Optimization of 3D diamond detectors with graphitized electrodes based on an innovative numerical simulation

Abstract

Future experiments at hadron colliders require an evolution of the tracking sensors to ensure sufficient radiation hardness as well as space and time resolution to handle unprecedented particle fluxes. 3D diamond sensors with laser-graphitized electrodes are promising candidates due to their strong binding energy, small atomic number, and high carrier mobility. However, the high resistance of the engraved electrodes delays the propagation of the induced signals towards the readout electronics, thereby degrading the precision of the timing measurements. So far, this effect has been the dominant factor limiting the time resolution of these devices, with other contributions, such as those due to electric field inhomogeneities or electronic noise, typically neglected. Recent advancements in graphitization technology, however, motivate a renewed effort in modeling signal generation in 3D diamond detectors, to achieve more reliable predictions. To this purpose, we apply an extended version of the Ramo-Shockley theorem, describing the effect of signal propagation as a time-dependent weighting potential, obtained by numerically solving the Maxwell's equations in a quasi-static approximation. We developed a custom spectral method solver and validated it against COMSOL MultiPhysics. The response of the modeled sensor to a beam of particles is then simulated using Garfield++ and is compared to the data acquired in a beam test carried on in 2021 by the TimeSPOT Collaboration at the SPS, at CERN. Based on the results obtained with this simulation workflow, we conclude that reducing the resistivity of the graphitic columns remains the priority for significantly improving the time resolution of 3D diamond detectors. Once achieved, optimization of the detector geometry and readout electronics design will become equally important steps to further enhance the timing performance of these devices.

Figures (18)

• Figure 1: Diagrammatic illustration of a three-dimensional diamond sensor, depicting a segment comprising four by four fundamental units. The figure illustrates electrodes connected to the polarization voltage (black) and grounded terminals (red). Proportions are illustrative; actual dimensions may vary.
• Figure 2: A detailed microscopic image of a 3D diamond sensor is presented. The specimen was slightly tilted during acquisition to ensure the complete visualization of the graphitized electrodes.
• Figure 3: Simulated trajectories of electrons (blue lines) and holes (red lines) generated by a 180 GeV/$c$ pion traversing a diamond sensor. The graphitized electrodes are depicted as gray or red cylinders, representing their connection to polarization voltage (positive in this case) and readout (grounded), respectively. The electrostatic field was derived by solving the Poisson equation using COMSOL MultiPhysics®, with drift paths computed by Garfield++.
• Figure 4: Signal induced on perfectly conductive electrodes embedded in a diamond dielectric traversed by a 180 GeV/$c$ pion. The signal model includes only processes 1 and 2, excluding propagation effects (process 3). The contributions due to the induction of electrons and holes are presented separately.
• Figure 5: A schematic representation of two electrodes used for detecting a traversing particle, depicted as an impedance network. Ionization charges are modeled using idealized pulse current generators. The total capacitance ($C$) and resistance ($R$) are distributed uniformly across $n$ identical elements.