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|Ultra Fast Calculation of Temperature Profiles of VLSI ICs in Thermal Packages Considering Parameter Variations|
|Keywords: Power Blurring, Convolution, Green's Function Method|
|Due to the aggressive scaling down of the CMOS technology, VLSI ICs become more and more vulnerable to the effect of non-uniform high temperatures which can significantly degrade chip performance and reliability. Therefore, we are interested in surface temperature profiles of VLSI ICs. In IC thermal analysis, heat conduction equation is conventionally solved by grid-based methods which are computationally expensive. In an effort to reduce the computation time, a matrix convolution technique, called Power Blurring (PB), has been proposed. This PB method has its theoretical basis on the Green’s function method and the methodological basis from image blurring used for image processing. It was reported that PB method reduced the calculation time by three orders of magnitude compared to the Finite Element Analysis (FEA). Furthermore, we find that it calculates the temperature profile with maximum temperature errors less than 1% for various types of power distributions. It requires a spatial impulse response, called the thermal mask, which can be obtained by using FEA tools such as ANSYS. The thermal mask is a function to be convoluted with power distribution for temperature profile. Thus, the PB method uses FEA repeatedly for the changes in parameters of thermal packages such as thermal conductivity, convection heat transfer coefficient, and silicon substrate thickness to obtain new thermal mask. Our test structure is divided into 49,323 elements and 1600 elements correspond to the surface of the silicon substrate. Hence, performing FEA repeatedly is time consuming. In this paper, we will describe the PB method and propose a method for parameterization of the thermal mask to avoid many FEA simulations under parameter variations. The PB method using parameterized mask shows good performances with maximum error less than 2.3% for various case studies and reduces calculation time from 17 seconds to 0.1 second for our test structure.|
|Je-Hyoung Park, Student
University of California at Santa Cruz
Santa Cruz, CA