Effects of Oxygen on Lattice Defects in Single-Crystalline Mg2Si Thermoelectrics

Lattice defect engineering has attracted attention due to its ability to develop thermoelectric materials with low thermal conductivity. For Mg2Si single crystals (SCs), Si vacancy (VSi) defects can be introduced and consequently result in the formation of dislocation cores. These lattice defects confer Mg2Si SCs with a lower thermal conductivity compared to Mg2Si polycrystals. To reveal a mechanism for the stabilisation of VSi in the Mg2Si SCs, we investigated the effects of oxygen (O) on lattice defects by performing electronic structure calculations, secondary ion mass spectrometry, X-ray photoelectron spectroscopy, and photoelectron holography. On the basis of these calculations, we predicted that O stabilised the formation of VSi when it was located at the Si site or at an interstitial site. All experiments confirmed the presence of O inside the Mg2Si SCs. However, O was suggested to be located not at the specific site in the crystal lattice of Mg2Si but at dislocation cores. The interaction between O and the dislocation cores in the Mg2Si SC is expected to immobilise dislocation cores, leading to the stabilisation of VSi formation.


Introduction
Lattice defect engineering is key to developing energy-harvesting materials such as photovoltaic, dielectric, and thermoelectric (TE) materials [1][2][3]. Lattice defects such as point defects and dislocation cores should be reduced in photovoltaic and dielectric materials to achieve high energy-conversion efficiency. Although the introduction of lattice defects into TE materials also affects TE properties (the Seebeck coefficient, electrical conductivity, and thermal conductivity) , it can improve TE performance mainly because lattice thermal conductivity (κ L ) decreases due to enhanced phonon scattering by lattice defects [5,11,16,19,23,24,[29][30][31]. Thus, investigating which point defect is formed and how it works in TE materials is important.
In this study, we focused on Mg 2 Si, which has attracted considerable attention as a potential TE material [3,8,21,32,33]. Mg 2 Si has an antifluorite type structure (space group: Fm3m), wherein the 8c(1/4 1/4 1/4) and the 4a(0 0 0) sites were occupied by Mg and Si, respectively. The most probable point of the defect in Mg 2 Si was theoretically predicted to be an interstitial defect in which the 4b(1/2 1/2 1/2) site was partially occupied by Mg [34][35][36]. This interstitial Mg (Mg i ) was present in synthesised Mg 2 Si-based polycrystals (PCs) [6,7,21,37]. However, recent studies have revealed that undoped and boron (B)-doped Mg 2 Si single crystals (SCs) contain Si vacancy (V Si ) defects [17]. In addition, V Si defects induce edge dislocation cores in these Mg 2 Si-based SCs [27]. As a result of the presence of V Si defects and dislocation cores, Mg 2 Si-based SCs exhibited lower κ L than Mg 2 Si

Calculation and Experimental Methods
We used the full-potential linearised augmented plane wave (FLAPW) method implemented in the Wien2k code [44] and the Korringa-Kohn-Rostoker (KKR) method under the coherent potential approximation implemented in the AkaiKKR code [45] to reduce the cost for the electronic structure calculation. Although the GW approximation, using the Green's function G and the screened Coulomb potential W, has been reported to be the most accurate method for the calculation of Mg 2 Si, Mg 2 Ge, and Mg 2 Sn [46], the FLAPW and/or KKR methods are known to be sufficient for determining the conduction type and comparing the total energy, E, of different crystal structure models [8,10,12,[18][19][20]22,25,28]. The local exchange-correlation potential in generalised gradient approximation was used for calculation through the FLAPW method. Twelve crystal structure models with a 2 × 2 × 2 cubic supercell were used, as shown in Figures S1-S3. Model where a-f is a constant (0 or 1). The numbers of k-points in the Brillouin zone for each model, Mg, and Si, were 108, 2028, and 3430, respectively. We also calculated the electronic density of states (DOS) to examine the conduction type. In the KKR method, the generalised gradient approximation and Perdew-Burke-Ernzerhof functional were used. The angular momentum cut-off was 2. The imaginary part added to the Fermi energy was set to The preparation procedure of the Mg 2 Si SC that contained V Si and dislocation cores is described elsewhere [17]. The depth profiles of O, carbon (C), hydrogen (H), Si, and MgSi in the prepared Mg 2 Si SCs were determined through SIMS (IONTOF, TOF-SIMS5-100) in negative polarity mode. The XPS spectra of the Mg 2 Si SC were acquired in a vacuum (1.2 × 10 −5 Pa) by using Al Kα radiation as a light source (ThermoFisher Scientific, Theta Probe). A cleavage surface was obtained just before the sample was introduced into the XPS chamber. Surface etching was performed in the chamber by using Ar ion milling. Photoelectron holography, a type of atomic resolution holography that can directly reveal a three-dimensional local structure around a target atom [47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63], was performed by using soft X-ray as a light source at the beamline 25SU [64] of the synchrotron radiation facility Super Photon ring-8 GeV (SPring-8), Japan. A wide-angle display-type retarding field analyser was used for the measurement [65]. A cleaved surface was obtained after the introduction of the sample into the vacuum chamber. The vacuum pressure during the measurement was 6.5 × 10 −8 Pa. From photoelectron holography, an atomic arrangement of O on W(110) [62] and a defect structure including O at the interface between Al 2 O 3 and diamond [63] was revealed. Thus, the position of O in the Mg 2 Si SC can be determined if a structure around O has a long-range order.

