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

Abstract

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.

Indirect time-of-flight pixel study: 3D Monte Carlo simulation approach

“…(ii) The stochastic transport of the electrons is computed through the "Advection-Diffusion Monte Carlo" method. 12 The doping concentration and electric field at the particle positions are interpolated using the data from the initial Poisson TCAD simulation. This data at the particle position is used to compute the drift velocity and the random diffusion at each time step.…”

“…Different approaches have been proposed to reduce the computation time of the standard methods. 11,12 The "Advection-Diffusion Monte Carlo" approach has been used in this work. 12 This method interprets the standard drift-diffusion-based-TCAD equations as Fokker-Plank equations applied to spatial probability density of electrons.…”

“…11,12 The "Advection-Diffusion Monte Carlo" approach has been used in this work. 12 This method interprets the standard drift-diffusion-based-TCAD equations as Fokker-Plank equations applied to spatial probability density of electrons. These equations are solved with a particle MC approach, providing a new stochastic method to compute the particle trajectory.…”

“…These equations are solved with a particle MC approach, providing a new stochastic method to compute the particle trajectory. 10,12 To model iToF pixels and simulate it utilizing 3D MC and drift-diffusion-based-TCAD, key figures of merit are identified.…”