An accurate non-uniformity characterization of the temperature field in microsystems based on singular value decomposition

Abstract

The significant thermal challenges faced by the new generation of high-density integrated microsystems have become hot research topics in current thermal design, management, and reliability of microsystems. The non-uniformity of temperature field (NUTF) is at the core of these challenges. Accurately characterizing the NUTF of microsystems has been a difficult task. This paper proposes an accurate characterization method for microsystem NUTF based on singular value decomposition (SVD) to enhance the effectiveness and accuracy of traditional NUTF characterization methods. The paper also investigates the impact of the non-uniform distribution of the microsystem's heat flux densities (HFDs) on the temperature field and its complexity using the singular value properties. The results demonstrate that the proposed method can quantitatively characterize the steady-state NUTF and the spatial-temporal transient NUTF of the microsystems. The decay rate of the singular values can effectively identify the non-uniformity of the microsystem's HFDs. The number of singular values above a threshold can quantitatively assess the complexity of the microsystem temperature field.