Results and Discussion
By using the FLAPW method, we investigated whether point defects in each supercell were stable or not. Figures S1-S3 show that the E of Models 2a (Mg 64 Si 32 +Mg i ), 3a (Mg 63 Si 32 ), and 4a (Mg 64 Si 31 ) were higher than that of Model 1 (Mg 64 Si 32 ). This result indicates that the formation energy of Mg i , V Mg , and V Si was positive (+0.197 eV/cell, +0.266 eV/cell, and +0.293 eV/cell, respectively). Consistent with the results of previous studies [34][35][36], V Si showed the highest E, i.e., it had the highest formation energy, among the point defects. However, Models 2b, 2c, 3b, 3c, 3d, 4b, 4c, and 4d, which all contained O, exhibited a lower E than Model Figure S3), respectively, were lower or equal to those of Models 2c and 3b, which contained Mg i /V Mg and O i , respectively. The formation energy of V Si +O i (Models 4b and 4c) was −0.211 eV/cell and −0.296 eV/cell, respectively. In other words, the incorporation of O stabilised the formation of V Si rather than Mg i and V Mg , regardless of whether O was located at the Si site or at the interstitial site. (The formation energy of each defect is summarised in Table S1). Next, we examined the conduction type of Models 1, 4a, and 4d by calculating their DOS through the FLAPW method. By introducing one VSi defect into Mg64Si32, p-type conductivity changed to n-type one (see Figure 2a,b). The band gap increased with the introduction of the VSi defect from 0.11 eV to 0.19 eV. Similar to the introduction of one Mgi into Mg64Si32 and Mg216Si108 [21], the substitution of one O for the Si site caused an in-gap state just at the bottom of the conduction band ( Figure 2c). Given that the Fermi level (EF) was located inside the conduction band, Mg64Si31+OSi was found to have n-type conductivity. These calculation results were reproduced using the KKR method, as shown in Figure 2d,e,f. Note that the fraction of VSi or OSi in the crystal structure models used for the calculation of Figure 2b,c,e,f was approximately 3%. By contrast, the VSi fraction in the prepared Mg2Si SCs was reported to be approximately 1%. Thus, we calculated the DOS of Mg2Si0.99 by using the KKR method ( Figure 2g). The n-type conductivity was confirmed, which was consistent with a previous calculation and used another KKR code [67]. The increase in the band gap was also found in the KKR calculation. The band gap of Mg2Si was 0.10 eV, whereas that of Mg2Si0.99 and Mg2Si0.97 was 0.15 eV and 0.20 eV, respectively. The band gap of Mg2Si and Mg2Si0.97 was in good agreement with the FLAPW calculation. For Mg2Si0.99+0.01OSi (Figure 2h), the in-gap state became smaller than that shown in Figure 2c,f, but EF continued to exist inside the conduction band. From the above calculations, we found that the presence of VSi or OSi led to n-type conductivity of Mg2Si. This result was consistent with the experiments showing that the prepared Mg2Si SCs had a negative Seebeck coefficient, i.e., they had n-type conductivity [17]. Figure 2i presents the lattice constant at the minimum E, which was used for the calculation of the results given in Figure 2a,h. The introduction of VSi or OSi reduced the lattice constant. Experimentally, the smaller lattice constant resulted in an increase in the VSi fraction in Mg2Si SCs [17]. A similar tendency was reported for the prepared Mg2Sn SCs, wherein the VMg fraction increased with the