294; doi: 10.3390/s16081294 http://www.mdpi.com/1424-8220/16/8/1294 ........................................................................................... 186 Chapter 3: Other Devices, Materials and Applications for Photon Counting Gerhard Lutz, Matteo Porro, Stefan Aschauer, Stefan Wölfel and Lothar Strüder The DEPFET Sensor-Amplifier Structure: A Method to Beat 1/f Noise and Reach Sub-Electron Noise in Pixel Detectors Reprinted from: Sensors 2016 , 16 (5), 608; doi: 10.3390/s16050608 http://www.mdpi.com/1424-8220/16/5/608 ............................................................................................. 201 Liisa M. Hirvonen and Klaus Suhling Photon Counting Imaging with an Electron-Bombarded Pixel Image Sensor Reprinted from: Sensors 2016 , 16 (5), 617; doi: 10.3390/s16050617 http://www.mdpi.com/1424-8220/16/5/617 ............................................................................................. 215 Bart Dierickx, Qiang Yao, Nick Witvrouwen, Dirk Uwaerts, Stijn Vandewiele and Peng Gao X-ray Photon Counting and Two-Color X-ray Imaging Using Indirect Detection Reprinted from: Sensors 2016 , 16 (6), 764; doi: 10.3390/s16060764 http://www.mdpi.com/1424-8220/16/6/764 ............................................................................................. 227 Shouleh Nikzad, Michael Hoenk, April D. Jewell, John J. Hennessy, Alexander G. Carver, Todd J. Jones, Timothy M. Goodsall, Erika T. Hamden, Puneet Suvarna, J. Bulmer, F. Shahedipour-Sandvik, Edoardo Charbon, Preethi Padmanabhan, Bruce Hancock and L. Douglas Bell Single Photon Counting UV Solar-Blind Detectors Using Silicon and III-Nitride Materials Reprinted from: Sensors 2016 , 16 (6), 927; doi: 10.3390/s16060927 http://www.mdpi.com/1424-8220/16/6/927 ............................................................................................. 241 Emna Amri, Yacine Felk, Damien Stucki, Jiaju Ma and Eric R. Fossum Quantum Random Number Generation Using a Quanta Image Sensor Reprinted from: Sensors 2016 , 16 (7), 1002; doi: 10.3390/s16071002 http://www.mdpi.com/1424-8220/16/7/1002 ........................................................................................... 262 v Jamie O. D. Williams, Jack A. Alexander-Webber, Jon S. Lapington, Mervyn Roy, Ian B. Hutchinson, Abhay A. Sagade, Marie-Blandine Martin, Philipp Braeuninger-Weimer, Andrea Cabrero-Vilatela, Ruizhi Wang, Andrea De Luca, Florin Udrea and Stephan Hofmann Towards a Graphene-Based Low Intensity Photon Counting Photodetector Reprinted from: Sensors 2016 , 16 (9), 1351; doi: 10.3390/s16091351 http://www.mdpi.com/1424-8220/16/9/1351 ........................................................................................... 270 Changhyuk Lee, Ben Johnson, TaeSung Jung and Alyosha Molnar A 72 × 60 Angle-Sensitive SPAD Imaging Array for Lens-less FLIM Reprinted from: Sensors 2016 , 16 (9), 1422; doi: 10.3390/s16091422 http://www.mdpi.com/1424-8220/16/9/1422 ........................................................................................... 297 Chapter 4: Image Reconstruction for Photon-Counting Image Sensors Bo Chen and Pietro Perona Vision without the Image Reprinted from: Sensors 2016 , 16 (4), 484; doi: 10.3390/s16040484 http://www.mdpi.com/1424-8220/16/4/484 ............................................................................................. 321 Myungjin Cho and Bahram Javidi Three-Dimensional Photon Counting Imaging with Axially Distributed Sensing Reprinted from: Sensors 2016 , 16 (8), 1184; doi: 10.3390/s16081184 http://www.mdpi.com/1424-8220/16/8/1184 ........................................................................................... 336 Stanley H. Chan, Omar A. Elgendy and Xiran Wang Images from Bits: Non-Iterative Image Reconstruction for Quanta Image Sensors Reprinted from: Sensors 2016 , 16 (11), 1961; doi: 10.3390/s16111961 http://www.mdpi.com/1424-8220/16/11/1961 ......................................................................................... 