Evolution of point defects in pulsed-laser-melted Ge1-x Sn x probed by positron annihilation lifetime spectroscopy

Direct-band-gap Germanium-Tin alloys (Ge1-x Sn x ) with high carrier mobilities are promising materials for nano- and optoelectronics. The concentration of open volume defects in the alloy, such as Sn and Ge vacancies, influences the final device performance. In this article, we present an evaluation of the point defects in molecular-beam-epitaxy grown Ge1-x Sn x films treated by post-growth nanosecond-range pulsed laser melting (PLM). Doppler broadening – variable energy positron annihilation spectroscopy and variable energy positron annihilation lifetime spectroscopy are used to investigate the defect nanostructure in the Ge1-x Sn x films exposed to increasing laser energy density. The experimental results, supported with ATomic SUPerposition calculations, evidence that after PLM, the average size of the open volume defects increases, which represents a raise in concentration of vacancy agglomerations, but the overall defect density is reduced as a function of the PLM fluence. At the same time, the positron annihilation spectroscopy analysis provides information about dislocations and Ge vacancies decorated by Sn atoms. Moreover, it is shown that the PLM reduces the strain in the layer, while dislocations are responsible for trapping of Sn and formation of small Sn-rich-clusters.


Introduction
In optoelectronics, the integration of silicon-compatible direct-band-gap materials into the complementary metaloxide-semiconductors technology would allow to fabricate lasers and optical interconnectors.Ge 1-x Sn x alloys are among the most promising materials to replace Si in future optoelectronics.These alloys enable an effective band gap engineering due to (i) alloying the indirect semiconductor Ge with the negative direct-band-gap material Sn [1,2]; (ii) strong n-type doping [3][4][5] or (iii) strain engineering [6,7].The conversion from an indirect-to a direct-band-gap material was experimentally shown on partly strain-strain relaxed Ge 0.9 Sn 0.1 by Ghetmiri et al [8].Unfortunately, the solid solubility of Sn in Ge in thermodynamic equilibrium is below 1.1 at.% [9] and compressive strain shifts the direct-band-gap transition to higher Sn concentrations [2].This means that the fabrication of direct-band-gap Ge 1-x Sn x alloys requires highly non-equilibrium processing techniques and methods to release the in-plane compressive strain.Currently, the main fabrication techniques for Ge 1-x Sn x alloys are molecular beam epitaxy (MBE) [10][11][12] and chemical vapor deposition [1,13].In order to avoid Sn segregation, the growth of the alloy is performed with high growth rates and at temperatures normally between 25 [14,15] and 390 • C [16][17][18], depending on the desired Sn concentration and growth method.This nonequilibrium growth causes the formation of different types of defects [16].Stain relaxation can be achieved in multiple ways: (i) using buffer layers with a lattice parameter in the range of the targeted Ge 1-x Sn x alloy; (ii) the formation of misfit or threading dislocations due to the growth of layers thicker than the critical thickness for pseudomorphic growth [19,20]; (iii) alloy engineering by adding smaller elements into the Ge 1-x Sn x alloy system, e.g.Si [21], P [6], or B [11]; (iv) using post-growth thermal treatment [7]; (v) strain release by the fabrication of nano-structures [1,22,23].In recent years, first success could be achieved by improving the growth process and using methods to gain partly strain-relaxed Ge 1-x Sn x alloys.Wirths et al [2] presented the first Ge 1-x Sn xbased laser, where lasing was observed up to 100 K from a sample containing 12.6% of Sn.Shortly after that, Chrétien et al [23] demonstrated compressively strained Fabry-Pérot Ge 0.84 Sn 0.16 micro-lasers with lasing action persisting up to 273 K [23].In general, the quality of the optically active layer mainly determines the laser performance and reliability, which depends on the presence of point defects like vacancies.
Recently, first results based on post-growth pulsed laser melting (PLM) on Ge 1-x Sn x alloys with a promising in-plane strain relaxation effect were published [7,24].The implementation of strain-relaxed PLM Ge 1-x Sn x as a virtual substrate could be a helpful approach for further improvements.However, the understanding of the mechanisms of defect formation in Ge 1-x Sn x alloys after PLM and their function in the system is crucial for the successful integration of Ge 1-x Sn x alloys within the Si technology.Positron annihilation lifetime spectroscopy (PALS) is one of the most sensitive techniques to investigate open volume defects like Sn and Ge vacancies [16].PALS offers the possibility to probe single vacancies (one missing atom).In addition, variable energy PALS (VE-PALS) allows studying the depth distribution of vacancies in the matrix [4].
In this paper, we study the evolution of open volume defects like Sn and Ge vacancies in MBE-grown Ge 1-x Sn x alloys after strain engineering by post-growth PLM.VE-PALS suggests the reduction of the concentration of mono-vacancy-Sn complexes and the average size of big vacancy clusters in the molten layer.Transmission electron microscopy (TEM) results show the formation of Sn-rich Ge 1-x Sn x filaments.The strain transition from compressive to tensile is confirmed by micro-Raman (µ-Raman) spectroscopy and discussed in detail in [7].The presented post-growth PLM may be applied for the fabrication of strain-relaxed or even tensile-strained virtual substrates for the growth of strain-free Ge 1-x Sn x layers.

Material fabrication
A 290 nm-thick Ge 0.89 Sn 0.11 layer was epitaxially grown by MBE on a (100)-oriented 4 inch p-type Si substrate with a sheet resistance of Rs = 10-20 Ω cm.The entire layer stack is shown in figure 1(a), and a detailed description of the process flow can be found elsewhere [7].Before the growth of the Ge 0.89 Sn 0.11 layer, we grew a 50 nm-thick Si virtual substrate followed by a 100 nm-thick Ge virtual substrate and a 300 nm-thick Ge-buffer layer and performed an in-situ post-growth thermal treatment at 750 • C for 5 min.Afterwards, the 290 nm-thick Ge 0.89 Sn 0.11 film was grown at 120 • C. The post-growth strain and defect engineering was performed by PLM using a XeCl excimer laser with a wavelength of 308 nm, a pulse length of 28 ns, and an energy density varying from 0.15 to 0.5 J cm −2 .The effective annealing area was 5 × 5 mm 2 , as visualized schematically in figure 1(c).

Characterization of materials
The influence of the PLM process on the microstructural and electrical properties of the Ge 1-x Sn x alloys as well as on the defects within them was studied using µ-Raman spectroscopy, TEM, Doppler broadening-variable energy positron annihilation spectroscopy (DB-VEPAS) and VE-PALS, and Halleffect measurements.
µ-Raman spectroscopy was performed on a Horiba LabRam n • 1/24 h system equipped with a Nd:YAG laser with a wavelength of 532 nm and a liquid-nitrogen-cooled CCD camera.All measurements were performed in backscattering geometry with a laser power of 1 mW focused on a circular area with 1 µm diameter.The phonon spectra were recorded in the wavenumber range of 50-550 cm −1 .The penetration depth of the green laser (532 nm) in Ge is approximately 20 nm from the surface [25].
TEM investigations of the as-grown and pulsed-lasermolten samples were done in cross-sectional geometry using a Titan 80-300 microscope (FEI) operated at an accelerating voltage of 300 kV.High-angle annular dark-field scanning transmission electron microscopy imaging and spectrum imaging analysis based on energy-dispersive x-ray spectroscopy (EDXS) were performed at 200 kV with a Talos F200X microscope equipped with a Super-X EDX detector system (FEI).Prior to (S)TEM analysis, the specimen mounted in a high-visibility low-background holder was placed for 10 s into a Model 1020 Plasma Cleaner (Fischione) to remove potential contamination.To record the bright-field TEM images, the TEM specimen was oriented in Si [1 10] zone axis geometry relative to the electron beam.