decrease in the lattice constant [16,27]. As expected from the above calculations, O can be Oi or OSi to stabilise VSi if it exists in the crystal lattice of Mg2Si. Next, we examined the conduction type of Models 1, 4a, and 4d by calculating their DOS through the FLAPW method. By introducing one V Si defect into Mg 64 Si 32 , p-type conductivity changed to n-type one (see Figure 2a,b). The band gap increased with the introduction of the V Si defect from 0.11 eV to 0.19 eV. Similar to the introduction of one Mg i into Mg 64 Si 32 and Mg 216 Si 108 [21], the substitution of one O for the Si site caused an in-gap state just at the bottom of the conduction band ( Figure 2c). Given that the Fermi level (E F ) was located inside the conduction band, Mg 64 Si 31 +O Si was found to have n-type conductivity. These calculation results were reproduced using the KKR method, as shown in Figure 2d-f. Note that the fraction of V Si or O Si in the crystal structure models used for the calculation of Figure 2b,c,e,f was approximately 3%. By contrast, the V Si fraction in the prepared Mg 2 Si SCs was reported to be approximately 1%. Thus, we calculated the DOS of Mg 2 Si 0 . 99 by using the KKR method ( Figure 2g). The n-type conductivity was confirmed, which was consistent with a previous calculation and used another KKR code [67]. The increase in the band gap was also found in the KKR calculation. The band gap of Mg 2 Si was 0.10 eV, whereas that of Mg 2 Si 0 . 99 and Mg 2 Si 0 . 97 was 0.15 eV and 0.20 eV, respectively. The band gap of Mg 2 Si and Mg 2 Si 0 . 97 was in good agreement with the FLAPW calculation. For Mg 2 Si 0 . 99 +0.01O Si (Figure 2h), the in-gap state became smaller than that shown in Figure 2c,f, but E F continued to exist inside the conduction band. From the above calculations, we found that the presence of V Si or O Si led to n-type conductivity of Mg 2 Si. This result was consistent with the experiments showing that the prepared Mg 2 Si SCs had a negative Seebeck coefficient, i.e., they had n-type conductivity [17]. Figure 2i presents the lattice constant at the minimum E, which was used for the calculation of the results given in Figure 2a,h. The introduction of V Si or O Si reduced the lattice constant. Experimentally, the smaller lattice constant resulted in an increase in the V Si fraction in Mg 2 Si SCs [17]. A similar tendency was reported for the prepared Mg 2 Sn SCs, wherein the V Mg fraction increased with the decrease in the lattice constant [16,27]. As expected from the above calculations, O can be O i or O Si to stabilise V Si if it exists in the crystal lattice of Mg 2 Si.
We acquired the depth profiles of O, C, H, Si, and MgSi by using SIMS, as shown in Figure 3, to investigate whether O was present or absent in the Mg 2 Si SC. O, C, and H were mainly detected below 200 nm, indicating that the surface of the Mg 2 Si SC was contaminated with O, C, and H. As the depth increased to 200 nm, the H intensity decreased to a noise level (<10 counts), and Si and MgSi were clearly detected instead. The C intensity also decreased and reached the noise level at 1600 nm. These results suggested that surface contamination with C and H could be eliminated by etching or cleaving the Mg 2 Si SC. On the other hand, O intensity decreased but remained constant above 1200 nm. Thus, O was expected to exist in the Mg 2 Si SC after etching or cleaving.
