The efficiency of thermoelectric devices in converting heat into the electricity is defined as the ratio of ``energy provided to the external load'' to ``heat energy absorbed at the hot junction''. The maximum efficiency of the power generator is achieved when the external load is matched with the device resistance :
The efficiency of a thermoelectric power generator, as any other heat engine, is less than the Carnot engine efficiency:
Indeed, the Carnot engine has the most efficient cycle for converting a given amount of thermal energy into work. In addition to the temperature difference, is also related to the average of , which is related to the material properties of the -type and -type materials used in the thermoelectric element. Figure 1.5 shows the maximum efficiency of the thermoelectric generator as a function of for and different . The efficiency increases with and . For , the maximum efficiency is about . The efficiency for high increases to and for and , respectively. The efficiency of Carnot cycle is plotted as well for comparison. We also note that the efficiency of some other common energy convertors is as follows: for hydro-electric technologies, for fuel cells, for wind turbines, and for tidal turbines . As a result, an average figure of merit higher than 3 is required, in order to compete with the rest of the commercial generators that are already in large-scale use in the market .
The thermoelectric device figure of merit and the efficiency are related to the material properties of the -type and -type semiconductors as well as the electrical and thermal contact resistances. For simplicity, the thermoelectric material figure of merit: