Predictive patterning via solid-state dewetting of transferred single-crystal films

Domain: biology
Published: 2026-03-28
Editorial outcome: minor_revision

Abstract
Designing and exploiting the dewetting of single-crystal films to create specific patterns for fabricating functional structures requires improved predictability and extensibility. In this study, we demonstrate that templated solid-state dewetting of single-crystal films can be guided to form regular patterns on arbitrary surfaces. This is achieved by adopting multiscale calculation schemes and implementing the dewetting results of single-crystal Pd(100) films transferred onto amorphous SiO2 substrates. The anisotropies of Pd surface energy and gas adsorption strength lead to <001> and <011> in-plane facets, favoring the latter as oxygen adsorption increases or the hydrogen flow rate is sufficiently high. This leads to anisotropic dewetting patterns whose geometric characteristics depend significantly on initial crystallographic alignment and annealing ambient. A combination of computational and experimental methods is used to design and guide dewetting to create electrode patterns with submicron channels for thin-film transistors, demonstrating their feasibility for fabricating functional structures on various substrates.

Introduction
Solid-state dewetting of single-crystal films occurs through the nucleation and growth of holes whose shapes are consistent with the crystallographic symmetries of the film surfaces, leading to morphologies with highly regular characteristics1-5. This has motivated research efforts to exploit the morphological evolution as a novel patterning process for creating regular structures. In most of these studies, the films were lithographically pre-patterned to apply geometric confinement to their crystallographically constrained morphological evolution, resulting in substantially enhanced regularity of the resulting structures6-10. The regular structures have sub-lithographic feature sizes and geometries with increased complexity owing to the various morphological instabilities involved in their formation and their dependence on the surface energy anisotropy of the film material. This renders the patterning process applicable to fabricating functional structures that cannot be achieved via conventional dewetting processes.

The potential of the dewetting process as a patterning method has not been sufficiently realized, for two main reasons. First, the choice of substrate is highly limited because the dewetting process requires crystallographic commensurability and chemical inertness between the film and the substrate materials, which are necessary for epitaxial growth and high-temperature annealing, respectively. For example, only single-crystal oxide substrates, such as MgO and Al2O3, have been used in studies on the dewetting of single-crystal metal films, limiting the applications of dewetted single-crystal metallic structures6,11,12. Furthermore, such single-crystal substrates are expensive, and their use for large-area patterning is not affordable. Second, despite significant progress, up-to-date reported simulation methods face challenges in precisely guiding the process conditions for creating the desired patterns through the dewetting of single-crystal films11-15. Simulation results based on a kinetic Monte Carlo (KMC) model captured the anisotropic nature of dewetting morphologies15-17; however, all KMC simulation parameters were empirically determined, and no theoretical framework was included to account for the chemical states of the film surfaces. These limitations make them unfeasible to consider the dependence of surface energy anisotropy on film materials and gas adsorption, which have been experimentally demonstrated to be critical in metal films.

Here, we demonstrate that these two shortcomings can be substantially improved through the transfer of large-area epitaxial metal films grown on Si substrates to target substrates and multiscale calculations, including density functional theory (DFT), molecular dynamics (MD), and the KMC methods. We present the formation of various regular patterns via solid-state dewetting of Pd(100) films transferred and patterned on oxidized heavily doped Si wafers. The approach using film transfer removes the need for single-crystal oxide substrates and the associated process constraints that have limited the applicability of prior studies. The geometric characteristics of the dewetting patterns are shown to strongly depend on the initial crystallographic alignments of the patterns and the annealing ambient conditions. The morphological evolution during dewetting is well predicted using multiscale calculation schemes that adopted the surface energy anisotropy of the film materials and its changes with oxygen adsorption. The initial pattern layouts and annealing processes are designed according to the calculation results to form Pd line patterns on which Au films are lifted-off, leading to the formation of Au electrode patterns with submicron channels for back-gate indium gallium zinc oxide (IGZO) thin-film transistors (TFTs). These results demonstrate the feasibility of designing and optimizing dewetting processes to create specific functional structures on arbitrary surfaces.

Results
Ambient-dependent dewetting behaviors of transferred Pd(100) films
Selective wet etching of the Cu layer in a Pd/Cu stack epitaxially grown on an Si(100) wafer leads to a floating Pd layer on the etchant, which can be transferred onto a target substrate (see the schematic in Fig. 1(a)). As shown in Fig. 1(b), Pd films were transferred and lithographically patterned over an area of a few cm2 on oxidized Si wafers. The X-ray diffraction (XRD) and selected-area electron diffraction (SAED) measurements shown in Figs. 1(c) and 1(d) indicate that the transferred films were nearly single-crystal Pd(100) films. The single crystallinity of the transferred films was further supported by the in-plane alignment of holes with <011> edges, which were formed after the thermal annealing (see Fig. 1(e)).

Figures 2(a) and 2(b) show the dewetting results of the patches lithographically patterned from the transferred Pd(100) films to be aligned along different crystallographic directions. These patches were annealed under two different annealing ambient conditions: 0.5 sccm H2 and 50 sccm Ar in Fig. 2(a); 2000 sccm Ar in Fig. 2(b). These two ambient conditions prevent extensive oxidation during the annealing. As shown in the figures, the retraction of the external edges and the growth of internal circular holes in the patches resulted in the formation of ring patterns when the initial edge orientations were parallel to particular directions that correspond to the <011> or <001> directions. In contrast, patches aligned along other directions dewetted to form an array of islands or nonuniform ring patterns. This is because the retracting and thickening edges are faceted parallel to the two directions in which they are crystallographically constrained to expose low-energy facets such as (111) and (100) along their surfaces. Edges and lines exposing low-energy facets are stable against Rayleigh–Plateau-type instability18,19, making ring patterns relatively stable6,7. An initial misalignment of patch edges from the specific directions leads to substantial width and thickness perturbation of the lines, resulting in the formation of particles via the Rayleigh–Plateau-type instability.

