From the nucleation of wiggling Au nanostructures to the dome-shaped Au droplets on GaAs (111)A, (110), (100), and (111)B

In this paper, the systematic evolution process of self-assembled Au droplets is successfully demonstrated on GaAs (111)A, (110), (100), and (111)B. On various GaAs substrates, self-assembled Au clusters begin to nucleate at around 300°C, and then, they develop into wiggly Au nanostructures at 350°C. Between 400°C and 550°C, the self-assembled dome-shaped Au droplets with fine uniformity are fabricated with various sizes and densities based on the Volmer-Weber growth mode. Depending on the annealing temperature, the size including the average height and lateral diameter and the density of Au droplets show the opposite trend of increased size with correspondingly decreased density as a function of the annealing temperature due to the difference in the diffusion length of adatoms at varied activation energy. Under an identical growth condition, depending on the surface index, the size and density of Au droplets show a clear distinction, observed throughout the temperature range. The results are systematically analyzed and discussed in terms of atomic force microscopy (AFM) images, cross-sectional line profiles, and Fourier filter transform (FFT) power spectra as well as the summary plots of the size and density.


Background
Due to their increased cross-section and surface area as well as the size-dependent quantum confinement, semiconductor nanowires (NWs) have been successfully utilized in numerous device applications such as solar cells, LEDs, and FETs [1][2][3][4][5][6][7][8]. Until now, various semiconductor NWs have been successfully demonstrated through diverse epitaxial growth approaches including chemical vapor deposition [9,10], molecular beam epitaxy [11,12], and pulsed laser deposition [13,14]. Vapor-liquid-solid (VLS) [15][16][17][18] method has been widely adapted as a common growth mechanism in the forth-mentioned epitaxial approaches. The first successful fabrication of Si whisker on Si (111) was reported by Wagner et al., and they introduced a novel concept of growth approach called the 'VLS' growth [15]. Later, Morales et al. successfully demonstrated the fabrication of crystalline Si NWs by utilizing the VLS approach [16]. In the VLS growth, Au droplets serve as catalysts, and regardless of the materials and substrates utilized, the vapor-phase atoms could diffuse into the liquid-phase Au droplets [17,18]; from the supersaturated Au alloy droplets, the crystallization of NWs can occur at the liquid-solid interface due to the higher sticking probability at the interface [19][20][21][22][23]. In addition, the metallic nanoparticles were utilized in plasmonic applications such as solar cells and light emission enhancement [24][25][26][27][28][29]. The diameter, size, configuration, and even the density of NWs can innately be determined by those of the Au catalysts, and thus, the control of Au droplets is an essential step for the successful fabrication of the desired NWs. However, to date, the systematic studies on the evolution of Au droplets on various GaAs substrates are deficient, and therefore, in this paper, the detailed study on the evolution of the self-assembled Au droplets on GaAs (111)A, (110), (100), and (111)B is investigated. In order to investigate the detailed evolution process, feasible annealing temperatures were systematically tested ranging from 100°C to 550°C as briefly illustrated in Figure 1.
Depending on the annealing temperature, the nucleation of self-assembled tiny Au clusters and wiggly Au nanostructures as shown in Figure 1c was clearly observed on various GaAs substrates. At increased annealing temperatures, the self-assembled Au droplets with fine uniformity were successfully fabricated on each GaAs index. The self-assembled Au droplets showed an opposite evolution trend of increased size including average height and lateral diameter with correspondingly decreased density as a function of annealing temperature, and the size and density evolution are systematically analyzed with the atomic force microscopy (AFM) images and cross-sectional line profiles as well as the summary plots. Under an identical growth condition, depending on the substrates utilized, the size and density of Au droplets show a clear disparity among various indices throughout the temperature range.

