Temperature-Driven Twin Structure Formation and Electronic Structure of Epitaxially Grown Mg3Sb2 Films on Mismatched Substrates

Mg3Sb2-based compounds are one type of important room-temperature thermoelectric materials and the appropriate candidate of type-II nodal line semimetals. In Mg3Sb2-based films, compelling research topics such as dimensionality reduction and topological states rely on the controllable preparation of films with high crystallinity, which remains a big challenge. In this work, high quality Mg3Sb2 films are successfully grown on mismatched substrates of sapphire (000l), while the temperature-driven twin structure evolution and characteristics of the electronic structure are revealed in the as-grown Mg3Sb2 films by in situ and ex situ measurements. The transition of layer-to-island growth of Mg3Sb2 films is kinetically controlled by increasing the substrate temperature (Tsub), which is accompanied with the rational manipulation of twin structure and epitaxial strains. Twin-free structure could be acquired in the Mg3Sb2 film grown at a low Tsub of 573 K, while the formation of twin structure is significantly promoted by elevating the Tsub and annealing, in close relation to the processes of strain relaxation and enhanced mass transfer. Measurements of scanning tunneling spectroscopy (STS) and angle-resolved photoemission spectroscopy (ARPES) elucidate the intrinsic p-type conduction of Mg3Sb2 films and a bulk band gap of ~0.89 eV, and a prominent Fermi level downshift of ~0.2 eV could be achieved by controlling the film growth parameters. As elucidated in this work, the effective manipulation of the epitaxial strains, twin structure and Fermi level is instructive and beneficial for the further exploration and optimization of thermoelectric and topological properties of Mg3Sb2-based films.


Introduction
Mg 3 Sb 2 -based compounds have attracted widespread attention in research areas of thermoelectrics and condensed matter physics due to their exceptional thermoelectric performances and novel topological properties. From the aspect of structure-property correlations, Mg 3 Sb 2 is one type of Zintl compounds with phonon-glass and electroncrystal (PGEC) characteristics [1][2][3][4], beneficial for its thermoelectric performance. In the past decade, a variety of strategies have been utilized to boost the thermoelectric properties of Mg 3 Sb 2 , such as tuning carrier density with dopants, band engineering [5,6], forming solid solutions [7][8][9], and interface engineering [6, [10][11][12], but research has seemed to hit a bottleneck. According to the latest theoretical calculations, a leap in the performance of Mg 3 Sb 2 requires innovative strategies based on epitaxial technology [13][14][15][16]. Zhang et al. have proposed that, the crystal field energy splitting of valence bands could be modulated by substrate-induced epitaxial strains in Mg 3 Sb 2 epi-films, bringing about the convergence of valence bands and the optimized zT of 0.7 [15]. In addition, based on Boltzmann transport calculations, Shan et al. have reported that the mono-layer Mg 3 Sb 2 would be endowed with strong electrical properties and a low lattice thermal conductivity due to the beneficial dimensionality reduction, resulting in a very high zT of 2.5 at elevated temperatures [13]. Furthermore, in the process of exploring new topological systems, Mg 3 Sb 2 was regarded as a suitable candidate possessing novel type-II nodal-line topological states, through appropriately modulating the spin-orbital coupling (SOC) strength of Mg 3 (Sb,Bi) 2 solid solutions [17]. Zhou et al. have successfully synthesized high quality Mg 3 Bi 2 films by the molecular beam epitaxy (MBE) technique, and have characterized the surface resonance bands by angle-resolved photoelectron spectroscopy (ARPES) [18]. However, the subtle control of the Bi/Sb ratio and the films' crystallinity remained as the big challenge in Mg 3 (Sb,Bi) 2 [17,19]. There are three obstacles regarding the epitaxial growth of Mg 3 Sb 2based films. (1) Due to the high saturation vapor pressure and chemical activity of the Mg, it is necessary to identify a series of substrates with matched lattice parameters that are chemically inert with Mg, as well as to effectively control the Mg content [20][21][22]. (2) To get desired epi-films with high crystallinity and with excellent compositional control, the optimal growth window for the growth of Mg 3 Sb 2 -based films should be thoroughly and carefully explored. (3) Epitaxial strains, twin structure and dislocations are usually discovered in epitaxial films under nanometer scale, which could largely influence the functional performances of materials [23,24]. Hence, it is necessary to clarify the tuning mechanisms of these structures in the epitaxially grown Mg 3 Sb 2 films.
