Controlled growth of hexagonal gold nanostructures during thermally induced self-assembling on Ge(001) surface

Nano-sized gold has become an important material in various fields of science and technology, where control over the size and crystallography is desired to tailor the functionality. Gold crystallizes in the face-centered cubic (fcc) phase, and its hexagonal closed packed (hcp) structure is a very unusual and rare phase. Stable Au hcp phase has been reported to form in nanoparticles at the tips of some Ge nanowires. It has also recently been synthesized in the form of thin graphene-supported sheets which are unstable under electron beam irradiation. Here, we show that stable hcp Au 3D nanostructures with well-defined crystallographic orientation and size can be systematically created in a process of thermally induced self-assembly of thin Au layer on Ge(001) monocrystal. The Au hcp crystallite is present in each Au nanostructure and has been characterized by different electron microscopy techniques. We report that a careful heat treatment above the eutectic melting temperature and a controlled cooling is required to form the hcp phase of Au on a Ge single crystal. This new method gives scientific prospects to obtain stable Au hcp phase for future applications in a rather simple manner as well as redefine the phase diagram of Gold with Germanium.

single crystal surfaces 14 and annealed at temperatures below the eutectic point of the Au/Ge system of ~634 K 15 . As the annealing temperature of the sample reaches ~634 K, part of the germanium substrate melts and forms a Au-Ge eutectic liquid, which then recrystallizes during cooling of the sample to room temperature (RT) 15 . Here, the structure and composition of nanostructures formed after RT deposition of 6 mono layers (ML) of Au on (2 × 1) reconstructed Ge(001) in UHV 16 and subsequent post-annealing at different temperatures (below and above the eutectic melting temperature of Au/Ge (634 K)-T e ) and cooling rates were investigated using a combination of electron microscopy techniques. The structure and formation of Au nanoparticles on a single crystal have garnered a renewed interest in nanotechnology 6 as these are the key catalysts in the growth of Ge, Si and III/V nanowires with tremendous applications for a new generation of nanoscale electronics and optoelectronics devices such as solar cells and battery electrodes 17 . The formed Au hcp 3D nanostructures could be also used as a growth template for hexagonal semiconductors 18 .
In the present study, Au islands of rectangular shape with edges oriented along [110] and [1][2][3][4][5][6][7][8][9][10] directions of the Ge(001) substrate (called Ge < 110> in the rest of the text) are created for a post-annealing temperature of 573 K (bellow T e ), as seen in Fig. 1a. When the post-annealing temperature exceeds T e , the islands reshape into an asymmetric polyhedral (see Supplementary Fig. S1), indicating the formation of a AuGe eutectic liquid during the high-temperature stage of the treatment 19 . The longest edge of the island is aligned along the Ge < 110> direction (as observed in Fig. 1b). EBSD measurements are performed to determine the crystallographic orientation and phase of each island. It is important to realize that the EBSD technique probes the subsurface region down to a depth of a few nanometers for gold. In Fig. 1(c,d), the resulting inverse pole figures (IPF) in the Z (out of plane) sample direction of the EBSD measurements for the sample post-annealed bellow (Fig. 1c) and above (Fig. 1d) T e are shown, respectively. For a low temperature, the Au crystallites were indexed unequivocally as belonging to the Au fcc structure, while for the sample annealed at a higher temperature, the Au crystallites could not be indexed in the cubic system, and the Au hcp phase has to be considered. Common orientations, independent of the annealing temperatures, of the Au crystallites are observed in the X, Y and Z sample directions, as depicted in Fig. 1e. For the case of temperatures lower than T e , the obtained EBSD results can be described as being constituted by two equivalent configurations of Au crystallites rotated by 90° in-plane, due to the substrate surface symmetry, (for details see Supplementary Figs S2   with epitaxial relation (101)Au fcc //(001)Ge and [001]Au fcc //[110]Ge (Fig. 1e). This crystallographic texturing was never directly observed but can be attributed to the preferential orientation of Au crystallites parallel to the germanium < 110> direction 14,20 . For the samples annealed at 673 K (see Fig. 1d), the EBSD results shows a combination of four possible different configurations of the Au crystallites rotated by 90° (for details see Supple  mentary Figs S2, S4 and S5, experimental and simulated pole figures and inverse pole figures) with the following two main orientation relationships: case I− (10-11) tilted by ~8deg Au hcp //(001)Ge, [2-1-10]Au hcp //[110]Ge and case II-(0001) tilted by ~30deg Au hcp //(001)Ge, [2-1-12]Au hcp //[110]Ge, see schematic in Fig. 1e. The relationship between the average grain size of the Au crystallites' crystallographic structure and the post annealing temperature, as revealed by EBSD, is presented in Fig. 1f. Here, two temperature regions are clearly visible: 1) For annealing temperatures below T e , the crystallites belong to the Au fcc phase, and their size (around 40 nm) is weakly dependent on the annealing temperature; 2) For annealing temperatures above T e , Au crystallites containing the Au hcp phase are formed. The size behavior of these crystallites presents a strong temperature dependence increasing from ~40 nm to ~120 nm in the studied temperature range (for details, see Supplementary Fig. S6). In addition, we have checked that the hexagonal form of gold was also present for different Au coverage i.e. 3, 12 and 18 ML as presented in Fig. 1g-i.
