DIT - University of Trento Design and characterization of novel silicon photodetectors for 3D imaging applications

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1 PhD Dissertation International Doctorate School in Information and Communication Technologies DIT - University of Trento Design and characterization of novel silicon photodetectors for 3D imaging applications Lucio Pancheri Advisor: Prof. Gian-Franco Dalla Betta Università degli Studi di Trento March 2006

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3 Abstract The high costs of existing optical 3D measuring systems prevent their use for low cost applications like those typical in the automotive and domotic fields. The most promising approach to lower the overall system costs seems to be the adoption of the Time-Of-Flight technique, which is suited for applications where high speed measurements of distances up to m are required, and relaxed constraints on measurement accuracy (a few centimeters) are accepted. Aim of this thesis work has been the design of new devices for 3D imaging sensors based on the TOF technique. The devices have been conceived to be integrated in a pixel together with an electronic readout channel, in order to fully exploit the advantages and low cost of CMOS technology. Three different devices were investigated: a CMOS compatible Metal-Semiconductor-Metal photodetector, an Electro-Optical Mixer based on closely spaced junctions and a Single Photon Avalanche Diode. Active pixels based on the last two devices have been designed and two linear image sensors have been fabricated and successfully tested. Experimental results shows that the proposed approach can allow for the realization of low-cost 3D image sensors with good performance and capable of real-time operation. Keywords [3D imaging, Time-Of-Flight, Metal-Semiconductor-Metal, Single Photon Avalanche Diode]

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5 Contents 1 Introduction The context The problem The solution Innovative aspects Structure of the thesis State of the Art Light detection with silicon Interaction between optical radiation and silicon Quantum efficiency Photodiodes CMOS image sensors Historical background CMOS imager architecture Passive and active pixels Time Of Flight technique TOF basic principle Direct Time of Flight Indirect Time of Flight Devices used in TOF 3D image sensors Lock-in CCD i

6 2.4.2 Photogate PMD Metal Semiconductor Metal Detecor Single Photon Avalanche Diode Time of Flight 3D Image Sensors Figures of merit Evolution of TOF 3D image sensors Switched capacitor approach Photogate approach SPAD approach CMOS compatible MSM Devices Device operation Device description DC characteristics Spectral responsivity Response to a light step Model description Results and discussion Model validation Frequency response Time-of-flight simulation Experimental results CMOS EOM based on closely spaced junctions Electro Optical Mixer design Measuring technique Readout circuit Experimental results Concluding remarks ii

7 5 CMOS Single Photon Avalanche Diode 3D imager Measuring techniques Direct Time Of Flight Indirect Time Of Flight Device design Image sensor design Pixel design Time-measuring pixel operation Photon-counting pixel operation Image sensor architecture Device characterization Test devices in 0.8 µm technology Test devices in 0.35 µm technology Sensor characterization Sensor linearity and time resolution Direct time of flight Indirect time of flight Conclusion 109 Bibliography 113 iii

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9 List of Tables 2.1 Static characteristics of silicon MSM photodetectors Dynamic characteristics of silicon MSM photodetectors Comparison between SPADs fabricated in CMOS technologies. ( ) Photon Detection Efficiency Ratios between the R constant of the three electrodes and R tot at different wavelengths Main characteristics of the designed OTA Measured breakdown voltage and dark current of test devices D1-D v

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11 List of Figures 2.1 Absorption length in silicon as a function of light wavelength Architecture of a CMOS image sensor CMOS pixel architectures: a) Passive pixel, b) Photodiodetype active pixel, c) Photogate-type active pixel Basic principle of the Time-Of-Flight technique Schematic structure of a Photo Gate PMD and surface potential at two different gate voltages Schematic structure of Metal Semiconductor Metal detector Working principle of a SPAD Schematic presentation of (a) passive quenching circuit (b) active quenching and recharge circuit SPAD cross section Basic principle of I-TOF using pulsed technique Schematic cross section and equivalent circuit of the MSM PDs in SOI (a) and CMOS (b) technology DC analysis of the SOI (a) and of the CMOS (b) MSM PDs. Contact S1 is grounded for the SOI PD and is biased at 2 V for the CMOS PD. The incident light wavelength is 860 nm Responsivity of the CMOS and SOI PDs vii

12 3.4 Transient response to a step of light of the CMOS MSM with a Schottky barrier of 0.6 V. Contact S1 and S2 are biased respectively at 1 V and 2 V. In the figure the components of the current at electrode S2 are shown. The optical power is 0.1 µw and the wavelength is 860 nm Dependence of the current rise time on Schottky barrier height. The optical power is 0.1 µw and the wavelength is 860 nm Schematic model of the SOI MSM (a) and the CMOS MSM (b) Transient behavior of the SOI (a) and CMOS (b) PDs. In both devices a step of light (λ = 860 nm, P opt = 0.1 µw) has been applied after a short time. In the CMOS device the substrate has been grounded and contact S1 has been biased at 2 V, while in the SOI device the voltage of contact S1 has been set at 0 V. In both devices the voltage of electrode S2 (V S2 ) has been switched as shown in the graph. The currents at electrodes S1 and S2 are marked respectively with black and white squares Ratio between AC (R) and DC (R 0 ) responsivity as a function of frequency at three different DC illumination levels Simulated correlation function employing the CMOS device as a balanced mixer. Modulation frequency was 20 MHz Measured I-V curves under different illumination conditions. On the right: zoom on the linear region I-V curves measured on a test Schottky diode Schematic cross section of the sensor Simulated hole density viii

13 4.3 Simulated electron current density under illumination Simulated I-V curves Simulated AC demodulation contrast at λ = 680 nm Simulated AC demodulation contrast at λ = 860 nm Block diagram of the pixel Schematic circuit of the pixel with the model of the EOM Simulation of pixel behavior Simulated performance of the system Half pixel layout Micrograph of the chip Measured I-V curves of one of the test devices (D = 1.5 µm) illuminated with a 860-nm light Measured and simulated demodulation contrast as a function of inter-finger distance D, with V = 1 V and λ = 860 nm Measured responsivity at the two electrodes Measured demodulation contrast as a function of wavelength Principle of I-TOF technique using gated SPADs Cross section of the SPAD in standard CMOS technology Block diagram of the proposed pixel Circuit schematic of the proposed pixel (a) Voltage drop at node IN after the detection of a photon. (b) Voltage at C Sample in time-measuring operation. (c) Voltage at C Sample in photon-counting operation Chip micrograph: (a) test structures, pixel array and readout (b) 10-pixels and part of the decoder (c) DDS stage Breakdown voltage and dark current of the avalanche photodiodes C1-C5 as a function of inter-well distance ix

14 5.8 Spectral responsivity of the avalanche photodiode A at two different bias voltages Photocurrent gain of the avalanche photodiode A as a function of light wavelength and applied bias voltage Dark count rate of the SPAD A as a function of excess bias Dark count rate of the SPAD A as a function of temperature Count rate of the SPAD A as a function of incident optical power density Spectral responsivity of device D4 at three different bias voltages Photocurrent gain of device D4 as a function of light wavelength and applied bias voltage Dark count rate of device E3 as a function of excess bias Pixel output averaged over the 64 pixel of the array. The error bars indicate the FPN, i.e. the standard deviation over the 64 pixels Distance measurement of a cooperative target after calibration Examples of 2D and 3D images Probability density function of photon detection time for 3 different pulse power levels. In the inset: PDF integral between 0 and 30 ns Comparison between theoretical and measured distance resolution and distance offset Pixel counts as a function of incident optical power density Images acquired by counting the number of photon detections over 3000 laser pulses. (a) laser pulse entirely included in the gate window; (b) and (c) laser pulse partially overlapping with the gate window, with different time delays x

15 5.23 3D image acquired with Indirect TOF technique xi

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17 Chapter 1 Introduction 1.1 The context 3D imaging systems are an appealing alternative to 2D systems, which were considered as the standard for many vision applications. A strong demand of contactless range imaging systems comes from the industrial field for applications like process control, robotic assembly and non contact inspection [1]. There is also a great interest in 3D vision systems in the automotive sector, where these sensors can be applied to intelligent navigation systems, obstacle avoidance and pre-crash functions [2, 3]. Other applications consist in surveillance, object shape recognition, virtual reality and 3D graphics [4]. These systems, if properly adapted, could also have a strong impact in the domotic field provided their overall cost is lowered. Current contactless distance measuring systems are based on either radar [5, 6], sonar [7] or optical [8] principles. Radar systems offer a high dynamic range and are robust to environmental conditions. However, they suffer from poor angular resolution. The same problem applies to sonar systems, in addition to the dependence on environmental conditions and propagation loss. Systems based on optical principles are usually costly, have a limited dynamic range and the presence of background light illumination lowers the measurement accuracy. However, optical range finders 1

18 CHAPTER 1. INTRODUCTION can achieve both a high range resolution and high lateral resolution. A first classification distinguishes between passive and active optical ranging techniques. Passive ranging techniques such as stereo vision require a strong computational effort and their performance is strongly determined by illumination conditions and by the contrast in the scene under measurement. Active ranging systems, on the contrary, use projection techniques to illuminate the area of interest and are therefore capable of acquiring range data also in the case of very low ambient illumination. Active optical ranging techniques can be subdivided into three families depending on the underlying physical working principle: interferometry, triangulation [9, 10, 11] and Time Of Flight (TOF) [12]. Interferometry is mainly used for very short distances in applications where high accuracy is needed. For long distances the TOF technique has been used for many years, in particular for military applications. Optical triangulation lies between the two and is therefore used for short-mid distances. 1.2 The problem Many different ranging system solutions have so far been proposed, but some key problems still remain partially unsolved. Among others, low cost, real-time operation and ambient light insensitivity are required to push 3D image sensors towards the consumer market. Although the choice of the technique is basically application driven, the common factor for active optical ranging systems is their mid to high costs. While this aspect may not be a problem in many industrial applications, it prevents the use of 3D vision systems in low cost applications like those typical for automotive and domotic fields. The most promising technique for a low-cost system working in real-time seems to be TOF, which is capable of high speed measurements of distances 2

19 1.3. THE SOLUTION up to m, if relaxed constraints on measurement accuracy (a few centimeters) are accepted. The recent progresses in TOF ranging systems have been based on the integration of photo-detectors and electronic readout circuits on the same die. Key factors to obtain a high frame rate with an acceptable resolution are the elimination of the scanner, which can be obtained by integrating a pixel array, and the capability to perform in-pixel signal processing. Recently, two commercial scannerless ranging systems have been presented 1. Although their performance is at the state of the art, their cost is still too high for automotive and domotic applications. 1.3 The solution Aim of this thesis has been the investigation of new device and system solutions to these problems. Since lowering the costs was one of the main objectives, the research concentrated on the use of standard CMOS technologies rather than custom technologies. This represents a challenge, since the performance of photodetectors in a standard technology are usually inferior if compared to dedicated technologies. However, the advantages of integrated electronics often overcome the disadvantages of the inferior detector performance. Three different approaches have been investigated in this thesis: the first two are based on the balanced mixer concept, while the third consists in the integration of a single-photon sensitive device and a readout channel at the pixel level. A first attempt has been made to explore the possibility of integrating Metal-Semiconductor-Metal (MSM) devices in a standard CMOS process. The second proposed solution is a CMOS Electro-Optical Mixer (EOM) structure that can be integrated with a differential readout channel. The

20 CHAPTER 1. INTRODUCTION third proposed approach has been the integration a the pixel level of a Single Photon Avalanche Diode (SPAD), a Time-to-Amplitude Converter and an averaging circuit. This research work has been carried out in collaboration with the Microsystems Division of the ITC-IRST (Trento, Italy). My main contributions have been in the design and electro-optical characterization of the proposed detectors, together with the theoretical analysis and measurement of the system performance. 1.4 Innovative aspects A common element linking the different solutions investigated in this thesis lies in the integration of non-standard detectors together with electronic readout channels in standard technologies. The analysis of MSM devices for array integration in a standard CMOS process has been explored for the first time and a simple yet accurate macromodel has been implemented. A novel EOM structure has been proposed, designed and implemented in a standard CMOS technology. Although a few SPAD-based imaging sensors have already been investigated, a monolithic sensor integrating SPAD and read-out channel at the pixel level has been developed for the first time. 1.5 Structure of the thesis The structure of this dissertation is given in the following. In Chapter 2 a brief description of the interactions between light and silicon is presented together with a short introduction to photodiodes. Then, an overview of CMOS image sensors is given, with attention to pixel and imager architectures. The principles of the TOF technique and its differ- 4

21 1.5. STRUCTURE OF THE THESIS ent implementations are then presented. The devices that can be used in a TOF system are reviewed, with particular attention to their CMOS implementation. The most important figures of merit of range imaging sensors are introduced and, finally, an overview of existing TOF 3D image sensors is given. Chapter 3 reports on the design of MSM devices in a standard CMOS technology. An analysis of the device by means of numerical simulations is shown. The development of a macromodel for circuit simulations is then reported together with the model validation by comparison with the simulations. Finally, the design and characterization of MSM test devices is shown. In Chapter 4 the design and characterization of a CMOS compatible EOM is reported, together with the architecture of an active pixel based on the proposed device. The operation principle of the detector is first presented, followed by an electro-optical analysis performed by means of device simulations. The architecture of a pixel based on a differential readout channel is presented together with a linear array image sensor. An electro-optical characterization of the detector is finally shown. Chapter 5 reports on the design and characterization of SPADs in CMOS technologies together with a SPAD-based linear image sensor. First, an analysis of the possible implementation of TOF technique using SPADs is presented. The design of some test avalanche photodiodes in two different CMOS technologies is reported. The architecture of a pixel including a SPAD, a Time-to-Amplitude converter and an averaging circuit is shown, followed by the description of an image sensor based on a linear array of the proposed pixels. An electro-optical characterization of the test avalanche photodiodes is then reported. Finally, a characterization of the proposed image sensor is presented. 5

22 CHAPTER 1. INTRODUCTION Publications related to the Ph.D. research: [1] L. Pancheri, C. Marzocca, M. Boscardin, G. F. Dalla Betta, Silicon PIN detector with integrated JFET-based source follower, Electronics Letters 40 (2004), pp [2] L. Pancheri, M. Scandiuzzo, G. F. Dalla Betta, D. Stoppa, F. De Nisi, L. Gonzo and A. Simoni, A silicon Metal-Semiconductor-Metal Macromodel for circuit simulations, Solid State Electronics 49 (2005), pp [3] L. Pancheri, G. F. Dalla Betta, M. Scandiuzzo, F. De Nisi, D. Stoppa, L. Gonzo and A. Simoni, CMOS Electro-Optical Mixer for Range Finders, Proceedings of AISEM 2005 Conference, Firenze (Italy), February [4] M. Scandiuzzo, F. De Nisi, L. Pancheri, D. Stoppa, L. Gonzo, G. F. Dalla Betta, A. Simoni, CMOS Distance Sensor based on Photon Mixing Device, Proceedings of SENSOR th International Conference, vol. 1, pp , Nürnberg (Germany) May [5] D. Stoppa, L. Pancheri, M. Scandiuzzo, A. Simoni, L. Viarani, G. F. Dalla Betta, A CMOS Sensor based on Single Photon Avalanche Diode for Distance Measurement Applications, Proceedings of the IEEE Instrumentation and Measurement Technology Conference (IM- TC05), pp , Ottawa (Canada), May [6] F. De Nisi, D. Stoppa, M. Scandiuzzo, L. Gonzo, L. Pancheri, G. F. Dalla Betta, Design of electro-optical demodulating pixel in CMOS technology, Proceedings of IEEE International Symposium on Circuits and Systems (ISCAS 2005), pp , Kobe (Japan),