344 vii About the Guest Editors Eric R. Fossum received the B.S. degree in physics and engineering from Trinity College, Hartford, CT, and his Ph.D. degree in engineering and applied science from Yale University, New Haven, CT. He was a member of the Faculty of Electrical Engineering, Columbia University, New York, NY until he joined the NASA Jet Propulsion Laboratory (JPL), California Institute of Technology, Pasadena, CA. There he invented the modern CMOS active pixel sensor camera-on-a-chip technology which is used in billions of cameras each year. He co-founded Photobit Corporation to commercialize the technology and served in several top management roles, including CEO. He was later CEO of Siimpel Corporation, developing camera modules with MEMS-based autofocus and shutter functions for cell phones. He was a Consultant with Samsung Electronics engaged in various projects including 3D RGBZ ranging image sensors. Since 2010, he has been a Professor with the Thayer School of Engineering, Dartmouth College, Hanover, NH, USA focused on photon-counting image sensors. He co- founded the International Image Sensor Society (IISS) and served as its first President. He has published over 290 technical papers and holds over 160 U.S. patents. He is a Charter Fellow of the National Academy of Inventors, a member of the National Academy of Engineering and was inducted into the National Inventors Hall of Fame. In 2017 Dr. Fossum received the Queen Elizabeth Prize for Engineering for his invention and development of CMOS image sensor technology. Nobukazu Teranishi received his B.S. degree and M.S. degree in physics from the University of Tokyo, Tokyo, Japan and is a professor at the University of Hyogo and Shizuoka University. Since 1978, he has developed image sensors at NEC Corporation (1978–2000) and at Panasonic Corporation (2000–2013) and different universities (2013–present). He and his group invented the pinned photodiode technology, vertical overflow structure, smear reduction structure, among others. They have developed image sensors for various applications, such as movie, digital still cameras, broadcast cameras, security, automobile, medical, scientific and space industries. They have also developed image sensors for infrared and X-ray use other than visible light. He has authored and co-authored 110 papers and has 46 Japanese patents and 21 US patents. Together with E. Fossum and A. Thuwissen, he founded the IISS (International Image Sensors Society), of which he is President. His leadership and image sensor technology development, including the pinned photodiode invention has been honored by government organizations as well as societies. He was awarded the National Invention Awards, Commendation by Minister of State for Science and Technology, Niwa-Takayanagi Award from the Institute of Image Information and Television Engineers (ITE), IEEE EDS J.J.Ebers Award, and is a Fellow of the ITE, and a Fellow of the IEEE. In 2017 Mr. Teranishi received the Queen Elizabeth Prize for Engineering for his invention and development of the pinned photodiode, widely used in CCD and CMOS image sensors. viii Albert J.P. Theuwissen received his degree in electrical engineering from the Catholic University of Leuven (Belgium) in 1977. From 1977 to 1983, his work at the ESAT-laboratory of the Catholic University of Leuven focused on semiconductor technology for linear CCD image sensors. He received the Ph.D. degree in electrical engineering in 1983. In 1983, he joined the Micro-Circuits Division of the Philips Research Laboratories in Eindhoven (the Netherlands). In 1991 he became Department Head of the Division Imaging Devices, covering CCD as well as CMOS solid-state imaging activities. He is the author or coauthor of over 200 technical papers in the solid-state imaging field and has been issued several patents. In 1995, he authored a textbook " Solid-State Imaging with Charge-Coupled Devices " and in 2011 he co- edited the book " Single-Photon Imaging ". In 1998, 2007 and 2015 he held the position of IEEE Electron Devices Society and Solid-State Circuits Society distinguished lecturer. He acted as general chairman of the International Image Sensor Workshop in 1997, 2003, 2009 and 2015. He was elected as the International Technical Program vice-chair and chair for respectively the ISSCC 2009 and ISSCC 2010. In March 2001, he was appointed as part-time professor at the Delft University of Technology, the Netherlands, where he teaches courses in solid-state imaging and coaches MSc and PhD students in their research on CMOS image sensors. In April 2002, he joined DALSA Corporation to act as the company’s Chief Technology Officer. After he left DALSA