In this work, the influences of MBE processing parameters on the phase structure and crystallinity of binary Mg 3 Sb 2 films were systematically investigated, while the ARPES band structure was illustrated in the films grown under various MBE parameters. The transition of layer-to-island growth mode with increasing the film thickness, and its relation with epitaxial strains, were revealed in our Mg 3 Sb 2 films. Moreover, the obvious twin structure in Mg 3 Sb 2 films could be effectively manipulated by the substrate temperature (T sub ), and hence, by the mass transfer process and epitaxial strains. Furthermore, the Fermi level (E F ) showed a substantial shift of~0.2 eV towards the conduction band as the Mg/Sb ratio (R) increased greatly, likely due to the suppression of Mg vacancies. This work clearly elucidated the rich nanostructure evolution during the epitaxial growth of Mg 3 Sb 2 films, and lays the foundation for exploring novel band structures of Mg 3 Sb 2 -based materials through strain engineering or forming heterostructures.

Materials and Methods
Mg 3 Sb 2 films with the highest crystallinity were mainly grown on Al 2 O 3 (000l) substrates in a commercial Molecular Beam Epitaxy (MBE) system (Octoplus 300, Dr. Eberl MBE-Komponenten GmbH, Germany), while the growth of Mg 3 Sb 2 films was also carried out on HOPG, BaF 2 (111) and Ge (111) substrates. The standard RCA cleaning method (omitting the HF etching step) is used to remove the inorganic and organic impurities on the surface of Al 2 O 3 (000l) substrates. High purity Mg (99.9%) and Sb (99.999%) were evaporated with the nominal Mg/Sn ratio R of 4:1~16/1 and at the Sb flux of 0.03 Å/s. The main experimental results were obtained from Mg 3 Sb 2 films grown under R = 4:1, if not explicitly stated. The T sub is selected as 573 K, 673 K and 773 K in this study. Two types of growth processes were selected: the one-step growth process and the growth and annealing process (annealed at 773 K after growth). The film growth process was monitored in situ by reflection high energy electron diffraction (RHEED). The crystal structure was examined using high-resolution x-ray diffraction (XRD, Smart Lab, Rigaku, Japan), including the θ-2θ scan, rocking curve and pole figure. The thickness and surface morphology of Mg 3 Sb 2 films were characterized by an atomic force microscope (AFM, Dimension FastScan, Bruker, Germany). The valence band structure of Mg3Sb2 films was measured at 10 K in an angle resolved photoemission spectroscopy (ARPES) apparatus that is connected to the MBE chamber by a UHV transfer line. The analyser (Scienta Omicron DA-30L, Sweden) with an energy resolution of 7 meV and an angular resolution of 0.2 • , the He-I monochromatic light source (Fermion Instruments, Shanghai) and the six-axis sample manipulator equipped a He closed-cycle helium refrigerator (Fermion Instruments, Shanghai) were utilized in the measurements. Scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) measurements were carried out in a UHV and low-temperature STM (LT-STM-AFM-N, CreaTec Fisher & Co. GmbH, Germany) operated at 77 K, which was connected to the MBE chamber by an UHV transfer line.