The annealing ambient conditions affected the in-plane orientation-dependent shapes of the dewetting patterns. As shown in Fig. 2(a), patches whose external edges were initially aligned along the <001> or <011> directions evolved into uniform ring patterns during the dewetting in 0.5 sccm H2 and 50 sccm Ar. The squareness of the ring patterns is slightly greater when the initial alignment direction is <001>. In 2000 sccm Ar with no H2, only the patches whose external edges were initially aligned along the <011> directions dewetted to form uniform ring patterns (see Fig. S1 in the Supplementary Information for enlarged images). Uniform ring patterns were observed when the external edge orientations corresponded to the orientations of the in-plane facets formed during the growth of the internal holes. Because the in-plane facet orientations depend on the annealing ambient conditions, the particular orientations where uniform ring patterns form differ under the two different ambient conditions, as shown in Figs. 2(a) and 2(b).

Annealing ambient-dependent in-plane facet orientations were clearly observed in the shapes of the holes formed during the dewetting of continuous Pd(100) films. Figures 2(c) and 2(d) show the holes formed during the dewetting of the continuous Pd(100) films under various annealing ambient conditions. The in-plane facets of the holes were aligned along the <011> directions in 2000 sccm Ar, whereas primary <001> and secondary <011> in-plane facets were observed in 0.5 sccm H2 and 50 sccm Ar. This is consistent with the dewetting results shown in Figs. 2(a) and 2(b). The morphological details of the dewetting patterns varied with the initial patch geometry, which was affected by process fluctuations during photolithography or wet etching (see Fig. S2 in the Supplementary Information). Nevertheless, the key differences in the anisotropic dewetting behaviors between the two annealing ambient conditions were consistently observed across patches with different initial geometries.

Effects of Pd surface energy anisotropy and oxygen adsorption
The effects of annealing ambient conditions on dewetting morphologies, including the shapes of dewetting patterns and growing holes, have been attributed to gas adsorption-induced changes in the surface energy anisotropy and faceting of metals20. The in-plane facet orientations in the holes remained <011> throughout the reduction of Ar flow rate from 2000 sccm down to 10 sccm, at which the oxidation-induced change of the surface was clearly observed by optical microscopy (OM), as shown in Fig. 2(c). This change could occur because reducing the Ar flow rate increased the adsorption of ambient oxygen. Conversely, increasing the H2 flow rate to 0.5 sccm in 50 sccm Ar led to the formation of primary <001> in-plane facets, as described in the previous section. However, the relative lengths of these <001> facets gradually decreased with increasing H2 flow rates of 0.5, 1, 1.5, and 2 sccm (see Fig. S3 in the Supplementary Information) and nearly disappeared at higher flow rates (3 and 5 sccm). Hydrogen is consumed in reducing surface oxides under annealing conditions in which its absence leads to oxidized surfaces. Excess hydrogen after reduction can be adsorbed on the surface or absorbed into the surface region. Hence, the amounts of oxygen and hydrogen adsorbates could depend on the hydrogen flow rates, which might be associated with the change of in-plane facets by the H2 flow rate.

X-ray photoelectron spectroscopy (XPS) was performed to investigate the chemical states of the annealed Pd(100) film surfaces. Figures 2(e) and 2(f) show the Pd 3d spectra measured from the samples shown in Figs. 2(c) and 2(d). As shown in the figures, reducing the Ar flow rate in the absence of H2 increased the fractions of Pd2+ and Pdδ+ species, which have been attributed to oxidized Pd in previous studies21-23. In particular, the fraction of Pd2+, which is usually assigned as PdO22,23, increased significantly. In the overlapping O 1s–Pd 3p region (Fig. 2(g)), the peak intensity near 530 eV, which corresponds to oxygen adsorbates and surface oxides, also increased as the Ar flow rate decreased. This observation supports the assignment of the high-binding-energy components in the Pd 3d spectra to oxidized Pd23,24.

Conversely, introducing 0.5 sccm H2 into the 50 sccm Ar stream decreased the fractions of Pd2+ (PdO) and Pdδ+ species while increasing the metallic Pd component (Fig. 2(f)), confirming the reducing effect of hydrogen. As shown earlier, the primary in-plane facet orientation was <011> in the absence of H2 and changed to <001> at 0.5 sccm H2 and 50 sccm Ar. The Pdδ+ peaks were shifted approximately by 0.5–0.6 eV to higher binding energies relative to the metallic Pd peaks. These shifts correspond to the reported values for oxygen-adsorption-induced shifts rather than those induced by hydrogen adsorption or absorption23,24. Hence, the abovementioned changes in the fraction of Pd2+ and Pdδ+ in the Pd 3d spectra suggest that oxygen adsorption promotes the formation of <011> in-plane facets.

Adventitious carbon and sulfur were also detected in most Pd films used in this study (see Fig. S4 in the Supplementary Information for representative spectra). No correlation was found between these contaminants and the specific hole morphologies, but sulfur can also shift the Pd 3d spectra to higher binding energies25, which may contribute to an increase in the Pdδ+ peak intensity. Hence, the Pd2+ peaks, whose intensities were shown to correlate with those of surface oxide in the O 1s spectra, are more reliable indicators of the extent of oxidation.

The decrease in the fraction of Pd2+ and Pdδ+ species were also observed in films annealed at higher H2 flow rates as expected, as shown in Fig. 2(f), indicating the role of H2 in reducing the oxidized species. Although the results shown in Figs. 2(c), 2(d), and S3 show that hydrogen has a critical effect on the reemergence of the dominant <011> in-plane facets, no distinct feature was consistently found in the XPS spectra of films annealed at higher H2 flow rates. This may be due to the limitation of ex-situ measurements, considering the films were exposed to ambient air prior to the measurements. In-situ surface cleaning and measurements under precisely controlled partial pressures of hydrogen will be required to clarify the role of H2 in the dewetting process.