in September 2007, he started his own company “Harvest Imaging”, focusing on consulting, training, teaching and coaching in the field of solid-state imaging technology (www.harvestimaging.com). In 2006 he co-founded (together with his peers Eric Fossum and Nobukazu Teranishi) ImageSensors, Inc. (a Californian non-profit public benefit company) to address the needs of the image sensor community (www.imagesensors.org). In 2008, he received the SMPTE’s Fuji gold medal for his contributions to the research, development and education of others in the field of solid-state image capturing. He is a member of the editor ial board of the magazine “ Photonics Spectra ”, an IEEE Fellow and member of SPIE. In 2011, he was elected as “Electronic Imaging Scientist of the Year”; in 2013 he received the Exceptional Service Award of the International Image Sensor Society; and in 2014 he was awarded with the SEMI Award. David Stoppa received the Laurea degree in Electronics Engineering from Politecnico of Milan, Italy, in 1998, and his Ph.D. degree in microelectronics from the University of Trento, Italy, in 2002. He is the Head of the Integrated Radiation and Image Sensors research unit at FBK where he has been working as a research scientist since 2002, and as Group Leader of the Smart Optical Sensors and Interfaces group from 2010 to 2013. Since 2000 he has been teaching courses at the Telecommunications Engineering Faculty of the University of Trento on Analogue Electronics and Microelectronics. His research interests are mainly in the field of CMOS integrated circuits design, image sensors and biosensors. He has authored or co-authored more than 120 papers in international journals, and presentations at international conferences, and holds several patents in the field of image sensors. Since 2011 he has served as a program committee member of the ‘International Solid -State Circuit s Conference’ (ISSCC) and the SPIE ‘Videometrics, Range Imaging and Applications’ conference, and was a technical committee member of the ‘International Image Sensors Workshop’ (IISW) in 2009, 2013, 2015 and 2017. He was a Guest Editor for IEEE Journal of Solid-State Circuits Special Issues on ISSCC’14 in 2015 and European Chair at ISSCC 2017. Dr. Stoppa received the 2006 European Solid-State Circuits Conference Best Paper Award. x Edoardo Charbon received his diploma from ETH Zürich, Switzerland, the M.S. from U.C. San Diego, and his Ph.D. from U.C. Berkeley in 1988, 1991, and 1995, respectively, all in electrical engineering and EECS. He was with Cadence Design Systems from 1995 to 2000, where he lead the company's initiative to develop information hiding for intellectual property protection. In 2000, he joined Canesta Inc., as Chief Architect, where he lead the development of time-of-flight 3D CMOS image sensors. From 2002 to 2008 he was assistant professor at EPFL; in 2008 he joined TU Delft as Chair of VLSI Design and, in 2015, EPFL as Chair of Advanced Quantum Architectures. He has authored and co-authored over 250 papers in journals, conference proceedings, magazines, and two books, and he holds 20 patents. Prof. Charbon was the initiator and coordinator of the EU projects Megaframe and SPADnet, which brought single- photon detectors to consumer and mainstream scientific and medical applications. His current research interests include 3D imaging, single-photon imaging, space-based detection, quantum- inspired circuits and systems, and cryo-CMOS technologies. Prof. Charbon has been a Guest Editor of numerous IEEE journals and is a member of the TPCs of ISSCC, ESSCIRC, ICECS, ISLPED, VLSI- SOC, and IEDM. He is a Distinguished Visiting Scholar with the W. M. Keck Institute for Space, California Institute of Technology, Pasadena, CA and a fellow of the Kavli Institute of Nanoscience Delft. xi Preface to “ Photon-Counting Image Sensors ” Papers presented at the 2015 International Image Sensor Workshop (IISW), in Vaals, the Netherlands, organized by the International Image Sensor Society (IISS), showed that photon-counting image sensors may represent the next step in the evolution of solid-state image sensors. In a photon- counting image sensor, it is possible to determine, with a high degree of accuracy, the number of photons that have struck a sensor photoelement during some interval of time. This is enabled by both