Prior to the film growth, the Mg 3 Sb 2 layer with thickness of several nanometers was deposited on the Al 2 O 3 (000l) substrate at 773 K, followed by a subsequent desorption at 1023 K until the substrate's RHEED patterns were recovered. We noted that the introduction of this passivation process is beneficial for the epitaxial growth of Mg 3 Sb 2 films with improved crystallinity, as shown in Figure S1. Such a process is broadly applicable for lattice-mismatched epitaxial growth, including WSe 2 and other TMDCs [25]. Figure 1a shows the crystal structure of α-Mg 3 Sb 2 (space group: P3m1, No. 164). Mg 3 Sb 2 compounds can be regarded as a special case of Zintl phase CaAl 2 Si 2 (AB 2 X 2 ) in which A and B are occupied by Mg1 (interlayer) and Mg2 (intralayer) atoms [26]. Since both the intralayer Mg2-Sb and interlayer Mg1-Sb are weak chemical bonds based on Bader charge analysis, Mg 3 Sb 2 exhibits a nearly isotropic 3D bonding network and pseudolayered feature [26]. This structural feature has been corroborated by recent discoveries, such as the nearly isotropic lattice thermal expansion [26], and the slightly higher compression ratio along the out-of-plane direction than that along the in-plane direction [27,28]. These findings highlight the unique chemical bonding characteristics of Mg 3 Sb 2 , distinct from the van der Waals (vdW) layered materials with weak interlayer interactions [29] and the 3D materials featuring strong anisotropic chemical bonds [30]. As a result, the pseudo-layered crystal structure endows Mg 3 Sb 2 with exceptional tolerance of epitaxially growing on substrates without strict lattice-matching requirements. As shown in Figure 1b,c and Figure S2, the Mg 3 Sb 2 films with strong (000l) orientation can be grown on lattice-mismatched substrates of Al 2 O 3 (000l), cleaved HOPG, Ge(111) and BaF 2 (111) substrates with in-plane lattice misfit of 4.6%, 8.1%, 12%, and −3.8%, respectively. According to the collected RHEED patterns, the Mg 3 Sb 2 film grown on Al 2 O 3 (000l) substrate possesses the highest crystalline quality, benefiting from the aforementioned passivation process and good anti-Mg corrosion resistance of the Al 2 O 3 substrate.

Lattice-Mismatched Epitaxial Growth of Mg 3 Sb 2
The crystalline structure of Mg 3 Sb 2 films grown on Al 2 O 3 (000l) substrates was investigated by high resolution XRD measurements, as illustrated in Figure 1b,c. Except for the peaks at~42 • and 21 • originating from the Al 2 O 3 substrate, the XRD (θ-2θ scan) peaks of films grown under different thermal processes can all be indexed to (000l) patterns of Mg 3 Sb 2 , confirming a strict c-axis orientation. Meanwhile, increasing T sub combined with the annealing process could drastically reduce the full-width-half-maximum (FWHM) of the rocking curve from 0.95 • to 0.11 • , implying the prominent improvement of crystalline quality. The film grown and annealed at T sub = 773 K has the narrowest rocking curve FWHM and the highest crystallinity among all films. In contrast, the film directly grown at T sub = 573 K possesses the worst crystalline quality, and the diffraction peaks of this film shift obviously towards lower angles, as shown in Figure 1b. This result indicates that the film directly grown at T sub = 573 K suffers from a tensile strain along the c-axis (ε ⊥ ) with the lattice parameter expanding by 5.4% (c = 7.62 Å as compared to c = 7.23 Å in the pristine Mg 3 Sb 2 ). Figure 1d displays the corresponding Raman spectra of the aforementioned Mg 3 Sb 2 films grown under different thermal processes. All the films present two characteristic Raman active peaks at the range of 50-200 cm −1 , similar to the recent result in Mg 3 Sb 2 based bulks [31]. An obvious Raman redshift is observed in the strained film grown at T sub = 573 K, while the frequencies of Raman spectra in the other films are nearly identical. The Raman peak shift is regarded as the indicator of strain state, in which the Raman peak position shifting to higher (or lower) frequencies reflects compressive (or tensile) strain being induced in the material [32]. Therefore, the Raman redshift verifies an increased bond length in the strained Mg 3 Sb 2 film grown at T sub = 573 K, consistent with the c-axis expansion of the Mg 3 Sb 2 structure detected from XRD measurements. The crystalline structure of Mg3Sb2 films grown on Al2O3 (000l) substrates was investigated by high resolution XRD measurements, as illustrated in Figure 1b,c. Except for the peaks at 42° and 21° originating from the Al2O3 substrate, the XRD (θ-2θ scan) peaks of films grown under different thermal processes can all be indexed to (000l) patterns of Mg3Sb2, confirming a strict c-axis orientation. Meanwhile, increasing Tsub combined with the annealing process could drastically reduce the full-width-half-maximum (FWHM) of