Modelling of integrated Peltier elements

On-chip integration of Peltier devices creates a number of additional parasitics, compared to conventional Peltier devices. The most important are thermal conduction through the supporting membrane and contact resistance. Analytical analysis shows that each parasitic decreases device performance, but only the contact resistance creates a significant shift in the optimum device current where the temperature reduction is maximised. To obtain an energetically correct lumped-element model, as presented in this paper, the electro-thermal Peltier effect must be linked to the thermo-electric Seebeck effect, which acts as a feedback parameter. The influence of this Seebeck voltage on a non-ideal current source, driving the Peltier device, is investigated and it is shown that the influence can be ignored if the current source has a reasonable impedance.