The type of defects and their concentration and depth distribution in the Ge 1-x Sn x alloys were investigated by DB-VEPAS and VE-PALS.DB-VEPAS measurements were conducted at an apparatus for in-situ defect analysis [26] of the slow positron beamline (SPONSOR) [27].Implanted into a solid material, positrons thermalize and shortly diffuse until they finally annihilate with electrons in delocalized lattice sites (interstitials) or localize in vacancy-like defects and interfaces.As a consequence of annihilation, two anti-collinear 511 keV gamma photons are emitted.Since at the annihilation site thermalized positrons have very small momentum compared to the electrons, a broadening of the 511 keV line is observed mostly due to the momentum of the electrons, which is then measured with a high-purity Ge detector (overall energy resolution of 1.09 ± 0.01 keV at 511 keV).This broadening is characterized by two distinct parameters, S and W, defined as fractions of the annihilation line in the middle (511 ± 0.74 keV) and outer regions (508.7 ± 0.30 keV and 513.30 ± 0.30 keV), respectively.The S-parameter is the fraction of positrons annihilated with low momentum valence electrons and represents vacancy-type defects and their concentration.The Wparameter approximates the overlap of the positron wave function with the high-momentum core electrons, enabling the direct analysis of defect atomic decoration.Plotting S as a function of the positron implantation energy, E p , provides depthdependent information of the defect density, whereas S-W plots are used to examine the atomic surrounding of the defect site and its size (type) [28].
The positron lifetime experiments were performed at the mono-energetic positron spectroscopy beamline of the radiation source ELBE (Electron Linac for beams with high Brilliance and low Emittance) at Helmholtz-Zentrum Dresden-Rossendorf (Germany) [29].Similarly to DB-VEPAS, positrons were accelerated and monoenergetically implanted into samples in the range between E p = 1-10 keV (E p = 0.05-35 keV for DB-VEPAS), which realizes depth profiling.A mean positron implantation depth was approximated using a simple material density ρ dependent equation (1) [30], <z> is an approximation of the depth and cannot be treated as an absolute measure, since it does not account for positron diffusion.However, it gives a reliable depth estimation for materials with large defect concentration, hence low positron diffusion length.A digital lifetime CrBr 3 scintillator detector operated by a homemade software, utilizing a SPDevices ADQ14DC-2X digitizer with 14-bit vertical resolution and 2 GS s −1 horizontal resolution, was used (the overall time resolution was about 230 ps) [31].The resolution function required for spectrum analysis was composed of two Gaussian functions with distinct intensities depending on the positron implantation energy, E p , and appropriate relative shifts.All spectra contain at least 5 × 10 6 counts.The lifetime spectra were analyzed as a sum of time-dependent exponential decays according to equation ( 2), convoluted with the spectrometer timing resolution [32] using a nonlinear least square approach provided by the PALSfit fitting software [33], The indices i correspond to the number of discrete lifetime components (defect sizes, types) in the spectra with individual lifetimes τ i and their relative intensities I i .A commercial undoped bulk Ge substrate was used as reference for DB-VEPAS and VE-PALS.
The Hall-effect measurements in van-der-Pauw configuration were performed using a HMS 9709 A measuring system from LakeShore.Close to the sample corners, 100 nm-thick circularly shaped Au contacts with a diameter of 3 mm were fabricated by thermal evaporation.The magnetic field was varied between −5 and 5 T.

