SPAD Simulation Pipeline

• SPAD simulation is a computational workflow that models photon, device, and system responses using methods like Monte Carlo photon transport and drift-diffusion analysis.
• It integrates physical sensor modeling with stochastic event simulation and noise incorporation to enable virtual prototyping and dataset generation.
• The pipeline validates performance metrics such as breakdown voltage and photon detection efficiency, supporting design optimization in imaging and quantum optics.

A Single-Photon Avalanche Diode (SPAD) simulation pipeline is a structured computational workflow for simulating the photon-level, device-level, and system-level response of SPAD sensors and SPAD-based systems. These pipelines are critical for the virtual prototyping of @@@@1@@@@, performance characterization, dataset generation, and algorithm evaluation in imaging, quantum optics, and device design. SPAD simulation workflows can range from Monte Carlo photon transport with sensor nonidealities, through rigorous device physics (drift-diffusion plus ionization), to cluster-level system modeling for context such as specialized hardware design. The archetype pipeline comprises flux modeling, stochastic photon events, sensor response (with noise sources and temporal effects), readout emulation, and modality-specific output. This article surveys the principal methodologies, algorithmic steps, and validation criteria from leading research pipelines.

1. Physical Principles and Device Modeling

SPAD simulation pipelines are grounded in optoelectronic device physics, beginning with the definition of the sensor's geometry, materials, doping profiles, and biasing conditions. For advanced device-centric studies, such as nanowire SPADs, the workflow consists of building a discretized p–i–n model, assigning spatial profiles for permittivity, bandgap, and dopant concentrations, and applying relevant boundary conditions (Ohmic contacts, symmetry at axes) (Li et al., 2023). The reverse-bias voltage V_bias is swept from sub-breakdown to well above breakdown to capture the dynamic range.

The time-dependent drift–diffusion simulation is at the core: solving Poisson’s equation for the electrostatic potential, and continuity equations for electron and hole densities. Carrier currents incorporate both drift and diffusion, with field-dependent mobility (Caughey–Thomas model) and impact ionization coefficients. Carrier generation and recombination are modeled with optical generation (G_opt), impact ionization (G_II from electric field), and Shockley-Read-Hall thermal processes (R_SRH). The time-evolving current I(t), field E(x), and carrier densities enable extraction of breakdown voltage V_B, avalanche build-up time τ_avalanche, and spatially resolved profiles.

2. Monte Carlo Photon-Level Simulation

For imaging and time-of-flight SPAD pipelines, stochastic simulation of individual photon arrivals is essential. Photon events (timestamp, pixel index, wavelength) are produced by upstream transient Monte Carlo rendering or by deterministic flux models scaled from scene radiance and device characteristics (Suonsivu et al., 19 Jan 2026). Each event undergoes probabilistic detection with a photon detection efficiency (PDE) that combines wavelength-dependent quantum efficiency, optical absorption, and bias-dependent avalanche probability (Hernandez et al., 2017).

PDE calculation often follows:

$$\text{PDE}(\lambda, V_e) = \eta(\lambda) \cdot P_t(V_e)$$

where $\eta(\lambda)$ models absorption and $P_t(V_e) = 1 - e^{-V_e/V_c}$ is the empirical trigger probability.

Detected photons are then timestamped with jitter drawn from an exponentially modified Gaussian impulse response, capturing both instrument response and statistical delays. Noise sources (dark counts as Poissonian, afterpulsing, pixel crosstalk), dead-time (quenching period post-avalanche), and optional temporal gates are applied. The simulation produces asynchronous timestamp lists, binary frames, or time-binned histograms (TCSPC) depending on modality.

3. Pipeline Implementation Steps and Algorithms

The SPAD simulation pipeline composes the following canonical steps:

Stage	Inputs/Actions	Outputs/Usage
Device Initialization	Geometry, doping, material parameters	Field mesh, boundary conditions
Photon Event Generation	Reference image, flux model, Poisson sampling	Photon event streams (time, pixel/wave)
Sensor Response Modeling	PDE, dead time, dark counts, afterpulsing, jitter	Time tags, binary detections, histograms
Post-Processing	ATP, PDE evaluation, DCR calculation	Efficiency, timing jitter, rate metrics
Output Formation	Modality-specific readout (TOA, 1-bit QIS, bins)	Output data or synthetic dataset

These workflows may be adapted or modulated according to application: nanowire breakdown modeling leverages drift-diffusion and McIntyre's equations for avalanche triggering probability (Li et al., 2023); transient imaging employs probabilistic event chains and explicit modeling of crosstalk, afterpulsing, and quenching (Hernandez et al., 2017); imaging pipelines incorporate illumination scaling, area corrections, detection probability, and binning for QIS modes or time-of-arrival histograms (Suonsivu et al., 19 Jan 2026).

Algorithmic expressions are provided for per-step calculations (e.g., photon arrival Poisson sampling, PDE rejection, dead time enforcement, afterpulse delay), as are exact pseudocode fragments for simulation routines.