the rocking curve from 0.95° to 0.11°, implying the prominent improvement of crystalline quality. The film grown and annealed at Tsub = 773 K has the narrowest rocking curve FWHM and the highest crystallinity among all films. In contrast, the film directly grown at Tsub = 573 K possesses the worst crystalline quality, and the diffraction peaks of this film shift obviously towards lower angles, as shown in Figure 1b. This result indicates that the film directly grown at Tsub = 573 K suffers from a tensile strain along the c-axis (⊥) with the lattice parameter expanding by 5.4% (c = 7.62 Å as compared to c = 7.23 Å in the pristine Mg3Sb2). Figure 1d displays the corresponding Raman spectra of the aforementioned Mg3Sb2 films grown under different thermal processes. All the films present two characteristic Raman active peaks at the range of 50-200 cm −1 , similar to the recent result in

Growth Mode and Epitaxial Strain Control
The growth of Mg 3 Sb 2 films on Al 2 O 3 (000l) substrate is classified as the Stranski-Krastanov (SK) mode featured with the layer-plus-island growth evolution during the film deposition, which is experimentally elucidated by AFM in Figure 2. During the initial growth period, the multipoint nucleation spontaneously forms at t ≈ 30 s with a nucleus size of 2~5 nm in height and 20~40 nm in diameter. The crystal nuclei grow quickly and coalesce into a flat Mg 3 Sb 2 slab when the film is grown for 1~15 min. As the film thickness further increases, 3D island grains form on top of the initial flat Mg 3 Sb 2 slab, implying a rough surface morphology. The SK growth mode implies the interaction between the Mg 3 Sb 2 layer and Al 2 O 3 substrate being distinctly stronger than that between Mg 3 Sb 2 layers. The strong interaction introduces a driving force favoring for forming flat Mg 3 Sb 2 layer during the initial growth. With increasing the film thickness of Mg 3 Sb 2 , the strong interaction between Mg 3 Sb 2 and Al 2 O 3 decays rapidly, and the island growth dominates the subsequent growth process. The SK growth characteristic is intimately related to the relaxation of strain in the case of mismatched epitaxy and to the control of the twin structure, which will be clarified in our Mg 3 Sb 2 films, as noted below.
coalesce into a flat Mg3Sb2 slab when the film is grown for 1~15 min. As the film thickness further increases, 3D island grains form on top of the initial flat Mg3Sb2 slab, implying a rough surface morphology. The SK growth mode implies the interaction between the Mg3Sb2 layer and Al2O3 substrate being distinctly stronger than that between Mg3Sb2 layers. The strong interaction introduces a driving force favoring for forming flat Mg3Sb2 layer during the initial growth. With increasing the film thickness of Mg3Sb2, the strong interaction between Mg3Sb2 and Al2O3 decays rapidly, and the island growth dominates the subsequent growth process. The SK growth characteristic is intimately related to the relaxation of strain in the case of mismatched epitaxy and to the control of the twin structure, which will be clarified in our Mg3Sb2 films, as noted below.   Figure 3 depicts the in situ RHEED patterns and the calculated in-plane lattice parameters a as a function of film thickness for our Mg 3 Sb 2 films. As for the film grown at 773 K, the spacing of RHEED patterns (labeled by dashed lines) remains the same as that of the Al 2 O 3 substrate when the film thickness is around 1 nm, indicating a tensile strained state. In addition, the spacing of RHEED patterns of the 100 nm thick film expands obviously as compared to the Al 2 O 3 substrate, which reflects the release of lattice strain during the film growth. On the contrary, the RHEED streaks remain unchanged with film thickness of 1 nm and 100 nm for the Mg 3 Sb 2 film grown at T sub = 573 K, indicating this Mg 3 Sb 2 film is in a full-strain state. Through the quantitative analysis of the in-situ RHEED patterns, we are able to clearly elucidate the evolution of a during the growth as well as to determine the critical film thickness h c above which the strain relaxation will occur. It is remarkable that a high T sub is crucial for releasing the epitaxial strain in Mg 3 Sb 2 , and the large epitaxial strain could remain in the thick film when the T sub is very low. The tensile epitaxial strain is retained even up to 70 nm for the Mg 3 Sb 2 film grown at T sub = 573 K, as highlighted by the unchanged a value across the entire thickness. In the film grown at T sub = 773 K, the a rapidly decays from a = 4.77 Å (the same as in the Al 2 O 3 substrate) to a = 4.56 Å (identical to the value in the pristine Mg 3 Sb 2 ) as the film thickness exceeds the h c , which is about 7 nm in this work. This phenomenon indicates the strain release process is related to the growth transition of the SK mode.
