Effect of hydrostatic pressure and alloying on thermoelectric properties of van der Waals solid KMgSb: An ab initio study

Using a combined approach of first-principles and Boltzmann transport theory, we conducted a systematic investigation of the thermal and electrical transport properties of the unexplored ternary quasi-two-dimensional KMgSb system of the $\mathrm{KMg}X$ ($X=\mathrm{P},\mathrm{As},\mathrm{Sb}, \text{and} \mathrm{Bi}$) family. In this paper, we present the transport properties of KMgSb under the influence of hydrostatic pressure and alloy engineering. At a carrier concentration of $\sim 8\times {10}^{19}{\mathrm{cm}}^{-3}$, we observed a close match in the figure of merit (zT; $\sim 0.75$, at 900 K) for both $n$-type and $p$-type KMgSb, making it an attractive choice for engineering thermoelectric devices with uniform materials in both legs. This characteristic is particularly advantageous for high-performance thermoelectric applications. Additionally, as pressure decreases, the zT value exhibits an increasing trend, further enhancing its potential for use in thermoelectric devices. Substitutional doping (replacing 50% of Sb atoms with Bi atoms) resulted in a significant $\sim 49\%$ (in-plane) increase in the peak thermoelectric figure of merit. Notably, after alloy engineering, the maximum figure-of-merit value obtained reached $\sim 1.45$ at 900 K temperature. Hydrostatic pressure emerges as an effective tool for tuning the lattice thermal conductivity ${\kappa }_L$. Our observations indicate that negative-pressure-like effects can be achieved through the chemical doping of larger atoms, especially when investigating ${\kappa }_L$ properties. Through our computational investigation, we elucidate that hydrostatic pressure and alloy engineering hold the potential to dramatically enhance thermoelectric performance in this compound.

Figure 1

The crystal structure of $\mathrm{KMg}X$ ($X$ = P, As, Sb, and Bi) in the $P4/nmm$ space group.

Figure 2

The lattice thermal conductivity ${\kappa }_L$ of KMgSb at (a) 1.0 GPa, (b) ambient, and (c) $-1.0$ GPa pressure. The black curves show the ${\kappa }_L$ calculated using third-order IFCs, and red curves represent values obtained using fourth- and third-order IFCs. Here, 3ph, three-phonon scattering; 4ph, four-phonon scattering; $a, b$, and $c$ are the lattice parameters.

Figure 3

The electronic band structures of KMgSb with van der Waals corrections and at (a) 1.0 GPa, (b) ambient, and (c) $-1.0$ GPa pressure. These band structures are obtained without including spin-orbit coupling (SOC) in the calculations.

Figure 4

The thermoelectric figure of merit (without SOC) of KMgSb at (a) and (b) 1.0 GPa, (c) and (d) ambient, and (e) and (f) $-1.0$ GPa pressure. The black, blue, and red curves represent zT at 300, 600, and 900 K temperatures, respectively. The solid and dashed curves show zT in the $a\text{−}b$ plane and along the $c$ direction, respectively. On the $x$ axis, we have used $n$ for the doping level.

Figure 5

(a) Phonon band structure and density of states (PhDOS), (b) Grüneisen parameter $\gamma$, (c) lattice thermal conductivity ${\kappa }_L$, and (d) cumulative lattice thermal conductivity ${\kappa }_c$ of ${\mathrm{KMgSb}}_{0.5}{\mathrm{Bi}}_{0.5}$ at 900 K.

Figure 6

The electronic band structure of ${\mathrm{KMgSb}}_{0.5}{\mathrm{Bi}}_{0.5}$ without (a) and with (b) spin-orbit coupling (SOC).

Figure 7

(a) and (b) The power factor (PF), (c) and (d) thermal conductivity (${\kappa }_e + {\kappa }_L$), and (e) and (f) thermoelectric figure of merit (zT) of ${\mathrm{KMgSb}}_{0.5}{\mathrm{Bi}}_{0.5}$. The black, blue, and red curves represent zT at 300, 600, and 900 K temperatures, respectively. The solid and dashed curves show zT in the $a\text{−}b$ plane and along the $c$ direction, respectively. On the $x$ axis, we have used $n$ for the doping level. These results are obtained without SOC.

Figure 8

The scattering-mechanism-dependent electronic relaxation time $\tau$ in ${\mathrm{KMgSb}}_{0.5}{\mathrm{Bi}}_{0.5}$, calculated at 300, 600, and 900 K for a $1.26\times {10}^{20}{\mathrm{cm}}^{-3} p$-type carrier concentration.