Modeling photon detection efficiency and temporal response of single photon avalanche diodes

Abstract

In this paper we present a physically-based model aimed at calculating the Photon Detection Efficiency (PDE) and the\ud temporal response of a Single-Photon Avalanche Diode (SPAD) with a given structure. In order to calculate these quantities, it is necessary to evaluate both the probability and the delay with which a photon impinging on the detector area triggers an avalanche. Three tasks are sequentially performed: as a first step, the electron-hole generation profile along the device is calculated according to the silicon absorption coefficient at the considered wavelength; successively, temporal evolution of the carriers distribution along the device is calculated by solving drift diffusion equations; finally, the avalanche triggering probability is calculated as a function of the photon absorption point.\ud Validation of the model has been carried out by comparing simulation and experimental results of a few generations of detectors previously realized in our laboratory. Photon detection efficiency has been measured and calculated for wavelengths ranging from 400nm to 1000nm and for excess bias voltages ranging from 2 to 8V. Similarly, temporal response has been investigated at two different wavelengths (520 and 820nm). A remarkable agreement between experimental and simulation results has been obtained in the entire characterization domain simply starting from the measured doping profile and without the need of any fitting parameter. Consequently, we think that this model will be a valuable tool for the development of new detectors with improved performances

Simulation of a high-efficiency and low-jitter nanostructured silicon single-photon avalanche diode

“…When a photon is absorbed in the p-type region or the n-type region, due to the absence of high electric field the photo-generated minority carriers move randomly before reaching the depletion region. This process has an effect on detection efficiency and timing jitter as discussed previously [27]. In this paper, we use the 1D random walk model to simulate such a process.…”

“…When a photon is absorbed in the depletion region, an avalanche is initiated immediately so that P c is close to 1. Since the depletion region is mainly in the intrinsic layer, the lifetime of photo-generated carriers is longer than the avalanche process such that the recombination effect can be ignored in this region [27]. When a photon is absorbed in the p-type region or the n-type region, due to the absence of high electric field the photo-generated minority carriers move randomly before reaching the depletion region.…”

“…Previous studies have revealed that the peak of the timing jitter histogram is coming from the photons absorbed in the depletion region, which undergo an avalanche growth process directly, and the tail of the timing jitter histogram is coming from the diffusion process in the neutral region. The contributions of timing jitter from the avalanche growth process (the peak of timing jitter histogram) can be modeled by a Gaussian function [27]. In our nanostructured SPAD, the absorption in the depletion region has been maximized for infrared wavelengths, most photons are absorbed in the depletion region, and the timing jitter will mainly be determined by these photons.…”

Photon-Detection-Probability Simulation Method for CMOS Single-Photon Avalanche Diodes

“…However, to optimize the PDP in a wavelength range aiming for certain applications, such as 905 nm for Si-based LiDAR, it needs a reliable tool based on the fundamental device physics and the material parameters. In fact, although there were a few theoretical models for the PDP calculation [15][16][17], a quantitative and reliable prediction of PDP has been a challenging task due to its complicated factors, including the doping profiles, the carrier transport above breakdown voltage, the non-uniform electric-field and impact-ionization distributions, and the spatially-dependent breakdown triggering probability. Pancheri et al compared two breakdown models to simulate bias-dependent PDP and an excellent consistence between their calculation and experiment was achieved [17] with a few fitting parameters.…”

A Simple Analytic Modeling Method for SPAD Timing Jitter Prediction

“…Moreover, the exponential jitter tail modeling caused by the device-neutral regions is less studied, although the modeling methods of Gaussian temporal response in the device avalanche region are investigated in depth. Also, a computational method was presented to focus on the tail modeling [14], but the key model parameters, such as electron and hole ionization rates come from fitting theoretical or empirical values that are not correlated with the device structures and processes, which may reduce the accuracy of the model to some extent. Obviously, the previously reported models are not capable of establishing simple analytical expressions for accurate prediction of the overall timing jitter characteristics.…”