Abstract
In a microelectronic device, thermal transport needs to be simulated on scales ranging from tens of nanometers to hundreds of millimeters. High accuracy multiscale models are required to develop engineering tools for predicting temperature distributions with sufficient accuracy in such devices. A computationally efficient and accurate multiscale reduced order transient thermal modeling methodology was developed using a combination of two different approaches: “progressive zoom-in” method and “proper orthogonal decomposition (POD)” technique. The capability of this approach in handling several decades of length scales from “package” to “chip components” at a considerably lower computational cost, while maintaining satisfactory accuracy was demonstrated. A flip chip ball grid array (FCBGA) package was considered for demonstration. The transient temperature and heat fluxes calculated on the top and bottom walls of the embedded chip at the package level simulations are employed as dynamic boundary conditions for the chip level simulation. The chip is divided into ten function blocks. Randomly generated dynamic power sources are applied in each of these blocks. The temperature rise in the different layers of the chip calculated from the multiscale model is compared with a finite element (FE) model. The close agreement between two models confirms that the multiscale approach can predict temperature rise accurately for scenarios corresponding to different power sources in functional blocks, without performing detailed FE simulations, which significantly reduces computational effort.
Published Version
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