Rectangular Approximation for Curved-Shape Power Density in Chip Thermal Analysis

This paper proposes a rectangular approximation method for curved-shape power density to rapidly calculate the temperature profile of the entire chip by using the 2D thermal model with the effective thermal characteristic length. The proposed method employs rectangular blocks to approximate the non-rectangular power density areas, thereby enabling the utilization of stepwise integration for the determination of the cosine series coefficients. In contrast to the conventional grid mesh approach, this rectangular approximation significantly reduces the number of required mesh elements, thus considerably enhancing computational efficiency. Numerical results reveal that the proposed method achieves a speed improvement ranging from 94×to 195× over the traditional grid technique, while maintaining comparable accuracy. Furthermore, the maximum absolute error observed in temperature predictions is limited to a mere 0.37K.