Formation of Mg2Si1−xSnx Thin Films by Co-sputtering and Investigation of their p-type Electrical Conduction

We obtained Mg2Si1-xSnx films on the c-plane sapphire and the (100) CaF2 substrates using the radio frequency (RF) magnetron co-sputtering method under various sputtering area ratio of Mg chips to Mg2Si (Sn) target and a subsequent two-step annealing process up to 400°C. The X-ray diffraction (XRD) and energy-dispersive X-ray spectrometry (EDS) analysis of the samples confirmed that the obtained films were ternary Mg2Si1-xSnx films with a composition of x ≈ 0.31. Optical microscopy and EDS mapping images of Mg2Si and Mg2Si1-xSnx (x = 0.31) films after annealing at 400°C showed remarkable Mg desorption from Mg2Si1-xSnx films, but not from Mg2Si films. The Hall effect measurements revealed that all Mg2Si1-xSnx films annealed at 400°C had a ptype conductivity. The first-principles calculations suggested that a combination of two different types of defects, Sn substitution at Si site (SnSi) and Mg vacancy (VMg), which acts as an acceptor, could be the origin of the p-type conductivity of Mg2Si1-xSnx films.


Introduction
Mg2Si is an environmentally friendly material with an indirect bandgap that ranges from 0.6 to 0.8 eV [1][2][3][4][5]. The dimensionless figure of merit (ZT) of Mg2Si is known to be high in the 500 K to 800 K range [6] and thus its application in thermoelectric conversion devices is expected. However, since Mg2Si has high thermal conductivity, it is necessary to increase phonon scattering to decrease the thermal conductivity of Mg2Si [7][8][9][10][11]. One possible way to decrease the thermal conductivity is by adding a third element (Sn) with a large atomic mass to Mg2Si. On the other hand, in the phase diagram of Mg2Si1-xSnx, the mixed-phase of Mg2Si and Mg2Sn is obtained in the composition range of 0.4 ≦ x ≦ 0.6 due to the presence of miscibility gaps [12]. However, it has been difficult to obtain a ternary solid solution of Mg2Si1-xSnx (0.4 ≦ x ≦ 0.6), especially by the crystal growth from the melt due to the large difference in the molecular mass of Mg2Si and Mg2Sn. There is a report on Mg2Si1-xSnx films (0.4 ≦ x ≦ 0.6) formed by co-sputtering using the three elemental targets of Si, Sn and Mg, and they have shown an n-type conductivity with an electron density in the order of 10 18 cm −3 [13]. In our previous study, we succeeded in obtaining ternary MgySi1-xSnx (0 < x < 0.5, 2> y >1) films, but all the samples exhibited p-type conductivity, probably due to the presence of Mg vacancy (VMg) [14][15]. The purpose of this study is to clarify the origin of p-type conductivity. We optimized the chemical composition of Mg in single-phase Mg2Si1-xSnx films during co-sputtering of Mg2Si, Sn and Mg. The relationship between the type of electrical conductivity and the formation energy of the Mg2Si1-xSnx crystals containing a few types of point defects was also evaluated by firstprinciples calculation.
Four Sn chips (3N, 10 × 10 × t1 mm) and various numbers of Mg chips (6N, 5 × 5 × t1 mm) were placed together on a Mg2Si target (3N, φ4 inch × t4.5 mm). The sputtering area ratio of the Mg chips to Mg2Si (Sn) target is defined as Mg/Mg2Si (Sn), and this ratio was varied from 0.0031-0.032. Two types of single side polished substrates were used in this study: one is a c-plan sapphire substrate (φ2 inches × t425 μm) for preforming X-ray diffraction (XRD), optical microscopy, and Hall effect measurements; the other is a (100) CaF2 substrate (10 × 10 × t0.5 mm) for performing scanning electron microscope (SEM)/ energy-dispersive X-ray spectrometry (EDS) analysis. No surface treatment was performed for the two types of as-received substrates before deposition. The deposition chamber was evacuated to 4 × 10 -5 Pa before starting the sputtering process. Pre-sputtering was performed for 10 min to clean the surfaces of the Mg2Si target as well as the Sn and Mg chips before deposition by sputtering. The Mg2Si1-xSnx films with a thickness of 300-400 nm were deposited on the c-plane sapphire substrates and the (100) CaF2 substrates by RF magnetron co-sputtering in Ar atmosphere. The deposition working pressure was maintained at 5 Pa. After the deposition, the samples were subjected to two-step annealing in constant Ar (97%)/H2 (3%) flow of 200 sccm: The first step was performed at 200℃ for 30 min to remove water remaining in the quartz tube of annealing system, and the second step was performed at 400℃ for 30 min to form Mg2Si1-xSnx films. After annealing, the ohmic electrodes were formed by soldering four indium dots of about φ1 mm at the four corners on the top surface of Mg2Si1-xSnx films, and the Hall effect measurement was performed at room temperature. The structural properties of the samples were characterized by XRD, optical microscopy, and SEM/ EDS analysis.

