  Traditional thermoelectric Peltier coolers exhibit a cooling limit which is
primarily determined by the figure of merit, zT. Rather than a fundamental
thermodynamic limit, this bound can be traced to the difficulty of maintaining
thermoelectric compatibility. Self-compatibility locally maximizes the cooler's
coefficient of performance for a given zT and can be achieved by adjusting the
relative ratio of the thermoelectric transport properties that make up zT. In
this study, we investigate the theoretical performance of thermoelectric
coolers that maintain self-compatibility across the device. We find such a
device behaves very differently from a Peltier cooler, and term self-compatible
coolers "Thomson coolers" when the Fourier heat divergence is dominated by the
Thomson, as opposed to the Joule, term. A Thomson cooler requires an
exponentially rising Seebeck coefficient with increasing temperature, while
traditional Peltier coolers, such as those used commercially, have
comparatively minimal change in Seebeck coefficient with temperature. When
reasonable material property bounds are placed on the thermoelectric leg, the
Thomson cooler is predicted to achieve approximately twice the maximum
temperature drop of a traditional Peltier cooler with equivalent figure of
merit (zT). We anticipate the development of Thomson coolers will ultimately
lead to solid state cooling to cryogenic temperatures.