The presence of O inside the Mg 2 Si SC was also confirmed by acquiring the XPS spectra before and after etching, as shown in Figure 4a. C and O peaks, in addition to Mg and Si peaks, were observed before etching. This finding indicated that the surface of the Mg 2 Si SC was contaminated and had oxidised. In fact, the surface of Mg 2 Si SC is known to oxidise when it is placed in the atmosphere [68]. After etching, the C peak disappeared, but the O peaks remained. Additional detailed information is provided in Figure 4b. Before etching, two peaks were observed in the C 1s XPS spectrum (upper-left figure). These peaks, which were assigned to C-O (290 eV [69] [71]. However, this assignment can be disputed, given the absence of Mg i in the Mg 2 Si SC [17]. Studies [72][73][74] have reported that the Mg-O and Mg peaks of Mg 2 Si components appeared in the Mg 2p XPS spectra at lower and higher binding energies, respectively. In consideration of these studies, as well as the O 1s XPS spectra in this study, we concluded that the components observed at 50  We further proved that O was present in Mg 2 Si SC through the use of photoelectron holography. Figure 5a shows the Mg 2p spectrum (dots), which could be deconvoluted into two components (blue and red curves). The spin-orbit splitting for each component was set at 0.6 eV. In consideration of the XPS results shown previously, we assigned the components at higher and lower binding energies to Mg-O and Mg in Mg 2 Si, respectively. The difference in the energy position between the two components was 1 eV and was consistent with that in the Mg 2p XPS spectra. The insets in Figure 5a are the holograms derived from each component (blue-black colour scale). In particular, the hologram for the component at a lower binding energy well coincided with the hologram simulated using the regular atomic arrangement of the Mg and Si atoms of Mg 2 Si around an emitter Mg atom (yellow-black colour scale). Thus, the assignment of the components in the Mg 2p spectrum was found to be valid. The Si 2p spectrum (dots) is shown in Figure 5b. The spin-orbit splitting for each component was set at 0.6 eV. Similar to a previous result [68], a component of Si for Mg 2 Si at the lowest binding energy and Si-O components at a higher binding energy were present in the Si 2p spectrum (coloured curves). The Si-O components were Si + , Si 2+ , Si 3+ , and Si 4+ at 0.5 eV, 0.9 eV, 1.3 eV, and 4.5 eV, respectively. The energy positions of these components were evaluated relative to that of the Si component and were found to correspond reasonably to values in the literature [75][76][77]. An inset in Figure 5b is an experimental hologram derived from the Si component (left) and a simulated hologram constructed on the basis of the regular atomic arrangement of the Mg and Si atoms of Mg 2 Si around an emitter Si atom (right). Given that the experimental hologram coincided with the simulated one, the assignment of the components was confirmed to be valid for the Si 2p spectrum. Although the cleavage surface was prepared in a vacuum, the Mg-O and Si-O components were found in Mg 2p and Si 2p spectra, respectively, verifying that O was present inside the Mg 2 Si SC. The remaining O in an Ar gas and/or the aluminum crucible was used for the preparation of the Mg 2 Si SC, which could be a source of O. We acquired the depth profiles of O, C, H, Si, and MgSi by using SIMS, as shown in Figure 3, to investigate whether O was present or absent in the Mg2Si SC. O, C, and H were mainly detected below 200 nm, indicating that the surface of the Mg2Si SC was contaminated with O, C, and H. As the depth increased to 200 nm, the H intensity decreased to a noise level (<10 counts), and Si and MgSi were clearly detected instead. The C intensity also decreased and reached the noise level at 1600 nm. These results suggested that surface contamination with C and H could be eliminated by etching or cleaving the Mg2Si SC. On the other hand, O intensity decreased but remained constant above 1200 nm. Thus, O was expected to exist in the Mg2Si SC after etching or cleaving.   We acquired the depth profiles of O, C, H, Si, and MgSi by using SIMS, as shown in Figure 3, to investigate whether O was present or absent in the Mg2Si SC. O, C, and H were mainly detected below 200 nm, indicating that the surface of the Mg2Si SC was contaminated with O, C, and H. As the depth increased to 200 nm, the H intensity decreased to a noise level (<10 counts), and Si and MgSi were clearly detected instead. The C intensity also decreased and reached the noise level at 1600 nm. These results suggested that surface contamination with C and H could be eliminated by etching or cleaving the Mg2Si SC. On the other hand, O intensity decreased but remained constant above 1200 nm. Thus, O was expected to exist in the Mg2Si SC after etching or cleaving.   Figure 5a, which is rather unclear compared with those derived from the Mg and Si components. We reconstructed a simulated hologram of Model 4c (Mg 64 Si 31 +O i ) and Model 4d (Mg 64 Si 31 +O Si ), as shown in Figure 6, to examine the position. The characteristic features in the simulated holograms were not identified in the experimental hologram. Thus, we could not conclude that O existed at a specific site of the crystal lattice of Mg 2 Si. Instead, O was highly likely to be present at the dislocation cores. O was likely diffused and segregated to the dislocation cores during crystal growth. O segregation resulted in the immobilisation of the dislocation cores through the reconstruction of Mg, Si, and O atom locations around the dislocation cores. The reconstruction process reduced the total energy, which, in turn, stabilised V Si . Note that reconstructed atomic arrangements lacked a long-range order; therefore, the hologram derived from the Mg-O component was featureless. In the future, other experiments, such as x-ray absorption spectroscopy and positron annihilation spectroscopy, will be performed to determine the position of O precisely.
