A method considering the light transmission of silicon dioxide film on the device surface can be proposed to address the large error between the existing photon detection probability (PDP) model and actual test results, which can accurately predict the detection probability of single-photon avalanche diodes (SPADs). Visible light communication requires a high-sensitivity receiver to receive optical signals, and single-photon detectors play an extremely important role in visible light communication because of their high sensitivity, high gain, and high visible light wide-spectrum response. Due to the time-consuming and cost-intensive bipolar-complementary metal oxide semiconductor-double diffusion metal oxide semiconductor (BCD) process workflow, prediction of SPAD performance is critical to optimize its design before fabrication. Although commercial semiconductor simulation software can usually simulate the electrical properties of SPADs, such as breakdown voltage, impact ionization rate, and electric field distribution, their statistical performance cannot be directly simulated. Additionally, since the internal operating mechanism of the semiconductor simulation software is not open, it is impossible to know the detailed simulation process, and it is also prone to non-convergence during the simulation. Therefore, it is of practical significance to model the performance parameters of SPADs. In fact, although there are some theoretical models for the calculation of PDP, due to the complex factors of its physical process, various models have large errors and are inconsistent with the experimental test trend in the short wavelength range. Thus, the photon-quantitative and reliable prediction of detection probability is challenging.

The PDP is defined as the product of the light transmission of a photon passing through the silicon dioxide layer on the silicon surface and the internal quantum efficiency of the device. The internal quantum efficiency of the device is the probability triggered when a photon is absorbed by the device and results in an avalanche. The internal quantum efficiency of P⁺/N well/deep N well SPAD is divided into three parts. In the neutral region P, photons are absorbed in the P⁺ layer on top of the SPAD to generate electron-hole pairs, and some photogenerated electrons will diffuse to the upper boundary of the depletion region, triggering an avalanche probability. In the depletion region, photogenerated electrons and holes drift in opposite directions under the action of a strong electric field in this region and trigger an avalanche after moving a very short distance. In the neutral region N, photogenerated holes can reach the bottom of the depletion region without being recombined, and initiate an avalanche trigger. In this study, the doping concentration provided by the device processing factory and the designed SPAD layout structure are imported into the TCAD tool to rebuild the two-dimensional device model. Through the function library that comes with Sentaurus Sdevice, parameters such as temperature, bias voltage, and incident light wavelength are set for electrical simulation, and the electric field intensity and width of the depletion region are obtained. Then, the electric field strength and the width of the depletion region are imported into the model built by Matlab software to obtain the internal quantum efficiency. The particle swarm optimization algorithm is adopted to obtain the fitting parameters of the transmission spectrum in the passivation layer of the silicon dioxide film, and finally acquire the PDP.

Firstly, two-dimensional process simulations are carried out through the Sentaurus SED based on the standard 0.18 μm BCD process and the SPAD device structure obtained from the process simulations. The simulated electric field distribution of the SPAD at an excess bias voltage of 1 V is simulated by Sentaurus Sdevice (Fig. 4) to extract the one-dimensional (1D) electric field distribution at the center of the device at an excess bias voltage of 1 V (Fig. 5). The electric field distributions at 0.5, 1.0, 2.0, and 3.0 V over-bias respectively are employed to calculate the avalanche trigger probability at each location in the depletion region (Fig. 6). The theoretical model of the PDP is improved by considering the effect of the silica passivation layer film on the incident light wavelength. The wavelength-dependent transmission of the silica film is fitted through a particle swarm optimization algorithm by comparing the theoretical model with experimental test results (Fig. 7). The PDPs contributed by each of the three components of the neutral P, depletion, and neutral N regions are calculated (Fig. 8), and the total PDP is the sum of the three components (Fig. 9). Finally, a PDP model with a low mean error is achieved (Fig. 10). The results show good agreement between the PDP predictions and experimental tests, with an average error of only 1.72%.

We discuss the PDP for simulating typical over-bias voltages from 0.5 to 3 V without substrate contribution. The model and experimental test results are compared at the over-bias voltage of 0.5 V with an average error of only 1.72%. The average error is defined as the average of the sum of the absolute errors for each wavelength. The improved model for PDP considering the transmission spectrum of a thin film of silica passivation layer provides a research direction for the development of new SPAD device structures. Results show that the model can reduce the non-convergence problems in commercial device simulation software, and greatly reduce the time and cost required to develop new structures for SPAD devices. Additionally, the building of models for electric field strength, avalanche trigger probability, and carrier lifetime can help dark counting analysis, thus enlightening related researchers.