Influence of Janus structure on the thermoelectric performance of the α-Se monolayer

Thermoelectric (TE) technology is renowned for its potential applications in waste-heat recovery, power generation, and refrigeration.¹ This has led to increased interest in discovering new high-performance TE materials and enhancing the TE performance of the present TE materials.^2–4 The measure of the TE performance of materials is characterized by the dimensionless figure of merit, $ZT= S 2GT/( κ e+ κ p$⁠), where $S$⁠, $G$⁠, $κ e$⁠, $κ p$⁠, and $T$ represent the Seebeck coefficient, electrical conductance, electronic thermal conductance, phononic thermal conductance, and temperature, respectively. Extensive experimental and theoretical studies have identified lots of effective strategies used to improve the $ZT$⁠, including the “phonon-glass electron-crystal,” “phonon-liquid electron-crystal,” band convergence, reducing dimensionality, and multi-nanostructure doping.^5–7 Despite these impressive advancements, the current $ZT$ values are still not enough high to achieve competitive conversion efficiency, which necessitates the further research and development of the TE technologies.

In recent years, group-VI elemental two-dimensional (2D) semiconductors including selenene and tellurene have attracted much attention due to their simple composition and novel properties.^8–10 Among them, the tellurene in $α$-phase and $β$-phase can exhibit tunable moderate bandgap, high carrier mobility, ultralow lattice thermal conductivity, and high TE performance.¹¹ Moreover, square selenene and tellurene have been investigated for their low thermal conductivity and interesting electronic structures that display non-trivial topological properties.^12,13 Furthermore, binary group-VI 2D compounds such as $α$- $Se 2$Te and $α$- $SeTe 2$ have been found to exhibit fantastic TE properties.^14,15 These studies indicate that the TE properties of the different structures composed of group-VI elements may deserve further investigation.

2D Janus materials, as new derivatives of 2D materials, have attracted increasing attention due to their mirror asymmetry.^16–20 Vu et al. systematically investigated the electronic, optical, and TE properties of Janus monolayers $In 2$XO (X = S, Se, Te) by using the first-principles calculations.²¹ In addition, Sun et al. proposed a new class of Janus silicene structures including $Si 2$HF, $Si 2$HCl, $Si 2$HBr, and $Si 2$HI, which are all direct bandgap semiconductors.²² Also, the 2D Janus transition metal dichalcogenides (TMDs) monolayers have been proposed for use in Rashba materials, sensors, hydrogen evolution reaction, and photocatalytic water splitting.^23–25 Note that the 2D Janus TMD monolayer such as Janus SMoSe has been synthesized experimentally via a controlled sulfurization process.²⁶ Meanwhile, theoretical studies have shown that the Janus monolayers such as Janus XSSe (X = Mo, In, Sn, $…$⁠), $α$- $SeTe 2$⁠, $α$- $STe 2$⁠, and $α$-TeSSe can exhibit reduced thermal conductivity compared to their pristine counterparts.^27–31 Therefore, it should be practical experimentally and theoretically that the Janus structure can be adopted to obtain high $ZT$ superior to the pristine materials.

In this paper, we will systematically investigate the TE properties of the Janus $α$- $SSe 2$ and $α$- $TeSe 2$ monolayers along the armchair and zigzag directions to explore the influence of the Janus structure. For comparison, the TE properties of the pristine $α$-Se monolayer will be also presented. The Seebeck coefficient $S$⁠, electrical conductance $G$⁠, thermal conductance $κ$⁠, and figure of merit $ZT$ of the Janus $α$- $SSe 2$⁠, Janus $α$- $TeSe 2$⁠, and pristine $α$-Se monolayers are all considered. Furthermore, the dependences of the $S$⁠, $G$⁠, $κ$⁠, and $ZT$ on the temperature will be investigated. For the first time, we demonstrate that the TE performances of the Janus $α$- $SSe 2$ and $α$- $TeSe 2$ monolayers are better than the pristine $α$-Se monolayer, implying the feasibility of improving $ZT$ by introducing the Janus structures.

