Theory and Analysis for Optimization of On-Chip Thermoelectric Cooling Systems

We established a novel theoretical analysis framework for optimizing the cooling system configuration of chips employing thermoelectric cooling (TEC) elements by extending the theory of inverse-positive matrices and the eigenvalue/eigenvector theory in linear algebra. In this brief, we present a new theorem and its formal proof, which is the key enabler to achieving a provably optimal solution for configuring bias current levels of TEC devices.