First-principles calculation
First-principles calculations combining density function theory and the projector augmented wave method were performed to investigate the electronic structures of the Mg2Si1-xSnx crystals, which contain point defects such as Mg vacancy (VMg) and Sn substitution at Si site (SnSi), using the software PHASE/0 (ASMS Co., Ltd.). We employed the generalized gradient approximation method proposed by Perdew-Burke-Ernzerhof (GGA-PBE) to deal with the exchange-correlation energy. The planewave cutoff energies used for the wavefunctions and charge densities were 340 and 3060 eV, respectively. The Brillouin zone (BZ) integration was performed using the tetrahedron method. Periodic boundary conditions were applied along the three lattice vectors. For the k-point sampling of numerical BZ integration, we used a 4 × 4 × 4 mesh for the 3 × 3 × 3 supercell (81 atoms in total). The energetic convergence threshold for the self-consistent field was 2.72 × 10 −8 eV. The convergence condition for structural optimization was 2.6 × 10 −2 eVǺ −1 . The Mg2Si Crystallographic Information File (Mg2Si coordinate and crystal structure), which can be downloaded from the material project database [16], was used to perform calculations. Figure 1 shows the Mg/Mg2Si (Sn) dependence of the XRD spectra for Mg2Si1-xSnx thin films formed on the c-plane sapphire substrates. From Fig. 1, all the peaks were observed between Mg2Sn and Mg2Si peaks, which indicates a formation of ternary Mg2Si1-xSnx films. As the Mg content increases, no significant change in the positions of the peaks was observed. Furthermore, no Mg or MgO peaks were observed. The composition ratio of x in Mg2Si1-xSnx was estimated using Vegard's law, and it was determined to be 0.31 (i.e., Mg2Si0.69Sn0.31) at Mg/Mg2Si (Sn) = 0.012. Figure 2 shows the optical microscope images of the surface of Mg2Si and Mg2Si0.69Sn0.31 films deposited on c-plane sapphire substrates before and after annealing. Before annealing, both films showed smooth surface morphology. After annealing at 400 ℃, surface voids were observed for the Mg2Si0.69Sn0.31 films, but not for the Mg2Si films. As for the Mg2Si1-xSnx films with Mg/Mg2Si (Sn) = 0.0031 and 0.0062, no surface voids were observed, but they were observed for the Mg2Si1-xSnx films with Mg/Mg2Si (Sn) = 0.012 and 0.032.

