  A thermoelectric device is a heat engine that directly converts heat into
electricity. Many materials with a high figure of merit ZT have been discovered
in anticipation of a high thermoelectric efficiency. However, there has been a
lack of investigations on efficiency-based material evaluation, and little is
known about the achievable limit of thermoelectric efficiency. Here, we report
the highest thermoelectric efficiency using 12,645 published materials. The
97,841,810 thermoelectric efficiencies are calculated using 808,610 device
configurations under various heat-source temperatures (T_h) when the cold-side
temperature is 300 K, solving one-dimensional thermoelectric integral equations
with temperature-dependent thermoelectric properties. For infinite-cascade
devices, a thermoelectric efficiency larger than 33% (~1/3) is achievable when
T_h exceeds 1400 K. For single-stage devices, the best efficiency of 17.1%
(~1/6) is possible when T_h is 860 K. Leg segmentation can overcome this limit,
delivering a very high efficiency of 24% (~1/4) when T_h is 1100 K.
