Ab initio density functional theory study of the electronic, dynamic, and thermoelectric properties of the crystalline pseudobinary chalcogenide ${\text{(GeTe)}}_x/\left({\mathrm{Sb}}_2{\mathrm{Te}}_3\right)(x=1,2,3)$

We use ab initio density functional theory calculations to understand the electronic, dynamical, and thermoelectric behavior of layered crystalline phase-change materials. We perform calculations on the pseudobinary compounds ${\left(\mathrm{GeTe}\right)}_x/\left({\mathrm{Sb}}_2{\mathrm{Te}}_3\right)$ (GST) with $x=1$, 2, and 3. Since the stable configuration of these compounds remains somehow unsettled, we study one stacking configuration for GST124 ($x=1$), three for GST225 ($x=2$), and two for GST326 ($x=3$). A supercell approach is used to check the dynamical stability of the systems while thermoelectric properties are obtained by solving the Boltzmann transport equation. We report that the most accepted stacking configuration of GST124, GST225, and GST326 have metallic character and for the case of $x=2$ and 3, those are the ones with the lowest energy. However, we find the metallic of GST326 configuration to be dynamically unstable. In general, our values of the Seebeck coefficient and thermal conductivity for compounds with $x=1$ and 2 agree very well with the available experimental data. The small differences that we observe with respect to experimental data are attributed to the disorder that is present experimentally and that we have not taken into account. We do not find a Dirac cone in the electronic band structure of GST225, contrarily to previous reports. We attribute this due to the theoretical strain induced by the choice of the pseudopotential.

Figure 1

Representation of the most accepted stacking arrangement of GST compounds. The green, blue, and purple balls represent Ge, Sb, and Te atoms. In this configuration, the Te-Te adjacent layers are surrounded by antimony atoms.

Figure 2

(a) Rhombohedral primitive cell (extended representation of atoms to illustrate the layered nature of the system). (b) Hexagonal representation with three formula units per cell. (c) First Brillouin zone with high-symmetry points.

Figure 3

Calculated electronic band structure and corresponding electronic density of states for GST124. The high-symmetry points are shown in Fig. 2.

Figure 4

Phonon density of states for the stable configuration of GST124 obtained with a $3\times 3\times 3$ supercell using the finite displacement method.

Figure 5

GST124 (a) Dependence of the trace of the Seebeck coefficient at three different temperatures upon doping with electrons (solid lines) and with holes (dashed lines). (b) Temperature dependence of the in-plane (solid line) and out-of-plane (dashed line) Seebeck coefficient at fixed carrier concentration. The experimental data were extracted from Refs. [34, 39]. (c) Temperature dependence of the components of the lattice contribution to the total thermal conductivity as well as the average of the trace of the thermal conductivity tensor and the experimental data. Experimental points were extracted from the work of Konstantinov et al. [40]. The lattice contribution to the thermal conductivity reported in experiments was obtained using the Wiedemann-Franz law.

Figure 6

Primitive rhombohedral representation of GST225 for the Kooi and De Hosson (left), the Petrov (center), and the inverted-Petrov (right) stacking configurations. The colors of the atoms are the same as in Fig. 1.

Figure 7

GST225 (a) Electronic band structure along high-symmetry lines for the proposed stacking configurations. (b) Phonon density of states for the three stacking configurations. Code color is the same for both panels.

Figure 8

GST225 (a) Carrier concentration dependence of the Seebeck coefficient at 300 K. Solid and dashed lines denote in-plane and out-of-plane $S$. (b) Temperature dependence of the in-plane (solid) and out-of-plane (dashed) Seebeck coefficient at experimental carrier concentration for the three proposed stacking configurations. Experimental data was extracted from Ref. [34]. (c) Lattice contribution to the total thermal conductivity for the three proposed stacking configurations. Experimental data was extracted from Refs. [34, 52].

Figure 9

From top to bottom: Nonprimitive hexagonal representation of the KH-326 and Petrov-326 structures; electronic density of states of the two proposed stacking configurations. (The Fermi level is taken as reference energy.)

Figure 10

Phonon band structure for the two stacking sequences. The KH-326 configuration is clearly unstable. The lower panel shows the KH-326 structure with arrows that denote the movement of the atom that produces the negative frequencies.

Figure 11

(a) Carrier concentration dependence of the Seebeck coefficient for GST326. Solid and dashed lines denote values for the KH-326 and Petrov-326 stacking arrangements, respectively. (b) Temperature dependence of the in-plane (solid lines) and out-of-plane (dashed lines) Seebeck coefficients for stacking configurations of GST326. The experimental data were extracted from Ref. [29].