23 1.5. STRUCTURE OF THE THESIS May [7] L. Pancheri, G. F. Dalla Betta, D. Stoppa, M. Scandiuzzo, L. Viarani, A. Simoni, CMOS distance sensor based on Single Photon Avalanche Diode, 2005 PhD Research in Microelectronics and Electronics (PRI- ME 05), Vol. 2, pp , Lausanne (Switzerland), July [8] G. F. Dalla Betta, M. Boscardin, A. Candelori, F. Fenotti, L. Pancheri, C. Piemonte, L. Ratti, N. Zorzi, An Improved Fabrication Technology for Silicon Detectors with Integrated JFET/MOSFET Electronics, IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS-MIC 05), Conference Record, paper N35-71, San Juan (Puerto Rico), October [9] D. Stoppa, L. Pancheri, M. Scandiuzzo, M. Malfatti, G. Pedretti and L. Gonzo, A Single-Photon-Avalanche-Diode 3D Imager, Proceedings of the 31st European Solid-State Circuits Conference (ESSCIRC 2005), pp , Grenoble (France), September [10] D. Stoppa, L. Pancheri, M. Scandiuzzo, L. Gonzo, G. F. Dalla Betta and A. Simoni, A CMOS 3-D Imager based on Single Photon Avalanche Diode, submitted to IEEE Transactions on Circuits and Systems I. 7

24 CHAPTER 1. INTRODUCTION 8

25 Chapter 2 State of the Art 2.1 Light detection with silicon Interaction between optical radiation and silicon Considering the interaction of light with matter, the quantum nature of light must be necessarily taken into account. Photons are the quantum particles carrying electromagnetic energy, which in vacuum travel at at the speed of light c = m/s. Photon energy E ph is related to its frequency ν and wavelength λ by the equation: E ph = hν = h c (2.1) λ where h is the Plank s constant. The most important forms of interaction between photons and matter are absorption, scattering, refraction, interference and diffraction. A photon beam travelling through a slab of material is attenuated because of absorption and scattering. The intensity I of the photon beam decreases with depth x according to Beer s law: I(x) = I 0 e αx = I 0 e x/l α (2.2) where I 0 is the beam initial intensity, α is the absorption coefficient, which 9

26 CHAPTER 2. STATE OF THE ART 1000 Absorption length [ m] Wavelength [nm] Figure 2.1: Absorption length in silicon as a function of light wavelength depends on photon energy and absorbing material, and L α = 1/α is called absorption length. Light detectors are often made of semiconductor materials, because of their low cost, ruggedness and advanced technology. The most used semiconductor in photon detection is silicon, though its application is mainly limited to the visible - near infrared range (λ = nm). Germanium and compound semiconductors are used for the detection of photons having a wavelength beyond 1100 nm. Absorption length in silicon as a function of light wavelength is shown in Figure Quantum efficiency An important figure of merit of a light sensor is the external quantum efficiency η ext, defined as the ratio between the number n e of electron-hole pairs generated by light and finally collected to form the electrical signal at 10

27 2.1. LIGHT DETECTION WITH SILICON the sensor output and the number of photons in the incident optical beam n ph : η ext = n e n ph. (2.3) η ext accounts for different effects related to light interaction with the semiconductor, among which the most important are: 1. Transmission efficiency, i.e. the fraction of photons that are able to reach the photosensitive region of the sensor; 2. Absorption efficiency, i.e. the number of electron-hole pairs generated by each photon reaching the semiconductor surface; 3. Collection efficiency, i.e. the fraction of photo-generated charge carriers that are collected at the sensor electrodes. Transmission efficiency is determined by the stack of layers covering the photosensitive area. Passing through the covering layers, light experiences multiple interferences and the transmitted and reflected amounts at a given wavelength depend on the thicknesses and refractive index of every layer in the stack [13]. In a standard CMOS process, there exist basically four types of materials that can cover the sensor area, namely aluminum, polysilicon, silicon oxide and silicon nitride. Due to its reflecting properties, aluminum is normally adopted as a light shield over the electronic devices outside the active area of photosensor. Normally, only inter-poly and inter-metal oxide layers together with the final passivation oxide (and/or nitride) layer cover the photosensor, even though polysilicon layers can be sometimes present. In non-standard, dedicated technologies, properly dimensioned multi-layer antireflecting coatings can be realized, that exploit constructive interference to improve the transmission efficiency. 11

28 CHAPTER 2. STATE OF THE ART Absorption efficiency is defined as the number of electron hole pairs generated by the fraction of photons reaching the semiconductor surface. Absorption efficiency is determined by two effects: the number of photons which generate electron hole pairs and the number of electron hole pairs generated by a single photon. The former is called intrinsic absorption efficiency (η i ), the latter intrinsic quantum yield (Q i ). The intrinsic absorption efficiency depends on the depth of the silicon active volume x and can be expressed as η i = 1 e αx. (2.4) As far as photons in the visible near infrared region of the spectrum are concerned, one electron hole pair will be generated by each incident photon; in this case, Q i = 1. Collection efficiency is defined as the fraction of optically generated minority charge carriers that are collected at the sensor electrodes before recombining. Since only the collected charge carriers contribute to the formation of a useful signal, while those which recombine are lost, the collection efficiency plays an important role in determining the external quantum efficiency. In semiconductors, charge carriers move by drift and diffusion; drift plays a dominant role in depleted region, diffusion in undepleted region. The mean distance travelled by a charge carrier before recombining in depleted and undepleted regions are the drift length L drift and the diffusion length L diff. When these lengths are long with respect to the distance a charge carrier needs to cover to reach the electrodes, the charge signal becomes largely independent on the incident point of absorption within the sensor volume. Drift and diffusion lengths are related to semiconductor physical parameters by the equations: 12

29 2.1. LIGHT DETECTION WITH SILICON L drifte = µ e τ e E (2.5) L diffe = D e τ e (2.6) where µ e represents the electron mobility, τ e the lifetime of electrons, E the electric field magnitude and D e the diffusion coefficient of electrons. Drift and diffusion length increase with increasing mobility and lifetime, thus improving collection efficiency Photodiodes The simplest, and probably the most used radiation sensor is the p/n junction photodiode. The optically generated charge carriers are separated by drift inside the junction depletion region or by diffusion within a diffusion length from the depletion region boundary in the neutral regions. Photodiodes can be operated in three different modes: photovoltaic, photoconductive and integrating mode. In the photovoltaic mode, the voltage drop at the diode electrodes in the presence of light is directly read out and there is no need to apply a bias voltage to the sensor. This mode of operation is used in industrial environments, where bias voltages would easily be affected by severe noise problems and their use is preferably avoided. In the photoconductive mode a reverse bias voltage is applied at the photodiode electrodes and the photocurrent is read out. This mode of operation is used in applications involving high speed and high optical power. To operate in the integrating mode, the diode is first reverse biased and then left floating, making the photocharge be integrated onto the photodiode capacitance. This mode of operation is used with weak optical signals and low operation speed, as in the case of digital cameras. One of the most useful figures of merit for photodiodes is the spectral 13

30 CHAPTER 2. STATE OF THE ART responsivity, R, defined as the ratio between the photogenerated current, I ph, and the incident optical power, P opt : R = I ph P opt. (2.7) The optical power is a function of the number of photons forming the optical beam, n ph, and of the energy of these photons, E ph : P opt = n ph E ph, (2.8) and the photogenerated current is directly proportional to the number of electron-hole pairs generated and collected, n e : I ph = n e q. (2.9) The spectral responsivity can thus be expressed as a function of the external quantum efficiency by the relation: R = n e q h c/λ n ph = n e n ph q λ h c = η ext λ(µm) (2.10) The response speed of a photodiode depends on how fast the optically generated charge carriers are collected by the electrodes. Since diffusion of carriers is much slower than drift, if a fast operation is needed the fraction of carriers generated in the depleted region must be much higher than that generated in the undepleted ones. In a reverse biased p/n junction a current flows also in the absence of illumination. This is called dark current and consists of three contributes. A first contribute is the thermal generation of carriers within the depletion region. A second contribute comes from the diffusion of the minority carriers from the neutral regions to the depletion region. The third contribute arises from the generation of carriers at the depleted surface beneath the silicon oxide passivation layer. Dark current affects the performance of 14

31 2.2. CMOS IMAGE SENSORS photodiodes in the presence of low optical power levels, because shot noise associated with dark current determines the low light detection limit of the sensor. 2.2 CMOS image sensors Historical background The first works on image sensors were carried out in the 60s, using NMOS, PMOS or bipolar processes [14, 15, 16]. Charge Coupled Devices (CCDs) were first reported in the 70s and were soon universally adopted over many other forms of image sensors. Among the reasons of their success were the simplicity and the small size of the CCD pixel, and the low Fixed Pattern Noise (FPN) if compared to other types of image sensors [17]. A large effort was applied to the development of CCDs during the 1970s and 1980s, while the CMOS sensors were only sporadically investigated. In the early 1990s, the growing interest of research and industry over CMOS image sensors led to great improvements in this kind of imagers [18, 19]. The advances of CMOS technologies together with the invention of the active pixel allowed the development of image sensors with good performances, low power consumption and added functionalities with respect to the CCD counterpart. The availability of low-cost Digital Signal Processing and the introduction of the Correlated Double Sampling (CDS) technique [20] has reduced the problem of FPN, thus making CMOS cameras competitive with CCDs in many fields of application CMOS imager architecture The architecture of a CMOS image sensor is shown in Figure 2.2. The core of the sensor is an array of pixels that is addressed one row at a time by row 15

32 CHAPTER 2. STATE OF THE ART selection logic. Pixels are read out through column buses by analog signal processors, which can perform several operations, including amplification, CDS, sample and hold, and FPN suppression. More advanced CMOS image sensors contain on-chip ADCs. Column selection logic is used to address the digital (or analog, if ADCs are not implemented) output of the chip for readout. The possibility of random access to the pixels permits several modes of image readout [17, 13]. Apart from progressive scan, which is the most common, with this architecture it is possible to perform a window readout, where only a small Region Of Interest (ROI) in the array is selected, and a skip readout, where every second (or third, etc...) pixel is read out. This modes of operation allow for an increased readout speed at a lower resolution. Pixel array Row select logic Analog signal processors Timing and control Column-parallel analog to digital converters Column select Digital output Figure 2.2: Architecture of a CMOS image sensor 16

33 2.2. CMOS IMAGE SENSORS Passive and active pixels Pixel circuits can be classified in passive pixels, that contain only the photosensitive element and a pass transistor, and active pixels, which contain at least an active amplifier. The passive pixel consists of a photodiode and a pass transistor, and is shown in Figure 2.3 (a). When the transistor is activated, the photodiode is connected to the vertical column bus. The readout is performed with a Charge Amplifier at the end of the column bus. Although a very high quantum efficiency can be obtained with this approach, the high parasitic capacitance of the column bus causes a high read-out noise, around 200 electrons rms, if compared to active pixels or CCDs. This effect is more pronounced in large arrays and when a fast read-out rate is used. V DD V DD TX RES PG RES TX n+ n+ n+ RS n+ RS p-sub p-sub p-sub COLUMN BUS COLUMN BUS COLUMN BUS (a) (b) (c) Figure 2.3: CMOS pixel architectures: a) Passive pixel, b) Photodiode-type active pixel, c) Photogate-type active pixel The simplest active pixel configuration uses a source follower as amplifying stage and can be designed both having a photodiode or a photogate as light sensing element. A schematic representation of the photodiodetype and photogate-type active pixel is shown in Figure 2.3 (b) and (c). A reset transistor and a row-select transistor are present in both pixel 17

34 CHAPTER 2. STATE OF THE ART Lens Modulated light source Syncronization circuit Lens Receiver and time measuring circuit Reflected light d Figure 2.4: Basic principle of the Time-Of-Flight technique configurations. In the photodiode-type active pixel, optically generated charge carriers are integrated onto the photodiode capacitance, while in photogate-type the electrons, first collected in the potential well below the gate, are transferred to an n diffusion, whose capacitance performs the charge to voltage conversion. The read-out noise in photodiode-type active pixels is around electrons rms and can be as low as electrons rms in photogate type active pixels. Several alternative active pixel concepts have been proposed, among which logarithmic pixels [21, 22], high-dynamic range pixels [23, 24] and pixels with integrated ADC [25, 26]. 2.3 Time Of Flight technique TOF basic principle Although the principle of TOF distance measurement dates back to 1903 [27], the first experiments using light as active source have been carried out in 18

35 2.3. TIME OF FLIGHT TECHNIQUE 1949 by Fizeau. Time of Flight technique is based on two properties of light, namely its straight line propagation and its finite speed. The underlying principle of TOF is shown in Figure 2.4. The measuring setup consists of a couple transmitter/receiver placed near to each other. The transmitter illuminates the scene to be mapped with a pulsed (or modulated) light source. The receiver detects the light reflected by the scene and calculates the time-delay between emitted and received light, thus reconstructing the distance. Time of flight can be classified into direct (D-TOF) and indirect (I-TOF), depending on the technique used for measuring the time delay between emitted and received modulated light Direct Time of Flight In a D-TOF system, the transmitter emits an optical pulse and at the same time sends a trigger signal to start a time counter. When the receiver detects the backscattered light pulse, it sends a stop signal to the counter. The distance is calculated from the time through the relation d = c t 2 (2.11) where c is the speed of light in air. Receivers employed in D-TOF systems usually employ standard photodiodes together with a high speed amplifier [8, 28, 29]. If a high distance resolution is required, a high bandwidth time counter must be employed. Solutions based on the intrinsic high sensitivity of Single Photon Avalanche Diodes have also been reported [30, 31]. In this case the amplifying stage is not needed, since the amplification is done intrinsically by the detector. 19

36 CHAPTER 2. STATE OF THE ART Indirect Time of Flight In an indirect TOF system, a modulated light source is used to illuminate the scene to be measured and the delay time is determined indirectly through the estimation of the phase difference between emitted and detected light. In the literature, systems using both pulsed [32, 33] and sine-wave [34, 35] light modulation have been demonstrated. In the latter case, the speed requirements for the light source and for the read-out electronics are less stringent, because a limited bandwidth must be available. High power LEDs can be used as a light source in the case of sine-wave modulation, while if pulsed light is needed, solid-state lasers are usually employed. An advantage of pulsed over sine-wave modulation is that it is possible to have very high peak optical power while keeping the average power low. This can accomplished using a low duty cycle and can help the satisfaction of eye safety requirements. The measurement range obtained with modulated light is limited by phase ambiguity problems. The distance range L that can be unambiguously measured is L = c/2f mod, where f mod is the modulation frequency. If, for example, a 20 MHz modulation frequency is employed, a distance range of about 7.5 m can be measured without ambiguity problems. The use of a lower modulation frequency can increase the measuring range at the price of a reduced range resolution. If the measuring range needs to be extended without loss in resolution, two measurements at different modulation frequencies can be performed. Phase evaluation can be done in two ways: by the correlation of the received light with a demodulation signal or by the sampling of the received light signal. 20

