PSI - Issue 79

Davide D’Andrea et al. / Procedia Structural Integrity 79 (2026) 283–290

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1. Introduction Direct Bonded Copper (DBC) substrates are widely used components in power electronics modules for their high current capability, excellent thermal conductivity, flexible patterning, and strong mechanical properties (Xu et al., (2016)). They consist of a ceramic substrate bonded to one or more copper layers on one or both sides. The ceramic substrate is typically aluminium oxide (alumina, Al₂O₃), although alternative materials such as aluminium nitride (AlN) or silicon nitride (Si₃N₄) may be employed depending on the application requirements. Ceramic layers are characterized by lower coefficients of thermal expansions if compared to that characterizing copper. For this reason, during normal operation, in which DBCs are subjected to thermal cyclic loading due to heat dissipation from power electronic devices, a thermo-structural phenomenon occurs. The copper layers alternately induce tensile and compressive stress fields at the interface with the ceramic substrate. This problem has already been investigated by several researchers (Han et al., (2020); Zhang et al., (2022)), who tried to enhance fatigue life of power electronics devices by optimizing copper’s geometrical shape and introducing dimple patterns. An interesting approach was used by Gaiser et al., (2015), who analysed DBC failure caused by delamination by means of fracture mechanics concepts in order to determine an optimal geometric configuration choosing dimple depths and copper tail angle to minimize Stress Intensity Factors (SIF) and J-Integral. In this work an experimentally measured crack in Alumina layer was modelled by finite element method and copper contribution to its propagation was treated as an external load. Klusák and Knésl, (2010) proposed to treat bi-material systems as bi-material notches and calculated Strain Energy Density (SED) averaged in the critical circular area at the notch tip, using a numerical based control radius. For many years SED has been used to formulate failure criteria for materials exhibiting both ductile and brittle behaviours and it has been found as a powerful tool to assess the static and fatigue behaviour of notched and unnotched components in structural engineering (Berto and Lazzarin, (2009)). In this work, DBC components geometric characteristics have been investigated by calculating SED in several parameters’ combination sampled by means of Latin Hypercubic Sampling algorithm. Machine Learning (ML) algorithms have been used to obtain a model to perform a shape optimization of DBC section.

Nomenclature DBC Direct Bonded Copper FEM Finite Element Method LHS Latin Hypercubic Sampling MAE Mean Absolute Error ML Machine Learning R 2 Coefficient of determination R c Control area’s radius SED Strain Energy Density SHAP SHapley Additive exPlanations SIF Stress Intensity Factor

2. Material and Methods A parametric 2D model of a DBC substrate module subsection has been developed using Ansys APDL language in order to allow the variation of dimple’s radius and position, as well as the bi -material notch opening angle. Since these components are only a few microns in size, unit system consistent with micrometre has been adopted. The bi material interface was modelled by sharing nodes along the common boundary between the two regions. Dimple’s position in the copper layer is regulated by the variable x distance , which is calculated as the sum of Cu increase and r dimple . In Figure 1 it is represented the geometry used for the analysis, where the copper layer is depicted in orange and the alumina layer in grey and the symmetry axis is represented with a dash-dotted line, while Table 1 reports the description and domain of each parameter.