In the last two decades, a number of semiconductor quantum and nanostructures (QNSs) by the strain-driven self-assembly based on Stranski-Krastanow (S-K) growth 1 have been demonstrated in the field of epitaxial growth using molecular beam epitaxy (MBE). As a result, various device applications have been demonstrated such as lasers, detectors, sensors, photovoltaic cells, light-emitting diodes, and solid-state quantum computation 2 3 4 5 6 7 . Meanwhile, droplet epitaxy (D-E) proposed by Koguchi et al. in 1991 8 has been relatively recently gaining increased interests due to its advantages over the conventional S-K growth approach for the fabrication of low-dimensional epitaxial semiconductor QNSs 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 . While the strain induced by the lattice mismatch is required in the S-K approach, it is not essential in the D-E approach for the fabrication of epitaxial QNSs. As a result, the selection of material system for QNSs by D-E approach is highly elastic and thus, a variety of unseen configurations of epitaxial QNSs have been demonstrated by D-E approach 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 . In addition, not only D-E approach can be used for lattice matched systems but also can be applied in the lattice mismatched systems. Quantum dots (QDs) and quantum rings are the most commonly studied epitaxial QNSs 9 10 11 12 13 14 . QD molecules 15 16 17 18 19 , low-density QDs 20 , ensembles of quantum ring geometry and droplet 21 , and various nanostructure complexes 22 23 have been demonstrated by the D-E approach. In addition, nanohole drilling and local etching effect 24 25 26 , selective etching using droplet as a mask 27 28 , various configurations of In nanocrystals 29 30 , running droplets 31 32 33 , and Ga-triggered oxide desorption 34 35 are only a few examples of D-E applications.

The fabrication of epitaxial QNSs is inherently dependent on the size, shape, and density of initial liquid phase metal droplets (MDs) and consequently, the control of the density and size of MDs becomes an essential research focus. The control of droplets on planar substrates has been somewhat widely studied 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 36 37 ; however, the fabrication of MDs on patterned surfaces lacks its investigation. This very naturally puts the control of MDs on patterned substrate as an attractive and essential research topic. In this paper, therefore, in extension of our previous results 38 39 , we extend the results of the sharp contrast of the size and density of Ga MDs on photo-lithographically patterned GaAs (100) by D-E approach using MBE. As evidenced by 3-D atomic force microscope (AFM) and high-resolution scanning electron microscope (SEM), the sharp contrast of the size and density of Ga MDs is clearly observed, showing an order magnitude higher density on the trench area (the etched area). Conversely, the size is much larger on strip top area (the un-etched area). By systematically varying the monolayer (ML) coverage, we demonstrate the control of size and density of Ga MDs on patterned GaAs (100) surface. The atomic surface roughness is around six times higher on the trench area (etched area) based on the cross-sectional line profile and root mean square (RMS) roughness analysis. The sharp contrast of size and density of Ga MDs is discussed in terms of surface adatom diffusion.

Figure  2 shows the sharp contrast of the density and size of Ga MDs at the interface between trench and strip top areas by the SEM images. The Ga MDs were fabricated with 20 ML at the surface temperature (T _sub) of 400°C. Figure  2 (b) is a cutout from the Figure  2 (a) and similarly, Figure  2 (c) is from Figure  2 (b). With an enlarged view of Figure  2 (c) at the interface between etched and un-etched areas, the sharp contrast in size and density is clearly observed between the strip top and trench areas. In Figure  2, (d) and (f) are further enlarged images of trench areas and in the same way in Figure  2, (e) and (g) are from strip top areas. By comparing the strip top and trench areas, the density of Ga MDs is relatively higher and the size is much smaller on the trench area. Meanwhile, the density of MDs is much lower and the size is much larger on the strip top area. As the image size of Figure  2 (f) is almost twice as large as Figure  2 (g), the size of MDs on strip top area in Figure  2 (g) is indeed much larger. Figure  3 shows EDS analysis of Ga MD samples with 20 ML deposition on both strip top area in Figure  3a and trench area in Figure  3b. The EDS analysis confirmed the presence of elemental signal of Ga and As and the higher Ga peaks as expected. The SEM insets and EDS mappings show good matching and the MDs are indeed consisted of Ga as clearly shown in Figure  3 (a-2) and (b-2).