The rectangular islands observed below T e result from a self-assembling process induced by the surface diffusion of Au atoms. On the contrary, above the eutectic temperature, the Au islands form from a liquid AuGe alloy droplets as observed previously by Sutter et al. 21 , inferring that the observed polyhedral Au islands originates from a recrystallization process accompanied by a necessary Ge segregation during cooling of the sample to room temperature. As the Au islands possess a defined crystallographic orientation relative to the Ge substrate, the Au/Ge interface has to play an important role for directing the growth and crystallographic orientation of the Au islands. This is different from the observation of randomly oriented Au nanostructures supported by a Ge pedestal when annealing Au clusters deposited on a Ge(111) single crystal 22 . To examine the exact atomic structure of this Au/Ge(001) interface, cross-sectional samples have been analyzed by high-resolution HAADF STEM imaging, where the contrast is proportional to the atomic number (thus, Au appears brighter than Ge). The HAADF STEM images revealed that on the samples annealed at 498 K (below T e ), only a small part of the Au island (~1 nm) is submerged into the germanium substrate, as presented in Fig. 2a. A similar effect of Au atoms migrating into the germanium substrate has been observed earlier by Wang et al. 23 and was attributed to the Au/ Ge mixing 14 . Moreover, the HAADF STEM image demonstrates, in Fig. 2a, that the epitaxial relationship between the island and the substrate is (101)Au fcc //(001)Ge in agreement with the EBSD results presented above.
The possible diffusion of Au atoms into the Ge substrate is further studied using statistical parameter estimation theory 24,25 . Here, the total scattered intensity by each atomic column is computed, as it scales with the average atomic number Z of an atomic column 26,27 . By assuming a constant sample thickness, this measure can be used to distinguish between columns containing Au atoms and pure Ge columns. Due to the noise inherent to the experiment, intermixing between the Au and Ge phases is studied atomic plane-by-plane across the interface using two sample t-tests 28 (see Supplementary Fig. S7 for details). The results presented in Fig. 2b indicate that no Au atoms are present in the Ge substrate, indicating that the interface is perfectly sharp and confirming the non-miscibility of Au in Ge 15,23 . For samples annealed above T e , more than half of each of the Au island is buried into the germanium substrate, as shown in Fig. 2c. From HAADF imaging, we determined that the Ge {001} and {111} planes are predominantly interfaced with the buried part of the Au island (for details, see Supplementary Figs S8 and S9). Moreover, for most of the studied Au islands, at the side opposite to their longest edge, a germanium crystalline rim is seen on top of the Ge substrate ( Fig. 2c,f). An Au hcp phase, which we will study in details in the following paragraph, is present in the topmost part of the islands. At the bottom of the Au island, the Au fcc (011) plane grows epitaxially on a Ge(001) surface, as shown by several HAADF STEM images. The combination of statistical parameter estimation theory with two-sample t-tests shows that in a small region, pure Ge columns are intermixed with columns containing Au. Note that Au atoms are only present in the columns following the fcc Au lattice. This leads us to the conclusion that Au atoms are most likely not diffusing into the Ge substrate; thus, excluding the presence of an AuGe alloy, as reported in earlier studies 21,29 (further detailed analysis is available in the Supplementary material, Fig. S7a). Moreover, our experimental findings indicate that the Au islands formed at annealing temperatures lower than T e can be considered as defect-free single crystals of fcc Au, whereas islands formed at higher annealing temperature contain regions of both the Au hcp and Au fcc crystallographic phases clearly resolved by STEM. At the bottom (earlier stage of the crystallization), the Au fcc phase is observed, forming at the Au fcc (011)/Ge(001) interface. At the regions facing the Ge(111) planes, the Au hcp phase is observed and grows on the Au fcc {111} planes giving the interfacial relationship (0001)Au hcp //(111)Au fcc , as seen in Fig. 2c. This growth results in an orientation relationship relative to the Ge substrate as already observed by EBSD, described as (0001) tilted