Microstructural investigation
Micro-Raman spectroscopy is used as a fast selection method to observe the PLM-initiated strain relaxation mechanism in Ge 0.89 Sn 0.11 reported in our previous work [7]. Figure 2 shows the µ-Raman spectra obtained from samples before and after PLM with energy densities varying from 0.15 to 0.5 J cm −2 .The Ge-Ge phonon mode in strain-free Ge are located at 300.5 ± 0.1 cm −1 [34].The peak position of the phonon mode in Ge can be shifted to lower or higher wavenumbers due to different phenomena like strain, alloying, disorder, or by phonon-plasmon interaction in heavily doped semiconductors.In general, compressive strain shifts the phonon mode to higher wavenumbers, while tensile strain causes a red shift [7,35].Alloying Ge with heavier elements like Sn shifts the phonon mode to lower wavenumbers [36].Therefore, µ-Raman spectroscopy is a contactless and nondestructive method to investigate the changes in composition and strain in solids.Analyzing the phonon spectra, the coexistence of different phenomena that can compensate the changes by each other has to be taken into account.On the one hand, the pseudomorphic growth of Ge 0.89 Sn 0.11 on Ge by MBE causes in-plane biaxial compressive strain.Therefore, the peak position of the as-grown Ge 0.89 Sn 0.11 layer is located at 296.6 cm −1 , instead of 291.3 cm −1 according to the theoretical calculation (see the vertical dashed line in figure 2).On the other hand, PLM may lead to a redistribution of Sn and strain relaxation, as discussed in detail in [7].The PLM process causes strain relaxation in the top part of the Ge 1-x Sn x layer, which can be observed by the shift of the phonon mode towards a lower wavenumber.The sample annealed with 0.15 J cm −2 is not affected by the pulsed laser, since the peak position coincides with the as-grown state.Annealing with 0.2 J cm −2 shows a slight red shift because the laser energy is close to the melting threshold.All other samples annealed with a pulsed laser energy density higher than 0.2 J cm −2 show the main phonon mode at about 291 ± 1 cm −1 , which is close to the theoretical peak position of strain-relaxed Ge 0.89 Sn 0.11 .Furthermore, a reduced Ge-Ge vibrational mode width can be observed after PLM for energy densities >0.15 J cm −2 .This can be attributed to a thermally activated rearrangement of Ge atoms in the lattice and the strain relaxation.Furthermore, a reduction in the width of the Ge-Ge vibrational mode was observed after PLM at energy densities >0.15 J cm −2 in figure 2. This can be attributed to a rearrangement of Ge atoms in the Ge 1-x Sn x lattice and strain relaxation.
The microstructure and element composition of the asgrown and PLM-treated samples were investigated using cross-sectional TEM-based analyses.In particular, figures 3(a) and (b) show superimposed Si, Ge, and Sn element distribution maps obtained from the upper part of the layer stack.The general setup matches the schematic presented in figures 1(a) and (b).Figures 3(c  small process instabilities during MBE growth, is related to a slightly varying Sn concentration. After PLM, the Ge 1-x Sn x surface is rearranged and larger defect structures are visible between the Ge 1-x Sn x /Ge interface up to about 100 nm below the Ge 1-x Sn x top surface (see figures 3(b) and (d)).The presence of these defect structures is not surprising since the strain relaxation comes with the formation of misfit dislocation networks and threading dislocations.According to the EDXS analysis (figure 3(b)), there is a Sndepleted region between the near-surface molten and nearsubstrate non-molten zone, which is visible in figure 3(e) as a sharp dip in the vertical Sn profile of the PLM-treated sample.Below the Sn-depleted zone, we find a Ge 0.89 Sn 0.11 layer with a microstructure similar to the as-grown state.Above the Sndepleted zone, there are Sn-rich clusters and filaments in a Ge 0.90 Sn 0.10 matrix.The filaments are well visible as sharp peaks in the horizontal Sn profile in figure 3(f).Similar filament structures were discussed by Narayan [37] for highly doped Si after PLM.He concluded, if the non-equilibrium solubility of the alloy exceeds a certain value, the solid-liquid interface becomes unstable and the structure experiences a cellular breakdown during the ultra-fast solidification.However, there are some reasons against this theory, as discussed in [24].The Sn-rich filaments in the present study are still part of the Ge 1-x Sn x crystal structure [7].Assuming, the filaments might be an early stage of phase separation, there should be a significant increase of the Sn concentration towards the surface, which is not visible in figure 3(b).Abdi et al reported similar Sn-rich Ge 1-x Sn x filaments in Ge 0.89 Sn 0.11 with an enhanced defect concentration and explained that a combination of pipe diffusion and spinodal decomposition might be the origin of the filaments [24].In fact, our filaments also contain some defect structures.On the other hand, the columnar fluctuation in the Sn concentration of the as-grown state might promote the filament formation after PLM.Apart from the filaments, the microstructure of the Ge 0.90 Sn 0.10 matrix close to the sample surface seems to be homogenous and comparable with the as-grown state [7].

Defect analysis
The influence of PLM on the defect concentration, defect depth distribution and electrical properties was examined by DB-VEPAS, VE-PALS and Hall-effect measurements.