high quantum efficiency and deep-sub-electron read noise. For some time, single-photon avalanche detectors (SPADs) have grown in performance and array size, with photoelement counts approaching 100,000 or more, today. Practical image capture at such array sizes can now be readily envisioned. SPADs also have an added advantage of allowing fine time resolution of photon arrival, enabling applications such as time-of-flight (TOF) range imaging and fluorescent lifetime imaging microscopy (FLIM). More recently, photoelements that do not require avalanche multiplication and instead use ultra-low capacitance to achieve voltage gain from captured photoelectrons, and/or use multiple sampling techniques to reduce read noise, have shown photon-counting capability. While not having the time resolution of SPADs, these devices offer the potential for large array formats and low power operation in a fabrication process consistent with modern backside-illuminated stacked CMOS image sensor manufacturing. MDPI Sensors and the International Image Sensor Society (IISS) have joined together to create an all-invited special issue reviewing the status of photon-counting image sensors as well as recent developments. The issue includes papers on avalanche gain devices such as SPADs, CMOS image sensors with deep sub-electron read noise, and other devices offering photon-counting capability. Also included are papers on recent progress in image reconstruction, an important aspect in the practical application of photon-counting image sensors. On behalf of the image sensor community, we extend our appreciation to the authors for accepting our invitation to contribute to the Special Issue. We hope that this collection of excellent papers on the topic of photon-counting image sensors is illuminating and useful in the years ahead. Eric R. Fossum, Edoardo Charbon, David Stoppa, Nobukazu Teranishi and Albert Theuwissen Guest Editors Chapter 1: Photon Counting with CMOS Image Sensors sensors Article Noise Reduction Techniques and Scaling Effects towards Photon Counting CMOS Image Sensors Assim Boukhayma 1, *, Arnaud Peizerat 2 and Christian Enz 1 1 Integrated Circuits Lab (ICLAB), École Polytechnique Fédérale de Lausanne (EPFL), Microcity, Rue de la Maladière 71, Neuchâtel 2000, Switzerland; christian.enz@epfl.ch 2 Laboratoire de l’ Électronique et Technologies de l’ Information (Leti), Commissariat a l’ Énergie Atomique (CEA), Rue des Marthyrs 17, Grenoble 38000, France; arnaud.peizerat@cea.fr * Correspondence: assim.boukhayma@epfl.ch; Tel.: +4-121-695-4397 Academic Editor: Albert Theuwissen Received: 25 January 2016; Accepted: 6 April 2016 ; Published: 9 April 2016 Abstract: This paper presents an overview of the read noise in CMOS image sensors (CISs) based on four-transistors (4T) pixels, column-level amplification and correlated multiple sampling. Starting from the input-referred noise analytical formula, process level optimizations, device choices and circuit techniques at the pixel and column level of the readout chain are derived and discussed. The noise reduction techniques that can be implemented at the column and pixel level are verified by transient noise simulations, measurement and results from recently-published low noise CIS. We show how recently-reported process refinement, leading to the reduction of the sense node capacitance, can be combined with an optimal in-pixel source follower design to reach a sub-0.3 e − rms read noise at room temperature. This paper also discusses the impact of technology scaling on the CIS read noise. It shows how designers can take advantage of scaling and how the Metal-Oxide-Semiconductor (MOS) transistor gate leakage tunneling current appears as a challenging limitation. For this purpose, both simulation results of the gate leakage current and 1 / f noise data reported from different foundries and technology nodes are used. Keywords: CMOS; image sensors; temporal read noise; 1 / f noise; thermal noise; correlated multiple sampling; deep sub-electron noise 1. Introduction The idea of an image sensor with photon counting capability is becoming a subject of interest for new applications and imaging paradigms [ 1 – 3 ]. Such a device must have an input-referred read noise negligible compared to a single electron. Among the state-of-the-art imaging devices, single photon detectors