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Page 12 of 21 Duparchy et al. Energy Mater. 2025, 5, 500134 https://dx.doi.org/10.20517/energymater.2025.51

reproducibility as no excess or loosely bound Mg is lost during the sintering step.

We have calculated the effective doping efficiency (η ) [Table 2] of Sb from the (measured) carrier
dop
concentration n and the nominal dopant concentration under the assumption that each Sb atom replaces
one Si/Sn atom and provides one electron, using η = with c = the dopant concentration. The
Sb
dop
effective doping efficiency is much lower for the synthesized Mg-poor samples than for the synthesized
Mg-rich materials, which could be caused by Sb becoming electrically inactive (i.e., does not act as a donor
anymore). However, if this was the case, comparing the different Mg-poor samples we should see an
increase of the doping efficiency with decreasing Sb content, which is not observed. Also, density functional
theory (DFT) calculations from Ayachi et al. indeed show a change from +1 to neutral for Sb and Sb for
[75]
Sn
Si
high Fermi levels (i.e., large carrier concentrations), but these charge transition levels are similar for
Mg-rich and Mg-poor materials, hence, Sb becoming inactive is probably not the reason for the decrease in
doping efficiency. A more plausible reason could be the formation of compensating defects with increasing
[29]
[48]
Sb content. This has been observed by Kato et al. and Dasgupta et al. who showed experimentally that
Mg vacancies increase with increasing Sb doping, for nominal Mg-rich samples. Also for Mg-poor samples
an increase of p-type Mg vacancies is expected with increasing carrier concentration caused by increasing
Sb content, leading to a partial compensation of the free electrons from Sb addition.

The transport data of Mg Si 0.233 Sn Sb 0.067 -II (sample on which Hall measurement was performed) were
1.95
0.7
investigated for differences in the microscopic material parameters using a single parabolic Band (SPB)
model with respect to previously reported data for Mg-rich samples and those extracted from the samples
[57]
after annealing, i.e., presumably Mg-poor . This composition was chosen as it leads to the best
thermoelectric performance in the material. As no thermal conductivity measurements were performed on
that sample, the data of Mg Si Sn Sb -I (with almost identical electrical properties) was utilized
0.7
0.067
0.233
1.95
instead.
The SPB model can be used for highly doped samples of Mg Si Sn with x~0.7 due to this composition
1-x
x
2
being closely located to convergence of CBs, as described in detail in many studies [21,57,76,77] . In our case we
used x = 0.7 + y with y being the Sb content (Sb is comparable in size to Sn rather than Si). The basic
parameters of this model are the reduced chemical potential (η), the mobility parameter (μ ) and the density
0
of states effective mass ( ), governed by
(3)

(4)

(5)

(6)

(7)

Here k represents Boltzmann’s constant, h is Planck’s constant, and F = are the Fermi integrals
i
B
of the order of i, and the reduced chemical potential η is given by η = where E F is the Fermi level. For
the calculation we have assumed a scattering parameter of λ = 0 corresponding to the energy
dependence of scattering with acoustic phonons (AP) and alloy scattering (AS) [78,79] .