37 2.3. TIME OF FLIGHT TECHNIQUE Demodulation by correlation With this technique, demodulation is performed by mixing the received optical signal with a demodulation signal and retrieving the phase delay from the output of the mixer. Let p(t) be the modulated optical signal incident on the detector. p(t) is a periodic function of time with period T. The demodulation function, g(t), is also periodic with period T. A detector - demodulator system measures the correlation function c(τ) between p(t) and g(t). c(τ) is defined by c(τ) = p(t) g(t) = p(t)g(t τ)dt. (2.12) The phase delay between p(t) and g(t) can be retrieved evaluating the correlation function c(τ) at different values of τ. Let s examine two examples of modulation, namely sine wave and square wave modulation. In the first case, the received light power can be expressed as p(t) = P 0 + P cos(ωt φ)) (2.13) where P 0 is the average optical power, φ is the phase delay, and P is the modulated optical power, while the demodulation function is expressed by g(t) = G 0 + G cos(ωt) (2.14) where G 0 and G are constants which depend on detector and mixer characteristics. The correlation function is expressed by P G c(τ) = P 0 G 0 T int + T int cos(ωτ φ) (2.15) 2 where T int is the integration time and P 0 G 0 T int is a constant arising from the integration of the continuous component of light (including background light) and from the non-ideality of the mixer. 21

38 CHAPTER 2. STATE OF THE ART A technique to eliminate the influence of P 0 and G 0 from the measurement is the use of a balanced mixer [36, 37]. In this case, an in-phase and an out-of-phase demodulation signals, having 180 phase delay, are simultaneously applied to the mixer, which is read out differentially. The resulting output signal c d (τ) can be calculated as the difference of the correlation functions c(τ) and c(τ + T/2): c d (τ) = c(τ) c(τ + T/2) = P G T int cos(ωτ φ) (2.16) which is independent on P 0 and G 0. Phase or frequency modulation techniques can be used to calculate the phase delay [38]. In the case of pulsed wave modulation, both p(t) and g(t) are square waves. Their correlation function is a triangular wave which is function of τ t, i.e. in selected time intervals c(τ) is a linear function of the delay time t. The most common system concept to measure TOF with correlation techniques is based on a standard photodiode, a high speed amplifier and a mixer [39]. Another approach sees the use of an external optical modulator, which performs mixing, and a camera, which detects the down-converted optical signal [40]. A different system concept makes use of standard photodiodes in a CMOS chip for light detection. Mixing is obtained exploiting the high speed shutter capabilities offered by CMOS technology [32, 33]. Other approaches make use of Inherently Mixing Detectors (IMDs), which integrate both detector and mixer in a single device [38, 41]. Demodulation by sampling Phase delay can be retrieved sampling the received optical signal synchronously. Sampling can be performed by integrating optically generated 22

39 2.4. DEVICES USED IN TOF 3D IMAGE SENSORS charges during short time windows centered at the sampling time T s. Systems employing this technique use photogate-based devices fabricated in CCD technology, which are able to perform light detection, charge transfer and accumulation [42, 35]. 2.4 Devices used in TOF 3D image sensors In this section some detectors that can be integrated in CMOS compatible technologies are briefly reviewed. First, the lock-in CCD, is presented. This device can be fabricated in a CMOS-CCD technology, obtaining a simple pixel architecture and small pixel dimensions. The concept of inherently mixing detector (IMD) has been introduced to group devices which unify in a single device both a photo-detector and a mixer [38]. Several devices have been proposed to be used as IMDs: gain modulated avalanche photodiodes [43], photogate photonic mixing devices (PG-PMD) [37] and Metal-Semiconductor-Metal (MSM) [36] photodiodes. The latter two, which are very promising in terms of possible degree of integration, device linearity and overall system cost, are here reviewed. Single Photon Avalanche Diodes (SPADs), which can be used in D-TOF systems, are briefly reviewed. Some implementations of SPADs in standard CMOS technologies have recently been demonstrated Lock-in CCD The lock-in CCD, introduced in ref. [42], is based on synchronous photocharge detection and storage. The first version was composed of a central photogate and four peripheral charge storage sites. The charges generated and stored under the central photogate can be transferred to one of the storage sites by means of four transfer gates, which can be operated 23

40 CHAPTER 2. STATE OF THE ART independently. This structure can perform synchronous sampling and accumulation of the photocharges in the storage sites. Four samples per period can be acquired, allowing the unambiguous reconstruction of the phase. A similar structure, but having only one storage site, is presented in ref. [35]. With this device, the four samples must be acquired sequentially in order to reconstruct the phase of the incoming light wave. An important figure of merit of the lock-in CCD is the demodulation contrast, which defines the ability of the mixing photodetector to separate the photogenerated charge according to the applied demodulation signal. Following the definition given by ref. [35], the contrast can be defined as C demod = measured amplitude measured offset (2.17) Demodulation contrast has been shown to decreases with increasing frequency and wavelength. For the device presented in [35], demodulation contrast is 40% at 630 nm and 20 MHz, but it becomes very small at wavelengths beyond 800 nm Photogate PMD The basic structure of a PG-PMD consists of a photosensitive area with two transparent gates on top and two read-out diodes at the sides of the active area [34]. The cross section of a PG-PMD is shown in Figure 2.5 together with the surface potential. The amount of photogenerated electrons collected by either of the read-out diodes is related to the the applied gate voltages. If complementary voltages are applied at the gate electrodes, a balanced mixing operation is possible. A structure with 3 gate electrodes operating on the same principle is presented in ref. [44]. 24

41 Potential 2.4. DEVICES USED IN TOF 3D IMAGE SENSORS V R1 V M1 V M2 V R2 n+ n+ p- V < M1 V M2 V > M1 V M2 Figure 2.5: Schematic structure of a Photo Gate PMD and surface potential at two different gate voltages Metal Semiconductor Metal Detecor MSM detectors essentially consist of a pair of rectifying Metal-Semiconductor contacts (Schottky diodes, [45]) connected in series back-to-back, having a voltage applied between their electrodes. The semiconductor region is left floating, so that the diode at the higher voltage (anode) is forward biased, the other one (cathode) is reverse biased. In dark conditions, the current flowing in the device is determined by the leakage current of the reverse biased diode. Under illumination, the photogenerated electrons and holes are collected respectively by the anode by the cathode, causing a photocurrent to flow from the anode to the cathode. The photocurrent direction can be reversed by simply inverting the bias. In practice, MSM photosensors normally feature an interdigitated structure, that, in order to be operated properly, requires the applied voltage to be large enough to fully deplete the semiconductor surface region be- 25

42 CHAPTER 2. STATE OF THE ART V 1 V 2 n- Figure 2.6: Schematic structure of Metal Semiconductor Metal detector tween the two electrodes, so that the photogenerated carriers can drift at a velocity close to the saturation value. In this operating conditions, the capacitance between the two electrodes is very low, allowing a very fast operation of the detector. The cross section of a typical MSM device is shown in Figure 2.6 MSM devices have first been proposed as Electro Optical Mixers in fiberoptics applications [46]. The photo-current flowing at the two electrodes depends on the the voltage difference V applied between the electrodes. At small applied voltages, current increases linearly with V, while beyond the reach-through voltage current saturation is observed. A MSM operated as EOM in a range-finding system has been demonstrated in ref. [36]. The main efforts in the development of MSM devices have so far been concerned with compound (III-V) semiconductors [47, 48], but also silicon MSMs fabricated in CMOS compatible technologies have been reported. Tables 2.1 and 2.2 resume the main characteristics of silicon Metal - Semiconductor - Metal photosensors reported in the scientific literature in the past few years. In 1991 Bassous et al. [49] proposed an MSM detector which was fabricated in a BiCMOS compatible technology. The device featured a fast dynamics at wavelengths lower than 700 nm, but above this 26

43 2.4. DEVICES USED IN TOF 3D IMAGE SENSORS Ref. Electrode Dark current Responsivity [A/W] material [pa/µm 2 ] [49] PtSi V bias = 4V λ=630nm, V bias = 5V [50] Ni V bias = 5V λ=960nm, V bias = 10V [51] Au V bias = 5V λ=830nm, V bias = 10V [52] TiW-Au V bias = 5V λ=790nm, V bias = 5V [53] Cr-Au V bias = 15V λ=830nm, V bias = 20V [56] Ti-TiW-Al V bias = 12V λ=860nm, V bias = 12V [55] Al V bias = 1V λ=800nm, V bias = 8V [54] Cr-Au V bias = 15V λ=830nm, V bias = 10V Table 2.1: Static characteristics of silicon MSM photodetectors the performance dropped because of the increasing absorption lenght of silicon. In the last years different approaches have been proposed to improve the performance of silicon MSMs in terms of responsivity, dark current and response speed. Sharma et al. [50] proved that a surface implant of fluorine to increase the radiation absorption would increase detector performance. Another approach to improve the device speed while keeping a good responsivity was the realization of the detector on a thin textured membrane [51]. Ho et al. [52] and Laih et al. [53] proposed the realization of the electrodes in grooves or trenches, in order to increase the electric field in depth, thus improving the device speed. In order to reduce the dark current, the deposition of a thin layer of hydrogenated amorphous silicon (a-si:h) has been proposed [53, 54]. Other MSM detectors have been realized in SOI [55] and polysilicon [56]. Only the device of [49], that is optimized for a lower wavelength (630 nm), is fabricated in a standard technology. The other reported photosensors are fabricated in CMOS compatible technologies, by adding to the basic process sequence few dedicated steps, that are not available in a standard technology, in order to improve the electro-optical performance at the wave- 27

44 CHAPTER 2. STATE OF THE ART Ref. Optical pulse response Bandwidth [GHz] time (FWHM) [ps] [49] λ=630nm, V bias = 5V λ=630nm, V bias = 5V [50] λ=760nm, V bias = 5V n.a. [51] λ=830nm, V bias = 10V λ=830nm, V bias = 10V [52] λ=790nm, V bias = 5V λ=790nm, V bias = 10V [53] λ=830nm, V bias = 15V λ=830nm, V bias = 15V [56] λ=850nm, V bias = 5V λ=850nm, V bias = 5V [55] λ=800nm, V bias = 15V λ=800nm, V bias = 15V [54] λ=830nm, V bias = 10V λ=830nm, V bias = 10V Table 2.2: Dynamic characteristics of silicon MSM photodetectors length of interest for short haul optical communications ( nm). Nevertheless, in spite of their outstanding performance, e.g., responsivity of 0.25 A/W and bandwidth of several GHz, it is worth stressing that these are single MSM photosensors and that the technological options adopted to improve their performance are not available in a standard process. In fact, the feasibility of MSM photosensors in CMOS processes, normally used for 2D imagers, can be difficult, due to several constraints. In particular, the metal electrode material is set by the technology and may result in high dark currents. Moreover, the same substrate is shared with transistors, and cannot be left floating, so that, in order for a true MSM operation to be achieved, the Schottky contacts could be fabricated on an n-well only Single Photon Avalanche Diode A Single Photon Avalanche Diode is basically an avalanche photodiode biased beyond its breakdown voltage V B by an amount V E, which is called excess bias. The working principle of a SPAD is illustrated in Figure 2.7. The absorption of a photon creates an electron-hole pair which triggers an 28

45 2.4. DEVICES USED IN TOF 3D IMAGE SENSORS Current Quenching photon Reverse voltage VB V B+ VE Recharge Figure 2.7: Working principle of a SPAD avalanche breakdown event. The SPAD must be connected to a circuit, called quenching circuit [57], whose task is lowering the applied voltage below the breakdown voltage in order to quench the avalanche discharge. Later, the quenching circuit must be able to restore the excess bias voltage, so that the SPAD could detect another photon. The quenching circuit can be passive, active or have mixed passiveactive features. The simplest circuit is a passive quench - passive recharge circuit, and is made of a high value resistor in series with the photodiode. This circuits has several disadvantages, in particular a slow recovery time and a count-rate dependent timing resolution. The use of active quenching circuits can improve the recovery time and the timing resolution obtained from a SPAD. The basic passive and active quenching configurations, independent from the actual circuit implementation, are shown in figure 2.8. The switches can be implemented with diodes, bipolar transistors or MOS- FETs. Gated operation can be obtained applying the excess bias voltage to the 29

46 CHAPTER 2. STATE OF THE ART (a) (b) V B +V E V B +V E R L S R R L h S Q h V B -V Q Figure 2.8: Schematic presentation of (a) passive quenching circuit (b) active quenching and recharge circuit SPAD for a time window, defined by a gate pulse. Both passive and active quenching circuits can be adapted for time-gated operation. SPAD structures are designed so as to avoid edge breakdown at the borders of the junction. In a planar technology two techniques are usually employed to this purpose: the first is the creation of a diffused guard ring at the edges of the junction [58, 59] and the second is the increment of the field at the center of the photodiode by means of an ion implantation that locally increases the electric field strength [60, 61, 62]. SPADs are typically classified in two groups: thin and thick SPAD, based on the depletion width of the p-n junction. In thin SPADs, the depletion region width is typically 1 µm the diameter ranges between 5 and 150 µm and the breakdown voltage from 10 to 50 V. In thick SPADs, the depletion region width ranges from 20 to 150 µm, the diameters from 100 to 500 µm and breakdown voltages from 200 to 500 V. The most important performance indicators for a SPAD are photon detection efficiency, dark count rate and time resolution. Typically, the maxi- 30

47 2.4. DEVICES USED IN TOF 3D IMAGE SENSORS mum photon detecion efficiency of thin junction SPADs is higher than 40% at 500 nm, while thick junction SPADs achieve a detection efficiency higher than 50% in the range nm. Dark count is mainly due to thermally generated carriers triggering an avalanche event, but the tunnelling contribution is not negligible in devices with a low breakdown voltage. Another technology-dependent parameter determining the dark count rate is the afterpulsing rate, which is caused by the release of charge carriers trapped during an avalanche discharge. The afterpulsing rate can be reduced limiting the current flowing during an avalanche discharge and keeping the off-time of the SPAD after an avalanche event sufficiently long. Recently, the feasibility of some CMOS technologies for the fabrication of good quality SPADs has been demonstrated [58, 59, 63]. This achievement opens the way to the monolithic integration of the SPAD with a readout channel, allowing a reduction of the stray capacitance present between the SPAD and the external circuit. Although fabricated in non-dedicated technologies, CMOS SPADs have good performances in terms of dark count rate, quantum efficiency and timing resolution. Two independent groups presented a SPAD in a 0.8 µm High Voltage CMOS technology [58, 59]. A schematic cross section of these SPADs is shown in Figure 2.9. In order to avoid edge breakdown, a guard-ring surrounding the p + implantation has been implemented using a p-tub layer inside a deep n-tub available in this fabrication processes. The active area is defined by means of an optical window opened in the metal light shield only in correspondence with the region where avalanche multiplication occurs. Comparing the work of Rochas et al. [58] and the work of Zappa et al. [59], it can be seen that, while the quantum efficiency is nearly the same, the SPAD of Zappa et al. has both a lower dark count and a better timing resolution (Table 2.3). While the low dark count can be attributed to the technology, the timing resolution is better because an active quenching 31

48 CHAPTER 2. STATE OF THE ART h metal shield p+ ptub p+ Deep ntub ptub n+ p sub Figure 2.9: SPAD cross section circuit is employed. A SPAD with a structure similar to that shown in Figure 2.9 has been fabricated in a standard CMOS 0.8µm technology by Rochas et al. [63]. The p-tub guard ring is obtained with the p-well implantation by violating the layout rules of the technology. This SPAD has the advantage of requiring a less expensive technology and occupying a lower area. However, its performance is inferior to SPADs fabricated in high voltage technology. Reference [58] [63] [59] Technology 0.8µm HV 0.8µm standard 0.8µm HV Diameter 7 µm 6 µm 12 µm Breakdown voltage 25 V 19 V 16 V Dark count rate 900 Hz Ve = 5 V < 300 Hz Ve = 2.5 V < 600 Hz Ve = 5 V Maximum PDE ( ) 500 nm Ve = 5 V 460 nm Ve = 2.5 V 500 nm Ve = 5 V Timing res. FWHM 60 ps 72 ps 36 ps Quenching technique passive passive mixed active-passive Table 2.3: Comparison between SPADs fabricated in CMOS technologies. ( ) Photon Detection Efficiency 32