may appear to be the best candidate for such an application [ 4 ]. Historically, micro-electronics could not provide readout chains with noise levels as low as deep sub-electron. Hence, the solution was to introduce a gain at the level of the photon-electron conversion. In photomultipliers tubes (PMTs) and single photon avalanche photodiodes (SPADs), the electron generated by the incident photon is accelerated and multiplied to a number of electrons from a few hundred in PMTs to millions in SPADs. Such a signal level can be easily detected and quantized into two logic levels, since the number of incident photons during the period of detection is assumed to be much less than one. However, these devices present the following disadvantages [ 5 ]. First, they are limited to the case of single photon detection. In other words, the arrival of one photon and multiple photons are not distinguished. Second, these devices suffer from a dead time and after pulse following each photon detection, blinding the device for a certain time. The third limitation is related to the low resolution Sensors 2016 , 16 , 514 3 www.mdpi.com/journal/sensors Sensors 2016 , 16 , 514 and fill factors of focal plane arrays using such devices. Additionally, they use high voltages, which are not compliant with standard CMOS image sensor (CIS) processes. During the last decade, CISs have seen their performance increasing remarkably in terms of dynamic range, speed, resolution and power consumption. With a lower cost and better on-chip integration, CISs replaced progressively the charge coupled devices (CCDs) in many applications and enlarged the market of electronic imaging devices. In terms of sensitivity, the quantum efficiency has been improved to reach levels as high as 0.95 [ 3 ]. The fill factors have been constantly improved. The dark current in the pinned photodiodes (PPDs) has been reduced to levels making the process of electron-hole pair generation noiseless for integration times around tens of ms. The read noise has also been dramatically reduced to reach deep sub-electron levels [ 6 – 8 ]. Hence, CIS technologies are advanced enough to envisage the photon counting possibility. Besides the quantum efficiency, this paper discusses the possibility of performing photon counting, with standard CIS, essentially from the read noise perspective. Starting from the analytical expressions of the input-referred noise, the noise reduction mechanisms at the circuit, device and process level are discussed and verified with simulation, measurements and data reported in recent works. The impact of the combination of different techniques is also analyzed, and the noise levels that can be reached with state-of-the-art technology in standard processes are quantified. This paper also shows how the technology downscaling can be used to reduce the read noise and how the gate leakage current could limit this advantage. 2. CMOS Image Sensors and Photon Counting Requirements Figure 1 shows the schematic of a conventional low noise CIS readout chain. The corresponding timing diagram is shown in Figure 2. It also shows the potential profile across the PPD, the transfer gate (TX) and the sense node (SN) during the three phases of operation: the integration, the reset and the transfer phases. During the integration time, the PPD accumulates the electrons generated by the incident photons. During the readout, the pixel is connected to the column through the row selection switch (RS), then the reset switch (RST) is closed in order to set the SN voltage higher than the pinning voltage of the PPD. The voltage level at the SN after the reset is read with the in-pixel source follower (SF) and sampled at the end of the readout chain. The potential barrier between the PPD and the SN is controlled by the transfer gate (TX). When the barrier is lowered, the charges accumulated in the PPD are transferred to the SN. The SN voltage level after the transfer is sampled at the output of the readout chain. The reset and transfer samples are then differentiated. This operation is called correlated double sampling (CDS) [9]. Thick oxide NMOS Column-level amplification C f Multiple sampling ADC Column level Circuits SN V RST TX RST RS PPD Pixel VDD I bias Column C L AZ C in Figure 1. Schematic of a conventional low noise CMOS image sensor (CIS) readout chain. RST, reset switch; TX, transfer gate; RS, row selection switch; SN, sense node; PPD, pinned photodiode; AZ, auto-zero; VDD, supply voltage . 