The relative changes of defect density (the S-parameter) and elemental decoration of defects (the W-parameter) across the sample thickness were studied by DB-VEPAS (see figure 4 and supplementary figure S 1).In general, the plotted annihilation line parameter S in figure 4(a) is directly proportional to the defect concentration.However, it depends on the defect size and tends to saturate for larger defect concentrations.We observe an increase of S as a function of PLM energy density applied on the film as well as a variation of the maximum S (E p ) position reflecting changes across the Ge 1-x Sn x layer thickness.This observation correlates with the higher amount of defects between 50 and 200 nm in the PLM 0.5 J cm −2 sample (see figure 3(d)).The concentration of open volume defects is higher compared to the as-grown state (lower slope and a maximum at E p = 7 keV) and a Ge-reference sample (lowest slope, no maximum).Interestingly the S-parameter at E p = 0.05 keV is for all PLM samples very similar as visible in figure 4(a) and table 1.Similar surface properties were also indicated by µ-Raman results in figure 2. The W-parameter can be used to evaluate atomic environment at the positron annihilation site and is presented in figure S 1.At E p = 10 keV we have a peak, which can be allocated to the Ge 0.9 Sn 0.1 /Ge interface because W of the Ge 0.89 Sn 0.11 approaches the W value of Ge-reference sample.For the PLM samples, we have additionally the Sn depletion region between the PLM affected Ge 1-x Sn x and unaffected Ge 0.89 Sn 0.11 layer (see figure 3(b)), which is however not clearly visible from positron annihilation spectroscopy (PAS) in figure S 1(b)).It is likely due to the fact that the Sn depleted layer is too thin and deeply buried for positrons to resolve it.In order to compare changes in defect density (S) and changes in the defect decoration types Table 1.The calculated S surf , S 1 , thickness d 1 , effective diffusion length L +,1 , and defect concentration cν for the germanium reference sample, Ge 0.89 Sn 0.11 as-grown state and Ge 1-x Snx samples after PLM with 0.3, 0.4 and 0.5 J cm −2 , respectively, were calculated with VEPFit code [38].In brackets a standard deviation for the last digit after comma is shown.S surf was calculated close to the sample surface at (Ep = 0.05 keV).Moreover, for both considered depths the local stoichiometry must contain Sn atoms as no obvious linear relation can be drawn between Ge reference and Ge 1-x Sn x data points.The VEPFit code [38] has been utilized for the analysis of positron diffusion length L + , which is inversely proportional to defect concentration c v .The code enables evaluation of defect densities as a function of depth in multilayer systems.The S (E p ) curves in figure 4(a) were fitted assuming a four-layer system by using the layer stack presented in figure 1 consisting of the strain-relaxed Ge 1-x Sn x (including Sn depleted Ge 1-x Sn x ), unaffected Ge 0.89 Sn 0.11 , Ge, and Si substrate.The selected parameter and calculation results are summarized in table 1.The layer thickness d 1 of Ge 1-x Sn x and Ge 0.9 Sn 0.1 was determined by RBS and TEM as explained in [7].and was fixed to these values for the calculation.The density of the strained Ge 0.89 Sn 0.11 and strain-relaxed Ge 1-x Sn x layers were determined by HRXRD and RSM results (see [7] and appendix D) to ρGe 0.89 Sn 0.11 = 5.14 g cm −3 and ρGe 1-x Sn x = 5.11 g cm −3 , respectively.For Ge (ρ Ge = 5.32 g cm −3 [39]) and Si (ρ Si = 2.33 g cm −3 [40]) literature densities were used.L + for the Ge-buffer layer and Si-substrate was fixed to 111 nm and 220 nm, respectively, based on the Ge single crystal substrate measurement and literature [41].The boundary between the Ge-buffer layer and the substrate was kept constant at depth of 700 nm, according to planned deposition conditions.For simplicity 15 nm was added to d 1 in case of PLM samples to account for the thickness of depleted layer.Such a thin layer has negligible influence on the positron annihilation as no clear variation of the S (Ep) curve shape has been isolated across the depth.According to the fitting results the calculated positron diffusion lengths of the PLM treated films are too short for positrons to directly arrive to the depleted layer, hence the defect density in the Sn depleted layer must be similar to the PLM treated Ge 1-x Sn x top or the Ge 0.89 Sn 0.11 bottom layers.d 1 for the as-grown Ge 0.89 Sn 0.11 was fixed to 290 nm and the obtained L +,1 = 37.4 nm served as a reference for the unaffected Ge 0.89 Sn 0.11 layer in the PLM treated samples (see figure 1(b)).Hence, the only free fitting parameter was the effective diffusion length in the top layer L +,1 .

