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As the scaling of silicon complementary metal-oxide-semiconductor devices becomes more and more challenging, both innovative device structures and new materials with high carrier mobility are needed to continue improving device performances. A metal-oxide-semiconductor field-effect transistor with germanium channel currently receives a resurgence of interest as a possible candidate for next-generation high mobility devices because germanium offers much higher mobility for both electrons and holes in comparison with silicon. While germanium solid-state device provides outstanding electrical benefits, it also offers significant challenges in thermal management and raises a major concern over the effect of on-chip hot spot on the reliability and performance of germanium chips. Current thermal management technologies, with a major focus on chip-level global cooling, offer very few choices for on-chip micro-scale hot spot cooling. The inherent thermoelectric properties of single crystal germanium support development of a novel thermal management strategy for micro-scale hot spot cooling which relies on thermoelectric self-cooling by electric current flowing into the back of the germanium chip. In this paper, the concept of germanium self-cooling for on-chip micro-scale hot spot is proposed and investigated. 3-D thermal-electric coupling simulations are used to evaluate the hot spot cooling performance on a germanium chip with a wide range of system parameters, including applied current, doping concentration, hot spot heat flux, micro-cooler size, and germanium chip thickness. The results suggest that localized thermoelectric self-cooling on the germanium chip can effectively reduce the temperature rise resulting from micro-scale high heat flux hot spots and shows a great promise as a novel on-chip cooling solution.