4 Sensors 2016 , 16 , 514 Figure 2 depicts also the different noise sources affecting the signal in the CIS apart from the photon shot noise. During the integration, the charge originating from the thermal generation of electron-hole pairs in the depleted region of the PPD (the dark current) can corrupt the signal. In state-of-the-art CIS, the dark current in PPDs has been reduced to a few e − / s. Hence, for exposure times below hundreds of ms, the dark current can be neglected. The reset of the SN leaves a kT / C noise charge held at the SN. This noise is as high as several electrons in the case of a SN capacitance of a few fF. However, for 4T pixels, it is canceled thanks to the CDS readout scheme, as depicted in the timing diagram of Figure 2. RS RST V reset V transfer AZ V out_amp T S Integration Reset V reset Transfer V transfer V reset TX SN (M-1)·T S Figure 2. Timing diagram of the conventional CIS readout chain of Figure 1 with noise mechanisms affecting the signal at the PPD and the readout chain levels. The charge transfer from the PPD to the SN can be affected by the noise related to the charge deficit due to incomplete transfer and lag [ 10 , 11 ]. Unlike the sampled reset kTC noise, this noise is not canceled by the CDS. The charge transfer noise has been extensively studied for CCDs [ 12 , 13 ] because an efficient charge transfer is crucial in such devices. In state-of-the-art CIS with 4T pixels, values of the lag as low as 0.1% have been reported. Thus, the lag can be neglected compared to the read noise in the low light context. The transient noise related to the lag is believed to behave as a shot noise [ 11 ], similarly to buried channel CCDs [ 13 ]. However, with a lag below 1%, this noise can be neglected in low light conditions. It is also believed that trapping mechanisms in the silicon oxide interface under the transfer gate also contribute to the transfer non-idealities [ 10 ,14 – 16 ], giving rise to a Random Telegraph Signal (RTS)-like noise. Finally, the readout of the SN reset and transfer voltages is affected by random fluctuations due to the readout chain noise; starting with the in-pixel SF and noise coupling of the TX and RST lines with the SN, the power supply noise and ending with the column-level circuitry and analog-to-digital converters (ADCs). The column-level amplification is introduced in order to minimize the contribution of the next circuit blocks to the input-referred total noise, e.g., buffers, sample-and-holds and ADC. The column-level amplifier also limits the bandwidth in order to minimize the thermal noise [ 8 ]. A switched capacitor amplifier is usually used. An auto-zero (AZ) is performed in order to reset its feedback capacitor and to reduce its offset and 1 / f noise [ 9 ]. When the AZ switch is opened, the noise is sampled at the integration capacitor and transferred to the output. This sampled noise is also canceled thanks to the CDS. Low noise CIS readout chains may also include correlated multiple sampling (CMS) that can be implemented with analog circuitry [ 17 , 18 ] or performed after the ADC [ 19 ]. CMS consists of averaging M samples after the reset and M other samples after the transfer with a sampling period T S , then calculating the difference between the two averages. 5 Sensors 2016 , 16 , 514 With a careful design, the readout noise originating from the pixel and column-level amplifier is the dominant noise source in CIS. Figure 3 shows the calculated probability of a true photo-electron count and a single photo-electron detection as a function of the input-referred readout chain noise by assuming a Gaussian distribution of noise and using the error function. Based on Figure 3, 90% accuracy requires a read noise below 0.4 e − rms for single photo-electron detection and 0.3 e − rms for photo-electron count. Recently reported works are today closer than ever to these limits [ 7 , 8 , 20 ]. A detailed noise analysis of the readout noise is therefore necessary in order to determine the key design and process parameters that can be used for further noise reduction. