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.

Bayesian optimization is used to investigate the optimal grating parameters of realistic SPADs, enhancing high absorption by positioning a resonance exactly at 940 nm. Bayesian optimization allows us to find optimal parameters while minimizing the numerical cost required.

A new methodology to accurately simulate the Photon Detection Efficiency and the Jitter tail of SPAD devices is presented. This method first relies on the use of the electric field lines to mimic the carriers' trajectories. A model for impact ionization and avalanche probability is then used on the obtained lines to simulate the probability of avalanche, coupled with the optical absorption, the PDE is then extracted. Finally, an advection-diffusion model is used to simulate the drift and diffusion of carriers within the device, which leads to the timing jitter due to the transport time from the photogeneration spot to the avalanche region. The results obtained numerically are compared with an extensive series of measurements and show a good agreement on a wide variety of device designs.

We present an efficient simulation method for electronic transport and avalanche in single-photon avalanche diodes (SPAD). Carrier transport is simulated in the real space using a particle Monte Carlo approach based on the Fokker–Planck point of view on an advection-diffusion equation, that enables us to reproduce mobility models, including electric fields and doping dependencies. The avalanche process is computed thanks to impact ionization rates implemented using a modified Random Path Length algorithm. Both transport and impact ionization mechanisms are computed concurrently from a statistical point of view, which allows us to achieve a full multi-particle simulation. This method provides accurate simulation of transport and avalanche process suitable for realistic three-dimensional SPADs, including all relevant stochastic aspects of these devices, together with a huge reduction of the computational time required, compared to standard Monte Carlo methods for charge carrier transport. The efficiency of our method empowers the possibility to precisely evaluate SPADs figures of merit and to explore new features that were untrackable by conventional methods. An extensive series of comparisons with experimental data on state-of-the art SPADs shows a very good accuracy of the proposed approach.

A semi-empirical model for the optical properties of SiGe alloys is proposed, based on physical considerations and the summation of Tauc-Lorentz and parametric oscillators. The key parameters of the oscillators are intuited from the optical transition and the symmetry points in the band structure. The model is fitted on extensive experimental data, for different temperatures, germanium concentrations and for both unstrained and strained on (100) Silicium wafer cases. This model can be used in optical simulation tools, in order to help the design of optoelectronic devices based on SiGe materials.

The statistical behavior of silicon-based single-photon-avalanche-diodes (SPADs) is investigated by using self-consistent 3-D Monte Carlo simulations.The coupling of Poisson and Boltzmann transport equations allows us to go beyond the analysis of avalanche breakdown and its timing and to extend the investigation to the quenching of the photodetector circuit.We find out that the quenching of SPADs is probabilistic and strongly depends on the surrounding circuit, in particular on the socalled quenching resistance.Independently of the SPAD deadtime, it appears that the extinction time needed to suppress any avalanche event may vary over a very large range.

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.