49 2.5. TIME OF FLIGHT 3D IMAGE SENSORS In designing a SPAD array care must be taken to limit the cross-talk effect. This effect arises from the emission of photons by one the SPADs during a discharge and their successive absorption by in the active region of another SPAD [64, 65]. If lateral isolation techniques, e.g. trench isolation, are not used, layout and circuit solutions must be considered to reduce the crosstalk probability. In particular, limiting the maximum current flowing in the SPAD during breakdown and keeping two adjacent SPADs not too close to each other strongly reduces the optical cross-talk effect. 2.5 Time of Flight 3D Image Sensors TOF 3D image sensor can be classified into three groups, on the base of system configuration. The first group includes single distance sensors equipped with a mechanical 2D beam deflection and scanning unit. The second group includes scannerless systems formed by an electro-optical modulator placed on front of a CCD or CMOS array. The optical signal, which is down-converted by the modulator, is detected by the array. The third group includes scannerless systems that perform detection and phase evaluation in a single chip Figures of merit The main performance parameters for a 3D image sensor are distance resolution, distance range, lateral resolution, Fixed Pattern Noise and frame rate. Distance resolution is connected to the noise in time (or phase) measuring circuit. If electronic noise is discarded, the ultimate resolution limit is given by shot noise, arising from the quantum nature of light. The intensity of backscattered light decreases with the square of the distance between the measured objects and the sensor. The need to have 33

50 CHAPTER 2. STATE OF THE ART a minimum amount of reflected light determines the maximum working distance of the system. Another limitation to the distance range is given by phase ambiguity if a modulated light source is employed. Lateral resolution is the minimum lateral distance at which two points in the observed scene can be distinguished. In a scannerless system, lateral resolution is determined by the number of pixels integrated in the array and the field of view. In many applications, a high lateral resolution is not required and relatively small 2D arrays or linear arrays would be sufficient. If a real-time image processing is required, the volume of data to process must be small and thus the number of pixels in the array must be not too large. Another important parameter is Fixed Pattern Noise (FPN). FPN is the variation of the response of all pixels under the same conditions of illumination and target distance. It is an important figure of merit in all image sensors and is caused by variations in the doping levels, geometrical mismatches and different boundary conditions of the pixels. A high frame rate is important in many applications where a continuous distance monitoring is required. To obtain real time operation, a frame rate of frames/s is required. Since distance resolution can be improved by averaging over a high number of acquisitions, an increased resolution can be obtained at the expense of a reduced frame rate. In big image sensors pixel readout is a time consuming task. In order to minimize the time required for the readout, averaging must be performed inside the pixels Evolution of TOF 3D image sensors The first approach of 3D imaging with TOF systems consisted on adding a beam scanning unit to a 1D range sensor [66, 67]. Systems based on this concept are bulky, sensitive to vibration and their cost is too high for consumer application. These shortcomings have restricted their use mainly 34

51 2.5. TIME OF FLIGHT 3D IMAGE SENSORS to industrial applications. The first scannerless TOF image sensor was implemented combining a standard 2D vision sensor with a fast gating electro-optical device like a micro-channel-plate (MCP). With this system, Muguira [40] was able to measure three dimensional distance maps up to 20 meters with an accuracy of a few centimeters and with a spatial resolution of pixels. This solution, however, is still too costly for most applications and furthermore operates at voltages of some hundreds of Volts. In the past few years several attempts have been carried out aiming at the realization of an integrated device implementing the TOF principle and capable of providing both 2D and range information of a given scene. The most recent works on the topic illustrate three different approaches to the problem. The first approach sees an extensive use of switched-capacitor based processing electronics integrated at the pixel level [32, 68, 69, 70]; this is allowed by the high integration capabilities of state of the art CMOS processes. Circuits include shutter capabilities obtained with MOSFET switches, charge packets sampling and accumulation in each pixel. The second approach exploits the charge transfer characteristics of photogates fabricated in CCD processes for easing signal demodulation at pixel level [44, 35]. Demodulation can be performed both by mixing or by sampling the incoming light signal. Charge packets storage and accumulation is performed in the charge domain: this accounts for a simplified pixel structure and small pixel dimensions. The third approach makes use of the high sensitivity of Single Photon Avalanche Diodes, which can detect very weak light pulses [31, 30]. In this case, TOF is measured directly by means of a time measuring circuit. 35

52 CHAPTER 2. STATE OF THE ART Switched capacitor approach Two groups have demonstrated 3D sensors using a simple photodiode as light detector and switched capacitor circuits to perform in-pixel demodulation, averaging and storage [32, 69]. The basic technique is illustrated in Figure The light source is a pulse modulated laser. Charge integration time is defined by two integration windows: in the first window the integrated charge depends linearly on the time delay t of the light pulses; the second window is dimensioned so as to integrate the charge generated in an entire light pulse. The ratio between the two signals S 1 and S 2 obtained with the two integrations is independent on the amount of light incident on the pixel and depends linearly on the time delay. In fact, this technique measures the correlation function between the light pulse and the integration window, which is a linear function of t. The sensor demonstrated by Elkhalili et al. [68] has 4 64 pixels. Pixels include a sample and hold circuit and a Correlated Double Sampling circuit is implemented at the column level. Pixel size is µm 2, measurement range is 8 m and reported range resolution is 5 cm in single- Emitted light pulse t T P Received light pulse S 1 Integration window 1 S 2 Integration window 2 Time Figure 2.10: Basic principle of I-TOF using pulsed technique 36

53 2.5. TIME OF FLIGHT 3D IMAGE SENSORS pulse mode and can be improved to 1 cm by averaging over 100 pulses. The frame rate is 195 frames/s with 100 pulses average and can be as high as frames/s in single pulse mode. The sensor described in [69, 33] is a array. Pixels have a symmetric structure and contain a sampling and averaging circuit based on a fully differential Operational Transconductance Amplifier. Pixel size is µm 2. A Double Delta Sampling (DDS) stage is implemented at the column level. The reported measurement range is 2 m-9 m, limited by the setup. Range resolution is 5% at 30 frames/s and decreases to 2% at 3 frames/s Photogate approach In 1997 Miyagawa et al. [44] presented a 32-pixel linear range finding sensor based on a PG-PMD device. Pixel size is µm 2. Pulse modulation was used for both the light source and the demodulation signal applied to the PMD gates. The light source is a LED with 592 nm wavelength, modulated at the frequency of 10 MHz. The sensor has a range resolution lower than 10 cm at the distance of 1.5 m. In 2001 Lange et al. [35] demonstrated a pixel sensor. Pixel size is µm 2. Each pixel, based on the photogate approach, performs demodulation of the incoming signal by sampling it at four different times for each modulation period and calculates the phase delay from this four signals. The system can use two arrays of 810-nm or 630-nm LEDs as light source, which are sine-wave modulated at 20 MHz. The distance range is limited by phase ambiguity to 7.5 m. Measured range resolution is 5 cm for both illumination units at a 10-Hz frame rate. 37

54 CHAPTER 2. STATE OF THE ART SPAD approach In systems using a high-gain detector such as a SPAD, time instead of phase is directly measured and time counting circuits are therefore used. Aull et al. [30] demonstrated pixel 3D image sensor. Every pixel consists in a passively quenched SPAD and a time counting circuit. Pixel size is µm 2. SPADs were fabricated in a dedicated technology and connected to the chip containing the read-out electronics using the bridgebonding technique. A pseudo-random counter operated at 500 MHz clock frequency was used as time-to-digital converter. A system for military applications based on this sensor is presented in [71]. The light source is a pulsed Nd:YAG laser (532 nm). A diffractive element is used to transform the laser beam into a spot array, whose echo is focused onto the pixels of the sensor. The nominal range of the sensor is 150 m with a range resolution of 40 cm. Frame acquisition rate is 16 khz, but raw data are typically accumulated for 0.25 s before being processed. The sensor presented in [31], based on an array of pixels, is fabricated in a 0.8 µm High Voltage CMOS technology. Each pixel includes a passively quenched SPAD and a comparator, while no counting circuit is integrated at the pixel level. Pixel size is µm 2. A time-to-digital converter is used to measure the delay time externally. The light source is a 635 nm pulsed laser. The distance range is 3 m with a distance accuracy of 1.8 mm. The reported frame acquisition time is 205 s. 38

55 Chapter 3 CMOS compatible MSM Devices Recently, a smart pixel concept based on a fully differential read-out technique has been proposed [69]. This approach, combined with the use of MSM photodetectors as balanced mixers, could largely improve the system performance of a range finding sensor. In order to successfully design these imaging systems, an accurate knowledge of the behavior of the photosensor is required. To this purpose, the characteristics of CMOS integrated MSM photosensors have been studied by means of numerical simulations, and a physically sound MSM macromodel to be used in circuit simulations has been developed and validated. The chapter is organized as follows. Firstly, the electro-optical characteristics of the MSM devices in steady state and dynamic regimes are described. Then, the electrical model of the device is presented. A comparison between the results obtained with the model and with device simulations is reported. A series of MSM test devices has been implemented in a 0.35 µm CMOS technology. Experimental results obtained on the test devices are finally presented. 39

56 CHAPTER 3. CMOS COMPATIBLE MSM DEVICES 3.1 Device operation Device description In this chapter the behavior of a CMOS compatible MSM PD realized in a n-well is analyzed. Since the doping of the well and the applied voltages allow the MSM to be operated only below the punch-through condition [72], the analysis has been restricted to this case. To improve our understanding of the device, its behavior has been compared to that of a SOI device operating in the same conditions. A standard CMOS technology on p-epi layer is considered. We have assumed a doping of the epi layer of cm 3, which corresponds to a resistivity of 10 Ω cm, and a thickness of 15 µm. The n-well has been assumed to have a gaussian doping profile with a peak concentration of cm 3 and a junction depth of 2 µm. The silicon layer in the SOI device has a thickness of 4 µm, whereas the electrode geometry is the same as for the CMOS PD. In order to have comparable leakage currents and capacitances between the two devices, the SOI layer doping concentration is uniform and equal to the peak concentration of the n-well. The schematic cross-section of the devices is shown in Figure 3.1, together with the electrical equivalent circuits. MSM devices are usually fabricated with interdigitated electrodes to obtain a high speed of operation. In order to reduce the time required for the simulation, the device structure has been simplified and only two fingers have been considered. The width of the fingers (W) is 2 µm and the distance between them (S) is also 2 µm. The length of the fingers is 50 µm. Since the exact characteristics of Schottky contacts for the considered technology are not known a priori, the simulations have been performed considering values of the Schottky barrier in the range from 0.55 V to 0.7 V [73]. Simulations were performed by means of the 2-D 40

57 3.1. DEVICE OPERATION a) I1 light I2 S1 S2 I I p1 n1 Ip2 In2 n-soi S1 S2 b) I1 light I2 p + Sub S1 I I p1 n1 n-well S2 Ip2 In2 p-substrate Ipsub S1 S2 Sub Figure 3.1: Schematic cross section and equivalent circuit of the MSM PDs in SOI (a) and CMOS (b) technology 41

58 CHAPTER 3. CMOS COMPATIBLE MSM DEVICES device-analysis program DESSIS, included in the T-CAD software package by ISE AG [74]. DESSIS solves Poisson s and carrier continuity equations, with electron- and hole-current densities given by the drift-diffusion model. All main physical effects of interest in device modelling are supported; among these carrier mobilities are functions of doping and electric field; carrier lifetimes are calculated as functions of doping. In the simulations, the effect of light has been modelled by activating the optical generation term in the carrier continuity equations. The optical signal has been modelled as a photon beam, which is orthogonally incident to the silicon surface between the two fingers DC characteristics If a voltage is applied between electrodes S1 and S2, the electrode with the highest voltage is forward-biased and the other is reverse-biased [72]. The voltage values that can be applied are limited by the technology, and usually don t exceed a few volts. With these voltages the space-charge regions of the two Schottky diodes don t reach the punch-through condition and the current is limited by the reverse saturation current of the Schottky contact. The saturation current density J S depends exponentially on the Schottky barrier height Φ Bn with the relation [45] ( J S = A T 2 exp qφ Bn kt ) (3.1) where A is the effective Richardson constant, T is the absolute temperature, q is the electron charge and k is the Boltzmann constant. Under illumination a photo-current I ph is generated, which is proportional to the optical power P opt incident on the detector. The fraction of the photocurrent lost because of the recombination in the undepleted region is called I rec. The remaining current flows at the electrodes. The ratio 42

59 3.1. DEVICE OPERATION of the recombination current to the total photocurrent depends on the hole diffusion length. When the SOI PD is illuminated, a photo-generated hole current flows through both electrodes [75]. We call I p1 and I p2 the hole currents flowing at the electrodes S1 and S2. The relation I p1 + I p2 = I ph I rec holds. Let S1 be the reverse biased and S2 the forward biased Schottky junction. At the contact S1 an electron dark current equal to the reverse saturation current I S of the Schottky diode flows. The photo-generated electrons are collected by electrode S2, through which a direct current flows. In the CMOS device part of the photo-generated hole current flows into the substrate contact and part into the two Schottky electrodes. The relation I p1 + I p2 + I psub = I ph I rec holds in this case. The electron current is collected by the forward biased Schottky contact and a dark current flows through the reverse biased Schottky diode and p-n diode. The hole current collected by the three electrodes is proportional to the incident optical power, with the relation I p = R(λ) P opt (3.2) where R(λ) is the responsivity, and depends on the incident light wavelength λ. Using the results of DC simulations the values of R 1, R 2 and R sub have been calculated for the electrodes S1, S2, and substrate at different wavelengths. The sum of the R values of the three electrodes, R tot, represents a proportionality constant between (I ph I rec ) and the incident optical power. In Table 3.1 the ratios between the R values and R tot are shown at different wavelengths. These values have been calculated with contact S1 biased at 1 V, S2 at 2 V and the substrate grounded. As can be seen in the table, the amount of hole currents collected at the Schottky contacts is higher at small wavelengths, because the carriers are generated near the 43

60 CHAPTER 3. CMOS COMPATIBLE MSM DEVICES semiconductor surface. As the wavelength increases, most of the carriers are generated in the substrate and are therefore collected by the substrate contact. λ [nm] R 1 /R tot [%] R 2 /R tot [%] R sub /R tot [%] Table 3.1: Ratios between the R constant of the three electrodes and R tot at different wavelengths The simulated DC characteristics of the SOI and CMOS PDs with a Schottky barrier of 0.6 V are shown in Figure 3.2. The I-V characteristics in the dark and with different light intensities at the wavelength of 860 nm have been simulated. In the simulations the contact S1 is biased at 2 V and the contact S2 is swept between 0 V and 4 V. In the CMOS MSM the p-substrate is connected to ground. As can be seen, for both devices there is a linear region of operation, corresponding to a small voltage difference between the electrodes S1 and S2. In this region the responsivity can be modulated with the electrode bias. Increasing the voltage difference a saturation region is reached, for which the responsivity is independent of the applied bias. In the SOI PD the currents flowing through the electrodes are zero when the voltage across the contacts is zero. This is not true in the case of the CMOS PD, for which, in the saturation region, the current flowing through the forward-biased contact is higher, because part of the current is collected by the substrate contact. In the central part of the linear region both S1 and S2 currents are positive, i.e., both Schottky junctions are forward biased. 44

61 3.1. DEVICE OPERATION a) 2 1 Current [na] 0-1 S1 dark 10 nw 20 nw S2 b) S2 Voltage [V] Current [na] dark 5 nw 10 nw S1 S S2 Voltage [V] Figure 3.2: DC analysis of the SOI (a) and of the CMOS (b) MSM PDs. Contact S1 is grounded for the SOI PD and is biased at 2 V for the CMOS PD. The incident light wavelength is 860 nm 45