Structural properties
EDS mapping analysis was performed to map out the lateral distribution of the elements of the rough surface area with surface voids for the Mg2Si0.69Sn0.31 films, while the EDS analysis was performed to determine the elemental composition of individual points of the smooth surface area without any surface voids for the MgySi1-xSnx films as a function of Mg/Mg2Si (Sn). It should be noted that the smooth area partially remained in the MgySi1-xSnx films with Mg/Mg2Si (Sn) = 0.012 and 0.032. CaF2 substrates were used for EDS measurements since CaF2 does not contain elemental oxygen and the constituent elements of the Mg2Si1-xSnx films. Figure 3 shows the EDS mapping images of Mg, Si and Sn measured on the rough surface area for the Mg2Si0.69Sn0.31 (Mg/Mg2Si (Sn) = 0.012) films deposited on the (100) CaF2 substrates after annealing at 400℃. Desorption of Mg, Si, and Sn atoms can be seen from the EDS mapping. This kind of desorption was also observed for films with Mg/Mg2Si (Sn) = 0.032 (data not shown here). For the MgySi1-xSnx films with Mg/Mg2Si (Sn) = 0.012 and 0.032, the rough surface area occupied about 50% and over 90% of the whole surface area, respectively. Table Ⅰ shows the chemical composition ratio of MgySi1-xSnx films deposited on the (100) CaF2 substrates with Mg/Mg2Si (Sn) = 0.012 before and after annealing. As for the annealed MgySi1-xSnx films with Mg/Mg2Si (Sn) = 0.012, two points with different surface morphologies, a smooth and rough surface area, were analyzed. The Mg composition ratio before annealing was 2.41, while the Mg composition ration decreased significantly after annealing from 2.41 to 2.05 and 1.74 for the films with a smooth and rough surface area, respectively. Similarly, the Sn composition ratio decreased after annealing. We consider the mechanism of desorption of the constituent elements from the surface of the MgySi1-xSnx films. It should be noted that in this study metallic Mg and Sn chips were used as a sputteringtarget material. The Mg-Sn system has a eutectic temperature of 203°C when the Sn molar ratio (Snx) is higher than 0.33 (Snx > 0.33) [17]. Furthermore, the vapor pressure of Mg is 10 12 times higher than that of Sn at 400°C [18]. Thus, excess isolated Mg atoms in Mg-rich Mg2Si1-xSnx films may result in eutectic reaction with isolated Sn atoms even at an annealing temperature of 400°C. The dominant desorption of Mg atoms as compared to Sn atoms may also occur during annealing at 400°C.
The chemical composition ratio of the MgySi1-xSnx films formed on the (100) CaF2 substrates was analyzed using EDS as a function of Mg/Mg2Si (Sn). EDS analysis was performed on the smooth surface area. Figure 4 shows the obtained composition ratio, x and y of the smooth surface for the  Table Ⅰ. Similarly, the Mg composition of the rough surface area for the MgySi1-xSnx films with Mg/Mg2Si (Sn) = 0.032 was smaller than 2, although the Mg composition of the smooth surface area for MgySi1-xSnx films with Mg/Mg2Si (Sn) = 0.032 is 3.43 as shown in Fig. 4. This indicates the formation of Mg vacancy (VMg) at the rough surface area for Mg2Si1-xSnx films with Mg/Mg2Si (Sn) = 0.012 and 0.032. The Mg composition value at the rough surface area differs, and this difference was related to the measurement point. Consequently, the systematical evaluation of the Mg composition value of the rough surface area will be needed.    Figure 5 shows the result of the Hall effect measurements for the MgySi1-xSnx films deposited on the c-plane sapphire substrates and annealed at 400℃, as a function of Mg/Mg2Si (Sn). Attention should be paid to the fact that the measured area includes both the rough and the smooth surface area. As mentioned above, the MgySi1-xSnx films with Mg/Mg2Si (Sn) = 0.0031 and 0.0062 only have a smooth surface area, while the MgySi1-xSnx films with Mg/Mg2Si (Sn) = 0.012 and 0.032 have a rough surface area about 50% and over 90% of the whole surface area, respectively. On the other hand, the chemical composition ratio, x and y for the MgySi1-xSnx films in Fig. 4 was measured at the smooth surface area. In Fig. 5, all the samples after annealing at 400℃ showed a p-type conductivity. The hole density and mobility showed a tendency to increase with increasing Mg/Mg2Si (Sn). Usually, the hole density decreases as the excess Mg content increases in Mg2Si due to an increase in interstitial Mg atoms, which act as a donor in Mg2Si. However, the hole density of the MgySi1-xSnx films increased as Mg/Mg2Si (Sn) increases as shown in Fig. 5. There are two possible reasons for this. The first reason is the low eutectic temperature of 203°C in the higher Sn molar ratio (Snx) sample where Snx was over 0.33 in the Mg-Sn system [17]. The other is the high vapor pressure of Mg, which is 10 12 times higher than that of Sn at 400°C [18]. Thus, excess isolated Mg atoms in the Mg-rich Mg2Si1-xSnx films may result in eutectic reaction with isolated Sn atoms, and dominant vaporization of Mg atoms may occur when annealing at 400°C. These phenomena may be enhanced by increasing the Mg content in the MgySi1-xSnx films which due to an increase in the number of Mg atoms surrounding the Sn atoms. To decrease in hole concentration, desorption of the Mg atoms during annealing should be suppressed: optimizations of deposition and annealing conditions are underway.

