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Kenneth Magallon Senados, [Takashi Aizawa](https://orcid.org/0000-0003-2357-5336), [Isao Ohkubo](https://orcid.org/0000-0002-4187-0112), Takahiro Baba, Akira Uedono, Takeaki Sakurai, [Takao Mori](https://orcid.org/0000-0003-2682-1846)

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[Defects modification in thermoelectric Mg<sub>2</sub>Sn (Ge) epitaxial thin films through modulation of Mg flux rate in MBE](https://mdr.nims.go.jp/datasets/9563daed-f364-4983-8a1b-e296303a81a0)

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Defects modification in thermoelectric Mg2Sn (Ge) epitaxial thin films through modulation of Mg flux rate in MBE     PAPER • OPEN ACCESSDefects modification in thermoelectric Mg2Sn (Ge)epitaxial thin films through modulation of Mg fluxrate in MBETo cite this article: Kenneth Magallon Senados et al 2025 J. Phys. Energy 7 035001 View the article online for updates and enhancements.You may also likeGrowth of uniform Mg-doped p-AlGaNnanowires using plasma-assistedmolecular beam epitaxy technique for UV-A emittersRitam Sarkar, Swagata Bhunia, DipankarJana et al.-AlGaN/GaN high electron mobilitytransistors with selective area grown p-GaN gatesYuliang Huang,  , Lian Zhang et al.-Vapour-liquid-solid growth of ZnO-ZnMgOcore–shell nanowires by gold-catalysedmolecular beam epitaxyO W Kennedy, E R White, M S P Shafferet al.-This content was downloaded from IP address 144.213.253.16 on 03/04/2025 at 04:24https://doi.org/10.1088/2515-7655/adc489/article/10.1088/1361-6528/ac7472/article/10.1088/1361-6528/ac7472/article/10.1088/1361-6528/ac7472/article/10.1088/1361-6528/ac7472/article/10.1088/1674-4926/37/11/114002/article/10.1088/1674-4926/37/11/114002/article/10.1088/1674-4926/37/11/114002/article/10.1088/1361-6528/ab011c/article/10.1088/1361-6528/ab011c/article/10.1088/1361-6528/ab011cJ. Phys. Energy 7 (2025) 035001 https://doi.org/10.1088/2515-7655/adc489Journal of Physics: EnergyOPEN ACCESSRECEIVED9 September 2024REVISED5 February 2025ACCEPTED FOR PUBLICATION23 March 2025PUBLISHED2 April 2025Original content fromthis work may be usedunder the terms of theCreative CommonsAttribution 4.0 licence.Any further distributionof this work mustmaintain attribution tothe author(s) and the titleof the work, journalcitation and DOI.PAPERDefects modification in thermoelectric Mg2Sn (Ge) epitaxial thinfilms through modulation of Mg flux rate in MBEKenneth Magallon Senados1,2,∗, Takashi Aizawa2, Isao Ohkubo2, Takahiro Baba2, Akira Uedono1,Takeaki Sakurai1,∗ and Takao Mori1,21 Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan2 Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba,Ibaraki 305-0044, Japan∗ Authors to whom any correspondence should be addressed.E-mail: senados.kenneth.magallon.tkb_gm@u.tsukuba.ac.jp and sakurai.takeaki.ft@u.tsukuba.ac.jpKeywords: thin film thermoelectric, Mg2Sn (Ge), epitaxial growth, defectsSupplementary material for this article is available onlineAbstractPrecise defect control is crucial for optimizing thermoelectric (TE) materials. However, thin filmprocesses differ from bulk synthesis, necessitating distinct approaches to defect management. Thisstudy investigates the impact of varying Mg flux rates in the molecular beam epitaxy (MBE)growth of epitaxial Mg2Sn (Ge) thin films, with Mg: Sn (Ge) ratios from 3.9 to 9.1 whilemaintaining constant Sn and Ge flux rates. Our results indicate that while the films mainlyconsisted of the Mg2Sn phase due to excess Mg compensating evaporation at the growthtemperature, the Mg flux rate significantly influenced film growth dynamics. X-ray diffractionanalysis showed that higher Mg flux rates increased microstrain and decreased vertical grain sizes,suggesting increased planar defect density. However, the full-width half maximums of rockingcurves tend to be reduced at higher flux rates, attributed to enhanced in-plane grain alignment andreduction of point defect density. Positron annihilation experiments revealed lower vacancy-typedefects at higher Mg flux rates, aligning with the rocking curve measurements. The higher Mg fluxrates enhanced surface migration and promoted larger horizontal grain growth. As these grainscoalesce, slight misalignments between