A systematic variation of Ga ML deposition on strip-patterned GaAs (100) is demonstrated and shown in Figures  4 and 5; the summary plots of density, diameter, and height are shown in Figure  6. Figure  4 shows 2-D flat AFM views of Ga MD formation on the strip and trench areas with 20 ML in Figure  4a,b and with 10 ML in Figure  4c,d and 5 ML in Figure  4e,f. For the side-view perspective, Figure  5 shows the 3-D side AFM views of Ga MDs similarly with 20, 10, and 5 ML. With 5-ML deposition, the average density was 2.8 × 10⁹ cm⁻² on trench area, while it was 3.8 × 10⁸ cm⁻² on the strip area. There was about an order of magnitude difference between the strip and trench areas. With an increase of ML to 10, the density was increased to 4.2 × 10¹⁰ cm⁻² on the trench and to 4.9 × 10⁹ cm⁻² on strip. Also, there was about an order of difference between the two areas in the average density of Ga MDs. With a further increase of ML deposition to 20, the average density was slightly decreased to 3.68 × 10¹⁰ cm⁻² on the trench area and to 3.9 × 10⁹ cm⁻² on strip area. In previous experiments, an increase of the average MD density was observed when ML deposition was increased 36 37 . Also, slightly reduced density was observed depending on the growth conditions, i.e., duration, G _rate, and T _sub. Here the T _sub was fixed at 400°C and the G _rate was also fixed at 0.5 ML/s for all samples. Thus, the growth duration was increased with increased deposition amount. With 5-ML deposition, the MDs begun to nucleate, and the density and size were increased when ML deposition was increased to 10, reaching the peak density. With a further increase of ML to 20, which is equivalent to the duration of 40 s in this experiment, the MDs could have sufficient time to diffuse and merge. Once the merging of MDs occurs, bigger MDs tend to absorb the smaller ones and this process can result in a reduced density, which is known as Ostwald-ripening 42 43 . To minimize Ostwald-ripening, the duration has to be reduced but this requires a variation of the growth parameter, G _rate in this case. For the diameters of MDs, the average diameters were larger on strip top areas as clearly seen in Figure  6b as well as in the AFM images of Figures  4 and 5. Both the strip and trench pattern show increased average diameters when ML was increased. At 5 ML on strip, the diameter was 40 nm and increased to 63 nm with 10 ML and to 105 nm with 20 ML. On the trench areas, the average diameters of Ga MDs were 38.2 nm with 5 ML, 60 nm with 10 ML, and 86 nm with 20 ML. As the ML deposition was increased, the gap between the strip top and trench areas became larger perhaps due to Ostwald-ripening as discussed. The increased diameter of Ga MDs is a common trend with increase in deposition amount 36 37 . Now, for the average height of Ga MDs as seen in Figure  6c, on strip top areas, it showed a constant increase. An increased height of MDs is also an acceptable result when ML deposition is increased in conditions of atomically smooth surfaces. However, the height of MDs on trench areas kept almost the same regardless of the ML variation in this experiment. This indicates that the amount of deposition was dedicated either to the expansion of diameter or to the increase of density if there was no intermixing or desorption involved in the process 36 37 . Considering the T _sub of MD fabrication, we could exclude the intermixing and desorption to some degree. The diameter of Ga MDs in Figure  6b does not seem to be unusual, indicating the blue line stays below the black. The density of MDs on the trench area (blue line in Figure  6a) shows that the increased deposition was mostly used for the increase of density; the blue line stays above black. Also, this behavior can indicate that the surface is not atomically smooth on the trench area.

Figure  7 shows the cross-sectional line profiles (CLPs) of bare GaAs (100) on strip area in Figure  7a and trench area in Figure  7b before Ga MD fabrication. Figure  7c is the CLP on the strip area and likewise, Figure  7d is on trench area shown as white lines in Figure  7a, b. The lengths of CLPs are 5 μm (x-axes on the graphs), and height was set at 10 nm for a straightforward comparison. As clearly seen in CLPs, the trench area is much rougher, confirming the previous speculation based on MD size analyses. The strip area showed an RMS roughness of 0.39, while the trench area was 2.26 which indicates that the trench area is approximately 5.8 times rougher. This large difference on the atomic surface roughness could be the major cause for the sharp contrast on the size and density of Ga MDs. A smoother surface can indicate a longer diffusion length and vice versa. When the diffusion length is longer, we generally observe lower density and larger size of MDs, for example, Ga and In MDs 36 37 . We can easily observe the effect of diffusion length when T _sub is increased and when other conditions were kept the same, as a higher T _sub indicates a longer diffusion length. For example, the MDs which are fabricated at 500°C as compared to 400°C should have larger dimensions and thus lower density and vice versa. In this experiment, the density is nearly an order of magnitude higher on strip areas almost constantly for 5, 10, and 20 ML. Also, the average diameters are larger on strip patterns as the surface is much smoother.

In conclusion, the sharp contrast of the size and density of Ga MDs on photo-lithographically patterned GaAs (100) was demonstrated and clearly observed by SEM and AFM. The EDS analysis confirmed that the MDs were consisted of Ga atoms. Also a systematic control of size and density was demonstrated by ML variation, and the behavior was discussed with atomic surface roughness, diffusion length, and surface diffusion. Ga MDs were fabricated by solid-source MBE, and the density of MDs was generally higher on the trench areas, and the size was larger on strip tops due to the approximately 5.8 × smoother surface morphology.

The authors declare that they have no competing interests.

JL, YH, SK participated in the experiment design and carried out the experiments. ML, MS, SS, EK JL participated in the analysis of data. GS, JL designed the experiments and testing methods. ML, JL carried out writing. All authors helped in drafting and read and approved the final manuscript.