The paper is organized as follows. In Sec. II, we describe the computational methods and details. Then, the results and discussion are presented in Sec. III. Finally, we outline the conclusion in Sec. IV.

In this section, we describe the parameter setting and theoretical methods used in this study. First, all the calculations of the geometric optimization and the TE transport properties of the Janus $α$- $SSe 2$⁠, Janus $α$- $TeSe 2$⁠, and pristine $α$-Se monolayers are performed using the Quantum Atomistix ToolKit (ATK) package, which combines the density functional theory with the non-equilibrium Green’s function (NEGF) method. The Perdew–Burke–Ernzerhof (PBE) method within the generalized gradient approximation (GGA) is used as the exchange-correlation functional. A cutoff energy of 150 Rydberg and a $3×1×7$ Monkhorst–Pack $k$-point mesh are employed. A vacuum slab of 20 Å is introduced to prevent the interactions between neighboring layers. Additionally, full atomic relaxation is performed until the forces acting on all atoms are less than 0.001 eV/Å. The van der Waals (vdW) correction proposed by Grimme is also considered during the calculations.³² 

Figure 1(a) shows the structure of the $α$-Se monolayer with the $P ¯3M1$ (164) symmetry group. From the pristine $α$-Se, the Janus $α$-SSe $2$ and $α$- $TeSe 2$ monolayers shown in Fig. 1(b) can be constructed by replacing all Se atoms in one outer sublayer with S or Te atoms. The dashed quadrangles in Figs. 1(a) and 1(b) represent the corresponding primitive cells, in which there are three atoms. From the side views, it can be found that in comparison with the symmetry in the $α$-Se monolayer, the Janus $α$-SSe $2$ and $α$- $TeSe 2$ monolayers are asymmetric because the two outer sublayers of the Janus structure are composed of different atoms. The lattice constant $a$⁠, buckling height $d$⁠, bond angle $θ$⁠, and bond lengths $l 1 , 2$ of the optimized structures are listed in Table I, which are in agreement with the literature.³⁶ The first Brillouin zone with high-symmetric points is shown in Fig. 1(c).

To assess the stability of the newly constructed structures, based on the primitive cell with three atoms, we calculated the phonon spectra of the Janus $α$-SSe $2$⁠, Janus $α$- $TeSe 2$⁠, and pristine $α$-Se monolayers, which are presented in Fig. 1(d). Clearly, no imaginary frequencies are observed, indicating that all the three structures obtained by structural optimization are dynamically stable. In order to check their stabilities at high temperature, we further carry out molecular dynamics (MD) simulations on the Janus $α$-SSe $2$⁠, Janus $α$- $TeSe 2$⁠, and pristine $α$-Se monolayers at the temperature of $T$ = 500 K under the constant-temperature and constant-volume (NVT) ensemble. The time-dependent evolutions of the total energies are plotted in Fig. 1(e). Evidently, in each case, the total energy only exhibits a small-amplitude fluctuation around a certain value within a 10-ps period. Meanwhile, the geometry of the monolayer structure remains nearly intact after a 10-ps dynamic evolution as shown in the inset of Fig. 1(e). This firmly demonstrates that the $α$- $SSe 2$⁠, $α$- $TeSe 2$⁠, and pristine $α$-Se monolayers should be thermally stable in the temperature range $T$ $≤$ 500 K.

