Two-dimensional electrical modeling of thermoelectric devices considering temperature-dependent parameters under the condition of nonuniform substrate temperature distribution

Since more aggressive thermal solutions, than would be required for uniform heating, are highly desired. Thermoelectric devices are regarded as an available thermal solution for high power electronic packages like processors. In this paper, a steady-state numerical model is derived for thermoelectric coolers (TECs) with parameters controlled by two-dimensional thermal profiles. Using the thermoelectric duality, we propose an improved electrical model with temperature-dependent parameter distribution in the presence of multi-couple pellets. Both electrical element and thermal behavior are simulated based on this improved model with TEC parameters modified according to the nonuniform temperature effects. The results demonstrate an excellent agreement with numerical calculation and the proposed electrical model. It proves that thermal profiles in the underlying silicon substrate have a linear effects on the temperature at the cold side of TECs. In addition, the optimum value of the temperature difference exhibits a negative interrelation with the electrical current flowing through TECs under a fixed hot junction temperature.