Page 159 - Read Online

Page 14 of 35 Martin-Gonzalez et al. Energy Mater. 2025, 5, 500121 https://dx.doi.org/10.20517/energymater.2025.32

have appeared in the literature on large PF performance in semimetals or materials with small bandgaps.
Most of these cases (that we describe below) have large PFs, but also large thermal conductivities and only
moderate zTs (with values not large enough to make it in the plot of Figure 1). Still, high PF materials could
be more significant in situations of power generation from abundant heat sources, whereas efficiency could
be less important.

[34]
A prominent example that has raised significant attention is the full-Heusler Fe VAl. In reference , for
2
example, an exceptional PF was reported, originating from a very high Seebeck coefficient, and it is claimed
that the n-type Fe VAl could provide zT even up to 5. This material is claimed to be semi-metallic from ab
2
initio calculations, although a large degree of its behavior can be understood by assuming a small bandgap
of 0.02 - 0.04 eV. In fact, with such a small bandgap, due to the large concentration of intrinsic defects (of
[56]
-3
the order of 10 cm ), nominally undoped samples appear metallic . Nevertheless, in Refs. [139,140] , it was
20
shown by density functional theory (DFT) calculations that partial Ti or Ta and Si co-substitution in
Fe V Ti Al Si and Fe V Ta Al Si drives an opening of a pseudo-gap, which could explain the large
1-y
y
y
x
1-y
1-x
2
x
1-x
2
experimental measurements of exceptionally large thermopowers and PFs of the order of
7.3-10.3 mW·m ·K at room temperature. Such large PFs are reported in a series of reports lately, stressing
-2
-1
the direction of opening small bandgaps in semimetals to improve PFs [56,139,140] . It is worth mentioning that
stabilizing the L ordered phase significantly enhances the TE performance of Fe VAl, exhibiting a two-fold
2
21
increase in the Seebeck coefficient compared to its disordered B2/A2 phases. This improvement is attributed
to the flattening of the DOS and the widening of the bandgap induced by the disorder-order transition .
[141]
We note here that half-Heuslers have some of the highest PFs of all TE materials and using these techniques
they can be improved even more. The reason this happens is that in those cases, the DOS(E) increases
sharply near the bandgap, which allows for very large Seebeck coefficients at significant conductivity. Note
also that there are several metallic/semi-metallic Heuslers that could offer large possibilities for materials
exploration. Recent works that have demonstrated exceptionally high PFs [34,139,140] stress the importance of
defect engineering to obtain a small effective bandgap, but which can also introduce impurity delta-function
states as a result of Anderson localization transitions in the material induced by defects. These can result in
effects like those observed in the presence of increased DOS due to resonant states (discussed below), which
are beneficial for the Seebeck coefficient and the PF.
Another example of how semimetals and/or narrow bandgap materials can provide very high Seebeck
coefficients and PFs is when a large degree of anisotropy in transport exists between the conduction and
valence bands [118,142,143] . Typically, bipolar transport degrades the Seebeck coefficient which undergoes a zero
crossing when the material changes polarity from n-type to p-type when changing the Fermi level position.
Furthermore, when the Fermi level is in the bandgap and near the charge neutrality point, where the
material is intrinsic (undoped), the carriers experience phonon-limited mobility, which is higher compared
to the mobility under heavy doping conditions. In addition, bipolar contributions from both electrons and
holes increase the conductivity. Advanced theory and simulations have shown that if quantities such as the
DOS, mobility, scattering rates, effective masses, etc., differ significantly between the conduction and
valence bands, then the zero crossing of the Seebeck coefficient and the charge neutrality point of high
mobility/conductivity occur at different Fermi level positions . This allows for a finite or even high
[143]
Seebeck at the high conductivity charge neutrality point, and exceptionally high PFs can be realized, even by
an order of magnitude higher compared to the unipolar values. Since the electronic thermal conductivity is
also large in the bipolar regime, the zT is shown to only increase at most by a factor of 2, which is still
significant, while this effect is more evident at higher temperatures . However, in general, bipolar
[143]
conduction degrades performance and needs to be avoided, because it reduces the Seebeck coefficient and
increases the electronic thermal conductivity through conduction of carriers of both polarities, in addition