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Allpix$^2$: A Modular Simulation Framework for Silicon Detectors
Simon Spannagel, Koen Wolters, Daniel Hynds, Niloufar Alipour Tehrani, Mathieu Benoit, Dominik Dannheim, Neal Gauvin, Andreas Nürnberg, Paul Schütze, Mateus Vicente Barreto Pinto
TL;DR
Silicon-detector simulation needs tools that combine detailed detector physics with computationally practical Monte Carlo workflows. Allpix2 addresses this through a modular framework integrating material interactions, charge transport, digitization, and configurable detector models. Comparisons with test-beam data show close agreement across track resolution, cluster size, charge, and residual-shape behavior, while transient-current simulation remains outside the current implementation.
Problem
Detailed detector simulations must represent both material effects and charge-carrier motion, but advanced tools such as TCAD are computationally demanding and difficult to integrate into Monte Carlo workflows.
Method
Allpix2 uses independent modules and a message broker to combine particle and material interactions, charge transport, electronics coupling, digitization, and configurable simulation components.
Results
The framework performs very well against data, with similar telescope resolutions and close agreement for DUT cluster size, charge, intrinsic resolution, and residual shapes.
Takeaways & Limitations
Allpix2 provides a lightweight, modular framework for studying silicon-pixel detector performance from particle interactions through signal formation.
Takeaways & Limitations
Charge groups are propagated without calculating transient currents induced on charge-collection implants, although induced-current simulation is ongoing.
Abstract
from arXiv · showhide
Allpix$^2$ (read: Allpix Squared) is a generic, open-source software framework for the simulation of silicon pixel detectors. Its goal is to ease the implementation of detailed simulations for both single detectors and more complex setups such as beam telescopes from incident radiation to the digitised detector response. Predefined detector types can be automatically constructed from simple model files describing the detector parameters. The simulation chain is arranged with the help of intuitive configuration files and an extensible system of modules, which implement separate simulation steps such as realistic charge carrier deposition with the Geant4 toolkit or propagation of charge carriers in silicon using a drift-diffusion model. Detailed electric field maps imported from TCAD simulations can be used to precisely model the drift behaviour of charge carriers within the silicon, bringing a new level of realism to Monte Carlo based simulations of particle detectors. This paper provides an overview of the framework and a selection of different simulation modules, and presents a comparison of simulation results with test beam data recorded with hybrid pixel detectors. Emphasis is placed on the performance of the framework itself, using a first-principles simulation of the detectors without addressing secondary ASIC-specific effects.
1. Introduction
Allpix2 addresses the need for detailed, Monte Carlo-compatible silicon-detector simulations by combining material effects with charge-carrier motion in a modular framework. It is designed to support both individual detectors and more complex simulation setups.
- Detailed silicon-detector simulations are important for understanding performance and optimizing detector design.
- TCAD provides advanced simulation capabilities but is computationally demanding and difficult to integrate with other tools for Monte Carlo studies.
- Allpix2 combines experimental material effects, such as multiple scattering and nuclear interactions, with detailed charge-carrier motion.
- The framework uses independent modules communicating through common objects and a message broker, allowing new simulation algorithms to be developed with limited knowledge of the underlying structure.
- The paper overviews the framework and typical simulation steps, then presents an initial validation with test-beam data.
2. Framework Architecture
Allpix2 separates shared framework infrastructure from detector- and physics-specific modules, enabling configurable simulations with reusable detector models and message-based data flow. Its architecture also records object provenance and supports practical configuration, visualization, and testing workflows.
- Architecture: The framework separates central infrastructure from physics simulation implemented in individual modules.
- Framework core: Core components provide module instantiation, detector geometries, messaging, and the user interface.
- Module instantiation: Unique modules handle global detector setups, whereas detector modules simulate processes within individual detectors.
- Detector geometries: Parameterized detector models can be changed without recompiling the framework or modifying program code, and can include hybrid, monolithic, or strip-like detectors with support layers.
- Messaging: Modules exchange results through a messaging system in which subscribed modules receive relevant messages and can dispatch new messages.
- Object history: Object history records full provenance, linking each simulated pixel hit to contributing charge carriers, energy depositions, particles, and Monte Carlo positions.
- Configuration: Configuration files use section headers and key-value pairs, while physical units are automatically converted into the framework’s internal units.
- Software quality: Continuous integration builds and tests the framework across supported platforms, including configuration, module, and framework functionality tests.
3. Simulation Flow
Allpix2 simulations execute configured modules sequentially for each event, while initialization steps can prepare geometry or other information before processing begins. The modular design supports both simple single-detector chains and more complex multi-detector setups.
- Simulation execution: Each simulation consists of modules with specific parameters executed sequentially for every simulated event.