large epitaxial strain could remain in the thick film when the Tsub is very low. The tensile epitaxial strain is retained even up to 70 nm for the Mg3Sb2 film grown at Tsub = 573 K, as highlighted by the unchanged a value across the entire thickness. In the film grown at Tsub = 773 K, the a rapidly decays from a = 4.77 Å (the same as in the Al2O3 substrate) to a = 4.56 Å (identical to the value in the pristine Mg3Sb2) as the film thickness exceeds the hc, which is about 7 nm in this work. This phenomenon indicates the strain release process is related to the growth transition of the SK mode. The change of strain state in Mg3Sb2 films grown at different Tsub could be interpreted by the semi-empirical model of metastable layers proposed by Dodson and Tsao [33][34][35][36]. The migration of misfit dislocation could be thermally activated, and dominates the strain relaxation process in mismatched hetero-epitaxial films. The density of misfit dislocations could be qualitatively estimated by the FWHM of the Mg3Sb2 (0002) rocking curve as shown in Figure 1c: where is the FWHM of the rocking curve, | | is the Burgers vector lengths equated to c-axial lattice constants and stands for the density of misfit dislocations, respectively [37][38][39][40]. The film grown at Tsub = 573 K shows a very high of 4.88 × 10 14 cm −2 while the strikingly decreases to 1.92 i. grown at T sub = 773 K with thickness of 1 nm; ii. grown at T sub = 573 K with thickness of 1 nm; iii. grown at T sub = 773 K with thickness of 100 nm and iv. grown at T sub = 573 K with thickness of 100 nm. The unchanged interval of RHEED streaks indicates the full strain state in the film grown at T sub = 573 K. (b) The in-plane lattice parameter a as a function of film thickness for films grown at T sub = 773 K and 573 K, quantified by the in situ RHEED measurements.
The change of strain state in Mg 3 Sb 2 films grown at different T sub could be interpreted by the semi-empirical model of metastable layers proposed by Dodson and Tsao [33][34][35][36]. The migration of misfit dislocation could be thermally activated, and dominates the strain relaxation process in mismatched hetero-epitaxial films. The density of misfit dislocations could be qualitatively estimated by the FWHM of the Mg 3 Sb 2 (0002) rocking curve as shown in Figure 1c: ρ s = β (002) 2 /(2π ln 2 × |b c |), where β is the FWHM of the rocking curve, |b c | is the Burgers vector lengths equated to c-axial lattice constants and ρ s stands for the density of misfit dislocations, respectively [37][38][39][40]. The film grown at T sub = 573 K shows a very high ρ s of~4.88 × 10 14 cm −2 while the ρ s strikingly decreases to 1.92 × 10 12 cm −2 in the Mg 3 Sb 2 film grown and annealed at T sub = 773 K. Hence, the thermal process, such as a high T sub and annealing, could effectively promote the dislocation migration and is beneficial for the relaxation of epitaxial strains in Mg 3 Sb 2 films. Generally, epitaxial films of semiconductors such as Si 1-x Ge x [41], Ga 1-x In x As [42] and Ga 1-x Al x N [43] along with multiferroic Sr 2 IrO 4 [44], SrRuO 3 [45] and HoMnO 3 [46] exhibit moderate biaxial epitaxial strains ε in the range of 0~4%. The prominent strain in the grown Mg 3 Sb 2 films is closely related to the chemical bonding characteristics of Mg 3 Sb 2 , including weak bonds and a nearly isotropic 3D bonding network. The above study shows the feasibility of strain manipulation in Mg 3 Sb 2 -based compounds utilizing the strong interaction at the film-substrate interface and the decisive role of T sub .