As mentioned previously, the formation of low-index facets along the film surfaces plays an important role in determining the anisotropic shapes of the dewetting patterns and holes. Figure 3 shows the cross-sectional surface morphologies of the holes and patterns corresponding to those presented in Fig. 2. In all cases, rim morphologies were observed around the holes, indicating that the dewetting process was predominantly governed by surface diffusion. In the case of patterns formed at 2000 sccm Ar, longer dewetting line patterns were used to observe facet morphologies along the <001> directions (see the scanning electron micrograph inset of Fig. 3(b)), because uniform ring patterns did not form in those directions. As shown in Figs. 3(a–d), the surfaces of the patterns aligned along the <011> and <001> directions have wider {111} and {100} facets, respectively, when annealed in 2000 sccm Ar than in 0.5 sccm H2 and 50 sccm Ar. The morphological evolution of faceted surfaces can be modeled to be driven by a gradient in a weighted curvature, which is defined as follows: \kappa = \sigma\Lambda/L, where \Lambda represents the facet length in the equilibrium crystal shape, L represents the actual facet length, and \sigma is the convexity factor (see Fig. S5 in the Supplementary Information)26. The wide facets indicate that surface energies at those orientations have prominent minima, implying that the \Lambda values are large therein. The weighted curvature is maintained as very large, where the surface normal corresponds to those orientations until a wide facet forms and the value of L becomes sufficiently large. Hence, the formation of a wide facet can significantly slow the surface diffusion flux from the edge front to the top film surface when the position of the facet is between the two locations, as in the case of the {111} facets in the patterns aligned along the <011> directions. When the facet orientation corresponds to the edge front, as in the case of the {100} facets in the patterns aligned along the <001> directions, a high weighted curvature at the edge front can enhance the surface diffusion flux. This leads to slow edge retraction in the <011> directions and consequently causes the internal holes to be bounded by <011> in-plane facets during their growth. This explains the difference between the two annealing ambient conditions in terms of the direction in which uniform ring patterns form. The above description based on the weighted curvature can be related to the Winterbottom construction, which generalizes the classical Wulff construction to supported films by incorporating the film–substrate interfacial energy. Within this framework, the dewetting process can be interpreted as a morphological evolution toward the equilibrium shape defined by the Winterbottom construction. This evolution is driven by gradients in the weighted curvature defined as the surface divergence of the Cahn-Hoffman vector14,27.

The cross-sectional surfaces along the thickened edges of the holes also exhibit facet morphologies consistent with those observed in the dewetting patterns. As shown in Figs. 3(e–h), wide {111} or {211} facets were also formed along the thickened edges of the holes bound by <011> in-plane facets. In the case of holes bound by <001> in-plane facets, which were only observed under one annealing ambient condition (0.5 sccm H2 and 50 sccm Ar), {110} facets were observed along the thickened edges. The contrasts shown in the scanning electron microscopy (SEM) images of the films annealed in H2 likely arose from hydrogen-induced surface roughening due to the increased homologous temperature28. Nevertheless, Pd SAED patterns shown in Fig. 3 were the same across different regions within each cross-section and exhibited no discernible changes with annealing conditions, suggesting that Si was not incorporated into the Pd films. The EDS line scan results shown in Fig. S6 also indicate that no Si incorporation occurred in the Pd patterns. This supports the idea that the aforementioned effects of the annealing ambient conditions on facet formation originated from the surface energy anisotropy of Pd.

Multiscale KMC simulations
The numerical calculation schemes used in this study were designed to capture the aforementioned effects of surface energy anisotropy and gas adsorption on dewetting morphologies by combining the KMC, MD, and DFT methods (see Fig. 4(a)). Figures 4(b, c) show the KMC simulation results corresponding to the dewetting patterns in Figs. 2(a, b). The KMC simulation results in Fig. 4(b) were obtained by setting the values of \zeta, kBT, and ES (= E*) based on the results of MD simulations for clean Pd, amorphous SiO2, and Pd/SiO2 slabs described in Figs. S7 and S8, where J represents the nearest-neighbor (NN) bond energy, kBT represents the thermal energy, E* is the energy difference between film-film and film-substrate NN bonds, and \zeta is the ratio of the next NN (NNN) bond energy to the NN bond energy15,29. The NN bond energy J was obtained by calculating the formation energy of two kink pairs using the conjugate gradient minimization method (see Note S1 and Fig. S7 in the Supplementary Information). The canonical ensemble MD simulations provided the values of the surface energies of film (EFV(film orientation)) and the film–substrate adhesion energy (EA) at a given temperature, which were used for evaluating \zeta and E* (see the Methods section and Figs. S7–S9 for details regarding the MD simulation conditions and procedures). The NVT MD simulation results are presented in Fig. 4(d). The values of \zeta and E* were calculated to be 2.422 and 0.85, respectively. The initial film thicknesses were set to three grid units, and the lateral pattern sizes were set such that the lateral size-to-thickness ratios were the same as the experimental values. The temperature T was first multiplied by a correction factor determined using the calculation results of \zeta-dependent roughening temperatures, which are based on the statistical mechanics model for step formation. Subsequently, an additional fitting factor c was applied to achieve simulation morphologies that are consistent with experimental results (see the Methods section and Note S1 in the Supplementary Information for details). These input parameters determine the hopping rates of the surface atoms in the KMC simulation, as explained in the Methods section.