them introduce strain within the crystal lattice. Toaccommodate this strain, planar defects such as stacking faults form, as indicated by the x-ray polefigure measurements. Despite the higher crystal quality and reduction in vacancy-type defects, thetotal thermal conductivity of the films decreased with increasing Mg flux rates. This suggests thatmodulating Mg flux rates in MBE-grown Mg2Sn thin films, it is possible to achieve enhancedcrystalline alignment and controlled formation of beneficial higher-dimensionality defects, whichtogether contribute to the reduction in thermal conductivity and improve the film’s overall TEperformance.1. IntroductionDefects in thermoelectric (TE) materials are pivotal in shaping their performance, influencing electrical andthermal conductivity, ultimately dictating TE efficiency [1–6]. The quest for optimal TE performanceconfronts significant challenges, notably the intricate interplay between material defects and structuraldimensions [7–9]. As a promising foundation of miniaturized TE devices, thin films offer scalability,flexibility, and seamless integration with device architectures, rendering them highly attractive forself-powered Internet of Things (IoT) applications [10–13]. However, the unique growth dynamics andsurface interactions inherent in thin film deposition techniques introduce novel challenges in balancingcrystal quality and defect management. Controlling defects in thin films demands a more nuanced approachcompared to bulk synthesis methods, owing to factors such as surface migration, epitaxial growth, andinterfacial interactions [14–18]. Advanced TE device designs, such as segmented TE modules, further© 2025 The Author(s). Published by IOP Publishing Ltdhttps://doi.org/10.1088/2515-7655/adc489https://crossmark.crossref.org/dialog/?doi=10.1088/2515-7655/adc489&domain=pdf&date_stamp=2025-4-2https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://orcid.org/0000-0002-1540-0862https://orcid.org/0000-0003-2357-5336https://orcid.org/0000-0003-2682-1846mailto:senados.kenneth.magallon.tkb_gm@u.tsukuba.ac.jpmailto:sakurai.takeaki.ft@u.tsukuba.ac.jphttp://doi.org/10.1088/2515-7655/adc489J. Phys. Energy 7 (2025) 035001 K M Senados et alhighlight the importance of optimizing material properties for specific operating conditions to achievemaximum efficiency and performance [19]. A comprehensive understanding of how defect formation andmanipulation differ in thin film materials is crucial for improving thin-film-based TE device performances.In thin film fabrication, the precise manipulation of defect densities and distributions may be achievablethrough tailored deposition techniques, growth conditions, and/or post-processing treatments [20–23].While conventional methods like physical vapor deposition, chemical vapor deposition, and sputteringprovide general applicability, their precision often falls short for certain applications. Notably, molecularbeam epitaxy (MBE) presents a promising avenue for defect control [24, 25]. Operating under ultra-highvacuum conditions, MBE facilitates the growth of epitaxial layers with high control over crystal structure andatomic arrangement. This method allows for depositing materials atom by atom or molecule by molecule,ensuring remarkably low defect densities and well-defined interfaces. Consequently, the MBE technique mayalso offer the potential to engineer defects in TE thin films, thereby fine-tuning electron and phonontransport properties to improve the TE performance of our thin films.MBE has been successfully employed to produce high-quality Mg2Sn epitaxial thin films, and itsapplicability to miniaturized TE devices has also been demonstrated [26–30]. This underscores the potentialof Mg2Sn-based thin films and their derivatives as promising candidates for low-cost, low-toxicity materialsin IoT applications, particularly within moderate temperature ranges. In our prior investigations, we haveanalyzed the surface chemical states, structures, and defect formations in epitaxial Mg2Sn1−xGex thin filmswhich are deemed necessary for successful integration in microscale TE devices [31, 32]. Specifically, one ofour findings indicates that several factors, such as the incorporation of Ge, can influence