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A Discrete Tangent based Sensitivity Analysis Method for Electronics Packaging Thermal Management
Keywords: Thermal management, CFD, Sensitivity Analysis
Thermal management of electronics packages governed by many operating parameters such as the powermap floorplans, material properties, and environmental conditions.  In most packages many of these parameters influence the package in complicated and interconnected manner.  It often requires generating, gathering, and analyzing design data from a large number of simulations or experiments to determine and quantify the critical parameters that govern the performance and their range of influence. CFD (Computational Fluid Dynamics) has become a vital tool to study, design, and optimize the packages. These analyses provide spatial and temporal detail of the conditions in the package helping the designer to make informed decisions regarding improving or optimizing the performance. However, CFD simulations can also be time consuming and expensive to perform especially when a large number of parameters are involved. Discrete tangent method is an approach that generates spatial derivatives with respect to selected parameters with every simulation. Derivatives of solution with respect to additional parameters are also generated at a small cost compared to the cost of full simulation at another value of the parameter. This rich data will save cost and effort required to characterize the package designs. This work presents an investigation of a flipchip package using Discrete Tangent method which provides solution and gradients of all variables in the package with respect to input and/or operating parameters. This rich data from a single simulation is useful identifying the strongest parameter which influence the performance both in overall terms and in detail. It will quantify the degree of influence of a parameter on the package and map the spatial influence of the parameter. The results for the sensitivity of the temperature profiles to input parameters such as the powermap, individual sources, leakage power, and environmental condition are presented. Results include the solution fields (or derived quantities) at the specified value of the sensitivity parameter (computed value), the gradient of the solution field with respect to this sensitivity parameter (derivative), and the extrapolated value of the field about the specified value of sensitivity parameter. The sensitivity results will be compared with results obtained from multiple single-point simulations using traditional simulators. The work also quantifies the time saved to obtain the range of sensitivity data for this demonstrative package simulation compared to the conventional approaches.
Prabhu Sathyamurthy, President
Amoeba Technologies Inc.
Austin, TX

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