by ~30deg Au hcp //(001)Ge, [2-1-12]Au hcp //[110]Ge. Figure 2e shows the radial power spectrum density (PSD) of this Au hcp region. There are two main peaks at 2.442 Å and at 2.233 Å, which can be uniquely identified as the (0002) and (10-11) reflections of the Au hcp phase 8 . The derived experimental lattice constants for Au hcp are a = 2.90 Å and c = 4.88 Å, which are in good agreement with other experimental 8 and theoretical values 13 . STEM images show that the Au hcp phase is always present at the top part of the island, which explains the absence of Au fcc phase in the EBSD measurements presented above. In light of the HAADF STEM images, models of the interfaces Au fcc (011)/Ge(001) and (0001) Au hcp //(111)Au fcc have been analyzed. At the bottom of the islands, the Au fcc (011) plane is growing epitaxial to a Ge(001) surface. In the plane of the interface, the Au fcc (100) and the Ge(110) lattice planes are in good agreement (4.078 Å/4.000 Å = 1.0195), and the two structures match well in this projection (see Fig. 3a). The Au hcp and Au fcc structures represent two different stacking sequences of close packing; hence, the interface between (0001)Au hcp and (111)Au fcc will be in perfect registry (see Fig. 3b). In contrast to the free standing Au hcp square sheets studied by Huang et al. 8 , the Au hcp nanostructures formed on Ge(001) are stable under electron irradiation. Furthermore, it has been found that both the annealing temperature and cooling rate are important in order to control the final phase content of Au nanostructures. Here, two series of measurements have been used: annealing at 673 K and 773 K and then cooling down to RT with constant rates of 0.1 K/min, 15 K/min and 700 K/min. The analysis of samples annealed at 673 K shows the existence of three different regions in the island structures: a pure unfaulted Au hcp phase; a hexagonal intergrowth domain consisting of a mixture of different stacking sequences which could be attributed to the pure Au hcp and Au fcc atomic planes simultanously; and a pure Au fcc phase close to the germanium substrate. For samples annealed at 773 K, significantly less regions having the Au hcp phase are observed in favor of an intergrowth domain content (see Figs S10 and S11). The structure of the pure unfaulted Au hcp phase can be seen in Fig. 4a. The interface between the intergrowth domain and the pure Au hcp is presented in Fig. 4b. The formed Au nanostructures were free of any germanium content within the precision of the performed EELS spectroscopy measurements Fig. 4c-e. Furthermore, the cooling rate is important in order to improve the formation of the pure Au fcc and Au hcp phases. At a fast cooling rate (i.e., 700 K/min), the domains of intergrowth between Au fcc and Au hcp are significantly increased compared to slower cooling, where the pure phase domains are larger, dictating this phenomenon to be thermodynamically controlled.
According to the experimental findings discussed here, a model explaining the formation of the observed half-buried Au islands on the Ge(001) substrate can be proposed, as presented in Fig. 5a-d. It is separated into 4 steps.
1. At the beginning of the annealing process, the deposited Au atoms aggregate into clusters due to surface diffusion of Au atoms on an Au rich surface and particle coarsening 19 . When the temperature exceeds the eutectic temperature of the system, a liquid Au-Ge droplet is formed by incorporation of Ge atoms from the substrate into the hot Au clusters, as described previously in nanowires 12 . According to the Au/Ge phase diagram, the concentration of germanium in the Au-Ge droplets is dependent on the annealing temperature 15 . In the  Fig. 3a. The developing Au fcc crystallite grows with little twinning, and its crystallization front is along its {111} facets, which are energetically favorable (i.e., they have the lowest surface energy) 32 . 3. The formation of these Au fcc crystallites leads to the germanium enrichment of the remaining liquid, so that the metastable hexagonal β -AuGe alloy is formed, similarly as directly first seen in the case of Au nanostructures supported on germanium nanorods by Marshall et al. 12 and accordingly to Okamoto et al. 15 , Sutter et al. 21 and Hajjar et al. 22 . 4. Upon further cooling, the metastable alloy separates into the Au hcp phase and pure Ge due to the easily diffused Ge atoms from the β -AuGe alloy, as was seen in the case of TEM in-situ studies on nanowires 12 .