defect formations inthese films. We observed a decrease in the concentration of vacancy-type point defects with increasing Geconcentration. This suggests that by examining different growth process variables, including Geconcentration, we can potentially control the defects in MBE-grown films.In the growth of high-quality films via MBE, numerous other variables can be independently controlled,with the flux rate being a key parameter adjusted by manipulating the evaporation rate of the sourcematerials [33]. Since MBE growth occurs under nonequilibrium conditions, the flux rates of source materialssignificantly influence the resulting film properties. For instance, in the epitaxial film formation of Mg2Sn,varying the Sn flux rate while fixing the Mg flux rate can yield different outcomes. It has been observed that alow Sn flux rate below 2 atoms·s−1·nm−2 is essential for achieving high-quality crystalline epitaxial films.Conversely, higher Sn flux rates have been associated with the formation of secondary orientations of Mg2Snand β-Sn phases [26].In this study, we closely examine how modulation of Mg flux rates in MBE growth of Mg2Sn (Ge)impacts the crystal quality and formation of defects in these epitaxial films. Although excess Mg, which has ahigh vapor pressure, would predominantly desorb during film growth, the modulation of Mg flux rates playsa significant role in influencing both film quality and the concentration of point defects.2. Experimental methodsMg2Sn (Ge) epitaxial thin films were grown using an MBE system (Eiko, EV-500) under vacuum conditionsof 10−6–10−7 Pa on sapphire (0001) substrates. The substrates were cleaned ultrasonically in acetone andsubsequently heated at 1000 ◦C for 1 h in the MBE chamber before growth. Mg2Sn (Ge) films were grownwith varying Mg flux rates from 6.0–18.0 atoms·s−1·nm−2, while maintaining the Sn (Ge) flux rate constant1.65 atoms·s−1·nm−2. The Ge fraction was kept at 5% with respect to Sn. Elemental magnesium (>99.95%),tin (>99.999%), and germanium (>99.999%) metals were evaporated using conventional effusion cells withpyrolytic boron nitride crucibles at 370◦C–410 ◦C for Mg, 1100◦C–1120 ◦C for Sn, and 1050◦C–1150 ◦C forGe. The substrate temperatures and the deposition times were fixed at 380 ◦C and 30 min, respectively. Thecrystal quality was evaluated by x-ray diffraction (XRD) patterns of θ–2θ scans, rocking curves, and polefigures measured by Rigaku SmartLab x-ray diffractometer. Nano-scale structural evaluation of thecross-section of the films was performed using a transmission electron microscope (TEM; Talos F200X G (2)(S)TEM, Thermo Scientific) at 200 kV acceleration voltage with a magnification accuracy of±10%. The hallcoefficient (RH) was measured using Van der Pauw’s method in DC mode at room temperature (RT), with a0.32 T magnetic field using a Bio-RAD-H5580 hall measurement machine with an RH measurementuncertainty of approximately 10%. The carrier concentration (p) and mobility (µ) were calculated byp= 1·[e·RH]−1 and µ= RH·[ρ]−1, where e and ρ are elementary charge and resistivity, respectively. Electricalconductivities, Seebeck coefficient, and power factors were measured by the four-probe method at RT using aZEM 3 (ULVAC Advance Riko) apparatus under a He atmosphere. The thermal conductivities weremeasured along the cross-plane by a pico-second time-domain thermoreflectance apparatus in afront-heating/front-detection configuration (Netzsch-Geratebau GmbH) whose measurement details aredescribed elsewhere [34–37]. The thermal conductivity was obtained by κ= λ · d ·Cp, where λ is the thermal2J. Phys. Energy 7 (2025) 035001 K M Senados et aldiffusion, d is density, and Cp is heat capacity in constant pressure of Mg2Sn [38]. Vacancy-type defects in thefilms were probed using positron annihilation spectroscopy (PAS). Details regarding the measurementsinvolving PAS and additional information on the measurement are described elsewhere [39–42].3. Experimental resultsMg2Sn (Ge) film growth was carried out under the Mg flux rate range between 8.5 and 15 atoms·s−1·nm−2.Our preliminary investigation revealed that films grown at flux rates below 8.5 atoms·s−1·nm−2 resulted inpoor film quality, probably due to secondary Sn phases as observed