Methods
In this study, the self-assembled Au droplets were fabricated on GaAs (111)A, (111)B, (110), and (100) representing the general zinc blende lattice indices in a pulsed laser deposition (PLD) system. To start with, various index samples were indium-bonded together on an Inconel holder side by side for uniformity per batch and then treated with a degassing process at 350°C for 30 min under 1 × 10 −4 Torr. Subsequently, a total amount of 2.5 nm of Au was equally deposited on the samples at a rate of 0.5 Å/s and at an ionization current of 3 mA under 1 × 10 −1 Torr in an ion coater chamber. With the aim of investigating the detailed evolution process of the self-assembled Au droplets, each growth was systematically carried out by varying the annealing temperatures (T a ) at 100°C, 250°C, 300°C, 350°C, 400°C, 450°C, 500, and 550°C, respectively. For the systematic growths, the substrate temperature (T s ) was ramped up to the target temperature at a ramp rate of 1.83°C/s under 1 × 10 −4 Torr by a computer-operated recipe, and after reaching each target, a dwell time of 450 s was equally given to the samples. After the termination of each growth, the T s was immediately quenched down to diminish the Ostwald ripening [30,31]. Following the fabrication, AFM was used for the characterization of surface morphologies, and XEI software was used for the data preparation and analysis of AFM top-view and side-view images and line profiles as well as the Fourier filter transform (FFT) power spectra. The FFT power spectrum represents the height information converted from the real spatial domain to the frequency domain, and thus, the horizontal (x) and vertical (y) information is converted by taking the reciprocal of the corresponding units of x and y from the AFM images; hence, the distribution of color patterns can present the distribution of frequent height with directionality.  Figure 2a,b,c,d along with the cross-sectional line profiles in Figure 2 (a-1) to (d-1), acquired from the white lines in Figure 2a, b,c,d. The insets in Figure 2 (a-2) to (d-2) show the FFT power spectra. In general, on GaAs (111)A from a relatively flat surface morphology in Figure 2a,b, with the increased T a , the surface morphologies were drastically changed and gradually developed into Au clusters in Figure 3c and wiggly Au nanostructures in Figure 2d. In more detail, after the Au deposition before annealing, the surface showed a quite smooth topography as clearly observed by the AFM image in Figure 2a, and the line profile in Figure 2 (a-1) and the corresponding FFT spectrum in Figure 2 (a-2) showed a quite broad round pattern due to the narrow random surface modulation. At the T a of 250°C, the diffusion of Au adatoms was induced as shown in Figure 2b, but the surface modulation was only slightly increased as evidenced by the line profile in Figure 2 (b-1). The FFT spectrum in Figure 2 (b-2) became smaller with a round pattern. With the increased thermal energy at 300°C, the diffusion of adatoms was further enhanced, and as a result, there was nucleation of tiny Au clusters with a slightly bumpy morphology as shown in Figure 2c and (c-1). Finally, at the T a of 350°C, as clearly seen with the AFM image in Figure 2d and the line profile in Figure 2 (d-2), a sharp transition from the Au clusters to the wiggly nanostructures occurred with a height modulation of approximately ±10 nm as clearly evidenced by the line profiles of Figure 2 (c-1) and (d-1). The FFT pattern size was further reduced with the increased height modulation and became a symmetric circle as there was no apparent directionality of Au nanostructures. The Au clusters and wiggly nanostructures can be formed based on the Volmer-Weber growth mode [32,33]. Given that the bonding energy among Au adatoms (E a ) is greater than that between Au adatoms and GaAs surface atoms (E i ), Au adatoms can be merged together to nucleate the Au clusters at a relatively lower T a , and the wiggly Au nanostructures can result at an increased T a . This transition of surface morphology associated with the nucleation of the Au clusters and wiggly nanostructures appears to be unique to GaAs. For example, on Si (111) neither this type of transition nor the Au clusters or the wiggly Au nanostructures were observed during the evolution of the self-assembled Au droplets while varying the T a between 50°C and 850°C [34], but very high density dome-shaped Au droplets were observed throughout the temperature range. In short, with the increased T a on GaAs (111)A, apparent transitions of surface morphologies at each T a were clearly observed and the height modulation was gradually enlarged as a function of T a ; a sharp transition was observed at 350°C with a surface modulation of approximately ±10 nm due to the increased diffusion of Au adatoms induced by the enhanced thermal energy.  