Cooling heat flux, COP, and cost optimization of integrated thermoelectric microcoolers with variation of thermoelectric properties

Thermoelectric (TE) microcoolers are solid state devices widely considered as strong candidates for precise temperature control and spot cooling in microelectronic circuits, especially for temperature sensitive devices such as laser diodes. Despite the excellent scalability and process compatibility of TE microcoolers for microelectronics, their utilization has been limited by their relatively moderate performance compared to vapor compression cycles due to the relatively small material figure-of-merit (ZT). In addition to crucial advantage of TE for a hotspot cooling, improving the ZT value of thermoelectric material has been the focus of research interest over the past few decades. Yet the independent impacts of three components of the ZT value have not been very clear. In this paper, we report the material cost impact of TE microcooler integration and coefficient-ofperformance (COP) change relative to modifications of the electrical conductivity, the Seebeck coefficient, and the thermal conductivity. This study is mostly focused on high heat-flux spot cooling based on the analysis of a practical TE microcooler integrated with a microchannel heat sink. Based on a one-dimensional analytic model, including the system thermal resistances, we maximize the cooling COP as functions of the drive current and the design thickness of a TE element. An example demonstrates the cooling performance for a 500 μm x 500 μm size integrated circuit with a temperature constraint of 65 °C maximum and an operating temperature of 74 °C for the heat sink. Increasing the ZT value linearly increases the maximum COP for a given temperature constraint and the maximum COP changes equally by varying any of the thermoelectric properties as expected. For the same ZT value, however, a lower thermal conductivity requires a thinner TE element for a design optimized for COP, e.g. changing the thermal conductivity from 1.5 W/mK to 0.75 W/mK reduces the optimum thickness from approximately 9 μm to 5 μm for 100 W/cm2 of heat flux. This result is encouraging for the utilization of TE for spot cooling since the TE cost directly relates to the mass usage of the material.