in the cross-section TEM image in figureS1(a). Conversely, films grown at the flux rates above 15 atoms·s−1·nm−2 also resulted in poor film quality,with clear separation between Mg2Sn and Mg phases, as shown in figure S1(b).Figure 1(a) shows the XRD patterns of Mg2Sn (Ge) films grown with varying Mg flux rates. All samplesexhibited strong Mg2Sn (nnn) peaks (n= 1–4), indicating that despite the variations in the flux rate ratio ofMg: Sn (Ge) by varying the Mg flux rate, and even though the relative Mg supply rate largely exceeded toreach 2 in the Mg/Sn (Ge) ratio, the resulting films consisted of the Mg2Sn phase as the main component.This occurrence is attributed to the excess Mg easily evaporating at the growth temperature of 380 ◦C.Figure 1(b) illustrates the changes in the Mg2Sn (111) peak, where an increase in intensity and a slight shiftto a lower diffraction angle are observed with increasing Mg flux rate. While the enhanced intensity of the(111) peak might suggest improved structural aspects of the Mg2Sn (Ge) films, it was however observed thatthe full-width half maximum (FWHM) broadened suggesting the presence of increasing strain orcompositional inhomogeneity at higher Mg flux rates which could introduce defects or phases with slightlydifferent lattice structures. Notably, when considering the XRDMg2Sn (111) peak intensities normalized byboth film thickness d (detailed in supplementary table S1) and substrate peak intensity Isaaphire(00012), i.e.Inorm = IMg2Sn(111)/(Isapphire(00012)d) [43], the normalized intensity, as shown in the inset of figure 1(b),reveals that the increase in peak intensity is primarily due to structural changes rather than variations in filmthickness. Complementary to this, the rocking curve measurements shown in figure 1(c) reveal a decrease inFWHM at higher flux rates, indicating improved in-plane grain alignment. This suggests that while the filmsexperience strain or inhomogeneity in the vertical direction, the overall in-plane crystalline alignment isenhanced with increasing Mg flux. In addition to the Mg2Sn (111) and the substrate peaks, a smalldiffraction peak appears at 34◦ in the high Mg flux rate (∼15 atoms·s−1·nm−2) samples (figure 1(a)), whichcan be assigned as Mg (111) diffraction. The peak shift of Mg2Sn (111) toward the lower diffraction angleindicates the expansion of Mg2Sn lattice.The microstructural parameters, including d-spacing and the FWHM of the rocking curve, were derivedfrom the Mg2Sn (111) peak in the θ–2θ XRD data, as depicted in figure 1(d). The analysis reveals a slightincrease in the d-spacing at higher flux rates, confirming lattice expansion. Higher Mg flux rates introducemore Mg atoms into the lattice, causing expansion and a modest increase in the FWHM of the Mg2Sn(111)peak in the θ–2θ XRD data from 0.173◦ to 0.185◦. This suggests a potential increase in strain orcompositional inhomogeneity due to localized lattice distortions at higher flux rates.The decrease in the FWHM of the rocking curve at higher flux rates suggests improved in-plane grainalignment due to enhanced surface diffusion and better lateral growth. However, the modest increase in theFWHM of the θ–2θ scan at higher flux rates points to increased lattice strain or compositionalinhomogeneity. The introduction of Mg atoms at higher rates may lead to structural adjustments within thelattice, contributing to the observed broadening.To elucidate the presence of defects, cross-sectional TEM observations of the grown films wereconducted. Figures 2(a)–(c) illustrates the representative TEM images of the films. Parallel Moiré patterns areseen in all the films grown. Moiré patterns are known to arise when two periodic structures with slightlydifferent lattice periodicities or orientations are superimposed, creating an interference pattern that appearsas regular stripes or grids in high-resolution images.In our study, these patterns may be influenced by structural variations within Mg2Sn, potentiallyincluding regions with differing Mg vacancy (VMg) concentrations, as suggested by previous studies [44–46].Introducing VMg into Mg2Sn slightly reduces the lattice constant, as the absence of Mg atoms affects localbonding and atomic spacing. This could create nanoscale