4. Noise Sources and Nonidealities

SPAD simulation rigorously incorporates intrinsic noise and nonideal effects through explicit modeling:

• Dark Count Rate (DCR): Simulated as Poissonian background, parameterized by measured values (e.g., 265 Hz typical for SPAD23) (Suonsivu et al., 19 Jan 2026), and up to $10^5$ counts/s (Hernandez et al., 2017).
• Afterpulsing: Stochastic retriggering post-avalanche, with probability $P_{ap}$ and delay distribution (often exponential) (Suonsivu et al., 19 Jan 2026, Hernandez et al., 2017).
• Dead Time: Sensitivity recovery period post-avalanche ($\tau_d$). Events within $t_{last} + \tau_d$ are rejected (Suonsivu et al., 19 Jan 2026).
• Jitter: Modeled by convolution with the exponentially modified Gaussian or as tabulated IRF; typical FWHM ≈ 20–120 ps (Suonsivu et al., 19 Jan 2026).
• Crosstalk: In arrays, firing in one pixel probabilistically triggers neighbors; implemented via pairwise event evaluation (Hernandez et al., 2017).
• Environmental Effects: Ambient background rates and spatial/temporal illumination variations may be incorporated.

5. Imaging and Dataset Generation Applications

Modern pipelines extend SPAD simulation to imaging modalities and dataset creation. For instance, the SPAD-MNIST dataset simulates pixelwise photon arrivals from canonical images at tunable light levels, incorporating fill factor, PDP, dead time, dark counts, and afterpulsing (Suonsivu et al., 19 Jan 2026). Modalities simulated include:

• TR-SPAD: Asynchronous timestamp streams per pixel with pile-up correction.
• QIS-SPAD: 1-bit binary frame readout over short integration windows.
• STR-SPAD: Synchronous time-of-first arrival per frame.

Flux estimators (count-based, passive free-running, inter-photon) reconstruct local flux from timestamp data. Performance evaluation is validated against experimental datasets from commercial sensors (SPAD23 and SPAD512²), where count histograms, timing statistics, and pixel-specific noise profiles match simulated results to within $\approx1\%$ error.

6. Performance Metrics, Validation, and Comparative Analysis

Simulation pipelines output quantitative device and system metrics fundamental for evaluating SPAD designs and applications:

• Breakdown voltage $V_B$: Onset voltage where current increases sharply (10–100x) (Li et al., 2023).
• Avalanche build-up time $\tau_{avalanche}$: Time for current plateau, extracted from logistic-type fit to $I(t)$ (Li et al., 2023).
• Photon Detection Efficiency $\langle PDE \rangle$: Region-averaged probability, e.g., up to $70\%$ for nanowire SPADs (Li et al., 2023).
• Deterministic timing jitter $\sigma_t$: Lower bound from avalanche onset positional scan (Li et al., 2023).
• Dark count rate DCR: Integrated over device, weighted by avalanche trigger probability (Li et al., 2023, Suonsivu et al., 19 Jan 2026).
• Localization precision and SNR: Imaging pipelines compute RMS error and SNR for molecule detection (Gyongy et al., 2016).
• Cluster-level throughput, cost, and TDP: For SPAD-inspired hardware platforms, metrics include throughput, TTFT, TBT, hardware cost/TDP normalized to H100 GPU baselines (Zhang et al., 9 Oct 2025).

Validation is performed by matching simulated data distributions—photon count histograms, timing metrics, aggregate device statistics—to experimental results under controlled illumination and biasing conditions. This ensures simulation fidelity and supports translation to unseen real-world data.

7. Adaptability, Extensions, and Pipeline Parameterization

SPAD simulation pipelines are designed to be highly parameterized and extensible. Geometries, electronic structures, and material models may be swapped for alternative device architectures (planar, nanowire, multi-dimensional arrays) (Li et al., 2023). In imaging applications, scene and sensor parameters (flux, area, fill factor, PDP, dead time, noise rates) are configurable per dataset (Suonsivu et al., 19 Jan 2026). Modalities (asynchronous, synchronous, gated) and noise models can be toggled for application-specific studies.

Specialized system-level simulations emulate hardware behavior for computational workloads, such as LLM inference with memory-/compute-disaggregated chips, modeling pipeline flows from die-level DSE to trace-based cluster scheduling (Zhang et al., 9 Oct 2025).

The pipeline can be employed for device design space exploration (DSE), cluster provisioning studies, robustness analysis under workload/model shifts, and synthetic dataset creation for learning-based applications and algorithm benchmarking. Execution times span minutes to hours per scenario due to fully synthetic, event-driven simulation.

---

Principal sources: (Li et al., 2023, Suonsivu et al., 19 Jan 2026, Hernandez et al., 2017, Gyongy et al., 2016, Zhang et al., 9 Oct 2025).