Figure 2 shows the electronic band structures and the projected density of states (DOS) of the $α$-SSe $2$⁠, $α$- $TeSe 2$⁠, and pristine $α$-Se monolayers, which are calculated based on the rectangular supercell with six atoms and with the two edges of the supercell along the zigzag and armchair directions. Clearly, the three monolayers exhibit similar band structures and are all indirect semiconductors. This should be reasonable because the substitution of Se atoms in one outer sublayer by the same group-VI elements like S or Te atom does not change the semiconducting attribution intuitively. However, the bandgaps of the $α$-SSe $2$ and $α$- $TeSe 2$ monolayers are 0.74 and 0.59 eV, respectively, which are smaller than the bandgap 0.96 eV of the $α$-Se monolayer. This reduction in bandgap, as well as the change of the entire band structures, should be the fundamental factor that will affect the TE properties of the pristine $α$-Se monolayer. In all the three monolayers, the conduction band minimum (CBM) is located at the $Γ$ point, while the valence band maximum (VBM) is situated on the $Γ$–Y line for the $α$-SSe $2$ and $α$-Se monolayers, and on the $Γ$–X line for the $α$- $TeSe 2$ monolayer. Furthermore, the projected DOS shown in Fig. 2(b) reveals that in the $α$-Se monolayer, the atoms in the two outer sublayers (Se1 and Se3) contribute equally due to the inversion symmetry of the structure. In contrast, in the Janus monolayers, the contributions of the two outer sublayers (S/Te and Se1) are different, as expected. Also, the middle sublayer Se2 atoms contribute much less than the outer S/Te/Se1 atoms around the VBM in the Janus monolayers, whereas the contributions of the Se2 atoms are nearly the same as those of the outer S/Te/Se1 atoms in the CBM.

Next, we consider the electronic transmission coefficients of the three monolayers along the armchair and zigzag directions in Fig. 3. For the $α$-SSe $2$⁠, $α$- $TeSe 2$⁠, and $α$-Se monolayers a wide valley with $T e$=0 is always observed along the armchair and zigzag directions near the Fermi level. However, the valley width of the $α$-SSe $2$ and $α$- $TeSe 2$ monolayers is different from that of the pristine $α$-Se monolayer, which is in agreement with the corresponding band structure shown in Fig. 2. In addition, the electronic transmission spectrum exhibits many plateaus, which indicates the existence of quantum effect. The $T e$ near the CBM and VBM should be critical in determining the TE properties.

We now turn to study the TE properties of the $α$-SSe $2$⁠, $α$- $TeSe 2$⁠, and pristine $α$-Se monolayers. In Figs. 4(a)–4(d), we show the Seebeck coefficient $S$⁠, the electrical conductance $G$⁠, the total thermal conductance $κ$ (⁠ $= κ e+ κ p$⁠), and the figure of merit $ZT$ of the $α$-SSe $2$⁠, $α$- $TeSe 2$⁠, and $α$-Se monolayers along the armchair direction at 300 K. The $α$-SSe $2$⁠, $α$- $TeSe 2$⁠, and pristine $α$-Se monolayers all exhibit one similar pair of $S$ peak and valley near the chemical potential $μ$ = 0 eV. The height of the $S$ peak and the depth of the $S$ valley, as well as the distance between the peak and valley positions, for the Janus $α$-SSe $2$ and $α$- $TeSe 2$ monolayers are smaller than those of the $α$-Se monolayer. In addition, a wide electrical conductance valley of $G=0$ mS can be observed near $μ$ = 0 eV for the $α$-SSe $2$⁠, $α$- $TeSe 2$⁠, and $α$-Se monolayers. Also, a wide $κ$ valley can appear in the same chemical potential scope where the $G$ = 0 mS valley is formed. For the $α$-SSe $2$ and $α$- $TeSe 2$ monolayers, the widths of the $G$ and $κ$ valleys are suppressed compared to the pristine $α$-Se monolayer. These variations in $S$⁠, $G$⁠, and $κ$ induced by the Janus structure can be attributed to the change of the bandgaps and the $T e$⁠, which can be understood according to the definitions of $G$⁠, $S$⁠, and $κ e$ shown in Eqs. (3)–(5). Finally, we can find that in the $α$-SSe $2$⁠, $α$- $TeSe 2$⁠, and $α$-Se monolayers two main $ZT$ peaks can be formed along the armchair direction. In comparison with the pristine $α$-Se monolayer, the maximum $ZT$ of the $α$- $TeSe 2$ monolayer only shows a slight increase while the maximum $ZT$ of the $α$-SSe $2$ monolayer can be sharply increased to 2.3 at $μ=−0.49$ eV. This indicates that the Janus structure is able to greatly improve the TE performance of the $α$-Se monolayer.