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Probability of True Electron Count Readout Noise [e - RMS ] electrons count single electron detection Figure 3. Probability of a true photo-electron count and single photo-electron detection as a function of the input-referred readout noise. 3. Read Noise in CIS In a conventional CIS readout chain, three readout noise sources can be distinguished: thermal noise, 1 / f noise and leakage current shot noise. For each noise source, the variance at the output of the readout chain is first calculated and then referred to the input as a noise charge. Hence, the pixel conversion gain is a key parameter in the noise analysis. The pixel conversion gain can be calculated using a small-signal analysis of the pixel. It is crucial to take into account the effect of parasitic capacitances. Figure 4 presents a schematic of a 4T pixel section view showing all of the parasitic capacitances connected to the sense node. These include the overlap capacitances of the transfer and reset gates, C Tov and C Rov , respectively, the sense node junction capacitance, C J , and the parasitic capacitance related to the metal wires, C W . These capacitances are independent of the in-pixel SF. Their sum is defined as: C P = C Tov + C Rov + C J + C W (1) p C e ·W C e ·W 2/3·C ox ·W·L p n p+ C Tov C J C Rov C W PPD Transfer Gate Reset Gate Source Follower n+ n+ n+ n+ Figure 4. Cross-section of a conventional 4T pixel showing the different parasitic elements contributing to the sense node capacitance. 6 Sensors 2016 , 16 , 514 Figure 5 presents a simplified small-signal schematic of the CIS readout chain of Figure 1. This small-signal schematic is used to calculate the conversion gain together with the noise and signal transfer functions. Based on the detailed analytical calculation presented in [ 8 ], the conversion gain of a conventional CIS 4T pixel can be expressed as: A CG = 1 n C P + C e · W + ( 1 − 1 n )( C e · W + 2 3 C ox · W · L ) (2) Here, n is the slope factor of the in-pixel SF [ 21 ] defined as G ms / G m , where G m and G ms are the SF gate and source transconductances, respectively. C e is the extrinsic capacitance per unit width of the in-pixel source follower transistor. It includes the overlap and fringing capacitances as depicted in Figure 4. C ox is the SF oxide capacitance per unit area. G m ·V G I n,GD I n,GS I in G ms ·V S C GS C P+ C GD I n,SF C in C col C f G mA ·V in I n,A C L H CMS (f) V col out D V in Pixel V SN G S Column Level Amplifier Thermal and 1/f noise Leakage current shot noise Figure 5. Small-signal analysis of the CIS readout chain depicted in Figure 1 showing the different readout noise sources considered in the analysis. 3.1. 1 / f Noise Under the long-channel approximation, the gate-referred 1 / f noise power spectral density (PSD) of a MOS transistor operating in the saturation region is commonly expressed as: S V g ( f ) = K F C 2 ox · W · L · f (3) Here, W and L are the gate width and length; C ox is the oxide capacitance per unit area; and K F is a 1 / f noise process and bias-dependent parameter. This empirical model is easy to use for hand calculation and remains valid even for advanced CMOS technologies for adequate gate widths and lengths [22]. The parameter K F can be expressed as [21,23]: K F = K G · k · T · q 2 · λ · N t (4) where k is the Boltzmann constant, T is the absolute temperature, q is the electron charge, λ is the tunneling attenuation distance ( 0.1 nm) [ 24 ], N t is the oxide trap density and K G is a bias-dependent parameter. It has been shown in [ 21 ] that K G is close to unity when the transistor is operating in the weak and moderate inversion regime. Most analog circuit simulators use the Berkeley Short-channel Model (BSIM) to predict the 1 / f noise behavior of circuits. It is important to establish a relationship between the parameters used by the simulator and the simple equation used for hand calculations in order to best exploit the noise calculation results. The oxide trap density is the key process-dependent parameter. In the BSIM model, it is referred to as the noise parameter A (noiA) [25]. It is well known that the 1 / f noise PSD is inversely proportional to the gate area. In low noise CIS readout chains, the transistors located outside the pixels array can be designed with gate dimensions much larger than the in-pixel source follower transistor. In this case, the latter becomes the dominant 7