Figure 3 shows the evolution of self-assembled Au droplets with further increased T a between 400°C and 550°C on GaAs (111)A. AFM top-view images in Figure 3a,b,c,d show the large areas of 3 × 3 μm 2 , and the insets of Figure 3 (a-1) to (d-1) are the enlarged areas of 1 × 1 μm 2 . The surface line profiles in Figure 3 (a-2) to (d-2), the FFT power spectra in Figure 3 (a-3) to (d-3), and the height distribution histograms (HDHs) in Figure 3 (a-4) to (d-4) are respectively presented. Figure 4 shows the summary plots of the average height (AH) in Figure 4a, the lateral diameter (LD) in Figure 4b, and the average density (AD) in Figure 4c of the self-assembled  Au droplets at each T a on various GaAs substrates. Table 1 summarizes the corresponding values. In general, between 400°C and 550°C, the self-assembled dome-shaped Au droplets were successfully fabricated as shown in Figure 3. Due to the enhanced diffusion of Au adatoms at increased thermal energy, given E a > E i , the wiggly Au nanostructures preferentially evolve into the dome-shaped Au droplets to minimize the surface energy [35]. In terms of the size and density evolution, as clearly shown in Figure 4a,b,c, the size including the AH and LD of the Au droplets was gradually increased, while the density was correspondingly decreased as a function of the T a on GaAs (111)A. In more detail, at an increased T a of 400°C, finally, the self-assembled Au droplets were fabricated and we can clearly observe the apparent transition from the wiggly Au nanostructures at 350°C to the dome-shaped Au droplets at 400°C. The AH was 23.4 nm, the LD was 128.6 nm, and the AD was 1.39 × 10 10 cm −2 as shown in Table 1. The HDH was approximately ±15 nm as shown in Figure 3 (a-4). At 450°C, the Au droplets grew larger in size and showed a lower density as shown in Figure 4. The AH was increased by × 1.09 and became 25.4 nm, and the LD was increased by × 1.04 and became 133.8 nm as shown in Table 1. The density was dropped by × 1.13 and became 1.23 × 10 10 cm −2 . Likewise, at 500°C, the size of the Au droplets was further increased, and the density was correspondingly decreased as shown in Figure 3c. The AH and LD were increased by × 1.14 and × 1.04 and became 28.9 and 138.5 nm, respectively, while the AD was decreased by × 1.04 and became 1.23 × 10 10 cm −2 . The HDH was now further extended with the increased size to over ±20 nm as shown in Figure 3 (c-4). Finally, with the 550°C annealing temperature, the Au droplets continually grew in size and the density was constantly decreased as shown in Figure 4. The AH and LD were increased by × 1.11 and × 1.04 and became 32.2 and 143.4 nm. Likewise, the AD was down by × 1.11 and became 9.9 × 10 9 cm −2 as shown in Table 1. The HDH in Figure 3 (d-4) now became clearly over ±20 nm wide along with the increased height of Au droplets. The self-assembled Au droplets on GaAs (111)A with the T a variation between 400°C and 550°C showed quite excellent uniformity as witnessed in the symmetric round FFT power spectra of Figure 3 (a-3) to (d-3) and showed an overall increased size with decreased density as a function of the T a . The size and density evolution induced by the variation of the T a can be simply explained with the following equation [36]. The diffusion length (l D ) can be expressed as

Results and discussion
where D is the surface diffusion coefficient and τ is the residence time of atoms. D can be written as D ∝ T sub where T sub is the substrate temperature, namely T a in this case. With the increased T a , the D proportionally increases and it results in an increased l D . With the increased l D , the density of the Au droplets can be decreased, given the stronger bonding energy between Au atoms (E a > E i ). In this thermodynamic equilibrium system, in order to keep the energy of the whole system in the lowest state, bigger droplets tend to absorb nearby adatoms to lower the surface energy, and thus, the size can grow larger and the density can be reduced until reaching the equilibrium. Thus, this type of size and density evolution was witnessed in Ga and In metal droplets [35,37,38] and nanostructures [39][40][41] on various semiconductor substrates. Figure 5 summarizes the evolution process of the selfassembled Au droplets on GaAs (110) induced by the variation of the T a between 250°C and 550°C, and similarly, Figures 6 and 7 show that on GaAs (100) and (111) B. In general, the evolution process of the Au droplets on GaAs (110), (100), and (111)B showed quite a similar behavior to that on GaAs (111)A in terms of the nucleation of Au clusters and wiggly nanostructures as shown in Figure 2 and the evolution of size and density as a function of the T a as summarized with the plots in Figure 4. For example, on GaAs (110) between 250°C and 350°C, the nucleation of Au clusters and wiggly Au nanostructures was clearly observed as shown in Figure 5b,c,d, and between 400°C and 550°C, the self-assembled dome-shaped Au droplets were successfully fabricated as shown in Figure 5e,f,g,h. The size of droplets on GaAs (110) was also constantly increased as a function the T a , while the density was correspondingly decreased as clearly shown in Figure 4. However, the size of Au droplets on GaAs (110) was slightly smaller than that on GaAa (111)A, putting