Detection and Manipulation of the Twin Structure
Along with the strain evolution with film thickness and T sub , a 60 • rotational twin structure is discovered in the Mg 3 Sb 2 films, which could be efficiently regulated by tuning the thermal process. Measurements of RHEED and high resolution XRD are utilized to trace the formation and to identify the tuning mechanism of the twin structure in Mg 3 Sb 2 films. As illustrated in Figure 4a, the normal domains and the twin domains differ in atomic stacking orders of ABC-BCA and ACB-CBA, respectively. In the RHEED patterns along the [1120] azimuthal direction, the diagonal feature of intensity modulation corresponds to the twin-free structure, while the mirror-symmetric RHEED pattern signifies the presence of Nanomaterials 2022, 12, 4429 7 of 12 twin structure (see Figure S3 and Figure 4b,c) [47]. For all of the displayed RHEED patterns, the symmetry feature is highlighted with arrows to reveal the presence/absence of the twin structure. Remarkably, in the Mg 3 Sb 2 film grown at T sub = 773 K, the RHEED patterns show a diagonal intensity modulation when the film thickness is below the h c , indicating a single domain structure. When the film thickness exceeds the h c , the twin structure forms rapidly so that the RHEED patterns become mirror symmetric (see Figure 4d,e). the thermal process. Measurements of RHEED and high resolution XRD are utilized to trace the formation and to identify the tuning mechanism of the twin structure in Mg3Sb2 films. As illustrated in Figure 4a, the normal domains and the twin domains differ in atomic stacking orders of ABC-BCA and ACB-CBA, respectively. In the RHEED patterns along the [1120] azimuthal direction, the diagonal feature of intensity modulation corresponds to the twin-free structure, while the mirror-symmetric RHEED pattern signifies the presence of twin structure (see Figures S3 and 4b,c) [47]. For all of the displayed RHEED patterns, the symmetry feature is highlighted with arrows to reveal the presence/absence of the twin structure. Remarkably, in the Mg3Sb2 film grown at Tsub = 773 K, the RHEED patterns show a diagonal intensity modulation when the film thickness is below the hc, indicating a single domain structure. When the film thickness exceeds the hc, the twin structure forms rapidly so that the RHEED patterns become mirror symmetric (see Figure 4d,e).  (b-e) RHEED patterns measured during the deposition of the Mg 3 Sb 2 film that is grown at T sub = 773 K. The intensity modulation highlighted by arrows reveals the presence/absence of the twin structure. The mirror symmetric diffraction pattern indicates the existence of twin structure, while the diagonal feature depicts the absence of twin structure. (b,c) indicate the film with twin-free structure at the initial stage of deposition, whereas (d,e) indicate the twinning structure gradually forms when the film thickness during the further deposition. Figure 5 shows the twin domain formation with increasing the T sub for Mg 3 Sb 2 films. The film grown at T sub = 573 K exhibits a macroscopic single-domain characteristic, yielding 3-fold symmetric diffraction spots at 0 • , 120 • and 240 • in the pole figure, as shown in Figure 5e. In comparison, under a higher T sub and by applying an annealing process, the twin structure forms in Mg 3 Sb 2 films and its diffraction spots appear at 60 • , 180 • and 300 • (see Figure 5f-h). Our results indicate that the content of twinning D twin increases drastically with increasing the T sub , which is 25%, 63% and 82% for films grown at T sub = 673 K and 773 K as well at T sub = 773 K and in situ annealed, respectively. The twin structure is closely related to the strain relaxation process, and its formation is obviously promoted by elevating the T sub and by annealing. Hence, thermal processes induce the improved mass transfer and the much reduced density of misfit dislocations is likely the mechanism responsible for the formation of the twin structure. The microscopic evidence of thermally promoted mass transfer is given by AFM and in situ STM measurements as shown in Figure 5a-d, Figures S4 and S5. On the one hand, the gain size increases greatly with increasing the T sub in Mg 3 Sb 2 films, e.g., from tens of nanometers to sub-micrometer with increase of the T sub from 573 K to 773 K. On the other hand, annealing at 773 K not only further increases the grain size, but also significantly improves the crystallinity of the Mg 3 Sb 2 film, forming a distinct layer structure with a flat surface. The Mg 3 Sb 2 film grown at 773 K and annealed at 773 K for 20 min exhibits the most prominent layered structure with layer thickness of~0.7 nm that is identical to the value of the single lattice spacing. and 773 K as well at Tsub = 773 K and in situ annealed, respectively. The