The formed Au nanostructures are free of any germanium content as checked by the EELS measurements Fig. 4c-e. The excess Ge from the alloy segregates at the opposite of the Au fcc crystallite and forms a crystalline rim at the alloy/Ge interface, as shown in Fig. 2c,f. Moreover, the excess Ge diffuses along the reconstructed substrate surface and extends the atomic terraces. This is evidenced by a drop in the intensity of RHEED spots during the cooling of the sample in the range from ~463 K down to ~433 K, see Fig. 4f. Our findings are consistent with the experimentally observed germanium out-diffusion from Au-Ge metastable phase which begins at ~448K 12 and the decay takes ~5 min 15 .
This scenario holds for lower cooling rates of 0.1-15 K/min, which indicates that this mechanism is thermodynamically stable and that our system is at a constant thermodynamic equilibrium during the cooling process. In the case of Au droplets on germanium nanorods, with finite amount of germanium available in the system as limited by the size of the germanium nanorod, the slow cooling resulted in the formation of the single crystalline segments of metastable γ -AuGe alloy 21 . However, for very fast cooling (i.e., 700 K/min), the pure Au hcp phase is not formed at the expense of an intergrowth of Au fcc and Au hcp . In contrast to fast cooling of the Au droplets on germanium nanorods presented by Marshall et al. 12 , Au hcp was observed. This might be related to the modification of the Ge diffusion kinetics due to the change of diffusion regime from a finite to an infinite Ge concentration at the source. In fact, the nanoscale Au-droplet phase diagram (valid for the nanorod system), with finite amount of germanium limited by size, deviated significantly from the phase diagram for bulk phase, as shown by E. Sutter and P. Sutter 33,34 . In our case, for an infinite amount of germanium available, the presence of the β -AuGe alloy, which is a precursor for the formation of pure Au hcp (as suggested by the Au/Ge phase diagram 15 ), is responsible for this change of regime. As the pure Au hcp phase is formed only when the annealing is above T e but below 773 K, we suggest that the formation of the β -AuGe alloy depends on the initial germanium concentration in the hot droplet. Considering our observations and the Au/Ge phase diagram 15 , the germanium content in the Au-Ge droplet should be higher than 28 at. % (at 663 K) but lower than 38 at. % (at 773 K) to form pure Au hcp . This is summarized in the derived Au/Ge phase diagram for the self-assembled Au nanostructures on the Ge(001) surface presented in Fig. 5e.
In summary, the formation of crystalline Au nanostructures on a germanium substrate during a thermally induced self-assembly process of 6 ML Au deposited on a Ge(001) surface was investigated. The Au islands change from a rectangular shape made of the Au fcc phase to a polyhedral shape belonging mainly to the Au hcp phase while the annealing temperature crosses ~634 K; this temperature corresponds to the eutectic temperature for the Au-Ge system. The formation of the hcp phase of Au was found to result from the decay of the β -AuGe metastable alloy when it is cooled down at a sufficiently slow rate (15 K/min or lower). We can conclude that the Au crystallization starts from one side of the germanium pit, i.e., the Ge(111)/Ge(001) plane corner, into the favorable Au fcc phase with {111} facets followed by the formation of the β -AuGe alloy under the influence of a depletion of Au from this crystallizing liquid. Finally, at a temperature of ~463 K, the metastable β -AuGe alloy separates into the Ge rim surrounding the island and the Au hcp phase on top of the Au fcc {111} facets. Confronting our observations to the known Au/Ge phase diagram, the germanium content in the Au-Ge droplet should be higher than 28 at. % (at 663 K) but lower than 38 at. % (at 773 K) to form pure Au hcp . The presented simple technology of Au hcp growth will enable the new development in the fabrication of defined templates of this very rare phase of Au and will enable investigation and development of new devices based on hcp gold. In (e) EELS spectrum is presented from area 1 (the Au island) and area 2 (germanium). It is seen that within the precision of the EELS spectroscopy the Au island is free of any germanium. (f) Change of the RHEED intensity, recorded during sample cooling, after post annealing of 6 ML Au/Ge(001) to temperature higher then Au/Ge eutectic. Monotonic increase of the intensities is seen for all type of surface reconstruction spots. In the temperature range of 470 K-423 K a drop of the intensity occurs, which takes ~8 min, later the intensities increase monotonically in the same way. The observed drop of RHEED intensity is assigned to the decay of the beta-Au-Ge metastable phase leading to formation of Au hcp and pure germanium.
