Istituto Nazionale di Fisica Nucleare
Sezione di Trieste

Simulation

Throughout the design process, work proceeds through cycles of design and verification simulation. There are multiple objectives to be met, ranging from the operation of the sensor and the electronics to that of the complete system.

Different tools are employed depending on the device or system component to be simulated: individual devices – such as sensors – are simulated using TCAD; electrical circuits via SPICE; and the complete system using custom-developed software that models the interactions of theassembly, drawing on outputs from the basic simulators nd integrating them with design data regarding the logic that connects them. Several types of simulation and their respective applications are presented below.

An X-ray detector must be sensitive within a specific photon energy range. From the perspective of the experiment in which it will be used, it is important to estimate its quantum efficiency based on its structure. The figure shows, on the left, the result of a TCAD simulation of a typical section of the active area of a linear drift sensor, highlighting the passive region between two drift electrodes. The profile of the insensitive regions allows for the calculation of quantum efficiency – as a function of energy and angle of incidence – which is plotted in the graph on the right.

Result of a TCAD simulation of a typical section of the active area of a linear drift sensor, highlighting the passive region between two drift electrodes

Ionization detectors often operate in hostile environments – for instance, due to the very radiation being measured or other types of radiation reaching the detector components. Semiconductor devices are susceptible to effects caused by displacement damage (nuclear collisions that displace atoms from the crystal lattice) and by the total dose accumulated in insulating parts. Damage of the former type leads to increased sensor current, whereas the total dose causes the generation of intense electric fields that can trigger electrical discharges, damaging the affected structures.

Simulating the interaction of radiation with the sensor material makes it possible to evaluate the effect of device exposure and estimate its operational lifespan within the limits required by the application. The graph on the left of the figure below shows the calculated hardness factor for a large-area linear drift detector bombarded by protons trapped in the radiation belts surrounding the Earth. The graph on the right, meanwhile, displays the differential displacement damage spectrum for the sensors of the two instruments proposed for the LOFT space mission.

Calculated hardness factor for a large-area linear drift detector bombarded by protons trapped in the radiation belts surrounding the Earth

Complex detectors require system-level simulations. In the case of a multi-element detector used to measure an intense radiation flux, it is necessary to account for the dead time of each element and the variation in intensity distribution across the different elements. Studying a measurement correction system for conditions involving a high dead-time fraction requires a robust system-level simulation of the detector. The following figure compares measurements from an element of the AXPiDe detector with its simulation; these data were obtained during a measurement campaign analyzing the fluorescence emitted by a metallic copper sample exposed to a 9 keV photon beam at the XAFX beamline at Elettra Sincrotrone Trieste.

Measurements comparison from an element of the AXPiDe detector with its simulation

To validate the detector simulation, measurements taken under extreme conditions were compared. The histogram on the left compares the spectrum acquired by the detector – using a peaking time of 0.7 µs and an incident photon rate exceeding 2 MHz – with the simulation: the simulation reproduces the spectrum’s shape excellently, including pile-up of various orders. The graph on the right compares the total dead time and the dead time attributable solely to the reset mechanism for the same detector element when using a peaking time of 1.5 µs: in this case, too, the simulation faithfully tracks the experimental data.

The creation of such a precise simulation enabled the development of a dead-time and pile-up correction system, which was verified via XANES analysis of the titanium K-edge absorption in a TiO₂ sample by measuring the titanium K_α fluorescence line at various distances from the sample.

Comparison of the spectrum acquired by the detector – using a peaking time of 0.7 µs and an incident photon rate exceeding 2 MHz – with the simulation

The three graphs on the left show the successive correction steps starting from the detector counts; at the closest position (pos1), the counts reach saturation. The graph on the right compares the four corrected measurements after normalization for the absorption jump at the K-edge. Any errors in data correction can be identified by the differing heights of the three peaks preceding the edge. The inset shows that the residual error is very small, thereby validating the system.

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