twin structure is closely related to the strain relaxation process, and its formation is obviously promoted by elevating the Tsub and by annealing. Hence, thermal processes induce the improved mass transfer and the much reduced density of misfit dislocations is likely the mechanism responsible for the formation of the twin structure. The microscopic evidence of thermally promoted mass transfer is given by AFM and in situ STM measurements as shown in Figures 5a-d, S4 and S5. On the one hand, the gain size increases greatly with increasing the Tsub in Mg3Sb2 films, e.g., from tens of nanometers to sub-micrometer with increase of the Tsub from 573 K to 773 K. On the other hand, annealing at 773 K not only further increases the grain size, but also significantly improves the crystallinity of the Mg3Sb2 film, forming a distinct layer structure with a flat surface. The Mg3Sb2 film grown at 773 K and annealed at 773 K for 20 min exhibits the most prominent layered structure with layer thickness of 0.7 nm that is identical to the value of the single lattice spacing.

Band Structure and the Tuning of E F
The characteristics of band structure and the tuning mechanism of E F are crucial for the regulation and optimization of electronic properties [48][49][50][51][52]. Here, utilizing the single crystalline films grown by MBE, we are able to determine the band features of Mg 3 Sb 2 by ARPES and STS measurements. Figure 6a,b depict the Fermi maps of constant energy contour at different binding energies E b and the STS spectra of the Mg 3 Sb 2 film grown at 773 K. The momentum dispersion of Fermi surfaces expands with increase of the E b , implying their valence band feature and p-type conduction of the grown Mg 3 Sb 2 film. In addition, we observe a circular hole pocket centered at the Γ point and a single band feature near the E F , which evolves into a complex band configuration composed of two valence bands (denoted as VB1 and VB2). The VB2 appears at the E b of~0.25 eV. The STS measurements in different regions unambiguously validate the electronic density of states (DOS) versus bias voltage. The spectra indicate a band gap of E g ≈ 0.89 eV, coinciding with the result from Mg 3 Sb 2 bulks [53]. The E F is located near the valence band maximum (VBM), corresponding to the ARPES result. The DOS near the conduction band maximum (CBM) is much higher than that near the VBM, in agreement with the higher DOS effective mass and superior electrical properties of n-type Mg 3 Sb 2 compared to that of the p-type counterpart [5]. in different regions unambiguously validate the electronic density of states (DOS) versus bias voltage. The spectra indicate a band gap of Eg  0.89 eV, coinciding with the result from Mg3Sb2 bulks [53]. The EF is located near the valence band maximum (VBM), corresponding to the ARPES result. The DOS near the conduction band maximum (CBM) is much higher than that near the VBM, in agreement with the higher DOS effective mass and superior electrical properties of n-type Mg3Sb2 compared to that of the p-type counterpart [5].  Figure 6c shows the energy-momentum dispersion along the K-Γ-K direction of Mg 3 Sb 2 films grown at different T sub and R. The growth parameters significantly alter the E F of Mg 3 Sb 2 films. The VBM is fully exposed in the film grown at T sub = 573 K and R = 24. Obviously, the VBM of Mg 3 Sb 2 is featured with two bands (VB1 and VB2) that show an energy interval of 0.3 eV, which is theoretically interpreted by the effect of crystal field energy splitting [15]. Since the saturated vapor pressure of the Mg element is two orders of magnitude higher than that of the Sb element under the adopted T sub (573 K-773 K) [54], the growth of Mg 3 Sb 2 films was always performed under a Mg-deficient condition. Since Mg vacancies (V 2− Mg ) possess the lowest formation energies among all point defects according to previous results [48], the formation of V 2− Mg is energetically favorable during the growth of Mg 3 Sb 2 films. As a result, the acceptor defects V 2− Mg would push the E F deeply into the VB, and result in a strong p-type conduction of Mg 3 Sb 2 films. The Mg 3 Sb 2 film grown at 773 K and annealed shows the strongest p-type conduction among all films, indicated by the highest energy positions of VB2. With increase of the R (i.e., the Mg flux) from 4 to 24 and decreasing the T sub from 773 K to 573 K, the formation of Mg vacancies is effectively suppressed, resulting in an obvious E F upshift of 200 meV. According to Luttinger's theorem [55], such a sizeable E F shift corresponds to the carrier density being altered by two orders of magnitude. This study manifests that the change of MBE processing parameters is an effective approach to manipulate the Mg content and hence the E F of the grown Mg 3 Sb 2 film.