Furthermore, we present in Figs. 4(a1)–4(d1) the $S$⁠, $G$⁠, $κ$⁠, and $ZT$ of the $α$-SSe $2$⁠, $α$- $TeSe 2$⁠, and $α$-Se monolayers along the zigzag direction. The influences of the Janus structure on $S$⁠, $G$⁠, and $κ$ along the zigzag direction are similar to those along the armchair direction. However, the $ZTs$ of the $α$-SSe $2$⁠, $α$- $TeSe 2$⁠, and $α$-Se monolayers along the zigzag direction exhibit three main peaks with the maximum $ZT$ peaks of the $α$-SSe $2$ and $α$- $TeSe 2$ monolayers slightly larger than that of the $α$-Se monolayer. To understand the reasons of these $ZT$ variations, we list in Table II the related parameters corresponding to the maximum $ZTs$ in Fig. 4. Along the armchair direction, the Janus structure will lead to an increase of both $Z eT$ and $ZT$⁠. Notably, the $ZT$ value of the $α$-SSe $2$ monolayer is twice as large as that of the $α$-Se monolayer due to its much higher $PF$⁠. As for the $α$- $TeSe 2$ monolayer, the sharp increase of $Z eT$ is due to the serious suppression of $κ e$ and the slight increase of $ZT$ is due to both the weak suppression of $PF$ and the strong suppression of $κ$⁠. Along the zigzag direction, the Janus structure can result in a decrease in $Z eT$ and an increase in the $ZT$⁠, which is different from the uniform increase of the $Z eT$ and $ZT$ along the armchair direction. For the $α$-SSe $2$ monolayer, the decrease in the $Z eT$ along the zigzag direction is primarily attributed to the larger $κ e$⁠. For the $α$- $TeSe 2$ monolayer, the decrease of $Z eT$ is caused mainly by the suppressed $PF$⁠. The increase of $ZT$ for the $α$-SSe $2$ monolayer is attributed to the enhanced $PF$⁠, and the slight increase of $ZT$ for the $α$- $TeSe 2$ monolayer is attributed to the serious suppression of $κ p$⁠. The competition between $κ e$ and $κ p$ induces the different variation of $Z eT$ from $ZT$⁠. Therefore, we can conclude that the Janus structure can uniformly enhance the maximum $ZT$ along the two different directions though the underlying reasons may be different.

In order to further evaluate the TE performance of the $α$-SSe $2$⁠, $α$- $TeSe 2$⁠, and $α$-Se monolayers, it is of critical importance to investigate the effect of temperature on their TE properties. In the following, we will systematically study how the temperature affects the $S$⁠, $G$⁠, $PF$⁠, $κ$⁠, and $ZT$ of the $α$-SSe $2$⁠, $α$- $TeSe 2$⁠, and $α$-Se monolayers.

Now, we first consider the temperature dependence of the Seebeck coefficient $S$⁠. In Fig. 5(a), the Seebeck coefficients $S$ of all the $α$-SSe $2$⁠, $α$- $TeSe 2$⁠, and pristine $α$-Se monolayers along the armchair direction will show an obvious pair of peak and valley at different temperatures 300, 400, and 500 K. Notably, the $S$ peak and valley appear near the chemical potential $μ$ = 0 eV, which is in agreement with the transmission gap shown in Fig. 3. As the temperature increases, the $S$ peak height and valley depth will become small, which is the same for the $α$-SSe $2$⁠, $α$- $TeSe 2$⁠, and $α$-Se monolayers. In Fig. 5(b), we investigate the temperature dependence of the $S$ of the $α$-SSe $2$⁠, $α$- $TeSe 2$⁠, and $α$-Se monolayers along the zigzag direction. Clearly, they show the similar temperature dependences to those along the armchair direction. Thus, one can conclude that along the two directions the same temperature dependence of $S$ can be observed for the $α$-SSe $2$⁠, $α$- $TeSe 2$⁠, and $α$-Se monolayers.