62 CHAPTER 3. CMOS COMPATIBLE MSM DEVICES Spectral responsivity The responsivity of the SOI PD is simply the ratio between the photocurrent flowing at the electrodes and the incident optical power, while in the case of the CMOS device, the responsivity is the ratio between the anode photo-current and the incident optical power. If the anode is electrode S2 and the dark currents are neglected, the photo-current flowing at the anode is given respectively by I 2 SOI = I p2 + I n2 = I p2 I p1 (3.3) I 2 CMOS = I p2 + I n2 = I p2 I p1 I psub (3.4) for the SOI and CMOS PD. The responsivity of the SOI and CMOS detectors are linked to the R constants by the relations 3.5 and 3.6: R SOI = R 1 R 2 (3.5) R CMOS = R 1 + R sub R 2 (3.6) These equations state that the hole current collected by the anode causes a reduction of the responsivity in both the CMOS and the SOI detector. Looking at Table 3.1, it can be seen that the reduction of the responsivity is higher at low light wavelengths. The simulated responsivity of the SOI and CMOS PDs is shown in Figure 3.3. The devices have been biased in the saturation region. The presence of dielectric coatings like silicon oxide or silicon nitride on silicon surface has not been taken into account. As can be expected, the responsivity of the SOI PD is lower, because of the small thickness of the silicon layer. The maximum of responsivity is shifted towards lower wavelengths if compared to the responsivity of the CMOS PD. 46

63 3.1. DEVICE OPERATION Responsivity [A/W] CMOS SOI Wavelength [ m] Figure 3.3: Responsivity of the CMOS and SOI PDs Response to a light step The two devices show a similar transient behavior, so we discuss the case of the CMOS device. An analysis of the transient response of the PDs to a step of monochromatic light has been performed. Figure 3.4 shows the response of the anode current to a long light pulse (5 µs) and a short light pulse (100 ns). The applied illumination power is 0.1 µw and the wavelength is 860 nm. The response to the long pulse shows that in the first part of the transient the displacement current is dominant. As the Schottky diode capacitance charges, the direct current flowing through the diode increases until it reaches the steady-state value. The higher the photocurrent, the faster the charge of the capacitance and therefore the time response. The response to a short pulse is dominated by the charge of the Schottky diode capacitance, induced by the photocurrent generated at the well-substrate junction. The pulse shape is therefore determined by the shape of the photocurrent generated at this junction. The first very fast 47

64 CHAPTER 3. CMOS COMPATIBLE MSM DEVICES part of the response (a few nanoseconds) can be attributed to the carriers generated in the depletion region. After that there is a slower increase of the current (tens of nanoseconds) due to carrier diffusion. This analysis shows that there are three time constants determining the time response of the device: the drift time, the diffusion time, and the time required to take the forward biased diode into conduction. The Schottky barrier height affects the current rise time in response to a light step. In Fig 3.5 the dependence of the rise time on the Schottky barrier height is shown. With a higher barrier height, a higher voltage drop across the forward biased Schottky junction is needed to let the same electron current flow. Therefore, an increased charge has to be stored in the diode capacitance, requiring more time to reach the equilibrium condition. As can be seen in Figure 3.5, the rise time is higher for the SOI PD than for the CMOS PD. This is due to the higher photo-generated current in the CMOS PD, that leads to a faster charge of the diode capacitance. 3.2 Model description Basing on the above described device behavior, a macromodel of the two MSM PDs has been realized and implemented in CADENCE circuit simulator. The schematic diagrams for the two models are sketched in Figure 3.6 (a) and (b). In these models each Schottky diode can be described independently, because there are no interactions between the two junctions, being the MSM operated below the punch-through condition. Each electrode is represented by an ideal diode in parallel with its capacitance and a current generator. The current generator is needed to simulate the hole current at the contacts, while the electron current is the current flowing through the Schottky diode and is given by the diode I-V equation. In the SOI PD model the hole currents Ip1 and Ip2 are forced by the genera- 48

65 3.2. MODEL DESCRIPTION Current [na] light on light off Time [ s] total electron hole displacement light on light off Time [ns] Figure 3.4: Transient response to a step of light of the CMOS MSM with a Schottky barrier of 0.6 V. Contact S1 and S2 are biased respectively at 1 V and 2 V. In the figure the components of the current at electrode S2 are shown. The optical power is 0.1 µw and the wavelength is 860 nm Rise time [ s] CMOS SOI Schottky barrier [V] Figure 3.5: Dependence of the current rise time on Schottky barrier height. The optical power is 0.1 µw and the wavelength is 860 nm 49

66 CHAPTER 3. CMOS COMPATIBLE MSM DEVICES Figure 3.6: Schematic model of the SOI MSM (a) and the CMOS MSM (b) tors, and are proportional to the optical power through the responsivities R 1 and R 2, whose values have been calculated from the results of the DC electro-optical simulations. The diode capacitances have been calculated from the simulation results and have been modeled according to normal, voltage-dependent relation C S = ( A SC S0 1 + V ) α (3.7) RS V BI where C S0 is the capacitance per unit area without applied voltage, A S is the area of the Schottky contact, V RS is the reverse bias voltage of the diode, V BI is built-in voltage of the Schottky junction and α is an exponent 50

67 3.3. RESULTS AND DISCUSSION ranging between 1/3 and 1/2. The model for the CMOS MSM device (Figure 3.6 (b)) is the same as the model of the SOI MSM device, with the addition of a block representing the well-substrate diode. The structure of this diode is the same as the structure of the two Schottky diodes. All the parameters of the model, which include the diode parameters, the capacitances and the constants R 1, R 2 and R sub, have been calculated from the numerical device simulation results. The model is very flexible: the electrical and optical parameters relevant to devices made from different technologies could be easily included. 3.3 Results and discussion Model validation In this part we report the results of circuit simulations employing the proposed macromodel and compare them with output of numerical device simulations. Having in mind the MSM photodetector operation within a pixel, three types of device operation have been taken into account: DC analysis, i.e., the current-voltage curves as the control voltage at one electrode is linearly swept in a quasi-static mode; transient analysis involving a light pulse at constant bias voltage; transient analysis involving a bias voltage switching at constant illumination conditions. Results from the circuit simulations and numerical device simulations have shown a very good agreement in all the considered situations both for the SOI and the CMOS n-well MSM devices. As an example, Figure 3.7 shows the transient behavior of the SOI (Figure 3.7 (a)) and CMOS (Figure 3.7 (b)) devices in response to a light step and to a switch of the 51

68 CHAPTER 3. CMOS COMPATIBLE MSM DEVICES a) b) Current [na] V S2 [V] Current [na] V S2 [V] light on light on Device simulation Model Device simulation Model Time [ s] Figure 3.7: Transient behavior of the SOI (a) and CMOS (b) PDs. In both devices a step of light (λ = 860 nm, P opt = 0.1 µw) has been applied after a short time. In the CMOS device the substrate has been grounded and contact S1 has been biased at 2 V, while in the SOI device the voltage of contact S1 has been set at 0 V. In both devices the voltage of electrode S2 (V S2 ) has been switched as shown in the graph. The currents at electrodes S1 and S2 are marked respectively with black and white squares 52

69 3.3. RESULTS AND DISCUSSION voltages between the Schottky electrodes. At the beginning the devices are in the dark, then a light pulse is applied. After current stabilization, the voltage of one electrode is switched 1 V above and below the voltage of the other electrode. The model reproduces very well both the response to the light pulse and the switching behavior. Moreover, from the initial and final (regime) current values, also the DC accuracy can be appreciated. In correspondence of the switching for the two devices there are current peaks, which arise from the charge and discharge of the capacitances. As can be seen, the recovery after the current peaks is faster in the SOI than in the CMOS device. This is due to the fact that in the SOI device the capacitances exchange the same amount of charge, leading to a very fast switching response. On the contrary, in the CMOS device, an extra-charge is needed to charge and discharge the well-substrate diode capacitance, leading to a slower switching response. If the voltages were switched in a symmetric way, the switching response would be similar to that of the SOI device, because the charge on the substrate-well diode capacitance would not change Frequency response The frequency-dependent modulated output current has been simulated using the proposed model. Figure 3.8 reports the simulated AC responsivity of the CMOS device. The ratio between AC and DC responsivity of the forward biased Schottky contact is reported at three different values of the DC illumination power P 0 at the wavelength λ = 860 nm. As can be seen in figure 3.8, there are three poles in the AC responsivity spectrum. The first pole (f T 1 ) is due to the product of the forward biased diode small-signal resistance r and the total capacitance seen from the well node. The second pole (f T 2 ) is due to the diffusive component of the photogenerated carriers and lies around 8 MHz. The third pole (f T 3 ) arises from the drift time in 53

70 CHAPTER 3. CMOS COMPATIBLE MSM DEVICES 1 f T1 R/R P 0 = 10 nw P 0 = 1 W P 0 = 100 W f T2 f T3 1k 10k 100k 1M 10M 100M 1G Frequency [Hz] Figure 3.8: Ratio between AC (R) and DC (R 0 ) responsivity as a function of frequency at three different DC illumination levels the diode depletion region and lies beyond 100 MHz. While the poles f T 2 and f T 3 are weakly dependent on the bias in the operating voltage ranges, the frequency of f T 1 varies linearly with the DC light power, because the small signal resistance of the forward biased diode is directly proportional to the DC photogenerated current. Thus, in order to have an effective current mixing, this pole must be beyond the mixing frequency. The SOI device presents similar characteristics (not shown), with the difference that in f T 1 the contribution of the well capacitance is missing Time-of-flight simulation A simulation of the device used as a balanced electro-optical mixer was performed. A small sine-wave modulation voltage (10 mv) was applied to the contacts, in order to operate in the linear region. A sine-wave modulated optical signal of 1 nw was sent to the sensor. Both voltage and 54

71 3.4. EXPERIMENTAL RESULTS Integrated charge [pc] Simulation Cosine fit Delay time [ns] Figure 3.9: Simulated correlation function employing the CMOS device as a balanced mixer. Modulation frequency was 20 MHz light modulation frequency was 20 MHz. An optical DC power of 50 µw was applied to the sensor, in order to achieve a sufficiently high bandwidth. The output currents were subtracted, low-pass filtered in order to isolate the DC component, and finally integrated for 100 µs. The output as a function of the time delay between the modulated light and modulation voltage is reported in Figure 3.9. As expected, the output is proportional to the cosine of the phase difference between voltage and light modulation signals. 3.4 Experimental results In order to experimentally verify simulation results, a series of test structures has been fabricated in a 0.35 µm CMOS technology. Since Schottky diodes are not provided in this technology, they have been designed as simple contacts omitting the implantation region. This constitutes a layout 55

72 CHAPTER 3. CMOS COMPATIBLE MSM DEVICES Current [na] Incident light power [a.u.]: S2 Voltage [V] Figure 3.10: Measured I-V curves under different illumination conditions. On the right: zoom on the linear region rule violation. A series of MSM test devices with variable finger width W and interfinger distance S have been designed. In all the structures, the n-well area is µm 2. Some test Schottky diodes have been included in the chip to assess the quality of Schottky contacts in this technology. Dark current measurements have been carried out on the MSM test devices. During the measurements the substrate was grounded, electrode S1 voltage was kept at 1.65 V (half of the 3.3 V maximum voltage to be used in this technology), and electrode S2 voltage was swept from 0 V to 3.3 V. In all cases the dark current was lower than 0.5 pa. Current-Voltage (I-V) curves under illumination have been measured on the test devices. The bias conditions were the same used in the dark current measurements and the devices were illuminated with an infrared LED (860 nm) at different power intensities. A set of I-V curves for one of the devices is shown in figure It can be seen that there is a good 56

73 3.4. EXPERIMENTAL RESULTS 1E-4 1E-5 Anode Cathode 1E-6 Current [A] 1E-7 1E-8 1E-9 1E-10 1E Voltage [V] Figure 3.11: I-V curves measured on a test Schottky diode agreement with the simulated I-V curves described in the previous sections. Current-Voltage curves have been measured on the test Schottky diodes. The measured reverse current was much lower than predicted by equation 3.1 with barrier heights in the range ev. In direct bias, the current flowing at the anode was higher than that flowing at the cathode, as shown in Figure The current gain, although very low, indicates the presence of transistor action, which should not occur in a Schottky diode. These observations suggest the presence of a p-n junction instead of a Schottky contact. The p-region could be due to the threshold-adjustment boron implantation, that creates a very shallow p layer in the active regions. To overcome this problem, different approaches can be tried. The first one requires a direct access to the technology in order to eliminate the threshold adjustment implantation in the area where MSM devices are present. As an alternative, a custom technology providing Schottky con- 57

74 CHAPTER 3. CMOS COMPATIBLE MSM DEVICES tacts can be employed to monolithically integrate detectors and electronics. A third, but more expensive solution is the fabrication of a MSM photodetector array in a custom technology and an array of readout channels in a standard technology. The two chips can then be joined using the bump bonding technique. 58

75 Chapter 4 CMOS Electro-Optical Mixer based on closely spaced junctions In this chapter, a fully CMOS compatible Electro-Optical Mixer (EOM) based on closely spaced junction is presented. This device can be used as an inherently mixing detector in balanced mixer configuration. Firstly, an analysis of the device by means of numerical device simulations is shown. The architecture of pixel containing an EOM and a differential readout channel is then presented. A chip containing EOM test devices and an image sensor based on a 128-pixel linear array has been designed and fabricated in a 0.35 µm CMOS technology. Finally, the experimental characterization of the EOM test devices is reported. 4.1 Electro Optical Mixer design The schematic cross section of the proposed EOM, consisting of two interdigitated n-well diffusions on a CMOS p-substrate, is shown in Figure 4.1. In submicron technologies a p-well is also often present outside n-well regions. The operation principle is based on the modulation of the optical responsivity of the two interdigitated n-well/p photodiodes, achieved by modu- 59

76 CHAPTER 4. CMOS EOM BASED ON CLOSELY SPACED JUNCTIONS light V 1 V 2 n+ n-well p-well D W p-sub section Figure 4.1: Schematic cross section of the sensor lating the respective space charge regions. In this way, the photogenerated charge is mixed between the two electrodes. The sensor static and dynamic performances have been analyzed by means of the simulation environment ISE-TCAD [74]. A CMOS 0.35 µm CMOS technology has been chosen, because it is sufficiently advanced to allow the integration of a complex in-pixel readout channel. The exact doping profiles were not known, but at least part of the profiles could be extracted from Capacitance-Voltage curves of p + /n-well and n + /p-well diodes previously fabricated in the same technology. The remaining profiles have been chosen arbitrarily in accordance with the other known technology parameters (junction depths and sheet resistances). The simulation domain has been defined as the section in Figure 4.1. Figure 4.2 shows the simulated hole density inside the semiconductor, when the two electrodes are biased at different voltages. In the figure, where V 1 = 2 V, V 2 = 1 V and the substrate is grounded, it is visible that 60

77 4.1. ELECTRO OPTICAL MIXER DESIGN Figure 4.2: Simulated hole density Figure 4.3: Simulated electron current density under illumination 61

