Optimization of Si/SiGe Microrefrigerators for Hybrid Solid-State/Liquid Cooling

Monolithic Solid-state microrefrigerators have attracted a lot of attention during the last ten years since they have the potential to solve some of the problems related to localized heat generation and temperature stabilization in optoelectronic, microelectronics or even biological microchip applications. Combination of the solid-state cooling with other conventional techniques like liquid cooling, offers an additional degree of freedom to control both the overall temperature of the chip and to remove hot spots. We present a new approach based on Thermal Quadrupoles Method to model the behavior of a single stage Si/SiGe microrefrigerator in the DC operating regime. The sensitivity and precision of this method come from its analytical expressions, which are based on the solution of Fourier’s heat diffusion equation in the Laplace domain. The microrefrigerator top surface temperature is calculated by taking into account all possible mechanisms of heat generation and conduction within the entire device. The 3D heat and current spreading in the substrate is taken into account. The parasitic heat leakage to the cold junction due to heat generation and heat conduction within the metal lead is also considered. The theoretical results are then compared with experimental ones for several microrefrigerator sizes. A good agreement is found between them. Based on the simulations, the structure of the microrefrigerator is optimized for lowering the overall chip temperature and removing high power density hot spots in several applications in conjunction with liquid cooling techniques.