Figure 6 shows the temperature dependence of the electrical conductance $G$ as a function of the chemical potential $μ$ along the armchair and zigzag directions. Clearly, the $G$ appears to be weakly dependent on the temperature, and a valley with $G$ = 0 mS will always be observed at different temperatures. The valley width, albeit different in the three monolayers, will always become slightly narrower with the temperature increasing, which can be found more clearly in the inset of Fig. 6, for example. Thus, we can readily draw a conclusion that the $α$-SSe $2$⁠, $α$- $TeSe 2$⁠, and $α$-Se monolayers show the same dependence of $G$ on temperature. Based on the $S$ and $G$⁠, the power factor $PF$ can be easily obtained, see Fig. 7. Due to the complex variations of $S$ and $G$⁠, different $PF$ peaks can be formed for the $α$-SSe $2$⁠, $α$- $TeSe 2$⁠, and $α$-Se monolayers along both the armchair and zigzag directions. The maximum $PF$ peaks for the $α$-SSe $2$⁠, $α$- $TeSe 2$⁠, and $α$-Se along both the armchair and zigzag directions will increase with the temperature increasing. These $PF$ peaks indicate where the high $ZT$ peaks may possibly appear.

In Fig. 8, we study the temperature dependence of the electronic thermal conductances $κ e$⁠. Similar to $G$⁠, the $κ e$ also shows a wide valley for the $α$-SSe $2$⁠, $α$- $TeSe 2$⁠, and $α$-Se monolayers. With the increase of $T$⁠, the valleys will be inclined to become narrower in width. Different from the dependence of $G$ on $T$⁠, obvious variations of $κ e$ outside the valley can be caused by the temperature increase. Specifically, the $κ e$ can be sharply increased as the temperature increases in the region of $κ e≠$ 0 mV/K for the $α$-SSe $2$⁠, $α$- $TeSe 2$⁠, and $α$-Se monolayers along the armchair and zigzag directions.

In Fig. 9, we show the variation of the phononic thermal conductance $κ p$ with temperature $T$ and the phononic transmission coefficients $T p$⁠. It is evident that the $κ p$ will increase and tend to saturate with increasing $T$ for the $α$-SSe $2$⁠, $α$- $TeSe 2$⁠, and $α$-Se monolayers. By comparing the high-temperature $κ p$ of the corresponding monolayers depicted in Figs. 9(a) and 9(b), we can find that the Janus structure can suppress $κ p$ to different extents. In Figs. 9(a1) and 9(b1), we show the phononic transmission coefficients $T p$⁠. Clearly, along the armchair and zigzag directions, the $T p$ of the $α$-SSe $2$ and $α$- $TeSe 2$ monolayers have been seriously changed in comparison with the $α$-Se monolayer. This variation of $T p$ will certainly induce the change of the phononic thermal conductance $κ p$⁠, which will further make influences on the TE properties of the pristine $α$-Se monolayer.

Now, we turn to study the influence of the temperature on the $ZT$ in Fig. 10. The heights and widths of the two main $ZT$ peaks of the $α$-SSe $2$⁠, $α$- $TeSe 2$⁠, and $α$-Se monolayers along the armchair direction will become larger with increasing temperature as shown in Fig. 10(a). Also, the two peaks will move toward each other in positions. Along the zigzag direction, the heights and widths of the three main $ZT$ peaks will also be inclined to become larger. The left two main peaks will move toward each other while the right peak seems not to move in position. This indicates that along the armchair and zigzag directions, the $ZT$ peaks of the three monolayers will show the similar temperature dependence except the right $ZT$ peak along the zigzag direction.

