SPAD Simulation: SPDE & DCR Reproduction

A repository for reproducing simulation results from Kang et al., ‘Dark Count Probability and Quantum Efficiency of Avalanche Photodiodes for Single-Photon Detection’.

Overview

This is a model to calculate the dark count rate (DCR) and single-photon detection efficiency (SPDE) for a gated SPAD. In this operation, the SPAD is periodically biased above and below it's breakdown voltage $V_B$. The key free parameters of the model are the primary dark current $I_{DM}$ and the avalanche breakdown probability $P_a$, which can be calculated from the McIntyre model [2].

Method

In Geiger mode, the SPAD is periodically biased above and below breakdown with a short voltage pulse. A detection event occurs when a carrier — either photon-generated or thermally generated — triggers an avalanche during the gate. This model assumes four independent sources fo such carriers:

1. Primary dark carriers generated inside the multiplication region during the gate pulse
2. Pre-pulse dark carriers generated before the pulse and amplified by the DC gain
3. Afterpulse carriers (type 1) released from traps during the gate pulse
4. Afterpulse carriers (type 2) released from traps before the gate pulse arrives

Poissonian statistics are assumed for light and dark counts, and an exponential decay for afterpulsing with a characteristic decay constant $\tau_d$. This value is different for III-V and Si SPADs, and should be obtained from literature.

Installation

# clone the repo
git clone https://github.com/thomasbourke1/dcr_simulation.git

# go into the project directory
cd dcr_simulation

# create a virtual environment to install dependencies
python -m venv venv

# activate virtual enviornment (Windows)
.\venv\Scripts\activate

# activate virtual environment (Mac / Linux)
source venv/bin/activate

# install project dependencies from pyproject.toml
pip install -e . 

Usage

Run run_dcr_spde.py to generate DCR plotted against SPDE.

References

[1] Kang, Y., H. X. Lu, Y. H. Lo, D. S. Bethune, and W. P. Risk. ‘Dark Count Probability and Quantum Efficiency of Avalanche Photodiodes for Single-Photon Detection’. Applied Physics Letters 83, no. 14 (2003): 2955–57. https://doi.org/10.1063/1.1616666.

[2] McIntyre, R. J. ‘On the Avalanche Initiation Probability of Avalanche Diodes above the Breakdown Voltage’. IEEE Transactions on Electron Devices 20, no. 7 (1973): 637–41. https://doi.org/10.1109/T-ED.1973.17715.