The behavior of the figure of merit (ZT) of the most famous n-type and p-type thermoelectric materials versus temperature has been illustrated in the following figure (Ref: http://www.its.caltech.edu/~jsnyder/thermoelectrics/).

In fact, materials with a higher ZT are better thermoelectrics. Nowadays, nanostructured thermoelectric materials and also nanocomposites show better thermoelectric characteristics. For example BiSbTe and PbTeTi show higher ZT than the amounts which is illustrated. Moreover, investigations are going on superlattice structures.

To reach ZT > 3 will require a breakthrough in the field.  This can be either in the form of some new material, or more likely, the result of nanostructuring.  To date, nano tructuring has improved ZT mainly by reducing thermal conductivity - more defects lead to more phonon scattering.  However, there is longstanding theoretical predications that truly small sizes (below 5 - 30 nm for most materials) will lead to quantum confinement for electronic transport.  This would lead to greater Seebeck coefficients, which are squared in calculating ZT.  Unfortunately, this has yet to be demonstrated experimentally in a meaningful thermoelectric material.  Many attempts have been made at making thermoelectric nano wires with the appropriate diameters, however, while this lead to high phonon scattering, so far it has proven difficult to achieve high electrical conductivity.  Our group believes that this is the result of poor crystalline structure within the grains of the nanowire materials.  You can check out some of our papers on my page.

Siegal,

I absolutely agree with you that it is necessary to do a breakthrough in the field if we want to reach a scalar figure of merit ZT > 3. The nanostructured materials with decrease the thermal conductivity would be an obvious improvement but I think that it is necessary go directly to the physical phenomena involved in the electronic transport if a full solution wants to be achieved