Efficiency and dissipation in a two-terminal thermoelectric junction, emphasizing small dissipation

The efficiency and cooling power of a two-terminal thermoelectric refrigerator are analyzed near the limit of vanishing dissipation (ideal system), where the optimal efficiency is the Carnot one, but the cooling power vanishes. This limit, where transport occurs only via a single sharp electronic energy, has been referred to as “strong coupling” or “the best thermoelectric.” Confining the discussion to the linear-response regime, it is found that “parasitic” effects that make the system deviate from the ideal limit, and reduce the efficiency from the Carnot limit, are crucial for the usefulness of the device. Among these parasitics, there are: parallel phonon conduction, finite width of the electrons' transport band, and more than a single energy transport channel. In terms of a small parameter characterizing the deviation from the ideal limit, the efficiency and power grow linearly, and the dissipation quadratically. The results are generalized to the case of broken time-reversal symmetry, and the major nontrivial changes are discussed. Finally, the recent universal relation between the thermopower and the asymmetry of the dissipation between the two terminals is briefly discussed, including the small dissipation limit.

Figure 1

The mathematical function of the efficiency, Eq. (19), as a function of $V{\eta }_C^{}$, for ${\gamma }_a=1$, $\gamma =10$, and $s=1$, for various values of $\zeta$, (a) $\zeta =0.01$, (b) $\zeta =0.1$, and (c) $\zeta =0.5$.

Figure 2

The efficiency as a function of the driving force, in the physical region. The values of $\zeta$ and $\gamma$ are marked on each panel; the four curves, in decreasing order, correspond to different values of the asymmetry parameter, in increasing order according to Eq. (13); ${\gamma }_a=0.994,0.998,1.002,1.006$ for the upper panel; ${\gamma }_a=0.945,0.985,1.025,1.065$ for the next panel; and ${\gamma }_a=0.81,1.04,1.27,1.5$ for the lower panel.