Sample name S
The calculated defect concentration (∼3.5 × 10 −5 atom −1 ) of the as-grown sample is relatively low due to a large L +,1 = 37 ± 3 nm, but is still three times larger than the undoped Ge-reference crystal.The slight loss of crystal coherency compared to Ge-reference is not surprising for materials deposited by MBE, since surface defects in the buffer or strain relaxation events in Ge 0.89 Sn 0.11 layer can lead to defects at the interface.After PLM with 0.3 J cm −2 , when the molten layer is about 100 nm, the defect concentration increases about 15 times.This suggest that the presented strain relaxation events leads to an abrupt formation of open volume defects.By increasing the PLM energy densities to 0.4 J cm −2 and 0.5 J cm −2 , the defect concentration c ν drops down due to annealing effects.Although on the first glance, a general increasing trend of the calculated S as a function of PLM energy density seems contradicting the drop of defect concentration, as we will show later, the raising density of larger vacancy clusters (see figure 5(c)) is likely the main cause of the S-parameter increase.This indicates that the high diffusion coefficient in the molten film may be also in combination with the assumed pipe diffusion mechanism reported by Abdi et al can be an effective way for strain relaxation and open volume accumulation [24].
In addition, we have studied the defect depth distribution in the as-grown and annealed samples using VE-PALS.Figure 5(a) shows the depth change of the average positron annihilation lifetime τ av , which is the weighted average defect size across sample thickness.τ av can be expressed by equation (3).The positron annihilation lifetime τ i refers to the characteristic annihilation sites (vacancy like defects of different sizes) and I i is the relative number of positrons trapped at these defect types.In the other words τ av indicates the density of vacancy like (open volume) defects, In general, the positron lifetime increases with increasing the size of the open volume defects and negativity of the defect charging state (more negative-slightly longer lifetime) [42].In figure 5(a) we obtain for τ av at 3 keV (∼42 nm) an increases from ∼275 ps in the as-grown sample to about ∼293 ps and ∼284 ps in the sample annealed with the pulsed laser energy densities of 0.4 J cm −2 and 0.5 J cm −2 , respectively.This is caused by an increase of the average size of defects after PLM compared to the as-grown state.For the positron implantation energies lower than 2 keV, all curves in figure 5(a) show a longer lifetime (close to the sample surface) because the signal is superimposed by the surface and its defect states [43][44][45].For higher positron implantation energies, only the defect states are visible (the most pure defect contributions can be obtained at the S-parameter maximum in figure 4(a).
From equation (3) we see that τ av is a combination of the discrete positron lifetime components τ i (τ 1 and τ 2 ), obtained by the spectra decomposition (figure 5(b)) and their relative intensities I 1 and I 2 (figure 5(c)).In general, positron lifetime scales with the local electron density, which is influenced by the size of open volume defects and their chemical composition, carrier concentration, and the defect charge state [42].In our case τ 1 is not a straight forward to define as it could represent a defect free GeSn material (bulk annihilation in figure 5(b)), a fully Sn-decorated Ge-mono-vacancy (V Ge + nSn Ge , where n is the number of Sn atoms substituting Ge) or GeSn with shallow trapping dislocations [46].On the other hand, τ 2 describes vacancy agglomerations (clusters containing certain number of vacancies).The positron lifetime components τ 1 and τ 2 as a function of depth reveal a defect size evolution due to annealing (see figure 5(b)).The first lifetime component τ 1 increases by not more than ∼16 ps across the depth after PLM with 0.4 J cm −2 which is followed by a τ 1 drop after PLM with 0.5 J cm −2 .It is accompanied by a reduction of its relative intensity I 1 by not more than ∼10% and indicates overall reduction of positron annihilation with defect states related to τ 1 .To understand the change of τ 1, the so-called atomic superposition (ATSUP) [47] calculations were performed for Ge (see table S I) and a Ge 0.9 Sn 0.1 cubic crystals.Here we used Ge 0.9 Sn 0.1 because the Ge 1-x Sn x the cross-section TEM line scan presented in figure 3(f) shows that Sn concentration in the matrix between filaments in the PLM treated sample is lower than that in the as-grown sample.The same was concluded from XRD data [7].
