This paper addresses the topology optimization of thermocouples for cooling applications, considering stress constraints to enhance reliability under service loads. We provide a first approach to derive sensitivities using SIMP (solid isotropic material with penalization) for thermo-electro-mechanical systems with temperature-dependent material properties. The proposed formulation decouples the thermoelectrical system from the mechanical degrees of freedom reducing computational memory usage from a fully coupled approach. The study focuses on the formulation of thermocouples for cooling applications using the Peltier effect, which considers electrical power limits, electrical working points, and material stress thresholds. Furthermore, while the thermoelectrical problem does not show the need for filtering techniques, including the mechanical degrees of freedom, we show that we recover undesirable porous optimized designs. We provide 2D thermocouple example optimizations with geometries and boundary conditions based on a practical case for the implementation of thermoelectric coolers in the Minimum Ionizing Particle Timing Detector (MTD) at CERN. The optimizations are performed with increased complexity, including the unfiltered thermoelectrical and thermo-electro-mechanical problems and a Helmholtz-filtered examples. The optimizations are compared with constant and nonlinear material properties with temperature and with respect to the consideration of air-conductance losses within the devices. Although more efficient topologies can be achieved without the need for volume constraints, we include an example with a constraint of 60% volume to understand its effect on the design and provide a methodology to reduce semiconductor-associated costs at lower efficiency costs. Finally, we explore the same formulation in 3D. The results provide guidelines for manufacturing compliant thermocouples, increasing their reliability without decreasing efficiency.

For the High-Luminosity (HL-LHC) phase, the upgrade of the Compact Muon Solenoid (CMS) experiment at CERN will include a novel MIP Timing Detector (MTD). The central part of MTD, the barrel timing layer (BTL), is designed to provide a measurement of the time of arrival of charged particles with a precision of 30 ps at the beginning of HL-LHC, progressively degrading to 60 ps while operating in an extremely harsh radiation environment for over a decade. In this paper we present a comparative analysis of the time resolution of BTL module prototypes made of LYSO:Ce crystal bars read out by silicon photo-multipliers (SiPMs). The timing performance measured in beam test campaigns is presented for prototypes with different construction and operation parameters, such as different SiPM cell sizes (15, 20, 25 and 30 μm), SiPM manufacturers and crystal bar thicknesses. The evolution of time resolution as a function of the irradiation level has been studied using non-irradiated SiPMs as well as SiPMs exposed up to 2 × 10¹⁴ n_eq/cm² fluence. The key parameters defining the module time resolution such as SiPM characteristics (gain, photon detection efficiency, radiation induced dark count rate) and crystal properties (light output and dimensions) are discussed. These results have informed the final choice of the MTD barrel sensor configuration and offer a unique starting point for the design of future large-area scintillator-based timing detectors in either low or high radiation environments.

Inorganic scintillators often use exotic, expensive materials to increase their light yield. Although material chemistry is a valid way to increase the light collection, these methods are expensive and limited to the material properties. As such, alternative methods such as the use of specific reflective coatings and crystal optical shapes are critical for the scintillator crystal design procedure. In this paper, we explore the modeling of a scintillator and silicon-photomultiplier (SiPM) assembly detector using GEANT4. GEANT4, an open-source software for particle–matter interaction based on ray-tracing, allows the modeling of a scintillator-based detector while offering methods to simplify and study the computational requirements for a precise calculation of the light collection. These studies incorporate two different geometries compatible with the barrel timing layer (BTL) particle detector that is being built for the compact muon solenoid (CME) experiment at CERN. Furthermore, the geometry of our model is parameterized using splines for smoother results and meshed using GMSH to perform genetic numerical optimization of the crystal shape through genetic algorithms, in particular non-dominated sorting genetic algorithm II (NGSAII). Using NSGA-II, we provide a series of optimized scintillator geometries and study the trade-offs of multiple possible objective functions including the light output, light collection, light collection per energy deposited, and track path length. The converged Pareto results according to the hypervolume indicator are compared to the original simplified design, and a recommendation towards the use of the light collection per energy deposition and track path length is given based on the results. The results provide increases in this objective of up to 18% for a constant volume for a geometry compatible with the current design of the BTL detector.

Heat pumping through thermoelectric devices has many advantages over traditional cooling. However, their current efficiency is a limiting factor in their implementation. In this paper, we approach the non-convex topology optimization of thermoelectrical elements for cooling applications through the method of moving asymptotes (MMA) to improve their cooling capabilities per watt usage. The optimization problem is defined for a given power budget, aiming for the minimum temperature with a known heat pumping need. The introduction of power as a constraint justifies the introduction of the voltage gradient across the thermocouple as a design variable to maintain the thermoelectrical device in its optimum power-to-heat extraction ratio. To better understand the convergence of this non-convex problem, we present a two-variable analytical thermoelectric optimization model. This example provides information on how to select the penalty parameters used to scale the three material coefficients involved in the problem to obtain lower objective values and better convergence using MMA. The analytical model shows the non-convexity of the problem and provides the recommendation to use penalization coefficients of the form p_k=p_σ>p_α=1 for the thermal conductivity, electrical conductivity, and Seebeck coefficients. We tested these penalization coefficients through optimizations of a model based on the 1MC10-031 commercial thermoelectric-cooler (TEC) using the finite element method (FEM). These penalization coefficients provided local minima without the need for volume constraints. With this procedure, we found designs that provided temperatures close to 10 degrees lower using 60% less semiconductor material volume compared to the initial design.

The barrel section of the novel MIP Timing Detector (MTD) will be constructed as part of the upgrade of the CMS experiment to provide a time resolution for single charged tracks in the range of 30-60 ps using LYSO:Ce crystal arrays read out with Silicon Photomultipliers (SiPMs). A major challenge for the operation of such a detector is the extremely high radiation level, of about 2 × 1014 1 MeV(Si) Eqv. n/cm2, that will be integrated over a decade of operation of the High Luminosity Large Hadron Collider (HL-LHC). Silicon Photomultipliers exposed to this level of radiation have shown a strong increase in dark count rate and radiation damage effects that also impact their gain and photon detection efficiency. For this reason during operations the whole detector is cooled down to about -35°C. In this paper we illustrate an innovative and cost-effective solution to mitigate the impact of radiation damage on the timing performance of the detector, by integrating small thermo-electric coolers (TECs) on the back of the SiPM package. This additional feature, fully integrated as part of the SiPM array, enables a further decrease in operating temperature down to about -45°C. This leads to a reduction by a factor of about two in the dark count rate without requiring additional power budget, since the power required by the TEC is almost entirely offset by a decrease in the power required for the SiPM operation due to leakage current. In addition, the operation of the TECs with reversed polarity during technical stops of the accelerator can raise the temperature of the SiPMs up to 60°C (about 50°C higher than the rest of the detector), thus accelerating the annealing of radiation damage effects and partly recovering the SiPM performance.