78 CHAPTER 4. CMOS EOM BASED ON CLOSELY SPACED JUNCTIONS Current [pa] I 2 I V 1 - V 2 [V] Figure 4.4: Simulated I-V curves the depletion region of junction 1 extends more deeply into the substrate than that of junction 2. Figure 4.3 shows the simulated electron current density under illumination (λ = 860 nm). The bias voltages are the same applied in Figure 4.2. It can be seen that a higher current density flows through junction 1. For the symmetry of the device, the situation is reversed if the voltages are exchanged. The I-V characteristics of the device under illumination are shown in Figure 4.4, where the voltage difference V = V 1 V 2 of the two EOM contacts is swept between -1 V and 1 V, maintaining a constant common mode voltage of 1.5 V. As can be seen, there is a linear dependence of the electrode currents on the voltage difference V. In order to evaluate the efficiency of the charge separation process, which represents a fundamental parameter for the distance measurement, the demodulation contrast χ has been defined as the ratio between the difference and the sum of the currents (I 1, I 2 ) at the two EOM electrodes: 62

79 4.1. ELECTRO OPTICAL MIXER DESIGN χ = I 1 I 2 I 1 + I 2 (4.1) The demodulation contrast χ is linearly proportional to the voltage difference V : χ = α V (4.2) where α represents the normalized demodulation contrast at V = 1 V. Moreover, the parameter χ depends on the distance D between the n- well fingers, on the well width W and on the incident light wavelength. Increasing the inter-finger distance D, χ is found to decrease as expected. To have a high contrast, n-well diffusions must be as close as possible, with the limitation given by punch through between the fingers. χ increases also decreasing the finger width W, whose minimum value is set by the technology. Varying the impinging light wavelength in the range nm, simulations show a slight increment of χ at increasing wavelengths. The frequency dependence of χ has been calculated by means of AC optical simulations. The AC currents i 1 and i 2 flowing at the electrodes as a function of an AC optical signal were calculated by the simulator. Electrodes 1 and 2 were biased at 2V and 1V, respectively. The frequencydependent demodulation contrast was then calculated from the relation: χ = i 1 i 2 i 1LF + i 2LF (4.3) where i 1LF and i 2LF are the AC currents flowing at the electrodes at low frequency. The simulated frequency-dependent demodulation contrast is shown in Figures 4.5 and 4.6 for incident light wavelengths of 680 nm and 860 nm and at different values of inter-finger distance D. It can be seen that, at the frequencies of interest in TOF applications (tens of MHz), the simulation contrast with λ = 680nm is close to the DC contrast, while if 63

80 CHAPTER 4. CMOS EOM BASED ON CLOSELY SPACED JUNCTIONS λ = 860nm χ is less than half the DC value. This behavior is due to different light absorption depths in silicon at different wavelengths. While at 680 nm most of the carriers are generated within 3 µm from the silicon surface, and are therefore quickly collected and mixed, at 860 nm the absorption length is about 20 µm and carrier diffusion is not fast enough to follow light modulation frequency. In order to perform simulations of the device together with a read-out channel, a simple electrical model of the EOM has been developed. Each junction has been modelled by the parallel of a diode, having a capacitance C D, and a current source representing the photo-generated current. In the device equivalent circuit, the current generated by the two current sources depend on the demodulation contrast χ according to the equations: I 1 = R 0 (λ)(1 + χ)p opt (4.4) I 2 = R 0 (λ)(1 χ)p opt (4.5) where P opt is the incident optical power, and R 0 is the responsivity when the device electrodes are at the same potential. Circuit simulations based on the model have been found to yield results in very good agreement with numerical device simulation predictions. 4.2 Measuring technique In I-TOF technique, a sinusoidally modulated light source is used to completely illuminate the object of interest placed at distance d. Assuming for simplicity the modulation phase delay θ = 0, the source output can be expressed by the relation: P T X = P T X0 + P MT cos(ω 0 t), (4.6) 64

81 4.2. MEASURING TECHNIQUE Demodulation contrast D = 1 m D = 2 m D = 3 m = 680 nm Frequency [Hz] Figure 4.5: Simulated AC demodulation contrast at λ = 680 nm Demodulation contrast D = 1 m D = 2 m D = 3 m = 860 nm Frequency [Hz] Figure 4.6: Simulated AC demodulation contrast at λ = 860 nm 65

82 CHAPTER 4. CMOS EOM BASED ON CLOSELY SPACED JUNCTIONS Figure 4.7: Block diagram of the pixel where f 0 = ω 0 /2π represents the modulation frequency, P T X0 the DC component, and P MT the modulation amplitude. Part of the radiation, diffused by the target, is collected by a proper optics, and arrives onto the EOM with a phase delay φ, as expressed by the relation: P RX = P RX0 + P MR cos(ω 0 t + φ) + P BK, (4.7) where P RX0 is the backscattered DC component, P MR the back-scattered modulation amplitude, and P BK the background illumination. Thus distance to target can be calculated from a phase measurement by means of the relation: d = cφ (4.8) 4πf 0 where d is the object distance, c is the light speed, φ is the phase difference and f 0 is the modulation frequency of the light power. Figure 4.7 shows the block diagram of the proposed pixel. The EOM, 66

83 4.2. MEASURING TECHNIQUE hit by light, generates two photocurrents as a result of the mixing process between the received light signal and the applied modulation voltages. These currents are low-pass filtered to isolate the distance information from the modulation frequency components, and then time-integrated to transform a weak current signal into a detectable voltage signal. Phase measurement is thus achieved by properly processing the signals at the device terminals. The EOM electrodes are modulated at the same frequency as the light source according to the relation: V = V 1 V 2 = V M cos(ω 0 t). (4.9) Considering equations 4.2, 4.4, 4.5 and 4.9 the EOM currents can be written as: I 1 = R 0 (λ)p RX [1 + αv M cos(ω 0 t)] (4.10) I 2 = R 0 (λ)p RX [1 αv M cos(ω 0 t)] (4.11) Replacing the terms in equations 4.10 and 4.11, and removing the components at frequencies ω 0 and 2ω 0, which are low-pass filtered, we obtain: I 1LP = R 0 (λ)(p RX0 + P BK ) + α 2 R 0(λ)P MR V M cos(φ) (4.12) I 2LP = R 0 (λ)(p RX0 + P BK ) α 2 R 0(λ)P MR V M cos(φ) (4.13) Integrating for a time T INT and subtracting the two terms of equations 4.12 and 4.13 we obtain: TINT 0 (I 1LP I 2LP )dt = αr 0 (λ)p MR V M T INT cos(φ) (4.14) Repeating the above operations setting the modulation phase φ = 90, it results: 67

84 CHAPTER 4. CMOS EOM BASED ON CLOSELY SPACED JUNCTIONS Figure 4.8: Schematic circuit of the pixel with the model of the EOM TINT 0 (I 1LP I 2LP )dt = αr 0 (λ)p MR V M T INT sin(φ) (4.15) The phase φ is thus recovered without ambiguity combining relations 4.14 and Readout circuit Figure 4.8 shows the schematic of the pixel read-out circuit. The EOM included in the pixels has W = 1.7 µm, D = 2.3 µm, and an area of 25 µm 25 µm. With these values each electrode has an associated overall capacitance C D of about 100 ff. The two EOM electrodes are connected to two modulation capacitances C MOD. In this way only the AC component 68

85 4.3. READOUT CIRCUIT of V M1,2 is applied to the EOM terminals through capacitances C MOD so that: V EOM1,2 = C MOD C MOD + C D V M1,2 (4.16) The adopted low-pass filter is a first-order RC circuit with a f 3dB frequency of 500 KHz. The resistor R F is made of high-resistivity poly-si, while the capacitor C F is realized with an NMOS device. In this way the filter dimensions are small enough to be integrated within the pixel. The current integrator is realized by means of a low power operational amplifier OTA and a feedback network composed of a capacitance in parallel with a pass-transistor. The value of the feedback capacitance, C INT, determines the gain factor of the charge amplifier. Note that the capacitance value should not be too small in order to avoid a high gain variability of the stage between the different pixels of the array, caused by process parameters fluctuations. In our design a 120 ff value has been chosen for this capacitance, which allows keeping the kt/c noise low. The core of the current integrator is a standard cascode OTA amplifier designed to achieve high gain and low noise while keeping the power consumption and the area occupation low [76]. The main characteristics of the OTA are reported in Table 4.1. The pixel behavior can be explained with the aid of the simulation Parameter Value Open loop gain > 93 db GBWP 1 MHz Phase margin (C LOAD = 100 ff) > 60 Systematic input offset 6 mv Power consumption 4.95 µw Table 4.1: Main characteristics of the designed OTA 69

86 CHAPTER 4. CMOS EOM BASED ON CLOSELY SPACED JUNCTIONS Figure 4.9: Simulation of pixel behavior result shown in Figure 4.9. It is worth noting that the two current sources present in the EOM schematic model of Figure 4.8 are indeed including the photocurrent modulation resulting from both the voltages V M1, V M2 and the back-scattered modulated light P RX. The measurement starts by resetting the integration capacitances C INT. In this phase the two feedback pass-transistors are switched on, for about 10 µs, through the phase V RES. Closing the feed-back loop makes the OTA work as a voltage-follower, thus forcing the DC level of the EOM at V REF. After that, the integration phase starts setting V RES low. The simulation shown in Figure 4.9 has been performed setting the modulation frequency f 0 at 20 MHz, the modulation amplitude of voltages V 1 and V 2 at 1 V peak-to-peak, and supposing the back-scattered optical 70

87 4.3. READOUT CIRCUIT 100 simulated phase [degree] real phase [degree] Figure 4.10: Simulated performance of the system signal to have the same frequency f 0 and a total phase delay φ of 60 with respect to V 1 signal. The modulated currents are low-pass filtered at 500 KHz and then integrated on the capacitances C INT for an integration time T INT of 346 µs. The two integrator output voltages V OUT 1 and V OUT 2 increase with a different slope depending on the DC current they are measuring. The difference between the two output voltages (performed off-chip) removes the back-ground light contribution thus preserving the phase delay information, according to equations 4.14 and The above measure is repeated after setting the modulation phase delay φ = 90. In this way, in the considered example, the total phase delay becomes 150 ( ). Combining the two measurements we can recover the phase delay related to the time of flight. In Figure 4.10, the results of simulations carried out at different φ values (0, 30, 60, 90 ) are reported, demonstrating the good accuracy achievable with this system. The systematic measurement error of about of 2 71

88 CHAPTER 4. CMOS EOM BASED ON CLOSELY SPACED JUNCTIONS 250 m 25 m Figure 4.11: Half pixel layout visible in Figure 4.10 is due to a voltage offset at the OTA inputs, but could be easily compensated off-chip. Care has been taken in designing the pixel layout in order to minimize mismatch effects, especially for the capacitors. The layout has a symmetric structure (only one half is shown in Figure 4.11). All the pixels but the EOM have been covered with a grounded metal layer working as a lightshield. A theoretical noise analysis has been performed to estimate the phase error: the resulting value, calculated at a 40 fps frame rate, a modulation frequency of 20 MHz, a demodulation contrast of 10 % and an optical power density of 10 nw/cm 2 over the EOM (without the ambient light contribution), is lower than 3. The pixel size, 500 µm 25 µm, and the power consumption, lower than 10 µw, make this approach suitable for linear array structures and low power applications. Although TOF imaging requires a sensor organized in a matrix configuration, a linear array of 128 elements has been deemed appropriate to validate the design approach and the system performance with low fabrication costs. 4.4 Experimental results A chip containing two linear pixel arrays and some test devices has been designed and fabricated in 0.35 µm 3.3 V CMOS technology in order to 72

89 4.4. EXPERIMENTAL RESULTS Figure 4.12: Micrograph of the chip validate the operation principle. A micrograph of the chip is shown in Figure The test devices include standard photodiodes and EOM devices having a µm active area, a finger width W = 1.7 µm and inter-finger distance D ranging from 1 µm to 3 µm with 0.5 µm steps. The longer array (128 pixels) is based on EOMs having D = 2.3 µm, while the smaller one is divided in groups of pixels containing EOMs with different inter-finger distances. Current-Voltage curves have been measured on the series of test EOMs under illumination. In the structure with inter-finger spacing D = 1 µm, a high current was measured at the electrodes, indicating the occurrence of punch through. The I-V characteristics of one of the devices (D = 1.5 µm) under illumination (λ = 860 nm) are shown in Figure 4.13, and exhibit an excellent linearity as predicted by device simulations. The measured demodulation contrast χ as a function of the inter-finger spacing D is shown in Figure The devices have been illuminated with an 860-nm light and χ has been calculated at a voltage difference V = 1 V applied between the electrodes. It can be seen that the measured χ is 73

90 CHAPTER 4. CMOS EOM BASED ON CLOSELY SPACED JUNCTIONS I1 Currents [pa] I V 1 -V 2 [V] Figure 4.13: Measured I-V curves of one of the test devices (D = 1.5 µm) illuminated with a 860-nm light 15 Demodulation contrast, [%] Measured Simulated 1,5 2,0 2,5 3,0 Interfinger distance, D [ m] Figure 4.14: Measured and simulated demodulation contrast as a function of inter-finger distance D, with V = 1 V and λ = 860 nm 74

91 4.4. EXPERIMENTAL RESULTS 0.15 D = 1.5 m Responsivity [A/W] V 2 =2V V 1 =1V Wavelength [nm] Figure 4.15: Measured responsivity at the two electrodes smaller than the simulated one, the observed difference being ascribed to the incomplete knowledge of the technological parameters for the adopted CMOS process. Spectral responsivity measurements have been performed on some test structures biasing the electrodes at two different voltages. The curves measured on the device with D = 1.5 µm are shown in Figure From the responsivity curves, χ has been calculated as a function of wavelength. Its value for two devices with different inter-finger spacing is shown in Figure It can be seen that χ increases with the wavelength for D = 2.5 µm, while it remains almost constant for D = 1.5 µm. This is consistent with device simulation results. 75

92 CHAPTER 4. CMOS EOM BASED ON CLOSELY SPACED JUNCTIONS 12 Demodulation contrast, [%] D=1.5 m D=2.5 m Wavelength, [nm] Figure 4.16: Measured demodulation contrast as a function of wavelength 4.5 Concluding remarks The observed mixing efficiency of the proposed detector, particularly in the structure with D = 1.5 µm, together with the excellent linearity of the device, are encouraging in view of the application. It should be stressed, however, that dynamic demodulation contrast measurements, not yet carried out, would be necessary to estimate the dynamic behavior of the device, which is fundamental to understand system performance. A dynamic characterization of the device is under way, together with the experimental study of the pixel array. 76

93 Chapter 5 CMOS Single Photon Avalanche Diode 3D imager In this chapter, an integrated image sensor based on Single Photon Avalanche Diodes as light detectors is presented. Firstly, the implementation of direct and indirect time-of-flight techniques and the intrinsic noise limitations are explored. Then, the design of a series of devices to investigate the feasibility of SPADs in 0.8 µm and 0.35 µm CMOS technologies is reported. The architecture of a pixel containing a SPAD and an integrated read-out channel is presented. A 64-pixel image sensor has been fabricated in a 0.8 µm CMOS technology to test the performance of the pixel. At the end, a characterization of test devices and of the image sensor is reported. 5.1 Measuring techniques SPADs are single-photon sensitive devices, and can be employed in a Direct TOF system to sense backscattered light pulses and generate a trigger signal stopping a time counting circuit, as done in [30, 31]. An alternative approach here proposed is to employ the SPAD in an Indirect TOF configuration. This technique is analog to the one used in [32, 33], with the difference that photon counting is performed instead 77