In order to clearly uncover how the Janus structure induced variation of the maximum figure of merit $Z T m a x$ is dependent on the temperature, we show in Fig. 11 the variation of the $Z T m a x$ vs the temperature along the armchair and zigzag directions. Roughly speaking, the $Z T m a x$ of the Janus $α$-SSe $2$ and $α$- $TeSe 2$ monolayers will be greater than that of the $α$-Se monolayer. As the temperature increases, the $Z T m a x$ difference between the $α$-SSe $2$ and $α$-Se monolayers will become large while that between the $α$- $TeSe 2$ and $α$-Se monolayers is kept almost invariant. Specifically, the $Z T m a x$ of the $α$-SSe $2$ monolayer along the armchair direction is much greater than that of the $α$-Se monolayer, and the $Z T m a x$ difference between them will be further enhanced with the increase of $T$⁠. This indicates that the Janus structure is beneficial to improving the $Z T m a x$ of the $α$-Se monolayer, and the Janus $α$-SSe $2$ monolayer along the armchair direction is of highly improved TE performance. By comparing Figs. 11(a) and 11(b), we can further find that the Janus structure can induce much sharper increase of $Z T m a x$ along the armchair direction than along the zigzag one. In addition, we want to emphasize that the reason why the $Z T m a x$ of the $α$-SSe $2$ (⁠ $α$- $TeSe 2$⁠) monolayer is larger than that of $α$-Se monolayer may be attributed to the sharp increase (decrease) of the $PF$ (⁠ $κ$⁠), as shown in Table II for example.

In summary, we have comparatively investigated the TE properties of the Janus $α$-SSe $2$ and $α$- $TeSe 2$ monolayers, and the pristine $α$-Se monolayer by means of the density functional theory and NEGF method. It is shown that the Janus $α$-SSe $2$⁠, Janus $α$- $TeSe 2$⁠, and pristine $α$-Se monolayers are all indirect semiconductors with the bandgaps suppressed by the Janus structure. Correspondingly, the Seebeck coefficient, electrical conductance, electronic thermal conductance, and power factor are all changed by the Janus structure, and the phononic thermal conductance is always suppressed. Consequently, our results show that the $ZT$ of the $α$-Se monolayer can be enhanced by the Janus structure. Note that the $ZTs$ of the Janus $α$-SSe $2$ and $α$- $TeSe 2$ monolayers along the armchair and zigzag directions are always greater than that of the $α$-Se monolayer in a broad temperature zone, firmly demonstrating that the Janus structure should be a potential scheme of improving the TE performance of materials. We believe that this scheme should be applicable in other similar layered materials. Regarding the experimental realization of the Janus structures, the selective substitution of all the atoms in one outer sublayer of a monolayer structure poses a challenging issue for experimental scientists. Moreover, further theoretical and experimental works are necessary on the assembly of the Janus structure with the substrates or electrodes in order to fabricate a TE device.

This research is financially supported by the National Natural Science Foundation of China (Nos. 12474038 and 11774029), the “Blue Fire Plan” (Dezhou) of Cooperative Industry-University Innovation of Education Ministry of China (No. 2021DZ006), and the innovation project of Shandong Province (No. 2022TSGC1353).

The authors have no conflicts to disclose.

Q. H. Liu: Formal analysis (equal); Software (equal); Writing – original draft (equal). H. L. Shi: Writing – review & editing (equal). Q. Z. Han: Writing – review & editing (equal). J. Yang: Resources (equal); Y. H. Zhao: Writing – review & editing (equal). L. J. Gong: Writing – review & editing (equal). H. Yang: Writing – review & editing (equal). R. S. Cheng: Writing – review & editing (equal). Z. T. Jiang: Funding acquisition (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.