As shown in Fig. 4(b), the thin-film patches aligned along the <011> or <001> directions dewet to form uniform ring patterns in the simulation results with \zeta of 2.422. These results are consistent with the experimental results obtained in 0.5 sccm H2 and 50 sccm Ar. As mentioned previously, uniform ring patterns were observed only in the <011> directions when the films were annealed under 2000 sccm Ar. This was associated with the formation of wider {111} facets along the surfaces of the lines aligned along the <011> directions. The formation of wider {111} facets indicates lower energies of the {111} surfaces. In the KMC algorithm, the change in the surface energy anisotropy can be implemented by increasing \zeta. The KMC simulation results became more consistent with the experimental results obtained in 2000 sccm Ar as the value of \zeta was increased to 7.5, as shown in Fig. 4(c). The increased value corresponds to a surface energy ratio of 1.119 between (100) and (111) surfaces, which is approximately 6% greater than the value at \zeta = 2.422. The simulation temperatures were increased and decreased from the values calculated using the statistical mechanics model by multiplying fitting factors greater and smaller than unity for \zeta = 2.422 and \zeta = 7.5, respectively, to achieve consistent agreement with experimental morphologies. Simulation results without the fitting factor are presented in Fig. S10 of the Supplementary Information. Morphologies obtained without applying the fitting factor were also qualitatively consistent with experimental results regarding the effects of orientation and \zeta on the line stability. However, key morphological characteristics, including the shape and connectivity of the rings and the number of particles, were not accurately reproduced. The morphologies of holes and thickened rims shown in Figs. 2(c), 2(d), 3(e), and 3(g) were also more accurately reproduced in the simulations when the values of \zeta and c were set as mentioned above (see Fig. S11 in the Supplementary Information).

The two different values of \zeta are associated with annealing in 0.5 sccm H2/50 sccm Ar and in 2000 sccm Ar, which can lead to hydrogen and oxygen incorporation, respectively. The value of c was set to be smaller than the unity in the case of \zeta = 7.5, indicating that the reduced temperature was higher in the simulations with no fitting factor. This likely arises because the experimental temperature was reduced by the roughening temperature at \zeta = 0.266 where the effect of oxygen adsorption was not considered. Oxygen adsorption could influence the roughening temperature of Pd(100), as suggested by the adsorption energetics examined in the following section. A more accurate estimation of roughening temperatures for oxygen-adsorbed Pd(100) surfaces may bring the value of c closer to unity.

It has been shown that a small amount of hydrogen absorption significantly increases the vacancy concentration30, which implies reduced cohesive energy that would lower the roughening temperature. Compressive stress exerted on the Pd films can also lower the roughening temperature31 while its relaxation is not a primary driving force for the dewetting process (see Note S2 in the Supplementary Information). Including these effects in the roughening temperature estimation might decrease the value of c. The explicit consideration of these effects in estimating the roughening temperature will be investigated in future studies.

It is also noteworthy that key differences between the simulation results in Figs. 4(b) and 4(c) did not originate from the different initial patch shapes. In the simulations, the greater ring stabilities in the directions adjacent to the <011> directions than those adjacent to the <001> directions were only observed in Fig. 4(c), where uniform rings formed only when initial patches were aligned along the <011> directions. These trends remain unchanged when the initial patches in Figs. 4(b) and 4(c) were swapped. (see Figs. S12(a) and 12(b) in the Supplementary Information). The results in Fig. S12(c) closely reproduced the experimental results in the left panel of Fig. S2(a), indicating that the particle formation observed in all directions can also be predicted and explained by the same underlying mechanisms driving the pattern formation in Figs. 2(a) and 2(b).

DFT-calculated adsorption energetics and their implications for dewetting
The results shown in Figs. 2 and 3 suggest that the extent of oxidation was greater on the film surfaces along which wider {111} facets were observed. This indicates that oxygen chemisorption could reduce the relative surface energies in the {111} orientations. Gas adsorption changes surface energy anisotropy because the adsorbate binding energy (BE) depends on the crystallographic orientation of the surface. Stronger binding on one surface leads to a greater decrease in the surface energy of the corresponding surface. To investigate whether this effect of gas adsorption is associated with the dewetting results shown in Figs. 2 and 3, we calculated the BEs of chemisorbed O and H adsorbates (O* and H*) on Pd slabs using spin-polarized DFT theory and analyzed their dependence on surface orientations (details regarding the DFT calculations are presented in the Methods section). As shown in Fig. 4(e), the BEs of O* and H* were calculated to be stronger on (111) than on others. They were stronger on (211), which is an intermediate inclined plane along the <011> edges, than on (110) and (210), which are analogous inclined planes along the <001> edges. This stronger binding on (111) and (211) lowers the relative energies of the surfaces compared with those of the other surfaces. The resulting surface energy anisotropy corresponds to a greater value of \zeta in the KMC model, which renders holes bound by <011> edges and leads to the formation of uniform ring patterns only in the <011> directions, as shown in Fig. 4(c).

As mentioned in the Methods section, the effects of adsorption on the surface energies were characterized by adding a correction term, given by the product of the BEs and the number of adsorbates per unit area to the surface energies obtained from MD. O and H surface coverages at 800 ℃ were estimated using Langmuir adsorption theory and assuming dissociative chemisorption (see Methods section for details). The surface-energy ratio between the (100) and (111) surfaces was calculated to be ~1.119, which corresponds to \zeta = 7.5, as the O coverages were ~0.0227 and ~0.0561 ML on (100) and (111) surfaces at an oxygen partial pressure of ~1.10 \times 10^{-3} atm at 800 ℃, respectively (see Note S3, Fig. S13, and Fig. S14 in the Supplementary Information for details).

As shown in Figs. 3(a), 3(c), 3(e) and 3(f), the (011) facet abuts the (111) facet during the retraction of the <011> edge, indicating that the relative widths of the {111} facets increase as the energy ratio of the (111) surface to the (110) surface decreases. This trend is consistent with the DFT-calculated O* BEs on the (111) and (110) surfaces. Such orientation-dependent binding is likely to cause oxygen chemisorption to significantly decrease the surface energy in the {111} orientations, leading to the formation of wide {111} facets and lagging edge retraction in the <011> directions.