94 CHAPTER 5. CMOS SINGLE PHOTON AVALANCHE DIODE 3D IMAGER of electron integration Direct Time Of Flight In a D-TOF system, the SPAD output is used as a trigger to stop a timemeasuring circuit, which can be either a Time to Amplitude Converter (TAC) [77] or a Time to Digital Converter (TDC) [78]. The sources of noise in this measurement are the statistics of photon arrival, SPAD s dark counts, background light sources, electronic jitter and laser pulse shape. In the following discussion, I will consider only the contribution of photon arrival statistics and laser pulse shape, that are the dominant ones for our chip, as will be demonstrated experimentally. The number of photons incident on a photodetector during a time T follows Poisson statistics as long as T is much longer than the coherence time τ c of the light source [79]. If a poissonian light with a constant power P L impinges on the active area of a SPAD, the detection of a photon after a time t from an arbitrary starting time t 0 has an exponential probability distribution [80]. The probability density function (PDF) is given by: f(t) = C exp [ Ct] (5.1) where the parameter C represents the average count rate due to incident photon flux. C is linked to incident optical power P L through the relation: C = η P L E ph (5.2) where η is the SPAD quantum efficiency and E ph is the photon energy. Let s now consider the case of a time-varying optical power P L (t). If the time dependence of P L (t) can be described by a time constant τ much greater than the coherence time τ c, then the light can still be considered 78

95 5.1. MEASURING TECHNIQUES poissonian. In this case, the parameter C is a function of time and equation 5.1 must be replaced by [ ] t f(t) = C(t) exp 0 C(t )dt (5.3) where equation 5.2 still holds, letting C and P L be functions of time. Let s assume that a laser pulse extinguishing in a time T P impinges on the active area of the device. Two limiting cases can be distinguished, basing on the value of the integral F (T P ) = TP 0 [ ] TP f(t) = 1 exp C(t )dt. (5.4) 0 The first case is F (T P ) 1. In this case, for most of the pulses no photons are detected. F (T P ) represents the probability that a photon is detected at the arrival of a single pulse. For a system working in this condition, a measurement is valid only in the cycles in which a photon is detected, while the other measurements must be discarded. The density function f(t) is approximately equal to C(t), and the time resolution is linked to the width of the optical pulse, to F (T P ) and to the number of measurements N. If σ tl is the laser pulse width, time resolution is given by equation σ t = σ tl N F (TP ) (5.5) N F (T P ) is the average number of photons detected during N laser pulses. The second limiting case is when F (T P ) 1. In this case the photon is detected every laser pulse and the time resolution of the measurement is given by the standard deviation σ t of f(t). In the case of a rectangular pulse with peak optical power P L and duration T P, time resolution is given by: 79

96 CHAPTER 5. CMOS SINGLE PHOTON AVALANCHE DIODE 3D IMAGER Emitted light pulse t T P Received light pulse t SH C 1 Gate 1 C 2 Gate 2 Time Figure 5.1: Principle of I-TOF technique using gated SPADs σ t = 1 C = E ph η P L (5.6) The mean of f(t) is also equal to 1/C and determines an offset in the measurement of the optical pulse arrival time. This offset, which depends on the incident optical power, causes a systematic error that must be removed or at least minimized to perform an accurate measurement. While time resolution can be improved by averaging over a large number of measurements, the offset is more difficult to remove. However, it can be minimized using high optical powers and SPADs with a high quantum efficiency or very short laser pulses Indirect Time Of Flight The possibility of using photon counting in an Indirect Time Of Flight system has not yet been explored. Hereafter, the noise limitations of the technique are analyzed. 80

97 5.1. MEASURING TECHNIQUES The basic principle of this technique is shown in figure 5.1. The number of photons detected with two different time gates over a number N of cycles is measured. In the first measurement the gate signal is shifted by an amount t SH with respect to the emitted light pulse. The number of photons C 1 detected when the gate is active is given by: C 1 = N C ( t + T P t SH ) (5.7) where t is the time of flight, T P is the pulse width and C is linked to the optical power P L incident on the detector by equation 5.2. The number of photons C 2 detected during N cycles with the second gate window is expressed by: C 2 = N C T P. (5.8) Combining equations 5.7 and 5.8, t can be expressed by equation ( C1 ) t = 1 T P + t SH. (5.9) C 2 The time resolution σ t of the measurement is related to the standard deviations σ C1 and σ C2 of C 1 and C 2. Since C follows a Poisson statistics, σ C2 is expressed by σ C2 = N C T P. (5.10) Let s define a parameter α so that C 1 = α C 2, with 0 α 1. From equations 5.7 and 5.8 it can be seen that α is a linear function of t. σ C1 can be expressed by the equation σ C1 = α N C T P. (5.11) Applying error propagation to equation 5.9, the time resolution of the measurement is given by: 81

98 CHAPTER 5. CMOS SINGLE PHOTON AVALANCHE DIODE 3D IMAGER σ t = T P α (1 + α) N C 2 (5.12) σ t reaches its maximum value for α = 1, which corresponds to the case t = t SH. Time resolution can be expressed as a function of incident optical power P L by substituting equation 5.8 into equation 5.12: σ t = α (1 + α) E ph T P N P L η. (5.13) In this case the time resolution of the system is inversely proportional to PL, while in the D-TOF approach (equation 5.6), σ t is inversely proportional to P L. This method, if compared to D-TOF, doesn t suffer from illumination-dependent systematic errors, and is thus more accurate. 5.2 Device design Different groups have demonstrated CMOS avalanche photodiodes having the structure shown in Figure 2.9. The processes used were a 2 µm BiCMOS [81] and a 0.8 µm High-Voltage CMOS [58, 59], in which a ptub inside ntub is available for the fabrication of the guard ring. An alternative approach using a standard twin-well 0.8 µm CMOS process is possible [63]. The guard-ring is formed by the p-well, which is isolated from the substrate by the merging of the central n-well region with a peripheral n-well ring, as illustrated in Figure 5.2. A chip containing test avalanche photodiodes and a linear SPAD-based image sensor has been designed. The choice of the fabrication technology has been determined mainly by two factors. Firstly, the performance of the SPADs should be reasonably good. Secondly, the readout electronics should be compact enough to be included in a pixel. A good compromise between the two requirements was found using a high-voltage 0.8 µm 82

99 5.2. DEVICE DESIGN light p-well n+ n-well p+ p-sub n-well merging p-well guard ring Figure 5.2: Cross section of the SPAD in standard CMOS technology 2P/2M CMOS technology. A series of avalanche photodiodes has been designed in this technology for testing purposes. They have a circular active area with 100 µm diameter. Since in the process chosen three different ntub diffusions (ntub, deepntab, shallow-ntub) are available, different device structures have been included in the chip: a structure with an active p + /deep-ntub area with a ptub guard ring (device A); a structure with an active p + /shallow-ntub area with a ptub guard ring (device B); a series of structures having an active p + /ntub area with the guard ring formed by merging the central ntub with a peripheral ntub ring. Five structures with different distance D between the central and peripheral ntubs were included. The values of D range from 0.4 µm to 0.8 µm with 0.1-µm steps (devices C1-5). The availability of SPADs in a more advanced CMOS technology would 83

100 CHAPTER 5. CMOS SINGLE PHOTON AVALANCHE DIODE 3D IMAGER V V spaddd quench R Voltage Comparator Time-to-Amplitude Converter Averaging Circuit OutLow OutHigh SPAD Figure 5.3: Block diagram of the proposed pixel allow the fabrication of a more compact readout circuit. To test this possibility, some test structures have been included in the chip described in chapter 4, fabricated in a 0.35 µm standard CMOS technology. Since a ptub inside ntub is not available in this technology, the ntub merging approach has been employed. Six structures with different distance D between the central ntub and the peripheral ntub ring were included (devices D1-6). The values of D range from 0 µm to 1 µm with 0.2-µ steps. The active area diameter of these structures is 100 µm. Four SPADs with a 5-µm active area, a 250-kΩ quenching resistor, a comparator and an output buffer have also been included (devices E1-4). In these structures, the inter-well distance D ranges from 0.2 µm to 0.8 µm. 5.3 Image sensor design Pixel design The block diagram of the proposed pixel is sketched in Figure 5.3. It consists of a SPAD, a quenching resistor R quench to limit the avalanche current, a voltage comparator for the avalanche event detection and a timeto-amplitude converter which measures the arrival time of the received 84

101 5.3. IMAGE SENSOR DESIGN Figure 5.4: Circuit schematic of the proposed pixel light pulse. To reduce the influence of jitter noise and limit the effect of thermally-generated spurious events, the measurement is repeated many times and the arrival-time information is averaged by means of two circuits dedicated to the count of low and high numbers of events, respectively. By so doing the time resolution of the system is increased by a factor N 1/2, where N is the number of pulses spread on the scene, but the overall measurement time is kept low because the read-out of the pixel array is not performed at every measurement cycle. This solution becomes of paramount importance as the number of pixels increases. The schematic diagram implementing the above mentioned functions is 85

102 CHAPTER 5. CMOS SINGLE PHOTON AVALANCHE DIODE 3D IMAGER shown in Figure 5.4. To avoid the use of high-voltage transistors, expensive in terms of area occupation, the cathode of the SPAD is connected through the quenching resistor to V spad+ (set close to V dd ), and the biasing above the breakdown voltage V B 27 V of the SPAD is assured by means of the external line V spad biased at a very negative voltage (about -25 V). The main drawback of this approach is that the maximum excess voltage (V e = V spad+ V spad V B ) available is below V dd Time-measuring pixel operation The operation principle of the pixel is described in the following. During the non-acquisition mode, unwanted avalanche events are avoided by keeping the SPAD below its breakdown bias voltage through transistor M n2 (SpadOFF = High). Then the measurement starts biasing the SPAD in the breakdown region (SpadOff = Low); to improve the settling time (the cathode would be slowly charged up to V spad+ through R quench only), transistor M p2 is switched on for a few nanoseconds. The voltage V spad+ can be externally adjusted to assure an optimal match with the threshold voltage of the comparator. When a light pulse is detected the avalanche current discharges the total parasitic capacitance at node IN causing a voltage drop across R quench as large as V E, sufficient to cause the commutation of the inverter amplifier M p3 -M n3 ; at this point the SPAD bias voltage is not high enough to sustain the avalanche and node IN is slowly recharged. An unbalanced driving capability of M p3 with respect to M n3 is obtained biasing M n3 with a small current (100 na). This allows for a fast first avalanche event detection while rejecting possible after-pulses. To rapidly restore the comparator state, transistor M n4, driven by the Res phase, has been added in parallel to M n3. The comparator output (Sample) is fed to the time-to-amplitude converter, where the conversion is realized by means of the cascode current 86

103 5.3. IMAGE SENSOR DESIGN mirror M n5 -M n8 -M n9 and the capacitance C Sample. At the beginning of the acquisition phase, the time counter is kept off by setting Res = High, so that the current I biast C flows through transistor M n6 and is not mirrored to C sample, which has been initially pre-charged through M n5 (EvalTC = Low). Then the detection phase starts setting Res = Low and EvalTC = High, and the current I biast C is mirrored to discharge C Sample. When a photon is detected the comparator output steps to V dd switching the mirror off and isolating C Sample. The bias current I biast C and the value of capacitance C Sample have been dimensioned so that the resulting voltage ramp exhibits a slope of about 100 mv/ns, which allows a time interval of 40 ns to be mapped on a 4-V voltage swing. At the end of the detection phase, the SPAD is biased below the breakdown voltage (SpadOFF = High), the voltage comparator and the time counter are reset (Res = High), and the pulse arrival-time information τ j is coded into the voltage signal V (τ j ) stored across C Sample. By turning M p5 on, the signal associated with V (τ j ) is then converted through the current mirror M p6 10 into two transient currents that are proportional to 1/10 and 1/100 and charge C Low and C High, respectively. The whole procedure is repeated N times (N Low = 10 or N High = 100) in order to obtain the average photon arrival time (τ j ); at the end of the N different acquisitions, the time-coded information stored onto C Low and C High is given by: V CLow = V CHigh = 1 NLow N Low j=1 V (τ j ) (5.14) N 1 High V (τ j ). (5.15) N High j=1 The pixel information is then buffered by means of two source follower amplifiers and two pass-transistor switches allow for the pixel address se- 87

104 CHAPTER 5. CMOS SINGLE PHOTON AVALANCHE DIODE 3D IMAGER (a) V IN V th T G Time V Csample (b) V Csample (c) Time T G Time Figure 5.5: (a) Voltage drop at node IN after the detection of a photon. (b) Voltage at C Sample in time-measuring operation. (c) Voltage at C Sample in photon-counting operation. lection. Finally, to compensate for the unavoidable mismatch effects among different pixels, a calibration phase can be preliminary performed by means of transistor M n1. By turning it on at a given time it is possible to force a synchronized commutation for all the pixels and to observe the different response of the array elements Photon-counting pixel operation Although specifically designed for time measurements, this circuit can also be used, with some limitations, as a gated photon counter. The working principle is described in the following. The voltage drop and recovery at node IN, following the detection of a photon, is shown if Figure 5.5 (a). If 88

105 5.3. IMAGE SENSOR DESIGN the comparator is activated by setting Res = Low when the voltage at node IN (V IN ) is lower than the comparator threshold voltage (V th ), the voltage at node Sample goes High, preventing the discharge of C Sample. The time T G during which V IN < V th depends on the SPAD recharge time and on the difference between V spad+ and V th, and can be adjusted in a limited range by varying V spad+. Considering the value of R quench and the capacitance of node IN, the value of T G is of the order of some tens of nanoseconds. If a photon is detected by the SPAD within a time T G before the activation of the comparator, C Sample is not discharged. In time-measuring operation, I biast C is set to a value that allows the discharge of C Sample in some tens of nanoseconds (Figure 5.5 (b)). In photon-counting operation, the current I biast C must be set to a value high enough that the discharge time of C Sample is much lower than T G (Figure 5.5 (c)). In these conditions, the voltage at C Sample can assume a high value if a photon is detected during the time T G or a low value if a photon is not detected, thus working as a gated counter with gate time T G. The binary information contained in C Sample can be transferred to C Low and C High. At this time, the output voltage can be directly read-out or N measurements can be done and accumulated by the averaging circuit Image sensor architecture Fast TOF imaging requires, of course, a sensor organized in a matrix structure, but to validate the system performance keeping the fabrication costs low, the proposed pixel has been implemented in a linear array of 64 elements. The pixel pitch is 38 µm, mainly limited by the minimum distance between two adjacent SPADs, while the pixel length is 180 µm. The SPAD included in the pixel has circular geometry with 5-µm active area diameter. It has been implemented with a p + /deep-ntub structure and a ptub guard ring. This structure is basically the same used in test 89

106 CHAPTER 5. CMOS SINGLE PHOTON AVALANCHE DIODE 3D IMAGER Figure 5.6: Chip micrograph: (a) test structures, pixel array and readout (b) 10-pixels and part of the decoder (c) DDS stage device A, although the diameter is much smaller. The quenching resistor R quench has been realized using the high resistivity polysilicon layer available with this technology. The 64-pixel array is addressed by a row decoder and the two outputs of each pixel are filtered out using a Double Delta Sampling stage (DDS) [82]. In the fabricated chip test devices A, B, C1-C5 and large-area test photodiodes have been included together with the image sensor. Three micrographs of the chip are shown in figure Device characterization A first characterization of test avalanche photodiodes has been performed in the sub-geiger mode. The measurements consist of static I-V curves, photocurrent gain and spectral responsivity. Where possible, dark count 90

