Thermoelectric power factor enhancement of calcium-intercalated layered silicene by introducing metastable phase

2D and layered materials, such as graphene, have been intensively studied in various fields due to their unique properties. ^1–7) Silicene, a 2D honeycomb buckled structure of Si atoms, has a massless Dirac band and is attracting attention as a promising 2D material that can exceed the attributes of graphene because its electronic band structure can be manipulated by deforming this unique buckled structure in silicene. ^4,6) Previous first-principle calculations revealed that various properties in silicene, such as carrier mobility, thermal conductivity and thermoelectric properties, could be enhanced due to the deformation of silicene structure by strain and defects. ^8–11) Therefore, it is greatly awaited to experimentally demonstrate the enhancement of its electrical properties by deforming the silicene structure. However, this realization has not been achieved due to its instability in air and the difficulty of fabrication on an insulating substrate. ^6,12) Therefore, recently, layered materials including silicene have been attracting attention as a stable layered silicene.

CaSi₂, calcium-intercalated layered silicene, is a layered crystal composed of alternately-stacked silicene and Ca layers, ^13–16) which shows higher oxidative resistance. The most stable phase of CaSi₂ is known as 6R-CaSi₂, which includes two types of silicene with higher and lower buckling heights, with values of 0.97 and 0.83 Å, respectively [Fig. 1(a)]. ^16,17) Due to the high structural stability, it is difficult to deform the silicene structure in 6R-CaSi₂. Recently, a fabrication technique using metastable 3R-CaSi₂ was developed. ^14,16,18,19) Metastable 3R-CaSi₂ includes only one type of silicene with a higher buckling height (0.97 Å). ¹⁷⁾ The two types of silicene in 6R-CaSi₂ are each rotated by 60° on the plane, while the crystal orientation of silicene in 3R-CaSi₂ is not rotated [Fig. 1(a)]. Thus, metastable 3R-CaSi₂ can be considered a crystal structure having a deformed silicene structure compared to that of stable 6R-CaSi₂. This implies that the electrical properties of 3R-CaSi₂ vary from that of 6R-CaSi₂. Actually, our calculation predicts that 3R-CaSi₂ exhibits a higher Seebeck coefficient (S) than that of 6R-CaSi₂, indicating that the electrical properties can be drastically changed by only sub-angstrom deformation of buckling height (Fig. 1). Therefore, we focus on the thermoelectric property enhancement related to the deformation of buckled structure in silicene by introducing metastable 3R-CaSi₂ into stable 6R-CaSi₂, with the aim of paving the way to eco-friendly Si-based thermoelectric material realization. ^20–29)

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In this study, we fabricate bulk 6R-CaSi₂ containing metastable 3R-CaSi₂ and then measure thermoelectric properties [S and electrical conductivity (σ)]. By introducing 3R-CaSi₂ into 6R-CaSi₂, the experimental S value along the direction parallel to the silicene layer is increased by a factor of ∼1.5. The calculation of energy dispersion relations reveals an originally high S value in 3R-CaSi₂ with a different electronic band structure from that of 6R-CaSi₂. The experiment observed that a larger S brings twice the enhancement of thermoelectric power factor (S² σ) in the CaSi₂ sample containing 9% 3R-CaSi₂. This study demonstrates that introducing a metastable phase with a different silicene structure enhances the thermoelectric properties of stable calcium-intercalated layered silicene.

CaSi₂ ingots were synthesized according to the following process. Ca (99.99 wt%) and Si (99.999 wt%) were mixed at the Ca/Si ratio of ∼0.5 in a Ta crucible under an argon atmosphere. The mixed source was melted by a high-frequency induction heating technique at 1353 K. Subsequently, it was cooled down to 773 K at various rates of ∼1–10 K min⁻¹. After the temperature (T) reached 773 K, it was naturally cooled down to RT. Therein, samples with different phases were formed by cooling rate control: 10 K min⁻¹ for the pure single-crystalline bulk 6R-CaSi₂ (sample #1) and 1 K min⁻¹ for the bulk 6R-CaSi₂ containing metastable 3R-CaSi₂ (sample #3). ¹⁶⁾ As an additional sample with a different ratio of 3R-CaSi₂ to 6R-CaSi₂ structures, sample #2 was prepared by annealing sample #3 at 873 K for 30 min in a vacuum.

X-ray diffraction (XRD) measurement was carried out using Cu Kα line with a wavelength of 1.5406 Å (Rigaku RINT2200VK/PC). The σ and S were measured using ZEM-3 (ADVANCE RIKO) in the T range 300–573 K.