Using an upper-bound estimate based on an Ar–H2 ambient, increasing the H2 flow rate to 3 and 5 sccm in 50 sccm Ar corresponds to partial pressures of ~0.0566 and ~0.0909 atm, which yield \zeta values of ~2.668 and ~2.798, respectively. These significantly smaller increases in \zeta compared to the O adsorption case are due to weaker BEs of H* and the resulting lower coverages. This suggests that the effect of hydrogen on the reemergence of the dominant <011> in-plane facets cannot be explained solely by H adsorption, although the less pronounced <011> facets observed under H2-containing ambient conditions are qualitatively consistent with the calculation results (see Fig. S15).

As shown in Fig. 4(e), the BE of O* is stronger on Pd(100) than on Pd(210) and Pd(110), meaning that the roughening temperature for Pd(100) could increase by oxygen adsorption. Such stabilization of Pd(100) also provides a plausible mechanism for the upward shift of the roughening temperature considered in the preceding discussion of the scaling factor c.

The BEs of S* and C* were calculated to be the weakest on (111) surfaces, as shown in Fig. S16. This further supports that the annealing-ambient dependent hole shapes are not associated with S or C adsorbates.

Quantitative comparison between experiments and KMC simulations
Figure 5 shows the experimental and simulation results for the dewetting of cross patches with internal circular holes. Annealing was performed in 2000 sccm Ar at 800 ℃. The value of \zeta in the KMC simulations was set to 7.5, which led to simulation results that were the most consistent with experimental results for the dewetting of square patches, as shown in Figs. 2(b) and 4(c). As shown in Fig. 5, these initial patches, having internal holes at specific positions and including both concave and convex corners, exhibit dewetting results with stronger dependence on their initial crystallographic alignments compared to those in Figs. 2(a) and 2(b). These results were also reproduced well by the KMC simulations. For example, the differences in the shape and width of the central ring and arms of the cross patterns between the <001> and <011> directions were consistently observed in the experimental and simulation results (see Fig. S17 in the Supplementary Information for more results).

Figure 6 shows the results of quantitative analyses evaluating the consistency between experimental and simulation results. As shown in Fig. 6(a), all feature sizes in the simulated cross pattern shown in Fig. 5(b) deviated by less than 10% from the corresponding feature sizes measured in the experimental pattern. Most features in the other simulated cross patterns also showed deviations below 10%, although some exceptions were observed. For example, in the cross patterns shown in Fig. 5(a), the widths of the arms and body lines were simulated to be significantly larger and smaller, respectively, than those in the experiment. This suggests that the anisotropic edge retraction and hole growth may not be quantitatively modeled solely by the surface energy anisotropy.

Figure 6(b) presents an analysis of ring patterns with different initial circular hole sizes (see Figs. 2(b), 4(c) and S18 for the complete sets of patterns). The numbers above each dewetting pattern indicate the rectangularities (R) in the interior region of the rings (see Fig. S19 for the details on the measurement). The rectangularities were significantly closer to unity for rings aligned in the <011> directions in both experimental and simulation patterns. The largest deviation was −6.14%, indicating a high quantitative consistency. The ring sizes and widths also deviated by less than 10% in all cases; the largest deviation was 8.33%, observed in the sizes of rings with the smallest initial hole and <011>-aligned external edges.

In the simulation results showing the largest deviations, which were observed in the cross pattern shown in Fig. 5(a), the edge retraction in the <001> directions was simulated to be significantly slower than in experiments. This led to noticeably wider arms in the simulation pattern. One possible approach to improving this quantitative deviation would be to include the effects of gas adsorption on the dynamic anisotropy. Figure 6(c) shows DFT calculation results for the vacancy formation energies on pristine (100) surfaces and those with an O adsorbate (see Fig. S20 in the Supplementary Information for the corresponding results for H, S, and C adsorbates). The vacancy formation energies were significantly lowered by oxygen adsorption. This lowering can render the exchange surface self-diffusion mechanism more favorable because the transition state in the exchange mechanism involves a vacancy beneath a dimer. The formation of a vacancy is not required in the hopping mechanism, which is known to dominate on the (100) surfaces of 3d transition metals.32 The enhanced exchange diffusion mechanism can therefore lead to faster edge retraction in the <001> directions relative to in the <011> directions. Incorporating adsorbate-induced changes in diffusivity on various facets, including the (100) facets, into the KMC model will be needed to improve quantitative accuracy.

Formation of electrode patterns via lift-off guided by dewetting patterns
Notably, single-crystal metal patterns presented in this study were created on amorphous SiO2 surfaces by inducing dewetting processes on the transferred films. This clearly demonstrates that the surface energy anisotropy of film materials and gas adsorption, rather than the anisotropy of film–substrate interfacial energy that exists on single-crystal substrate surfaces, play critical roles in determining the geometric characteristics of regular dewetting patterns. Furthermore, their ability to create regular dewetting patterns on arbitrary surfaces extends their applicability. For example, metallic patterns formed on thermally oxidized heavily doped Si substrates can be used to create functional structures that constitute back-gated TFTs.

We designed initial film patches that could dewet to form line patterns separating the areas of the source, drain, and channel of a TFT; as such, their negative patterns could be used as electrodes. As shown previously, edges remained stable during retraction in the <001> and <011> directions. The retraction was shown to be faster in the <001> directions when the films were annealed in 2000 sccm Ar, which can be beneficial for reducing the line pattern width faster. Hence, the initial patches were designed to align along the <001> directions. Figure 7(a) shows the KMC simulation results for the designed patches. The simulation was performed using the same input parameters that were employed in the simulations presented in Fig. 5. The central line in the patch evolved to form uniform line patterns whose linewidths decreased over time to the sub-lithographic range. The external edges also retracted without introducing morphological instability. As shown in Fig. 7(b), corresponding patterns were experimentally obtained by the dewetting of the Pd patches in 2000 sccm Ar, consistent with the KMC predictions. The sub-lithographic features of the structures were attained by surface self-diffusion from the pattern edge to the top film surface, which increased their heights during dewetting and made them more suitable as liftoff masks. This process, which is schematically described in Fig. 7(c), allows the creation of functional sub-lithographic structures that are unattainable using conventional dewetting processes. Figure 7(d) shows Au source/drain electrodes with submicron channel lengths, which were formed by liftoff processes involving 50-nm-thick Au film deposition and selective etching of Pd. The formation of channels down to submicron scales demonstrates the controllability of our templated dewetting approach.