Scientific RepoRts | 7:42420 | DOI: 10.1038/srep42420 Methods Au/Ge sample preparation. The samples were prepared in a UHV MBE system at Institute of Physics Jagiellonian University, Krakow, Poland. The Ge(001) substrate surfaces were cleaned by cycles of low-energy ion beam bombardment and annealing in order to achieve atomically flat terraces. Deposition of 6 ML of Au by the Molecular Beam Epitaxy with 0.12 ML/min resulted in formation of a crystalline, continuous Au overlayer as verified by RHEED and LEED. Just after the deposition, the 6 ML Au/Ge(001) samples were post-annealed in UHV conditions (10 −10 mbar) to temperatures ranging from 498 K to 773 K, for which the initial continuous Au layer can reform into nanoscale Au islands. The temperature was increased with constant rate of 10 K/min and decreased in the cooling process with a rate of 15 K/min. Then, the samples were transferred in-situ by means of a UHV transfer system from a UHV MBE system to the SEM chamber (1*10 −6 mbar).
Sample characterization. The Au/Ge(001) samples were characterized by SEM (FEI Quanta 3D FEG) equipped with a EBSD system (EDAX TSL DigiView camera) at the Institute of Physics Jagiellonian University, Krakow, Poland, which allows structural examination from the near surface of the sample (for Au, it is of a few nanometers). The EBSD diffraction patterns were collected at a 70° sample tilt at 15 keV beam energy. The diffraction patterns were automatically indexed by EDAX TSL OIM DC 7.2.1 software, according to the Au fcc phase and the Au hcp phase. The software algorithm during indexing selects the best matching phase automatically 35,36 . The sample geometry was chosen in a such a way that X, Y and Z are parallel to the [110], [1][2][3][4][5][6][7][8][9][10] and [001] crystallographic directions of the Ge single crystal substrate, respectively, as indicated in Fig. 1(a,b). IPF maps were subject to two clean-up algorithm procedures to ensure that reliable data were displayed, where grain CI standardization was applied and neighbor CI correlation with CI (0.4). The analysis of the experimental EBSD pole figures and inverse pole figures resulted in the derivation of the epitaxial relations for the formed nanostructures. The Au grain size was calculated from the EBSD data as an average grain feret diameter. For the 498 K sample, the Au grain size was calculated from the STEM cross section measurements. Samples were also investigated with a 5500 Agilent Atomic Force Microscope at ambient conditions. In order to study the internal structure of the Au/Ge(001), cross section samples were prepared using the FIB technique. At first, a protective carbon layer was deposited on the surface inside the SEM before an exposure to the atmosphere to avoid any change to the native structure of the samples. After this, a Pt protection layer was deposited first by e-beam deposition and then by ion-beam deposition to ensure minimal damage to the surface of the sample.
High Angle Annular Dark Field (HAADF) imaging was performed in a Probe Corrected Scanning Transmission Electron Microscope (STEM) FEI Titan at the University of Antwerp, Belgium, operated at 300 kV. This imaging mode provides structural images where intensities are proportional to both the thickness and mean atomic number Z. Statistical parameter estimation theory was used to calculate the total scattered intensity of the individual projected columns 24,25 . A linear scaling of these intensities with the atomic number Z was assumed to quantify the chemical structure of the Au/Ge interface 26,27 . A statistical analysis by two-sample t-test 28 using the mean scattered intensity of the different columns in each atomic layers was performed to determine which layers have columns containing Au atoms.  (001) surface, sample cooling rate as a function of sample annealing temperature and germanium content in Au/Ge liquid The relative sizes of Au hcp (red), intergrowth domain(green) and Au fcc (blue) regions of the island after recrystallization of the liquid are marked. When changing the sample annealing temperature and sample cooling rate, the Au hcp relative sizes change.
Scientific RepoRts | 7:42420 | DOI: 10.1038/srep42420 To investigate the presence of germanium in the Au nanostructures, EELS measurements were performed. EELS was preferred to EDX due to the possible contribution of secondary fluorescence effects of the highly energetic Au K line giving rise to an artificial germanium signal in the Au. The EELS spectra were acquired at 300 kV with a convergence angle of 20 mrad and a collection angle of 100mrad. The spectra were acquired in Dual EELS with the same exposure time of 0.1 s/pixel and a dispersion of 0.5 eV/pixel. The spectra were then spliced together using the DM routine. The spectra obtained for region 1 and region 2 were power-law background subtracted in the region from 100 to 1150 eV.