Thermoelectric optimization of $\mathrm{AgBiS}{\mathrm{e}}_2$ by defect engineering for room-temperature applications

The hexagonal phase of $\mathrm{AgBiS}{\mathrm{e}}_2$ has been discovered as a promising thermoelectric material for room-temperature applications. However, its basic conduction type is still ambiguous, and its current ZT value is pretty low. To improve the thermoelectric performance of $\mathrm{AgBiS}{\mathrm{e}}_2$, we apply band engineering to modify its band structure by introducing defects to increase the band degeneracy. From the calculated intrinsic point defect formation energies of $\mathrm{AgBiS}{\mathrm{e}}_2$ at different growth conditions, we clarify that the conducting behavior of $\mathrm{AgBiS}{\mathrm{e}}_2$ is a $p$-type semiconductor, and the Ag vacancy is the dominated acceptor. Based on scrutinizing the band structure of $\mathrm{AgBiS}{\mathrm{e}}_2$, two kinds of methodologies can be used to modify its band structure to achieve high band degeneracy: (i) shifting the Fermi level into the valence band using intrinsic defects, and (ii) converging several valence-band maxima by introducing extrinsic defects. We find that the intrinsic Ag vacancy is helpful to significantly increase the power factor, leading to a large ZT for Ag vacancy-doped $\mathrm{AgBiS}{\mathrm{e}}_2$: the maximum ZT value is increased to 0.3–0.5 at near room temperature. Based on analyzing the bonding characters and atomic energy levels in the compound, we predict several extrinsic dopants (Cu, Rh, and Pd) that can be used to converge three valence-band maxima. Our work provides methodologies to improve the room-temperature thermoelectric applications of $\mathrm{AgBiS}{\mathrm{e}}_2$ by tuning its band structures using intrinsic or extrinsic defects.

Figure 1

Accessible range of chemical potential (red shaded region) for the equilibrium growth conditions of the hexagonal $\mathrm{AgBiS}{\mathrm{e}}_2$ phase. The specific points are chosen for the representative chemical potentials to be used for the defect formation energy calculations.

Figure 2

Formation energies of neutral defects in $\mathrm{AgBiS}{\mathrm{e}}_2$ as a function of the chemical potential at points A–E shown in Fig. 1 and Table 1.

Figure 3

Theoretically calculated formation energies of intrinsic charged point defects in $\mathrm{AgBiS}{\mathrm{e}}_2$ as a function of the Fermi level, with chemical potentials under the (a) Ag-rich [point A (0, −0.68 eV, −0.21 eV) in Fig. 1], (b) Se-rich [point B (−0.11 eV, −0.99 eV, 0) in Fig. 1], and (c) Ag-rich/more Se-poor [point C (0, −0.12 eV, −0.49 eV) in Fig. 1] conditions.

Figure 4

(a) Calculated band structure of the pristine $\mathrm{AgBiS}{\mathrm{e}}_2$ along high-symmetry points in BZ. The black dashed line represents the Fermi level. The calculated isoenergy surfaces for $\mathrm{AgBiS}{\mathrm{e}}_2$ near the VBM are shown at (b) VBM−0.01 eV, (c) VBM−0.06 eV, and (d) VBM−0.11 eV.

Figure 5

The band structures of (a) pristine $\mathrm{AgBiS}{\mathrm{e}}_2$ and (b) Ag vacancy after band unfolding.

Figure 6

Theoretically calculated thermoelectric properties ($\sigma , S, S^2\sigma$, and ZT) of $\mathrm{AgBiS}{\mathrm{e}}_2$ and Ag vacancy defect system as a function of temperature and concentrations.

Figure 7

(a) Projected density of states of $\mathrm{AgBiS}{\mathrm{e}}_2$. (b) Schematic of interatomic interactions between the main valence states for energy-band formation, where the bonding and antibonding states are formed in the shaded region. The position of the energy levels in the shaded region of (b) corresponds to states in (a). The Ag-$d$ atomic level sits at its $d$-band center $(\sim -3.0\mathrm{eV})$, and other atomic orbital levels are positioned relative to Ag-$d$. In $\mathrm{AgBiS}{\mathrm{e}}_2$, the Ag $d$-band is narrow and occupied, which facilitated the analysis, and we estimate the $d$-band center by averaging the valence $d$-band DOS.

Figure 8

Projection of the $\mathrm{AgBiS}{\mathrm{e}}_2$ band wave functions onto the Ag-$d$ orbitals (the big red dots).