The electronic structures of 3R- and 6R-CaSi₂ were computed using the Vienna ab initio simulation package (VASP) ^31,32) with the Perdew–Burke–Ernzerhof (PBE) functional ³³⁾ [Fig. 2(a)]. Structure optimization was performed until the residual force was less than 0.01 eV Å⁻¹. With these settings, the lattice constants of 3R- and 6R-CaSi₂ were calculated to be a = 3.842 Å, c = 15.854 Å and a = 3.877 Å, c = 30.371 Å, respectively. These values were consistent with the previous calculations ^34–36) and experimental result. ¹⁸⁾ For the calculation of thermoelectric properties, the electronic structures were recomputed on dense k-mesh of 480 × 480 × 120 and 480 × 480 × 60 for 3R- and 6R-CaSi₂, respectively, by employing the Wannier interpolation technique implemented in the Wannier90 package. ³⁷⁾ As shown in Fig. 2(a), there was no difference between the energy dispersion relations computed by Wannier90 and by VASP, demonstrating the high reproducibility of the energy dispersion relation computed by Wannier90. The thermoelectric properties were calculated by introducing the computed energy dispersion into the BoltzWann module integrated in the Wannier90 package. ³⁸⁾ The transport properties were calculated using a Boltzmann transport equation under the constant relaxation time approximation.

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As shown in Figs. 2(a) and 2(b), it was confirmed that both 3R- and 6R-CaSi₂ have semimetal band structures. A closer look near E-E_F = 0 (E: carrier energy, E_F: Fermi level) shows that the bands with electron pockets of 3R-CaSi₂ near M and L points are uplifted compared with those of 6R-CaSi₂. Previous studies revealed that these bands with electron pockets are formed by the hybridization of Ca and Si bands. ³⁹⁾ Therefore, the hybridization makes these electron bands different in 3R- and 6R-CaSi₂, which have different silicene structures [Fig. 1(a)]. On the other hand, the tops of the valence bands of 3R-CaSi₂ near E_F in the Γ-M, K-Γ and H-A regions move downwards from E_F compared with those of 6R-CaSi₂. Therefore, it is considered that the hole concentration in 3R-CaSi₂ is smaller than that of 6R-CaSi₂. In CaSi₂ with the negative sign of the Seebeck coefficient [Fig. 1(b)], the dominant carrier for transport is electrons. Then, it is considered that the contribution of bipolar conduction ²⁷⁾ in 3R-CaSi₂ is smaller than that in 6R-CaSi₂. This indicates that 3R-CaSi₂ likely has a higher S than 6R-CaSi₂. Figure 2(c) shows the density of states (DOSs) in 3R- (black solid line) and 6R-CaSi₂ (red dotted line). Both 3R- and 6R-CaSi₂ have steep stair-like DOSs near E_F, which are beneficial for high S. The stair-like DOS also exists at E-E_F ∼−1 eV, originating from flat bands at ∼−1 eV in the Γ-A region, indicating the quasi-2D property in CaSi₂. Thus, it is found that both 3R- and 6R-CaSi₂ have quasi-2D DOS that can bring high S. In addition, 3R-CaSi₂ likely has higher S than 6R-CaSi₂ because of the smaller contribution of bipolar conduction as mentioned above.

Figure 3 shows an XRD 2θ-ω scan of three CaSi₂ samples. The 2θ-ω scan of sample #1 displays the diffraction peaks from the (00l) planes (l = 6, 9, 12, 15, 18) of 6R-CaSi₂ without those originating from 3R-CaSi₂ (squares), whereas samples #2 and #3 exhibit diffraction peaks from the (00l) planes of 3R-CaSi₂ (triangles) in addition to those of 6R-CaSi₂. In order to acquire the mixing ratio of 3R- and 6R-CaSi₂ in each sample quantitatively, reciprocal space mappings (RSMs) were obtained around 00 12_6R-CaSi2 : 2θ of 33.0–36.0 degrees and Δω of −7 − +7 degrees [Figs. 4(a)–4(c)]. A single peak of 00 12_6R-CaSi2 was observed in sample #1 [Fig. 4(a)], while diffraction peaks of 00 12_6R-CaSi2 and 006_3R-CaSi2 were observed in sample #2 [Fig. 4(b)] and sample #3 [Fig. 4(c)]. Several 006_3R-CaSi2 peaks were observed in sample #3, unlike in sample #2 with a single 006_3R-CaSi2 peak. This indicates that 3R-CaSi₂ crystals were introduced into 6R-CaSi₂ endotaxially in sample #2, ^40,41) and that 3R-CaSi₂ inclusions in sample #3 were poorly endotaxially introduced because the transformation from 6R- to 3R-CaSi₂ with high controllability is very difficult. We analyzed the integrated peak intensities of 3R- and 6R-CaSi₂ (I_3R and I_6R) in RSMs and estimated the mixing ratio of 3R structures as R_M = I_3R/(I_3R + I_6R), as shown in Fig. 4(d). As a result, it was found that samples #1–3 had R_M values of 0%, 9% and 29%, respectively. The fact that sample #2 had smaller R_M values than sample #3 indicated that vacuum annealing decreased the amount of the metastable 3R-CaSi₂. ¹⁶⁾ Thus, CaSi₂ samples with different R_M values were formed.