To demonstrate the functionality of the patterned electrodes, we fabricated a back-gate IGZO TFT as a proof-of-concept device. Figure 7(e) presents the output and transfer characteristics of this device. This proof-of-concept demonstration, incorporating a 30-nm-thick IGZO layer and using heavily doped p-type Si substrates with a 300-nm thermal SiO2 layer as back gates, exhibits clear n-type semiconducting behavior with an ON-OFF ratio of approximately 106 and current saturation33. Further optimization of materials and processing conditions is needed to enhance the device performance (additional data is available in Fig. S21 of the Supplementary Information). Nevertheless, these results demonstrate that the solid-state dewetting processes of pre-patterned single-crystal films can be predictably guided to create structures suitable for the fabrication of functional devices on amorphous substrates.

Methods
Thin-film growth and transfer
Epitaxial Pd(100) films with a thickness of 120 nm were deposited on 30-nm-thick Cu(100) buffer layers grown on epi-polished single-crystal Si(100) substrates via electron-beam (e-beam) evaporation. 99.997% pure Cu and 99.95% pure Pd pellets were used as evaporation sources. The Si substrates were dipped in a 25% HF solution before being introduced into the deposition chamber to strip surface oxides and passivate them via hydrogenation. The chamber was pumped down to a base pressure of high 10-7 Torr, and the films were deposited at room temperature and at a rate of 0.5 Å/s, which was measured using a quartz crystal sensor. The chamber pressure varied between 1 \times 10-6 and 4 \times 10-6 Torr, as measured by an ion gauge.

As mentioned in the main text, the Cu films were deposited not only to enable the epitaxial growth of the Pd films but also to form sacrificial layers selectively etched to separate the epitaxial Pd films for transfer. The as-deposited epitaxial stacks of Pd and Cu films were floated on Cu etchants, which consisted of 2 M ammonium persulfate (reagent grade 98%, Sigma–Aldrich) aqueous solutions, to selectively remove the Cu films. This process resulted in the Pd films floating on the surface of the etchant, while the Si wafer sank. The floating Pd films, after being transferred from the etchant solution to DI water for rinsing, were transferred onto heavily B-doped p-type Si(100) substrates with 300-nm-thick thermal oxide layers. The surfaces of the target substrates were pretreated with O2 plasma to render them hydrophilic, mitigate wrinkling, and facilitate uniform adhesion of the transferred Pd films. The O2 plasma treatment was performed for 30 min in an oxygen plasma cleaner (PDC-32G-2, Harrick Plasma) at a working pressure of 5.8 \times 10-1 Torr and a radiofrequency power of 18 W.

Pattern formation via dewetting and liftoff processes
The transferred Pd films were patterned using conventional photolithography, followed by the wet etching of the exposed areas. Wet etching was performed for 1 min in diluted aqua regia solutions comprising 3, 1, and 6 parts of 37% hydrochloric acid, 60%–62% nitric acid, and deionized (DI) water, respectively. The samples were soaked in acetone for 30 min and subsequently rinsed with isopropyl alcohol and DI water.

The patterned and as-transferred Pd films were thermally annealed in a quartz tube furnace at 800 ℃ for 90 min under various ambient conditions of Ar and H2 to induce solid-state dewetting and create regular patterns. The temperature inside the quartz tube and gas flow rate were measured and controlled using a K-type thermoprobe and mass flow controllers. The flow rates of H2 and Ar were varied to investigate the effects of the extent of gas chemisorption on dewetting.

50 nm-thick Au films were deposited on dewetted samples to create negative patterns via liftoff processes. The Au films were also deposited at room temperature via e-beam evaporation under the same conditions employed for the deposition of the Pd and Cu films. The Au films deposited on the Pd patterns were removed by soaking the samples in a wet etchant (Ni etch type 1, Transene Company, Inc.), which selectively etched Pd in approximately 2 min. Short ultrasonication is often needed to enhance the liftoff process.

Structural and compositional analyses of Pd films and patterns
The crystallinity of the Pd films was characterized using X-ray diffraction (XRD, Phillips X'Pert-PRO) and selective area electron diffraction (SAED) patterns acquired in a transmission electron microscope (TEM, JEOL JEM-2100F). The crystallinity of the dewetting patterns was examined by SAED. Energy-dispersive X-ray spectroscopy (EDS) line-scan data were obtained in the same TEM and analyzed using the Oxford Instruments AZtec software package. The sample preparation for cross-sectional transmission electron microscopy was performed using an FEI Nova NanoLab focused ion beam (FIB). The morphologies and shapes of dewetting patterns and holes were observed using TEM, scanning electron microscopy (SEM, FEI Nova NanoLab; Hitachi SU8010), and optical microscopy (OM, Olympus BX41M). XPS was performed using an Al K\alpha X-ray beam (photon energy of 1486.6 eV) in an ultrahigh vacuum spectrometer (Thermo Scientific K-Alpha) to analyze the surface chemical compositions of Pd films annealed under different ambient conditions. Peak deconvolution was performed in CasaXPS using mixed Gaussian–Lorentzian line shapes and a standard Shirley background.

Formation and electrical characterization of IGZO TFTs
IGZO TFTs were formed by depositing 30-nm-thick IGZO films onto the aforementioned Au electrode patterns via sputtering. The IGZO targets used in the sputtering were formed with an In2O3:Ga2O3:ZnO ratio of 1:1:1 (mol%). The films were deposited under a working pressure of 2 \times 10-3 Torr and a power of 60 W. The sputtering gas atmosphere was maintained at 9 sccm Ar and 1 sccm O2. Prior to electrical measurements, the TFTs were annealed at 350 ℃ for 1 h in air to remove structural defects in IGZO films without inducing crystallization33. Their current–voltage (I–V) characteristics were measured using a probe station (MS TECH, MST5000) and a semiconductor characterization system (Keithley, 4200-SCS) at a pressure of 5 \times 10-2 Torr.

