The performance limits and design techniques of multistage thermoelectric devices

A method of calculating the performance limits of multi-stage thermoelectric devices is derived by a direct thermodynamic approach and a comparison is made between multi-stage and single stage devices. The results are then applied to the design of feasible multi-stage devices that closely approximate these limits. The calculations indicate that at present there is little advantage in using more than one stage in a thermoelectric generator. In the case of a thermoelectric refrigerator however, a practicable multi-stage device should be able to produce a temperature reduction about twice as great as that obtainable with a single stage device. This at present corresponds to a maximum temperature reduction of approximately 135°C for the multi-stage device. The approximate limits of feasible temperature reduction are calculated as a function of the value of the figure of merit Z. This calculation indicates that even if materials are improved by an order of magnitude or more it will probably never be feasible to construct a thermoelectric refrigerator that can cool to cryogenic temperatures while operating from a room temperature ambient.