the (110) line below the (111)A in Figure 4a,b, and as a result, based on the thermodynamic description, the density was slightly higher throughout the whole temperature range, marking the (110) line above the (111)A in Figure 4c. For example, at 400°C, the AH, LD, and AD were 22.6 nm, 122.5 nm, and 1.48 × 10 10 cm −2 , which are 3.42% and 4.47% smaller in size and 6.47% higher in density as compared to those on GaAs (111)A. Similarly, at 550°C, the size and density of droplets on (110) were 31.2 nm (AH), 141 nm (LD), and 1.07 × 10 10 cm −2 (AD), which are 3.11% smaller in AH and 1.67% smaller in LD and 8.08% higher in AD. In short, the self-assembled Au droplets on GaAs (110) clearly showed smaller size and correspondingly higher density as compared to those on GaAs (111)A throughout the T a range. In the meantime, on GaAs (100) and (111)B, the nucleation of Au clusters and wiggly nanostructures was also clearly observed between 250°C and 350°C as shown in Figures 6b,c,d and 7b,c,d, and the selfassembled Au droplets were also successfully fabricated between 400°C and 550°C as shown in Figure 6e,f,g,h and 7e, f,g,h. In the same way, on both GaAs (100) and (111)B, the size of the Au droplets was constantly increased as a function of T a and the density was correspondingly decreased. Depending on the surface index, there appeared a clear difference in size and density between the indices, and this trend constantly appeared throughout the T a range as clearly shown in Figure 4. the diffusion length (l D ) can be directly related to the T a and thus can affect the size and density of Au droplets. The l D can also be related to the root mean squared (RMS) surface roughness (R q ) caused by several factors such as the dangling bond density, atomic step density, and surface reconstruction [42][43][44][45][46]. If the R q value of one surface is relatively lower, the surface would possess longer l D , and it can result in a larger size and a lower density of Au droplets.  Figure 4. Similarly, we can relate the decreased size and the increased density of Au droplets on GaAs (100) as compared to those on (110) with the increased R q . However, the (111)B surface showed similar R q to the (111)A, and the results nevertheless showed the smallest size with the highest density. The type-A GaAs surface is characterized to be Ga-rich, while the type-B surface is Asrich [42]. The Ga-rich surface can possess a higher interface energy than the As-rich surface based on the atomistic modeling of the Au droplet-GaAs interface [47], and thus, the reduced diffusion of Au atoms on type-B surface can lead to a lower l D ; hence, the smaller size of droplets with a higher density can result. In short, on various GaAs surfaces, the evolution process of the self-assembled Au droplets was clearly demonstrated, and they showed quite similar behaviors in terms of the size and density evolution while keeping the difference between indices throughout the whole T a range. Figure 6 Temperature effect on the evolution of self-assembled Au droplets on GaAs (100). Au droplets were fabricated by annealing between 250°C and 550°C for 450 s with 2.5-nm Au deposition. The evolution process is presented with (a-h) the AFM top-view images of 1 × 1 μm 2 and the line profiles in (a-1) to (h-1) with the corresponding FFT power spectra in (a-2) to (h-2). AFM top-view images of 3 × 3 μm 2 are shown in (e-3) to (h-3), and the insets of AFM side-view images of 1 × 1 μm 2 are shown in (e-4) to (h-4).

Conclusions
The evolution of the self-assembled Au droplets has been successfully demonstrated on GaAs (111)A, (110), (100), and (111)B through the variation of annealing temperature throughout the feasible annealing temperature (T a ) range between 250°C to 550°C. The resulting Au nanostructures were systematically analyzed in terms of AFM images, cross-sectional line profiles, height distribution histograms, and FFT power spectra. The unique nucleation stages of the Au clusters and wiggly nanostructures were observed on various GaAs surfaces at the T a range between 250°C and 350°C, and the selfassembled dome-shaped Au droplets with excellent uniformity were successfully fabricated between 400°C and 550°C. The average height and lateral diameter of the Au droplets were gradually increased with the increased T a , and the average density was correspondingly decreased at each T a point. The nucleation and the formation of Au droplets were described based on the Volmer-Weber growth mode, namely E a > E i . The evolution of the size and density of Au droplets was described in terms of the l D of Au adatoms in relation with the thermal dynamic equilibrium along with the T a . In addition, an apparent distinction in the size and density of Au droplets between various GaAs indices was clearly observed, and it was maintained throughout the T a range GaAs (111)A > (110) > (100) > (111)B in size and vice versa in diameter, and the trend was described in relation between the R q and l D . This study can find applications in the nanowire fabrications on various GaAs surfaces.