- Simulation execution: Modules may run initialization code before the simulation chain, including processing information needed for electric-field generation.
- Simulation setups: A typical silicon-detector simulation can be expanded from a simple use case to complex configurations with different modules and multiple detectors.
- Additional geometry: Additional geometry information can be supplied by modules that store materials and other objects alongside detector models.
- Additional geometry: The GeometryBuilderGeant4 module converts internal detector models into Geant4-compatible geometry using predefined configuration-driven sequences.
- Additional geometry: Separating Geant4 geometry construction into its own module minimizes external dependencies and permits operation without that dependency for further data processing.
3.2. Visualisation of the Setup
Allpix2 supports visual inspection and detailed electric-field modeling for detector setups, including multi-detector configurations and TCAD-derived fields. These capabilities help represent geometry, field profiles, and charge-transport conditions within the simulation chain.
- Setup visualization: VisualizationGeant4 displays detector geometry together with primary and secondary Geant4 particles, helping verify configuration and placement in complex setups.
- Electric fields: Electric fields are added by a dedicated module rather than treated as detector geometry, allowing different fields or bias voltages to be applied to the same detector type.
- Electric fields: Allpix2 supports both linear electric fields and imported TCAD field maps.
- Simulation chain: A single-detector chain proceeds from geometry and field construction through charge deposition, propagation, collection, digitization, and result storage.
- Multi-detector setups: A three-detector setup can use simpler reference-device simulations alongside a more detailed device-under-test chain with TCAD fields, drift-diffusion, capacitive coupling, and multiple thresholds.
- Detector geometry: Hybrid-detector bump bonds can be modeled as joined spherical and cylindrical volumes between the sensor and readout ASIC.
- Electric fields: TCAD field distributions are converted from adaptive meshes to uniformly spaced grids to reduce interpolation computation time.
- Electric fields: The resulting field is replicated across pixels and accessed transparently through the detector model for any three-dimensional point.
3.4. Deposition of Charge Carriers
Allpix2 uses Geant4 through DepositionGeant4 to model particle interactions and convert energy deposits into linked charge-carrier information.
- 3.4. Deposition of Charge Carriers: DepositionGeant4 interfaces with Geant4 to generate and propagate particles throughout the volume surrounding the detector setup.It configures particle properties from the user-provided configuration.
- 3.4. Deposition of Charge Carriers: Using one fifth of the setup’s minimal detector feature size by default improves the description of secondary-particle effects on cluster size.This setting concerns the simulation resolution used by DepositionGeant4.
- 3.4. Deposition of Charge Carriers: The module can use any available Geant4 physics list, with optional PAI modelling for very thin sensors.PAI denotes the Photoabsorption Ionisation model.
- 3.4. Deposition of Charge Carriers: Energy deposits in sensitive volumes become charge-carrier deposits and retain links to primary and secondary particle trajectories.Secondary information includes particles such as delta electrons.
3.5. Propagation of Charge Carriers
Allpix2 provides fast and detailed approaches for charge-carrier propagation, including field-transparent integration that can use complex TCAD field maps. Current propagation omits induced transient currents.
- 3.5. Propagation of Charge Carriers: Allpix2 implements two charge-carrier propagation methods with different levels of complexity.Propagation through the sensitive volume is a key component of semiconductor detector simulation.
- 3.5. Propagation of Charge Carriers: ProjectionPropagation analytically estimates drift time in a linear field and adds Gaussian lateral diffusion before placing carriers at the sensor surface.For thick, planar sensors, this fast approximation is sufficiently precise when detectors serve as references.
- 3.5. Propagation of Charge Carriers: GenericPropagation steps user-defined carrier groups through the sensor using Jacoboni mobility, Runge-Kutta field integration, and diffusion at each drift step.The mobility is recalculated at each position.
- 3.5. Propagation of Charge Carriers: Because the electric field is requested as 3D vectors, GenericPropagation can use field maps from TCAD without exposing the field-evaluation method.This supports observing charge flow along field lines in complicated profiles, including depleted CMOS devices.
- 3.5. Propagation of Charge Carriers: Propagation currently omits transient currents induced on charge-collection implants, although Ramo weighting-field treatment is under implementation.The abstraction is considered sufficient for many detector-performance applications.
3.6. Transfer from Sensor to Readout Chip
Allpix2 separates sensor-to-chip signal transfer from charge propagation and digitisation, allowing the simulation chain to represent different interconnect technologies.
- 3.6. Transfer from Sensor to Readout Chip: The transfer step adds flexibility for detectors using different sensor-to-readout interconnect technologies.It sits between charge-carrier propagation and front-end digitisation.