regions with slightly different lattice periodicities.If such regions form semi-coherent interfaces, interference between their periodic lattice modulations maycontribute to the observed Moiré patterns. However, other structural factors, such low-angle grainboundaries, may also be involved.The fast Fourier transform (FFT) of the regions enclosed in yellow lines, shown as an inset in the TEMimage, reveals a diffraction pattern characteristic of a single-crystal region, with additional spots around thefundamental diffraction spots attributed to contributions from the parallel Moiré patterns. Figure 2(a) showsa relatively uniform structure with less pronounced stress and fewer defects. As the Mg flux rate increases in3J. Phys. Energy 7 (2025) 035001 K M Senados et alFigure 1. (a) XRD patterns of Mg2Sn (Ge) thin films with varying Mg flux rates. (b) The peaks change on Mg2Sn (111), (c) x-rayrocking curve at (111) and (d) microstructural analysis of XRD (111) peak.figure 2(b), more defects and strain contrast are visible, indicating increased lattice distortions. In figure 2(c),at the highest Mg flux rate, Moiré patterns are still observable; however, additional features which appear tobe more complex than the surrounding areas are also visible. The diffraction pattern of this region exhibitsextra spots, suggesting the presence of longer-range ordering in the crystal lattice. The longer-range ordering,observed in the TEM image, appears to extend over a region approximately 15–25 nm in size, which could bedue to the formation of a metastable modulated structure. This structural modulation might also contributeto the broadening of the (111) peak observed in the XRD pattern, as it introduces additional strain or defectsinto the lattice. The formation of this state could be a result on non-equilibrium conditions during the highMg flux deposition but while this feature may indicate a metastable state, further analysis is needed toconfirm the exact nature of these structures.To further analyze the structural distortions, we performed an Inverse FFT (IFFT) analysis on one Moirépattern region enclosed in red in figure 2(b), with results shown in figure 2(e). IFFT was performed toenhance the visualization of lattice distortion and dislocations at the interfaces, which may contribute to theobserved Moiré patterns. The IFFT reveals the presence of dislocations in the Moiré patterns. Thesedislocations, consistent with semi-coherent interface models [45], contribute to the periodic latticemodulations responsible for the observed Moiré patterns.While our findings suggest that vacancy-induced structural variations may contribute to the formation ofMoiré patterns, other mechanisms, such as low-angle grain boundaries characterized by slightmisorientations between adjacent grains, may also play a role. However, our current data does not provideconclusive evidence to distinguish between these mechanisms, and further investigation is needed.To investigate the changes in the concentration of vacancy-type defects in the films, we performed PASmeasurements using a monoenergetic positron beam. Figure 3 shows the sharpness (S) parameter of theMg2Sn (Ge) films as a function of incident positron energy (E). The S-parameter is used to analyze the defect4J. Phys. Energy 7 (2025) 035001 K M Senados et alFigure 2. (a)–(c) Cross-sectional high-magnification TEM images of Mg2Sn0.95Ge0.05 thin films grown at three different Mg fluxrates, with FFT patterns of the regions enclosed by yellow squares shown as insets. (d) Higher magnification of the regionoutlined in red in (b). (e) IFFT image of the region in (d), highlighting dislocations.Figure 3. S parameter as a function of the incident photon energy E of the thin films.5J. Phys. Energy 7 (2025) 035001 K M Senados et alFigure 4. X-ray pole figures of Al2O3 {104} and Mg2Sn (Ge) {220} thin films with varying Mg flux rate.concentration or defect-related characteristics in a material. The results indicated that there was a depthdistribution of vacancy-type defects in the films, which are VMg as we previously suggested [32]. For positronenergies below approximately 4 keV, positrons predominantly annihilate within the films, while at higherenergies they penetrate