Theory of Nernst generators and refrigerators

Formulas for efficiency and coefficient of performance are derived for devices based on the Nernst and Ettingshausen effects. The equations reduce to those of Harman and Honig in the limits of small figure of merit and refrigerator current, but they do not limit to the Carnot values. To obtain a better device theory, one must solve a two-dimensional partial differential equation in which the current density is allowed to vary with position. A maximization procedure for the figure of merit is shown for a one-band non-degenerate semiconductor. Experimental data indicates that HgxCd1-xTe alloys are perhaps the best materials for such devices at present.