- 3.6. Transfer from Sensor to Readout Chip: SimpleTransfer groups carriers within a pixel boundary and implant depth for monolithic or DC-coupled hybrid detectors.The module represents signal formation for these detector configurations.
- 3.6. Transfer from Sensor to Readout Chip: Capacitive-Transfer models cross-coupling between neighbouring pixels in capacitively coupled hybrid detectors.It can emulate additional signals and pixel hits caused by stray capacitances.
3.7. Digitisation of the Signal
A generic digitisation module converts transferred sensor charge into configurable front-end responses rather than modelling a specific ASIC.
- 3.7. Digitisation of the Signal: The generic digitisation module simulates front-end pixel-electronics responses from the charge transferred to each pixel.Its configurable parameters support a variety of chip architectures.
- 3.7. Digitisation of the Signal: Digitisation can combine charge with electronic noise, apply a threshold with optional dispersion, and convert electrons into ADC units.These parameters model thresholding, gain, and counter precision.
- 3.7. Digitisation of the Signal: A fixed offset combined with the conversion settings can represent a typical Time-over-Threshold digitisation response.The response is mapped onto a customisable-precision counter.
3.8. Storing the Simulation Result
Allpix2 stores simulation results in ROOT trees and preserves configuration and detector information so simulations can be reproduced and inspected. Stored intermediate data can also be replayed to vary later digitisation settings without recomputing the full chain.
- Each ROOT tree stores information for a specific detector and message type, while the writer records the framework, module configuration, and detector setup.This enables verification of simulation settings from the data file.
- Simulation data can be selectively stored, including or excluding details such as deposited-energy positions and primary-particle entry and exit points.
- Stored messages can be replayed to restart the simulation from an intermediate stage and test variable digitisation settings without rerunning the full chain.ROOTObjectReader dispatches the stored messages back into the framework.
- Output modules support reconstruction and analysis frameworks including EUTelescope, Proteus, and Corryvreckan.Corryvreckan was used for the results presented in the following section.
4. Comparison with Testbeam Data
The Allpix2 simulation reproduces key beam-telescope and DUT observables using a first-principles setup with only a few tuned parameters. Agreement with data is strong for tracking, cluster size, charge, and intrinsic resolution, while some detector-specific effects remain outside the simulation scope.
- Experimental setup and simulation inputs: The simulation uses beam and geometry inputs, Geant4 physics, operating parameters, and tuned charge-digitisation parameters without modelling several ASIC-specific effects.A Gaussian smearing term and a gain factor of 1.03 were used for comparison with charge-calibrated data.
- Experimental setup and simulation inputs: The comparison models a six-plane Timepix3 telescope, two n-in-p DUTs, and track-to-cluster association using χ2 and spatial selection criteria.The DUTs are 50 µm and 100 µm thick, while telescope planes use 300 µm silicon sensors.
- Track reconstruction: A telescope track resolution of about 2 µm was obtained from Monte Carlo truth and agrees with the corresponding data-based telescope residuals.The simulated random detector shifts and rotations were also reproduced correctly by alignment.
- DUT observables: The simulated cluster-size distributions show excellent agreement with data, including high-size tails dominated by higher-order effects such as delta-electron emission.Small differences for three- and four-pixel clusters may be reduced by tuning simulated threshold values.
- DUT observables: The simulated cluster-charge distributions closely resemble the Landau-shaped data distributions, with further improvement expected from modelling per-pixel threshold and gain variations.The charge comparison covers both 50 µm and 100 µm sensors.
- DUT observables: The simulated residual RMS values are 15.2 µm and 13.6 µm for the 50 µm and 100 µm DUTs, versus 14.4 µm and 12.8 µm in data.After subtracting track resolution quadratically, the intrinsic simulated resolutions are 15.0 µm and 13.4 µm for the thinner and thicker DUTs.
5. Conclusions & Outlook
Allpix2 combines detailed particle–material interactions with charge transport and signal formation in a lightweight, modular framework. Validation against data shows close agreement after adjusting only a few known parameters, while further physics and electronics extensions are planned.
- Allpix2 combines detailed simulation of particle and detector-material interactions with charge-carrier motion and signal formation.
- Its initial validated modules cover Geant4 particle propagation and energy deposition, charge transport, readout coupling, digitisation, and data input/output.
- Simulation and data agree closely for beam-telescope track resolution, DUT cluster size, charge, intrinsic resolution, and residual shape after adjusting only a few known parameters.
- Primary-particle position information enables assessment of charge transport, digitisation, and track-reconstruction effects on detector performance.
- Planned extensions include laser-induced charge deposition, transient induced currents using Ramo weighting fields, radiation damage, digital front-end effects, and high-Z sensor support.