deeper, eventually annihilating near the substrate, where the S parameter approachesa value of approximately 0.42.The energy position of the transition from film to substrate annihilation (e.g. where S(E)≈ 0.48)depends on the film thickness, which is detailed in supplementary table S1. Thicker films require higherpositron energies for positrons to penetrate to the substrate, resulting in a delayed transition, whereasthinner films exhibit this transition at lower energies. For example, the undoped Mg2Sn sample, exhibitedthe lowest thickness, leading to an earlier transition to the substrate compared to the thicker Ge-alloyedfilms. While a simple proportionality might be expected, the observed variation in energy (6.5–9 keV) islarger than the 13% thickness increase (186–210 nm). This deviation may arise due to several factors such asvariations in film density, interface roughness, or other factors affecting positron penetration depth. Whilethe general trend between film thickness and required positron energy follows expectations, the observeddeviation suggests that additional factors, such as interface effects or density variations, may influencepositron penetration. Further investigation would be needed to model this relationship more precisely.At very low positron energies (E < 0.5 keV), positrons may annihilate from bound surface states,typically corresponding to an S parameter of approximately 0.50. This surface-state annihilation is observedin all samples but is more pronounced in films grown at lower Mg flux rates. At low Mg flux rates, the Sparameter transitions to the bulk annihilation value (≈0.58) more quickly. This is due to shorter positrondiffusion lengths, consistent with higher concentrations of vacancy-type defects. Vacancies act as positrontraps, reducing the distance positrons can travel before annihilation. For positron energies in the rangeE = 0.5–4 keV, corresponding to annihilation within the films, no significant change in the S values wasobserved for samples grown with Mg flux rates of 6.5–10.0 atoms·s−1·nm−2. However, for samples grown atflux rates of 12.0–15.0 atoms·s−1·nm−2, the S values at E < 3 keV decreased.This reduction in S values at higher Mg flux rates can be attributed to two factors. First, excess Mg atomsat high flux rates may diffuse into the lattice, interact with existing vacancies, and reduce their concentration.Second, with fewer vacancies, positron diffusion lengths increase, allowing positrons to probe deeper into thefilm before annihilating. This dual effect enhances lateral grain alignment, leading to larger, better-alignedgrains and improved lateral crystal quality. However, as indicated by the small diffraction peak at 34◦ inXRD, residual Mg metal begins to accumulate at these high flux rates, potentially leading to the formation ofstacking faults.The x-ray diffraction pole figures of the thin films, depicted in figure 4, reveal that stacking faults beganto emerge when the Mg flux reached approximately 10.0 atoms·s−1·nm−2. This is evidenced by theappearance of the antiphase minor domain: [1̄1̄2]Mg2Sn∥ [101̄0]sapphire, coexisting with the major domain.Anti-phase minor domain spots, highlighted in yellow in figures 4(b)–(d), appear at directions 60◦ apartfrom the major domain spots. These stacking faults may exhibit increased occurrences at much higher flux6J. Phys. Energy 7 (2025) 035001 K M Senados et alFigure 5. (a) Carrier concentration and mobility and (b) electrical conductivity, Seebeck coefficient and power factor as afunction of Mg flux rate measured at RT.rates, as also indicated by the PAS results showing a decrease in the S-parameter as a reference. Whilestacking faults are typically associated with reducing crystallinity due to their disruptive nature, they play acrucial role in managing strain within the crystal lattice in our Mg2Sn (Ge) films with increasing Mg flux.Enhanced surface migration at higher Mg flux rates may promote larger horizontal grains, improvingin-plane grain alignment and reducing the FWHM of the rocking curve. However, the same higher flux alsointroduces more vertical defects. Rapid incorporation of Mg atoms during vertical growth causes strain anddisruptions, leading to non-ideal stacking sequences and