SC were ascribed to the Si-O and Mg-O components. By etching the surface, the broad O 1s peak changed into double peaks (lower-middle figure) due to a decrease in C-related contamination. In other words, the C-O component at 532 eV disappeared, making the Si-O and Mg-O components more evident after etching. The remaining Si-O and Mg-O components indicated that O existed inside the Mg2Si SC. The removal of surface oxidation was confirmed by comparing the Mg 2p XPS spectra before and after etching (upper-right and lower-right figures, respectively). A broad peak was observed in the spectra. This peak could be separated into two components at 50 eV and 49 eV. Such components were also found in an Sb-doped Mg2Si0.4Sn0.6 PC and were assigned to the Mg of Mg2Si (50 eV) and Mgi (49 eV) components [71]. However, this assignment can be disputed, given the absence of Mgi in the Mg2Si SC [17]. Studies [72][73][74] have reported that the Mg-O and Mg peaks of Mg2Si components appeared in the Mg 2p XPS spectra at lower and higher binding energies, respectively. In consideration of these studies, as well as the O 1s XPS spectra in this study, we concluded that the components observed at 50    nents were Si + , Si 2+ , Si 3+ , and Si 4+ at 0.5 eV, 0.9 eV, 1.3 eV, and 4.5 eV, respectively. The energy positions of these components were evaluated relative to that of the Si component and were found to correspond reasonably to values in the literature [75][76][77]. An inset in Figure 5b is an experimental hologram derived from the Si component (left) and a simulated hologram constructed on the basis of the regular atomic arrangement of the Mg and Si atoms of Mg2Si around an emitter Si atom (right). Given that the experimental hologram coincided with the simulated one, the assignment of the components was confirmed to be valid for the Si 2p spectrum. Although the cleavage surface was prepared in a vacuum, the Mg-O and Si-O components were found in Mg 2p and Si 2p spectra, respectively, verifying that O was present inside the Mg2Si SC. The remaining O in an Ar gas and/or the aluminum crucible was used for the preparation of the Mg2Si SC, which could be a source of O.   O segregation resulted in the immobilisation of the dislocation cores through the reconstruction of Mg, Si, and O atom locations around the dislocation cores. The reconstruction process reduced the total energy, which, in turn, stabilised VSi. Note that reconstructed atomic arrangements lacked a long-range order; therefore, the hologram derived from the Mg-O component was featureless. In the future, other experiments, such as x-ray absorption spectroscopy and positron annihilation spectroscopy, will be performed to determine the position of O precisely. In summary, using the FLAPW and KKR methods, we theoretically predicted that the presence of O stabilised the formation of Mgi, VMg, and VSi in Mg2Si SCs. The formation energy of VSi+Oi (Models 4b and 4c) and OSi (Model 4d) was lower or equal to that of the other lattice defects, indicating that Mg2Si SCs with VSi were stabilised through the incorporation of O. The OSi defect showed the lowest formation energy of the −0.583 eV/cell. The calculated DOS indicated that the electrical conduction of Mg2Si changed from p-type

Supplementary Materials:
The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/nano13071222/s1, Figure S1: Volume dependence of the total energy for the four crystal structure models relative to the minimum energy of Model 1. Crystal structures are drawn by using VESTA [66]; Figure S2: Volume dependence of the total energy for the five crystal structure models relative to the minimum energy of Model 1; Figure S3: Volume dependence of the total energy for the five crystal structure models relative to the minimum energy of Model 1; Table S1