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Page 10 of 23 Shanmugasundaram et al. Energy Mater. 2025, 5, 500100 https://dx.doi.org/10.20517/energymater.2024.304

temperatures. Ag-substituted samples have a S approximately 150% higher than undoped Mg Zn Sb , due
2
1.2
1.8
to hole excitation into heavier bands, enhancing VB convergence . Thus, this finding suggests that VB
[59]
convergence adds a substantial benefit to the S and TE performance across a wide temperature range.
The contribution of impurity or secondary phase was confirmed by the reduced E ( ) using the S
F
(σ × exp ) and σ ( ) values, as shown in Figure 3C. At room temperature, positive
values indicated an increased hole concentration. At higher temperatures, negative values suggested the
influence of minority charge carriers, highlighting the significant role of secondary Sb in contributing to
bipolar conductivity. Figure 3D represents the σ and S vs. Ag content at 303 K, which confirms the typical
semiconductor behavior of the as-prepared samples .
[60]
Density functional theory representation of Ag Mg Zn Sb
x 1.8-x 1.2 2
The periodic density functional calculations were performed to gain insight on the TE properties of
Mg ZnSb compounds. The optimized geometries and formation energy of undoped, Zn, and Zn-Ag
2
2
substituted Mg Sb systems are shown in Supplementary Figure 4A-E. Here, the computed band diagrams,
2
3
PDOS plots, and electron density difference of Mg ZnSb and Ag-Mg ZnSb systems are provided in
2
2
2
2
Figure 4. The VB at the high symmetry point Γ and the CB at A indicate the indirect nature of the band
explained in Figure 4A . The VB and CB of Mg ZnSb and Ag- Mg ZnSb systems are composed of the
[61]
2
2
2
2
p-orbital of Sb and s-orbital of Mg, respectively. The obtained temperature-dependent S trend has been
significantly changed after Ag doping due to the following phenomenon: VB convergence, which is highly
consistent with the previous reports [62,63] . It is a potential strategy, where the multiple VB maxima (VBM)
(i.e., light and heavy VBs) of the material exist at nearly the same energy level which enhances the DOS near
the E , resulting in enhanced S. On the other hand, the convergence of multi-band improves the mobility of
F
holes and increases the σ. Therefore, the significant enhancement of S and σ enhances the overall power
factor (PF) and TE performance. This VB convergence can be introduced via doping impurities, alloying, or
strain engineering, respectively . The Mg Sb intrinsically exhibits a wide band gap of ~0.6-0.8 eV and
[64]
2
3
lower valley degeneracy (N = 1), which renders the TE performance . In this present investigation, the S of
[65]
v
undoped Mg Zn Sb sample decreased with temperature indicating the semiconductor behavior, whereas
2
1.8
1.2
Ag-doped samples show an increasing trend with temperature due to the following reasons. Here, the
substitution of isovalent Zn atom replaces ~60% Mg atoms and only settles in the tetrahedral [Mg Sb ] 2-
2
2
sites, resulting in reducing the band gap from 0.28 eV (Mg Sb ) to narrow the band gap of 0.16 eV
3
2
(Mg Zn Sb ) with increased valley degeneracy [Supplementary Figure 5A] . The DOS and PDOS for the
[63]
2
1.2
1.8
Mg Sb system explain the presence of Mg-s, Mg-p, Sb-s, and Sb-p orbitals, as shown in Supplementary
2
3
Figure 5B-D. Substituting the heavy element Ag at anionic Mg2 site of Mg Zn Sb system introduces
+
1.8
2
1.2
additional acceptor levels and exhibits the convergence of heavy VB Γ and lighter VB A near E of the band
F
structure. The VB modification enhances the DOS and improves the TE performance of the Ag-substituted
Mg Zn Sb system . In addition, this phenomenon helps increase the DOS m* of the system which
[45]
2
1.8
1.2
significantly improves the S of 103 µV/K to 257 µV/K with a temperature of Ag-substituted Mg ZnSb 2
2
system.
In this case, the VBM was located at the Γ and A points displayed in Figure 4B, indicating a significant
improvement in the electrical transport behavior of Mg Sb after the substitution of Zn, and Ag into the
2
3
Mg2 sites. It also enriches the number of bands in the DOS, which lowers the thermal excitation of the
electrons and enables more opportunities for electron transitions, thereby enhancing the electrical transport
characteristics in the low-temperature domain and agreeing with experimental results. In addition,
Supplementary Figure 6A-D shows the optimized geometries of Zn at Mg and Sb sites, and Zn-Ag at Mg
and Sb sites of Mg Sb .The bonding behavior between the foreign dopants (i.e., Zn and Ag) in the Mg Sb 2
3
3
2
has been revealed from the PDOS analysis. Figure 4C and D shows the VB and CB regions of the energy