Device Packaging 2019

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Automated Discovery of Negative CTE Microstructures
Keywords: CTE , Multi-Material, Additive Manufacturing
Conventional discovery of negative coefficient of thermal expansion material structures involves a combination of manual design and numerical simulations. Humans typically provided the basic structural mechanisms defined by a small set of parameters to control the expansion of geometry locally throughout a volume towards the goal of a macroscopic thermal expansion that it significantly less than the materials used, while simulations are subsequently employed to verify and optimize the structure within reasonable bounds for fabrication. Once constructed, tests can be performed to confirm the expected reduction in thermal expansion. While such structures have been designed and fabricated out of sets of one, two or more materials, the range of material properties they can be used to obtain are limited due to the overwhelmingly large set of materials and structural combinations available. To map them all conventionally would take an inordinate amount of effort. One approach to deal with the complexity of the solution space is to use optimization techniques like Topological Optimization, which can automate the process of achieving desired parameters within defined constraints, but to keep the problem manageable such optimization is usually limited to a single domain, e.g. structural or thermal. To facilitate the discovery of new negative CTE multi-material microstructures, we have developed a computational framework which automates the process and significantly lowers the barrier to incorporation of designer thermal expansion material structures into new designs. The process begins with the selection of materials to be included for consideration in a multi-material composite and the definition of their thermal and structural properties provided on technical data sheets or from lab experiments. Composite structures are then randomly generated within an FEA solver which extracts stiffness and CTE parameters to build an initial map of the property space. This space of a few hundred or thousand data points is then expanded through sampling that preferentially pushes the boundary of achievable CTE, and systematically fills in the gaps between previously discovered regions to achieve a desired density of known structures in the parameter space. Families of mechanism are identified though machine learning algorithms, which further generate related samples through continuous optimization to rapidly realize material property combinations that are available for use further down the line in the design of complex multi-material systems. This particular study focused on a system of three materials in two dimensions with idealized material properties, though the solver is capable of working with larger sets of materials with more complex characteristics and three dimensional geometries. The first two materials where similar in stiffness, but had an order of magnitude difference in coefficient of thermal expansion. The third material is a material with significantly lower stiffness. This mix of expansive and compressible materials are the basic building blocks for negative CTE structures, but using the automated material discovery we can identify many more families of negative CTE mechanisms. Overall, we show that microstructures with CTE as low as -8 have been discovered for materials with starting relative CTEs of 1 and 10. The resulting structures have low stiffness, below 30% of bulk stiffness.
Isaac Ehrenberg, Technical Staff
Cambridge, Massachusetts
United States

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