Conclusions
In summary, high crystalline quality Mg 3 Sb 2 films were successfully epitaxially grown on lattice-mismatched Al 2 O 3 (000l) substrates by the MBE technique. The growth of Mg 3 Sb 2 films showed a layer-to-island morphological evolution with increase of film thickness, and could be interpreted by the Stranski-Krastanov (SK) growth characteristic. Films grown and annealed at a high T sub of 773 K possessed a flat surface and distinct layered structure, implying a strong mass transfer process at elevated temperatures. The strong interlayer interaction between the film and the substrate plays a vital role in the manipulation of epitaxial strains and the formation of twin structure in the grown Mg 3 Sb 2 films. On the one hand, the Mg 3 Sb 2 film grown at 573 K was in a full tensile strain state, and lacked the twin structure. On the other hand, the Mg 3 Sb 2 film grown and annealed at 773 K was completely strain relaxed when the film thickness was above a critical value of~7 nm, and contained obvious twin structures with a large D twin of up to 82% in the ultimate case. This is ascribed to the effects from thermally activated mass transfer and the effective migration of misfit dislocations. The band structure characterizations confirmed an intrinsic p-type conduction of the grown Mg 3 Sb 2 films, which is due to the Mg deficiency during the film growth and the formation of donor-like Mg vacancies. Moreover, decreasing the growth temperature and increasing the Mg/Sb flux ratio could remarkably enhance the Mg content in the grown films and suppress the formation of Mg vacancies, leading to an obvious Fermi level downshift of~0.2 eV. This work elucidated the tuning effects regarding epitaxial strains, twin structure, film crystallinity and Fermi level of Mg 3 Sb 2 films, and thus laid an important foundation for rationally manipulating their microstructure, electronic band structure and thermoelectric performance.
Supplementary Materials: The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/nano12244429/s1, Figure S1: The RHEED patterns of Mg 3 Sb 2 films grown on Al 2 O 3 (000l) substrates with and without passivation treatment; Figure S2: The RHEED patterns of Mg 3 Sb 2 grown on different substrates; Figure S3: Schematic illustration of the RHEED measurement and the RHEED patterns for twin-free structure and twin domains; Figure S4: STM surface morphology and structure evolution of Mg 3 Sb 2 films grown at 773 K; Figure S5: Layer structure of the Mg 3 Sb 2 film grown at 773 K and annealed at 773 K for 20 min.
Author Contributions: S.X. and Y.O. contributed equally to this work. W.L. and X.T. co-supervised this project. S.X., F.Y. and Y.O. performed the MBE growth. Y.O. and F.Y. and W.L. performed the ARPES measurements and analysis. S.X., J.L. and X.L. carried out the STM measurements and analyzed the data. Y.L. and Z.W. assisted with the high resolution XRD measurements and analysis. S.X., W.L., X.T. and Y.O. wrote and edited the manuscript. All authors have read and agreed to the published version of the manuscript.