107 5.4. DEVICE CHARACTERIZATION rate measurements in the geiger mode have been done using a passive quenching configuration Test devices in 0.8 µm technology I-V measurements on test device B (p + -ptub in shallow-ntub) indicate the presence of punch through between the p + -ptub region and the substrate. The low doping level of the shallow ntub causes the punch through of the junctions to happen at voltages lower than the breakdown voltage. It is thus impossible to use this structure as an avalanche photodiode. A series of I-V curve measurements in the dark has been carried out on test devices C1-C5, fabricated with the ntub-merging approach. The curves have been measured on 5 different dies. The breakdown voltage V B has been extracted as the voltage at which a reverse current of 1 µa flows through the diode. In Figure 5.7 both V B and the dark current flowing with the diode biased 1 V below V B are shown as a function of inter-well distance D. The error bars indicate the standard deviation over the 5 measured dies. The measured breakdown voltage, ranging from 18 to 19.5 V, is higher than that measured on a simple p + /ntub diode (about 12 V), and increases with increasing inter-well distance D. Measurements under illumination show a very low photocurrent gain, indicating that there is almost no avalanche multiplication in the active region. According to this measurement, breakdown still occurs at the borders of the junction, preventing these structures from being used as avalanche photodiodes. The reason of this failure could be the excessive distance between the edges of p + and ntub regions, but to fully understand the problem an accurate knowledge of the doping profiles would be needed. I-V measurements on device A (p + -ptub on deep-ntub) have been performed on 5 different dies. The breakdown voltage at room temperature 91

108 CHAPTER 5. CMOS SINGLE PHOTON AVALANCHE DIODE 3D IMAGER p 19.5 Breakdown Voltage [V] Dark current [A] 200p 100p Inter-well distance [ m] Inter-well distance [ m] Figure 5.7: Breakdown voltage and dark current of the avalanche photodiodes C1-C5 as a function of inter-well distance is V ± 0.09 V, while the dark current is 8.7 pa ± 1 pa at 26 V bias voltage. In this device, the variability of both parameters in different dies is much lower than in the series C1-C5. Moreover, the leakage current is one order of magnitude lower than in devices C1-C5. The spectral responsivity of device A is shown in Figure 5.8 at two different voltages. At 0 V bias the maximum responsivity is about 0.1 A/W at the wavelength of 540 nm, while at 26 V the maximum responsivity is shifted at lower wavelengths (480 nm). The photocurrent gain as a function of wavelength and bias voltage is shown in Figure 5.9. An increment of the gain at low wavelengths is observed, which is due to the increment of the ratio between electron-initiated and hole-initiated avalanche events. At low wavelengths, the number of electrons generated into the p + region increases with respect to the holes generated into the ntub region. Thus, there is an increase in the number 92

109 5.4. DEVICE CHARACTERIZATION 10 V B =0 V V B =26 V Responsivity [A/W] Wavelength [nm] Figure 5.8: Spectral responsivity of the avalanche photodiode A at two different bias voltages of electron-initiated avalanche events, having a higher multiplication gain, with respect to hole-initiated events [83]. Therefore, an overall increase in the mean gain is observed. Device A was tested in the geiger mode of operation in a passive quenching configuration with voltage-mode output [57]. A 200-kΩ quenching resistor and a 1-kΩ resistor for signal extraction have been used. A comparator was mounted on a board near to the chip, in order to minimize the stray capacitances. Figure 5.10 shows the dark count rate of the SPAD as a function of excess bias voltage at room temperature. A characterization of dark count rate as a function of temperature has been performed putting the SPAD in a climatic chamber and sweeping the temperature from -20 to +40 V. The results at 3 different excess bias voltages are shown in Figure SPAD dark counts approximately double every 10 C, indicating their origin in 93

110 CHAPTER 5. CMOS SINGLE PHOTON AVALANCHE DIODE 3D IMAGER V B = 26 V = 555 nm Photocurrent gain Photocurrent gain Wavelength [nm] Bias voltage [V] Figure 5.9: Photocurrent gain of the avalanche photodiode A as a function of light wavelength and applied bias voltage SRH generation. If this result is reported to the area of the SPAD included in the pixel, a dark count rate lower than 1 khz is obtained, which is negligible for the proposed application. The SPAD was then illuminated with a wide-spectrum thermal light to see the linearity of operation. The resulting count rate as a function of incident optical power density is reported in Figure Unfortunately, the linearity range is narrow, because the dark count rate (which represents the low limit) and the saturated count rate (which determines the high limit) differ only by two orders of magnitude. 94

111 5.4. DEVICE CHARACTERIZATION 10 6 Dark count rate [Hz] Excess bias, Ve [V] Figure 5.10: Dark count rate of the SPAD A as a function of excess bias 10 6 Dark count rate [Hz] Ve [V]: 1V 2V 3V Temperature [ o C] Figure 5.11: Dark count rate of the SPAD A as a function of temperature 95

112 CHAPTER 5. CMOS SINGLE PHOTON AVALANCHE DIODE 3D IMAGER Count rate [s -1 ] p 100p 1n 10n 100n Optical power density [W/mm 2 ] Figure 5.12: Count rate of the SPAD A as a function of incident optical power density Test devices in 0.35 µm technology I-V measurements on devices D1-D6 has been performed. The breakdown voltage and dark current measured with an applied bias 1 V below breakdown are reported in table 5.1. As can be seen, the guard ring becomes effective for D greater than 0.6 µm. While in devices D1-D3 the breakdown voltage is around 9 V, an increase of about 2 V is observed in devices Device D [µm] V B [V] Dark current [A] D D D D D D Table 5.1: Measured breakdown voltage and dark current of test devices D1-D6 96

113 5.4. DEVICE CHARACTERIZATION Responsivity [A/W] V B =0 V V B =8.3 V V B =10.3 V Wavelength [nm] Figure 5.13: Spectral responsivity of device D4 at three different bias voltages D4-D6. The dark current in devices D4-D6 is also reduced by more than two orders of magnitude if compared to devices D1-D3. The spectral responsivity of device D5 is shown in Figure 5.13 at three different voltages. At 0 V bias the maximum responsivity is 0.09 A/W at the wavelength of 470 nm. The interference fringes observed in the figure reveal the presence of a thick passivation layer. An equivalent oxide thickness of 8.54 µm can be calculated from the distance of the fringe maxima. The photocurrent gain as a function of wavelength and bias voltage is shown in Figure As in the case of device A, an increment of the gain at low wavelengths is present. In this case, however, the wavelengths at which the increment is observed are lower than those measured on device A, since the junction in device D4 is shallower than in device A. A characterization of dark count rate has been performed on devices E1-E4. Figure 5.15 shows the measured dark count rate as a function 97

114 CHAPTER 5. CMOS SINGLE PHOTON AVALANCHE DIODE 3D IMAGER V B =8.3 V V B =10.3 V 100 = 555 nm Photocurrent gain Photocurrent gain Wavelength [nm] Bias voltage [V] Figure 5.14: Photocurrent gain of device D4 as a function of light wavelength and applied bias voltage of voltage for device E4 (D = 0.8 µm). Since the integrated comparator threshold is 1.25 V, the count rate couldn t be measured when V e is below this level. The dark count rate is very high, in the MHz range. According to [65], for the SPADs with a low breakdown voltage the dark count is determined by trap-assisted tunnelling. In this devices, the electric field at the junction is high enough that the rate of electron injection from the p + region into the space-charge region becomes higher than SRH generation rate. The dark count rate caused by tunnelling can be expressed as the product of the number of electrons injected per unit time and the breakdown probability P e due to an injected electron. The tunnelling current density can be expressed by the relation [84]: ( J t = qcv R Fm 3/2 exp F ) 0 F m (5.16) 98

115 5.4. DEVICE CHARACTERIZATION 10 7 Dark count rate [Hz] Comparator threshold 10 4 Measurement Theory Excess voltage [V] Figure 5.15: Dark count rate of device E3 as a function of excess bias where c and F 0 are two constant, V R is the reverse bias voltage, and F m is the maximum electric field. The breakdown probability can be calculated as described in reference [85]. This simple model has been used to interpret the experimental data. The electric field has been calculated as a function of V R under the abrupt junction approximation [45]. The doping level N D of the n region has been used as a fitting parameter. The hole and electron ionization coefficients, which determine the breakdown probability, have been calculated with the model proposed by Van Overstraeten and De Man [86]. A good agreement between measured data and theory has been found for a doping level N D = cm 3, as shown in Figure

116 CHAPTER 5. CMOS SINGLE PHOTON AVALANCHE DIODE 3D IMAGER 5.5 Sensor characterization Sensor linearity and time resolution The sensor has been assembled in a camera system board and preliminarly tested using a 50-mW, 658 nm, 100-ns pulsed laser. The current I BiasT C was set to 20 µa and an excess bias voltage V e = 3 V was applied to the SPAD. A first test was carried out with the laser at a fixed distance from the sensor by varying the time delay t L of the laser pulse. The output of the sensor as a function of t L, averaged over all the pixels, is shown in Figure The High and Low outputs have been obtained by setting respectively 100 and 10 in-pixel averages. The error bars indicate the FPN, measured as the standard deviation over the 64 pixels. Its maximum value is around 15% for both outputs, indicating that a calibration is necessary to reduce the mismatch between the pixels. The linearity region is about 30 ns wide for output High, a bit narrower for output Low. In the linear region, output High exhibits a mean sensitivity of 58 mv/ns, and a pixel noise of 17 mv, corresponding to a 290-ps time resolution. The sensitivity of output High is 85 mv/ns and the pixel noise is 73 mv, so that the corresponding time resolution is 850 ps. The calculated time resolution is determined by several factors: laser pulse jitter, shot noise, SPAD and measuring circuit time resolution. The measured time resolution of 290 ps, corresponding to 4.3 cm range resolution, is suitable for the proposed imaging application of the pixel. If the resolution needs to be increased, an average over more acquisitions can be performed. 100

117 5.5. SENSOR CHARACTERIZATION Output High Output Low Output voltage [V] Time delay [ns] Time delay [ns] Figure 5.16: Pixel output averaged over the 64 pixel of the array. The error bars indicate the FPN, i.e. the standard deviation over the 64 pixels Direct time of flight The distance measurement of a cooperative target has then been performed using the laser described in the previous section. A series of measurements have been taken with the mirror placed at different distances from the sensor. The acquired data have been used to calibrate the sensor output in order to reduce the FPN. The measured mirror distance after calibration is shown in Figure The pixel noise is ± 2.9 cm, while residual FPN is 3 cm. Although the laser power previously used was high enough to measure the distance of a cooperative target, a more powerful laser must be employed to illuminate non-cooperative objects. An uncollimated, 905 nm, 100 ns pulsed laser source having a mean power of about 250 mw was used to flood illuminate the scene under measurement. A photographic 101

118 CHAPTER 5. CMOS SINGLE PHOTON AVALANCHE DIODE 3D IMAGER Measured distance [cm] Real distance [cm] Figure 5.17: Distance measurement of a cooperative target after calibration objective has been mounted in front of the sensor. The intensity map of two objects, a teddy-bear and a plastic glass, is shown in Figure 5.18 (a) and (b). The 3-D image of the teddy-bear, coded in gray-level intensity, is shown in inset (c). The acquisition has been performed by a vertical scanning of the linear array. It can be seen that in the regions where illumination is sufficiently high the measurement is correct, while in the regions where the backscattered light power is lower the object appears farther than it actually is. The same effect can be seen looking at the section of the glass in inset (d). The behavior of the sensor can be interpreted using the theory presented in section 5.1. In this case, the laser pulse is not perfectly square, but the leading edge of the pulse can be modelled with the exponential function: P L (t) = P L0 [ ( 1 exp t )] τ (5.17) The shape of the pulse has been measured using a fast photodiode and an 102

119 5.5. SENSOR CHARACTERIZATION Figure 5.18: Examples of 2D and 3D images oscilloscope, giving a time constant τ = 4 ns. The probability density function of photon detection time can be calculated including equations 5.17 and 5.2 into equation 5.3. The resulting distribution at three different maximum powers P L0, calculated by numerical integration, is shown in Figure The mean of this distribution represents the time measurement offset, while the standard deviation determines the time resolution. In order to compare theory and experimental data, the optical power incident on the pixels and the SPAD photon detection efficiency have been evaluated. The power incident on the devices has been measured by means of a calibrated photodiode. The photon detection efficiency of the SPAD at 905 nm has been measured by exploiting the photon-counting mode of operation of the pixels. The measured efficiency was 0.62%, comparable with an efficiency around 1% reported in other works [58, 59]. Distance offset and resolution have been measured experimentally using the 905 nm laser. The current I biast C was set to 40 µa, so that the range of 103

120 CHAPTER 5. CMOS SINGLE PHOTON AVALANCHE DIODE 3D IMAGER Probability density function 1.5x x x10 7 P L0 = 1nW P L0 = 5nw P L0 = 10nW Integral 0-30ns P L0 [nw] Time [ns] Figure 5.19: Probability density function of photon detection time for 3 different pulse power levels. In the inset: PDF integral between 0 and 30 ns. the time-to-amplitude converter was about 30 ns. The measured sensitivity in the linear region was 105 mv/ns. The noise was calculated as the standard deviation over 1000 acquisitions. Since the range of the time-to-amplitude converter is about 30 ns, the theory is not applicable to interpret the measurements if the tail of the PDF exceeds 30 ns. The inset of Figure 5.19 shows the integral of the PDF between 0 and 30 ns as a function of P L0. It can be seen that for values of P L0 greater than about 6 nw the probability that a photon is detected within 30 ns is almost 1 and thus the theory can be applied. Distance offset and resolution have been calculated by numerical integration as the mean and the standard deviation of the PDF. A comparison between measured and theoretical distance offset and noise is shown in Figure Since in the experiment the output signal is the average over 100 measurements, the calculated noise has been scaled by a factor N =

121 5.5. SENSOR CHARACTERIZATION 20 Theory Experiment 300 Theory Experiment Pixel noise [cm] Distance offset [cm] Theory validity limit 0 Theory validity limit P L [nw] P L [nw] Figure 5.20: Comparison between theoretical and measured distance resolution and distance offset. A good agreement can be observed between measured and experimental offset and noise where the incident power is higher than 6 nw Indirect time of flight The photon counting operation of the sensor has been analyzed by illuminating the sensor with a white thermal light at different power intensities. The measurements have been performed without in-pixel averaging, by reading out output Low. In this way, the difference at the output between the two binary levels is about 400 mv. The number of counts over acquisitions as a function of incident optical power density is reported in Figure The measured noise is also reported in the figure and compared to the square root of the signal counts. In the linear region there is an excellent matching between the two curves, indicating a poisson distributed count rate. 105

122 CHAPTER 5. CMOS SINGLE PHOTON AVALANCHE DIODE 3D IMAGER Signal counts, C Noise counts, N sqrt(c) Counts n 10n 100n 1µ 10µ Incident optical power [W/mm 2 ] Figure 5.21: Pixel counts as a function of incident optical power density Counting operation of the sensor has been used to test the performance of the sensor with the indirect time-of-flight technique. The 905-nm laser has been used to illuminate the scene under measurement. Three different images, acquired by varying the time delay of the 100-ns laser pulse, are shown in Figure In inset (a), the pulse is entirely included in the gate window, which is about 150 ns wide. In insets (b) and (c), the laser pulse and the gate window are partially overlapping. A 3-D image of the scene has been reconstructed from images (a) and (b), as described in section 5.1. The distance map depends linearly on the ratio between the intensity maps (b) and (a). A perspective view of the reconstructed 3-D image is shown in Figure A precision of about 10 cm at 2 m is obtained, and could be further improved by averaging over a higher number of laser pulses. Further measurements employing a faster laser source have been planned to investigate the ultimate limit in the performance of the proposed sensor. 106

123 5.5. SENSOR CHARACTERIZATION Figure 5.22: Images acquired by counting the number of photon detections over 3000 laser pulses. (a) laser pulse entirely included in the gate window; (b) and (c) laser pulse partially overlapping with the gate window, with different time delays. Figure 5.23: 3D image acquired with Indirect TOF technique 107