Comprehensive Modeling and Characterization of Photon Detection Efficiency and Jitter Tail in Advanced SPAD Devices

Abstract

A new method to reliably simulate the PDE and jitter tail for realistic three-dimensional SPAD devices is presented. The simulation method is based on the use of electric field lines to mimic the carriers' trajectories, and on one-dimensional models for avalanche breakdown probability and charges transport. This approach allows treating a three-dimensional problem as several one-dimensional problems along each field line. The original approach is applied to the McIntyre model for avalanche breakdown probability to calculate PDE, but also for jitter prediction using a dedicated advection-diffusion model. The results obtained numerically are compared with an extensive series of measurements and show a good agreement on a wide variety of device designs.Index Terms-avalanche breakdown probability, breakdown voltage, jitter, photon detection efficiency (PDE), single-photon avalanche diode (SPAD), Technology computer-aided design (TCAD) I. INTRODUCTION AND DEVICE STRUCTURESS INGLE-Photon Avalanche Diodes (SPAD) are key optoelectronic detectors for medical imaging, camera ranging, and automotive laser imaging detection and ranging (LiDAR) applications. Currently, the device leading the market of SPADs is a micrometric silicon (Si) PN junction associated with nearby CMOS electronics biasing the system above the breakdown voltage (BV) [1].The main figure of merit for the sensor sensitivity is the photon detection efficiency (PDE), which is the probability that a photon hitting the SPAD is detected. It can be evaluated by multiplying the probability that an incoming photon hits the photosensitive area of the sensor, the fill factor (FF), by the probability that the photon is absorbed within the Manuscript submitted the February 8th 2022. The authors gratefully acknowledge VIZTA project (https://www.vizta-ecsel.eu/) for

A Fokker–Planck-based Monte Carlo method for electronic transport and avalanche simulation in single-photon avalanche diodes

“…In our algorithm, we compute the integral P ii (z ′ |z) on the fly, consistently with the trajectory, and whenever P ii (z ′ |z) reaches or exceeds the random value r, an electron-hole pair is created at the current position of the parent carrier. The capacity of the multiplication model to be used consistently with the transport simulation is mandatory to accurately model the operation of state-of-the-art devices with highly bent electric fields, for which considering straight lines for carrier trajectories is very inaccurate [28]. The extraction of impact ionization coefficients in Silicon was performed by several authors either from measurements or from BTE Monte Carlo simulations.…”

“…Such a map is shown in figure 8(b), for each point the color represents the probability for an electron injected at this location to eventually trigger an avalanche. These kinds of maps were already produced by means of deterministic methods, such as solving the McIntyre equations over electric field lines [28]. Those methods could not take into account the statistical intrinsic behavior of the particles.…”