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Figure 5(a) reveals that both CaSi₂ samples with R_M of 9% and 29% exhibited about 1.5 times higher S values than the CaSi₂ sample with R_M of 0%. The calculated S values of 3R- (dashed line) and 6R-CaSi₂ (dotted line) at the chemical potential of 0 eV at 300 K are also plotted in Fig. 5(a). Based on this calculation, it is predicted that 3R-CaSi₂ has a higher S than 6R-CaSi₂ [Fig. 1(b)]. While the S value of the 6R-CaSi₂ sample (R_M = 0%) was close to the calculated value of 6R-CaSi₂, the S of samples with R_M = 9% and 29% were higher. This S enhancement is possibly caused by the introduction of 3R-CaSi₂ with higher S.

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Figures 5(b) and 5(c) show T dependences of σ and S in the CaSi₂ samples, respectively. The thermoelectric properties were measured along the direction parallel to the silicene layer. The decreasing tendency of σ against T indicated that the electrical conduction of all the CaSi₂ samples was metal-like. Sample #2 with R_M of 9% exhibited almost the same σ value as sample #1 with R_M of 0%, namely single-phase 6R-CaSi₂, which came from the endotaxial introduction of 3R-CaSi₂ in sample #2. On the other hand, the σ value of sample #3 with R_M of 29% was less than half the value of the other two samples. This σ degradation is likely attributed to the poor endotaxial introduction of 3R-CaSi₂ in sample #3 with an R_M of 29%, unlike sample #2 with an R_M of 9% as mentioned above [Fig. 4(c)]. The endotaxial introduction of metastable phase is key for high σ.

Figure 5(c) shows that the S values of CaSi₂ with R_M of 0% were similar to the calculated ones in the entire T range. On the other hand, the samples with R_M of 9% and 29% exhibited higher S values than sample #1 with an R_M of 0% and the calculated ones of 6R-CaSi₂, although the S values of the samples with R_M of 9% and 29% were lower than the calculated ones of 3R-CaSi₂. This highlights that S of 6R-CaSi₂ is increased by introducing metastable 3R-CaSi₂ with a higher S than that of 6R-CaSi₂. Another effect for S enhancement might be the boundary effect between two phases, such as the energy filtering effect. ^42,43) However, the introduction of 3R-CaSi₂ with higher S into 6R-CaSi₂ is an effective way to enhance S. As a result of this S enhancement, sample #2 with an R_M of 9% exhibited the maximum S² σ (9.2 μWcm⁻¹K⁻²) in Fig. 5(d) near RT. This value was twice as high as the S² σ of the single-crystalline 6R-CaSi₂ sample (R_M = 0%). These results demonstrate that the endotaxial introduction of metastable 3R-CaSi₂ into 6R-CaSi₂ matrix enhances thermoelectric properties.

In conclusion, we fabricated bulk 6R-CaSi₂ containing metastable 3R-CaSi₂ with a different silicene structure to that of stable 6R-CaSi₂. The endotaxial introduction of 3R-CaSi₂ into 6R-CaSi₂ enhanced the S value by a factor of ∼1.5 and kept the σ value along the direction parallel to the silicene layer. The calculation of energy dispersion relations revealed an originally high S value in 3R-CaSi₂ with different electronic band structure to 6R-CaSi₂. The experiment observed S enhancement resulted in twice the enhancement of S² σ. This study demonstrated that endotaxially introducing metastable phase enhances thermoelectric properties in stable calcium-intercalated layered silicene. This paves the way to the realization of eco-friendly silicene thermoelectric material.

Acknowledgments