Thermomechanical design validation for quad pixel modules for the ITk

The current programme of upgrades to the ATLAS detector to take advantage of the opportunities presented by the High Luminosity LHC (HL-LHC) will include a complete replacement of the tracking system. This upgrade will install an all-silicon tracker called the ITk, the innermost five layers will be made up of Si Pixel (Si-Pix) detectors. These detectors will be exposed to an extremely challenging operational environment and as such will need to be cooled to very low temperatures to ensure that they will operate for the full lifetime of the experiment. The detectors and their support structures are made from materials with a range of Coefficient's of Thermal Expansion (CTE's) from ∼-0.5 ppm °C -1 for the carbon fibre support structures to several tens of ppm °C -1 for epoxy based adhesives. This means that large changes in temperature will introduce large differential movements between the components which could potentially damage the detectors. FEA was used to model the response to temperature cycling of a pixel detector module attached to the local supports material. The design space covers several parameters including the thickness of the copper traces in the PCB and the thickness and stiffness of the adhesives to ensure that the stresses induced by the CTE mismatch of the components does not cause catastrophic failure of the module. Here we present work carried out to guide the design of the flex PCB and the module testing regimes and compare the results to measurements with prototype modules.