promoting the formation of stacking faults. Theseconditions decrease vertical coherence length and increase the FWHM of the θ–2θ scan.The RT Hall measurements of the films are plotted in figure 5(a). A slight decrease in carrierconcentration with increasing Mg flux rate was observed. The decrease can be attributed to increasing grainboundary density. However, as we can observe, carrier mobility increased despite the decrease in carrierconcentration, which is thanks to the enhancement of the crystallite quality and fewer large-scale defectsformation at preferable higher Mg flux rates. The RT TE properties measurement in figure 5(b), shows thatthe electrical conductivity remains relatively stable which is because the decrease in carrier concentration wascompensated for by an increase in carrier mobility. This maintains a stable product of p-type carrierconcentration (p) and mobility (µ) thus keeping the conductivity constant. An initial decrease in the Seebeckcoefficient was observed in the films grown at the Mg flux rates from 8 to 10 atoms·s−1·nm−2, followed by aconsistent increase from 10 to 15 atoms·s−1·nm−2. This initial decrease of Seebeck coefficient from rates8–10 atoms·s−1·nm−2 might be related to the introduction of stacking faults which initially increasescattering, reducing the average energy of carriers and contributing to the Seebeck effect. However, in filmsgrown at higher flux rates beyond 10 atoms·s−1·nm−2, the Seebeck coefficient increases, likely due toimproved crystalline alignment, which reduces the scattering of higher-energy carriers. This suggests that atthese higher flux rates, the beneficial influence of enhanced crystal order and a decrease in point defectsoutweigh the scattering introduced by the stacking faults. Moreover, the significant impact of the changes inthe film properties by modulation of Mg flux rate can be clearly seen in the total thermal conductivity κtotalof the films shown in figure 6. As the Mg flux rate increased, we observed a decrease in the total thermalconductivity of the films which can be attributed to both the improved crystalline alignment of the films andthe progressive modification of defect types. Initially, the films predominantly featured zero-dimensionalpoint defects, such as vacancies, and one-dimensional like defects like dislocations. However, with higher Mgflux rates, the defects in the films were modified into two-dimensional planar defects which include stackingfaults, which significantly contributed to enhanced phonon scattering and the resultant reduction in thermalconductivity.4. DiscussionThe results indicate that Mg2Sn (Ge) films exhibit varying structural and TE properties based on the Mg fluxrate during growth. The observed structural changes suggest that modulating the Mg flux during the growthof Mg2Sn (Ge) films results in enhanced in-plane crystal alignment, nano-structural modificationsassociated with changes in lattice strain and grain boundaries, and the formation of higher dimensionality7J. Phys. Energy 7 (2025) 035001 K M Senados et alFigure 6. Total thermal conductivity at RT for Mg2Sn (Ge) thin films.defects, transitioning from vacancy-type and dislocation defects to dislocations, stacking faults and possiblemetastable phases. As stacking faults and grain boundaries become more prevalent, and the vacancy-typepoint defects are reduced, these results to an improvement of crystalline alignment and coherence andenhance carrier mobility. While stacking faults and grain boundaries typically scatter carriers and reducemobility [47], in this study, the improved crystalline alignment and reduced vacancy defects may havemitigated their usual negative effects, resulting in the observed increase in mobility. This leads to moreefficient carrier transport and higher average energy of carriers, resulting in a consistent increase in theSeebeck coefficient at higher Mg flux rates. Overall, we observe that higher Mg flux rates are required for thepreferable TE properties of the films.In general, the presence of these defects can reduce the electronic contribution to thermal conductivity κeby scattering charge carriers, but this effect is generally smaller compared to phonon scattering, thus, thealterations in the κtotal