DFT calculations
Spin-polarized DFT calculations were performed using the projector augmented-wave method with plane-wave basis sets and the Perdew–Burke–Ernzerhof exchange-correlation functional within the generalized gradient approximation35 as implemented in GPAW (version 19.8.1 and 22.1.0)36. The Atomic Simulation Environment (ASE, version 3.20.1 and 3.22.1) package37 was used to create model structures for the DFT calculations. The equilibrium lattice constant of Pd was calculated to be 3.946 Å with a plane-wave cutoff energy of 700 eV, an 8 \times 8 \times 8 Monkhorst–Pack k-point sampling38. Slab calculations of Pd(111), Pd(100), and Pd(110) were performed using 2 \times 2 \times 4 supercells, with the cutoff energy and k-point sampling set to 500 eV and 7 \times 7 \times 1, respectively, following the parameters used in our previous work39. 3 \times 2 \times 4 supercells were used for Pd(211), and four-layer slabs containing 16 Pd atoms for Pd(210). 30-Å-thick vacuum layers were inserted on each side of the slab in the surface normal direction, and a dipole-layer correction was included to prevent interaction between periodic images of the slabs along the surface normal directions. For the Pd bulk and slab calculations, a Fermi–Dirac smearing of 0.1 eV was employed. The self-consistent field convergence criteria were set to 10^{-4} eV and 10^{-6} for the total energy and electron density, respectively. The geometries of the molecules, clean slabs, and slabs with adsorbates were optimized using a quasi-Newton algorithm implemented in ASE until the maximum force was \le 0.02 eV/Å. The bottommost layer of the slab was fixed during the geometry optimization. The BEs of the oxygen and hydrogen adsorbates were calculated after geometry optimization as follows:
BE(O*) = E(Pd slab+O*) - E(Pd slab) - 0.5 \times E(O2) (1)
BE(H*) = E(Pd slab+H*) - E(Pd slab) - 0.5 \times E(H2) (2)
where O* and H* represent the adsorbates, and E represents the total energies of the systems indicated in parentheses.

The surface energies (Esurf+O) of the Pd planes with O adsorbates were approximated using the following equation:
Esurf+O = Esurf + BE(O*) \times (NO*/A) (3)
where Esurf represents the surface energies of the clean Pd planes calculated using MD, and NO* and A represent the number of O adsorbates and the area of the supercell, respectively. The O surface coverage was calculated as a function of oxygen partial pressure using Langmuir theory as follows:
\thetaO* = \sqrt{exp[(\muO2 - 2BE(O*))/kBT]} / (1 + \sqrt{exp[(\muO2 - 2BE(O*))/kBT]}) (4)
where \muO2 and BE(O*) represent the chemical potential of oxygen molecules and the BE of O*, and kB and T are the Boltzmann constant and temperature. The chemical potentials of gas molecules at 800 ℃ were estimated using the NIST–JANAF thermochemical data40, with the tabulated values interpolated and the pressure dependence treated assuming ideal-gas behavior. The calculated surface coverage was used to obtain the value of NO*/A. The same calculation was performed for H adsorbates. See Note S3 in the Supplementary Information for details.

DFT calculations for determining the formation energies of vacancy (Evacf) were performed using 4 \times 2 \times 4 Pd(100) slabs with the same parameters as for the adsorbate binding energies. Clean slabs and those with O, H, S and C adsorbates were used to investigate the effect of adsorption on the vacancy formation energy. The vacancy formation energies were calculated as follows:
Evacf = E(Pd slab+vacancy) + 0.25 \times E(bulk) - E(Pd slab) (5)
where E(bulk) is the total energy of a periodic supercell consisting of four atoms. The bulk energy was calculated using the same cutoff energy as in the slab calculations and a 12 \times 12 \times 12 k-point mesh.

MD simulations
MD simulations were performed using LAMMPS software (version 29 Sep 2021)41 to obtain the input parameters for the KMC simulations. The model structures for the MD simulations were built using the ASE package. For all ensemble simulations, periodic slabs were used, and their temperatures were equilibrated at 800 ℃ using Nose–Hoover thermostats. The timestep was always set to 1 fs, and each simulation was run for 100 ps, unless otherwise specified. Vacuum layers of 40–80 Å were inserted at the top and bottom of each slab to model the surfaces. Each ensemble simulation was performed 10 times with different seed numbers to obtain the mean values of the system properties.

The equilibrium lattice constant of Pd at 800 ℃ and 1 bar was calculated to be 3.943 Å by averaging the results of NPT ensemble simulations in which periodic 20 \times 20 \times 20 slabs of Pd(100) with no vacuum layer were relaxed for 100 ps. The formation energies of two kink pairs with one- and two-atom heights (Ekink1 and Ekink2) were calculated using conjugate gradient minimization method to obtain the values of J and \zeta in Pd. The structures were relaxed until energy convergence was achieved. As shown in Fig. S7, Pd(1811) slabs with two kink pairs were created by manually moving one or two ledge atoms at a fixed position along a step toward the front of another ledge atom. Formation energies were determined by subtracting the energy of the Pd(1811) slab from that of the Pd(1811) slab with two kink pairs.

To obtain the input parameters for KMC simulations, we ran canonical ensemble simulations of two types of slabs for each of Pd(100) and Pd(111), as shown in Fig. S8(a), the total energies of which are denoted as Eslab1 and Eslab2, respectively. The surface energies (EFV) of Pd were determined from the calculated total energies, as follows:
EFV = (Eslab2 - Eslab1) / (2A) (6)
where A represents the surface area of one side of the slab.

