The use of 3D Monte Carlo simulations for the study of an indirect time of flight (iToF) pixel revealed underlying information compared to conventional simulation tools. Experimental tendencies and results are systematically compared with results obtained numerically. During the sensor operation, iToF pixels reconstruct the depth information using an optical signal modulated in intensity at high operation frequencies of hundreds of MHz. A demodulation operation samples the photogenerated charges at different times in a single pixel. An efficient transfer is dependent of the charge carrier path in the pixel volume. Through the coupling of 3D Monte Carlo with a commercial Poisson solver and optical simulation tools, a complete and accurate simulation methodology was developed allowing the estimation of iToF main figures of merit such as demodulation contrast, parasitic light sensitivity and quantum efficiency. The method consists of generating a light impulse and studying the distribution and collection of each unitary charge in time through MC simulations. Detailed information can be obtained in the 3D volume of a pixel for the photogenerated carriers. The efficiency of charges transfer from the pixel volume to sensing nodes is given at the operation frequency by the demodulation contrast. The electrostatic potential barriers reducing the transfer efficiency can be easily identified and lost photogenerated carriers can be estimated. The prediction accuracy of Monte Carlo simulation is further improved through the coupling of photogeneration and electron mobility profiles extracted from optical simulation and drift-diffusion-based-technology computed-aided design tools respectively. A non optimized small pitch pixel was optimized thanks to these advanced multi-physics simulations.
KEYWORDS: Single photon avalanche diodes, Monte Carlo methods, Quenching, Simulations, Stochastic processes, Modeling, Ionization, Power consumption, Picosecond phenomena, Capacitance
We present a study of the main SPAD figures of merit using a multiscale approach, from Monte Carlo simulations to SPICE simulations. We explore novel stochastic approaches capable of predicting accurately experimental measurements such as the Breakdown Probability, and the jitter. Additionally, the SPAD avalanche dynamics that is a stochastic process, is discussed within a transient Monte Carlo simulation perspective. We also derived a VerilogA model, making possible the analysis of the stochastic responses of the SPAD, including the buildup of the avalanche but also its quench. This latter quench probability of these diodes once in avalanche, rarely discussed in literature, is related to the dynamics of the voltage change of the floating cathode node. If the cathode voltage recovery (after the debiasing due to the quench circuit) is quicker than the time needed for the carrier evacuation within the avalanche junction, small additional avalanches can occur.
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