Result of the first-principles calculation
First-principles calculation was performed to clarify the origin of p-type conductivity for the MgySi1-xSnx films. Two types of Sn-related point defect in the silicide lattice were considered: for Sn substitution at Si site (SnSi) and for Sn substitution at Si site with Mg vacancy (SnSi + VMg). Figure 6 shows the DOS profiles of SnSi (Mg54Si19Sn8) = Mg2Si0.7Sn0.3 and SnSi + VMg (Mg49Si19Sn8) = Mg1.81Si0.7Sn0. 3. SnSi (Mg54Si19Sn8) shows the intrinsic property, while SnSi + VMg (Mg49Si18Sn9) shows a p-type conductivity, judging from the positions of their fermi-levels (Ef). From the total energy obtained by first-principles calculation, we calculated the formation energy of the point defects in the Mg2Si1-xSnx crystals. The formation energy (ΔE) of SnSi and SnSi+VMg can be calculated using Eqs. (1) and (2), respectively. Here, E(material) denotes the total energy of the single crystalline material. Table Ⅱ shows the type of conductivity and the formation energy of the Mg2Si1-xSnx crystals that contain a few types of point defects, which were obtained by first-principles calculation. There were no significant influences of the lattice points occupied by two types of defects, SnSi and VMg, on the DOS profiles and the total energies. The formation energy of SnSi+VMg (Mg49Si18Sn9) (0.342 eV/cell) is smaller than that of VMg (Mg49Si27) (0.343 eV/cell) and SnSi (Mg54Si18Sn9) (0.470 eV/cell), which indicates that Mg49Si18Sn9 could be easily formed when compared with the Mg vacancy in Mg2Si and pure ternary Mg54Si18Sn9. Thus, we believe that the origin of the p-type conductivity for MgySi1-xSnx films could be due to a combination of two types of defects: Sn substitution at Si site (SnSi) and Mg vacancy (VMg).

Conclusion
We studied the origin of the p-type conductivity for MgySi1-xSnx films formed by RF magnetron co-sputtering and subsequent two-step annealing as a function of Mg/Mg2Si (Sn). The XRD analysis indicates the formation of ternary Mg2Si1-xSnx films and the composition ratio of x derived from Vegard's law and EDS analysis was almost constant at 0.31, which is independent of Mg/Mg2Si (Sn). In the XRD spectra, no Mg and MgO peaks were observed. Optical microscopy and EDS mapping images showed that the Mg desorption occurred for Mg2Si0.69Sn0.31 films after annealing at 400 ℃, but not for Mg2Si films. The Mg composition at the smooth area for MgySi1-xSnx films annealed at 400℃ increased from 1.37 to 3.43 as Mg/Mg2Si (Sn) increased, but the Mg composition at the rough surface area for MgySi1-xSnx films annealed at 400℃ was less than 2.0. The Hall effect measurements revealed that all Mg2Si1-xSnx films annealed at 400℃, which include both the rough and smooth surface area, had a p-type conductivity. Furthermore, a hole density and the hole mobility showed a tendency to increase with increasing Mg/Mg2Si (Sn). While annealing at 400°C, the excess isolated Mg atoms in the Mg-rich Mg2Si1-xSnx films may result in eutectic reaction with the isolated Sn atoms due to a low eutectic temperature of 203°C in the Mg-Sn system, and eventually dominant vaporization of the Mg atoms may occur due to high vapor pressure of Mg, which is 10 12 times higher than that of Sn at 400°C.
The formation energy of SnSi+VMg (Mg49Si18Sn9) (0.342 eV/cell) is smaller than that of VMg (Mg49Si27) (0.343 eV/cell) and SnSi (Mg54Si18Sn9) (0.470 eV/cell), which indicates that Mg49Si18Sn9 could be easily formed when compared with Mg vacancy in Mg2Si and pure ternary Mg54Si18Sn9. Thus, we believe that the origin of the p-type conductivity could be due to a combination of two types of defects: Sn substitution at Si site (SnSi) and Mg vacancy (VMg).