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Kumar et al. Energy Mater. 2025, 5, 500109 https://dx.doi.org/10.20517/energymater.2025.22 Page 9 of 17

Figure 5. (A) Seebeck coefficients as a function of n with the Pisarenko plots of the hot-pressed BST+HEA (x = 0, 0.1, 0.5, and 1.0
H
x
vol%) samples for the Pa- and Pe-directions; (B) Fermi energies E and the mean free paths of the carrier λ ; (C) room-temperature
e
F
2
power factors S σ; (D) electrical grain connectivity G conn. as a function of the HEA concentrations at room temperature. HEA: High
entropy alloy; BST: Bi Sb Te .
0.4
1.6
3
where r is the scattering factor (r = -1/2 for acoustic phonon scattering) [39,42] . The E is not significantly
F
affected by the additions of the HEA nanoparticles in the BST matrix, as presented in Table 1. In contrast to
the less susceptible λ for the Pe-direction, the λ in the Pa-direction of the BST+HEA is increased compared
e
e
to the pristine BST. The results of the λ clearly show that the HEA nanoparticle distribution is effective for
e
enhancing the σ in the Pa-direction of the BST through the increased λ .
e
The enhanced λ , without the changes in the n and E , can be attributed to the effect of the enhanced
H
e
F
electrical grain connectivity [25,27,28] . Since the BST grains and the HEA nanoparticles are homogeneously
mixed in the BST+HEA samples, the electrical resistivities of the BST+HEA are strongly affected by the
metallic HEA nanoparticles.
The temperature-dependent scattering of the electrical resistivity can be roughly estimated by the
characteristic change in the resistivity Δρ = ρ(T ) - ρ(T ) [25,27,28] . Using the temperature-dependent
high
low
electrical resistivities ρ(T) of the BST+HEA samples, the characteristic change in the resistivities Δρ was
x
obtained, as shown in Supplementary Figure 3A and B. However, the Δρ does not provide a clear
understanding of the electrical transport characteristics of the composites. To address this, a modified factor
for the electrical grain connectivity G is introduced to quantify the contribution of the grain connectivity
conn.