primarily stem from the decrease in lattice thermal conductivity κl contribution.A similar behavior in the κl has been reported in GeTe-based TE materials wherein the evolution ofdefect structures from lower dimensionality defects to hierarchical domain structures via active control of Gevacancies results to sharp decrease in thermal conductivity [48]. From the Debye-Callaway model, whichaccounts for phonon scattering by defects, the theoretical κl can be expressed asκl =kB2π 2ν(kBTh̄)3θD/Tˆ0x4exτ−1C (ex − 1)2dx (1)where x= h̄ω/kBT is dimensionless, ω is the phonon frequency, h̄ is the reduced Planck constant, ν is theaverage sound velocity, θD is the Debye temperature, and τC is the sum of the relaxation times of differentphonon scattering mechanisms [49]. In the context of defect engineering, the pivotal factor lies in themanipulation of relaxation time τC, and defects are strategically introduced to amplify the phonon scatteringby minimizing τC to reduce phonon mean free path. From here we see that the dimensionality of defects is akey parameter in understanding their impact on TE properties. If scattering processes can be analyzedseparately, then the total relaxation time is:τ−1C =∑iτ−1i = τ−1U + τ−1N + τ−1PD + τ−1DC + τ−1B + τ−1SF . . . (2)where τi denotes the relaxation time corresponding to various phonon scattering mechanism, such asUmpklapp and normal phonon-phonon scattering (τU and τN), point defect scattering (τPD), dislocationcore scattering (τDC), grain boundary scattering (τB), and stacking faults (τST). Thus, the formation of higherdimensionality defects at higher Mg flux rates, such as stacking faults and increase in grain boundary densityby the decrease in vertical grain size, can effectively lower κtotal of the films through additional phononscattering provided by these defects.8J. Phys. Energy 7 (2025) 035001 K M Senados et al5. ConclusionsEpitaxial Mg2Sn (Ge) thin films were grown using MBE, with Mg flux rates varied from 8.5 to 15.0atoms·s−1·nm−2, while maintaining a constant Sn (Ge) flux rate. The crystal properties and defect formationwere investigated. Our study demonstrates that higher Mg flux rates improve lateral grain size and enhancein-plane crystal alignment. However, these higher flux rates also promote the formation of vertical defects,including stacking faults, which concurrently reduce and decrease vertical grain size and elevate microstrainwithin the lattice. The nuanced interplay between enhanced horizontal grain alignment and the introductionof higher-dimensionality defects resulted in a measurable decrease in thermal conductivity, an outcome thatmay favorably impact TE efficiency. Modulating Mg flux rates is demonstrated as an effective strategy foroptimizing defect formation and enhancing the crystal quality of Mg-based thin films.Data availability statementAll data that support the findings of this study are included within the article (and any supplementary files).AcknowledgmentThe research is funded by the JST Mirai Grant No. JPMJMI19A1. A part of this work was supported by‘Advanced Research Infrastructure for Materials and Nanotechnology in Japan (ARIM)’ of the Ministry ofEducation, Culture, Sports, Science and Technology (MEXT) Proposal Number JPMXP1224NM5157.Thanks to Takanobu Hiroto for the assistance in obtaining the x-ray rocking curve measurements and x-raypole figures, Noriyuki Okada for TEM sample preparation, and Makoto Oishi for TEM images acquisition.The first author expresses his sincerest gratitude to the Japanese Government for their financial support incarrying out this research through the Monbukagakusho (MEXT) Scholarship program.ORCID iDsKenneth Magallon Senados https://orcid.org/0000-0002-1540-0862Takashi Aizawa https://orcid.org/0000-0003-2357-5336Takao Mori https://orcid.org/0000-0003-2682-1846References[1] Liu Z, Mao J, Liu T-H, Chen G and Ren Z 2018 Nano-microstructural control of phonon engineering for thermoelectric energyharvestingMRS Bull. 43 181–6[2] Shi X L, Zou J and Chen Z G 2020 Advanced thermoelectric design: from materials and structures to devices Chem. 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Introduction 2. Experimental methods 3. Experimental results 4. Discussion 5. Conclusions References