The calculated positron lifetime as a function of the lattice parameter and the number of Sn atoms decorating V Ge are presented in the tables S II and S III and plotted in figures 5(d)-(f), respectively.The details about our simulations and the calculation results can be found in the supplementary materials sections B and C.
From the ATSUP calculation we obtain that the calculated lifetime in Ge 0.89 Sn 0.11 is increasing with the lattice parameter for both bulk and V Ge (see figure 5(d)), as expected.The numbers of Sn substitutions of Ge in Ge 0.9 Sn 0.1 has only a minor influence on the positron lifetime for bulk, but a substantial reduction is observed for V Ge (figure 5(e)).Finally, positron lifetime scales with the vacancy cluster size in a similar way for Ge 0.9 Sn 0.1 as for Ge (figure 5(f)).With this results we reveal that the change of τ 1 is likely a superposition of lattice parameter variation (figure 5(d)) and a change of the Sn distribution at V Ge (figure 5(e)).Therefore, the component τ 1 combines the positron annihilation in bulk and at the Sn-decorated V Ge .Experimentally, the reference lifetime in bulk Ge is in the range of 224-228 ps [48] and decreases with increasing Sn concentration [16], which is in line with our calculations.Moreover, we assume that the average area of filaments i.e. regions with high Sn content (equivalent to the shorter positron lifetime due to larger Sn decoration of V Ge ) increases with PLM energy.They are not observed in the asgrown sample at all.There the positron lifetime is the shortest and likely represents bulk annihilation.The slight variation of lifetime between different PLM energy densities, on the other hand, is likely related to a variation of the average number of Sn atoms bonded with V Ge existing at the direct interface with filaments and the Ge 1-x Sn x matrix in between.
Further, the relative intensity I 1 decreases after the PLM (see figure 5(c)), which reflects the overall reduction of the Sn-vacancy complex concentration.In general, after PLM τ 2 is reduced in all samples.This means that the average size of larger vacancy clusters decreases, but simultaneously the relative intensity I 2 increases (see figure 5(c)), indicating larger fraction of positrons annihilating with vacancy agglomerations modified due to PLM.The τ 2 is in the order of 400 ps referring to the vacancy clusters with about three to four agglomerated vacancies (see figure 5(b) and table S III).Larger concentration of vacancy clusters can increase scattering and reduce the mobility of charge carriers as shown by the Hall effect measurements [49].
The results of the Hall-effect measurement are summarized in table 2. The hole concentration in the as-grown state is 3.3 × 10 18 cm −3 at 300 K because of unintentional ptype doping during the growing process of Ge 1-x Sn x .This background doping is already one magnitude higher than indicated in earlier reports [50].After PLM, the hole concentration is increased to 4.1 × 10 18 cm −3 (0.4 J cm −2 ) and 4.9 × 10 18 cm −3 (0.5 J cm −2 ) at 300 K. Simultaneously, the mobility is reduced from 304 cm 2 Vs −1 down to 231 cm 2 Vs −1 .This can be caused by a higher background doping or the filament formation.

Conclusions
Compressively strained single-crystalline Ge 0.89 Sn 0.11 was successfully fabricated via MBE on Si with the help of a Ge virtual substrate and buffer layer.After PLM, the Ge 1-x Sn x layer on the surface is single-crystalline and strainrelaxed.Using PAS, the overall defect concentration in the as-grown sample was determined to about 3.5 10 −5 atom −1 .
After PLM at 0.3 J cm −2 the defect density increases to ∼54 × 10 −5 atom −1 followed by a substantial decrease for higher energies to ∼27 × 10 −5 atom −1 for 0.4 J cm −2 and ∼16 × 10 −5 atom −1 for 0.5 J cm −2 .Moreover, PLM raises the average defect size for energy densities lower than 0.4 J cm −2 , which is followed by a small drop for higher PLM energy densities.Furthermore, after PLM more electrically active p-type dopants are achieved, which could be related to a reduction in the number of Sn atoms decorating Ge monovacancies.PLM generates a larger density of vacancy agglomerations consisting of 3-4 vacancies and increases the scattering possibilities that hinder and reduces the mobility of charge carriers.The combination of thick MBE-grown Ge 1-x Sn x with an additional deep PLM treatment is a promising approach to fabricate strain-relaxed Ge 1-x Sn x or Si 1-x-y Ge y Sn x -buffer layers.

Figure 1 .
Figure 1.Process flow and schematic of the layer stack cross-section of the Ge 0.89 Sn 0.11 material grown on Si by MBE before (a) and after post-growth nanosecond-range PLM with energy densities above the melting threshold (b).Schematic of the post-growth PLM process (c).
) and (d) show the bright-field TEM images recorded from the areas marked with the white-dashed squares in figures 3(a) and (b), respectively.In the as-grown state, about 80 nm above the Ge 1-x Sn x /Ge interface, first vertical structures with a columnar signature appear (see figures 3(a) and (c)).Line scan analyses, presented in figures 3(e) and (f), confirm that the columnar structure, which could be caused by

Figure 3 .
Figure 3. Cross-sectional TEM-based analysis of the as-grown sample ((a), (c), and (e)), and after PLM treatment with an energy density of 0.5 J cm −2 ((b), (d), and (f)).Panels (a) and (b) show representative superimposed Ge (blue), Sn (red), and Si (cyan) EDXS-based element distributions, while (c) and (d) present the bright-field TEM images of the regions marked with white-dashed squares in (a) and (b), respectively.The diagrams in (e) and (f) depict the vertical and horizontal line scans, indicated in (a) and (b) with orange and green arrows, respectively.

Figure 4 .
Figure 4. Annihilation line parameter S of the Ge-reference, as-grown Ge 0.89 Sn 0.11 and after PLM with an energy density of 0.3, 0.4, and 0.5 J cm −2 (a) as a function of positron implantation energy Ep and mean positron implantation depth <z> with corresponding fits.(b) S-W plot of the maximum values from S (Ep ≈ 4 or 7 keV) and W (Ep ≈ 10 keV) dependencies compared to the bulk value (Ep = 35 keV) for Ge reference sample.

(
W), we plotted both in figure4(b) at two characteristic depths of each sample.The discussed depth are (i) lower depth corresponding to the S (E p ) maximum (indicated by the arrow in figure4(a)) and (ii) the deeper depth-W (E p ≈ 10 keV) (see figure S 1(b)).The data points from the lower depth exhibit a linear relation to each other, which indicates that they share a similar defect type as the reference sample.Deeper in the film a trend in direction towards the Ge reference sample is found.Hence, the observed change at E p ≈ 10 keV is related to the increased defect decoration by Ge (less decoration of Sn).

Figure 5 .
Figure 5. Average positron annihilation lifetime τav of the samples in the as-grown state and after PLM with an energy density of 0.4 J cm −2 and 0.5 J cm −2 as a function of positron implantation energy Ep and mean positron implantation depth <z> (a).Discrete positron lifetime components τ 1 (closed symbols) and τ 2 (open symbols) obtained by spectra decomposition of τav (b).Relative intensities I 1 and I 2 of the components τ 1 and τ 2 (c).ATSUP calculations of positron lifetime as a function of lattice parameter a for bulk Ge 0.9 Sn 0.1 and V Ge configurations (d), a number of Sn nearest-neighbors (≤4) and next-nearest-neighbors donors decorating Ge atom and V Ge in Ge 0.9 Sn 0.1 (e), and in function of vacancy agglomeration size for a Ge and Ge 0.89 Sn 0.11 crystals (f).The calculated lifetimes from (f) of bulk Ge 0.9 Sn 0.1 and vacancy cluser sizes with 3 (V3) and 4 (V4) vacancies are highlighted in green in (b).