The total energies of the slabs of Pd(100), amorphous SiO2, and a stack of two (EPd, ESiO2, and EPd/SiO2) were calculated to obtain the Pd/SiO2 adhesion energies by running canonical ensemble simulations (see Fig. S8(b) for the structures used in the simulations). The amorphous structure of the SiO2 slab was obtained by running a two-step canonical ensemble simulation, in which a beta quartz slab was heated at 5000 K for 100 ps and subsequently cooled to 300 K in 200 ps. The values of EA were calculated using the total energy values of the three slabs, as follows:
EA = (EPd + ESiO2 - EPd/SiO2) / A (7)
where A represents the interfacial area. For the slab energy calculations used in Eqs. (6) and (7), the total energies were averaged over the final 10 ps of each simulation.

In all MD simulations, the Pd–Pd interactions were described using a 12-6 Lennard–Jones (LJ) potential with the coefficients reported by Heinz et al.42. The Si–O and O–O interactions were described by overlaying the Beest–Kramer–van Santen (BKS) potential43 with an 18-6 LJ potential and the coefficients reported by Yu et al.44. The cutoffs for the Buckingham and Coulomb interactions in the BKS potential were set to 5.5 Å and 10 Å, respectively. The long-range part of the Coulomb interaction was computed using the particle–particle particle–mesh method with a relative force accuracy of 1 \times 10-4. Pd–Si and Pd–O interactions were described using 12-6 LJ potentials. The \epsilon and \sigma parameters were derived using the geometric-mean mixing rule from the LJ parameters reported by Heinz et al.42 for Pd–Pd interactions and by Rappe et al.45 for Si–Si and O–O interactions. The cutoffs were set to 3\sigma, corresponding to 9.3 Å for Pd–Si and 8.4 Å for Pd–O.

KMC simulations
The hopping frequency is given by:
\nu = \nu0 exp(-(n+m\zeta)J + \delta z E* / kBT) (8)
where n and m are the numbers of the nearest and next-nearest neighbors (NN and NNN, respectively), \zeta is the ratio of NNN bond energy to NN bond energy, J represents the NN bond energy, kBT represents the thermal energy, E* is the energy difference between film-film and film-substrate NN bonds, and \delta z is the Kronecker delta. \delta z is 1 if z = 0; otherwise, it is 0. E* \approx -a2S where S and a are the spreading coefficient and the lattice parameter, respectively. The values of J, \zeta, and E* were calculated using the following equations:
EFV(100) / EFV(111) = (1+4\zeta) / {\sqrt{3}(1+2\zeta)} (9)
ES / {J(1+4\zeta)} = (2EFV(100) - EA) / 2EFV(100) (10)
J = Ekink1 / 2 (11)
where EFV(100) and EFV(111) represent the energies of the (100) and (111) surfaces, respectively15.

The kink, surface, and adhesion energies in the expressions were calculated, as described in the MD simulation section. The roughening temperature of Pd(100) was estimated by calculating the temperature at which the free energy of an atomic step vanishes in a statistical mechanics model for step formation in a simple cubic lattice. In the model, the step free energy \beta is given as
\beta = 1/(2a) [J(1+2\zeta) - 2kBT ln[1 + exp(J(2\zeta-1) / 4kBT) / sinh(J(1+2\zeta) / 4kBT)]] (12)
where a is the lattice constant, kB is Boltzmann constant, and T represents the temperature15,46.

The simulation temperature TKMC was set as follows:
TKMC = cTexp (Tr(\zeta) / Tr(\zeta = 0.266)) (13)
where Tr represents calculated roughening temperatures and Texp represents the experimental annealing temperature, which was 1073.15 K. Tr is a function of \zeta, and the value of \zeta entered in the denominator was determined to be 0.266 by calculating Ekink1 and Ekink2, as mentioned in the MD simulation section. A fitting factor c was applied to obtain KMC simulation results that were further consistent with the experimental results.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The experiments presented in this paper shed new basic insights into the dewetting of metal films. For example, they show very clearly how the initial orientation of the edges of the films affects dewetting mechanisms . They also demonstrate that edge orientation can dominate the effects of substrate epitaxy. I found the experimental design to be clever and novel. I thus have no hesitation in recommending publication in Nature Communications. I do, however, have some comments that the authors might want to address before publication:\n1) The annealing that induces dewetting is performed at 800˚C. At that temperature I would expect that surface concentrations of relatively weakly adsorbed species such as H (and maybe O) to be very low. The authors could estimate these concentrations from their DFT calculations of adsorption energies. Are the expected concentrations high enough to changes the orientation dependent surface energies enough to support their hypothesis about how surface energy affect dewetting?\n2) Small concentrations of adsorbed species can however have dramatic effects on surface dynamics (by changing defect formation energies) and thus Have the authors considered this possibility? Can they rule it out?\n3) The presentation of the XPS results were a bit incomplete. What were the surface concentrations of impurities such as C, S and O? Carbon is a very common contaminate in Pd and it would be important to know how much carbon was detected and how it varied with annealing recipe. (And as I mentioned above, trace amounts of O and S can have dramatic effects on surface diffusion.)", "reviewer_2": "This manuscript presents a study on the dewetting of patterned Pd films transferred onto amorphous SiO₂ substrates. Selected configurations are investigated to understand the impact of anisotropies under varying gas-adsorption conditions. A multiscale simulation framework is employed to reproduce experimental observations and provide insights into spontaneous patterning. While the overall process and techniques are well-established in the literature, some elements of novelty may lie in the proposed predictive multiscale framework, which is based on different simulations, and in the approach of transferring Pd films onto amorphous SiO2, potentially enabling new applications.\nThe main claim of this work, entering both experiments and simulations, is the achievement of \"predictive patterning\" via solid-state dewetting. From an experimental standpoint, this claim has been explored in earlier studies (e.g., Ye et al., Advanced Materials 23, 1567–1571 (2011)), which demonstrated deterministic outcomes in patterned solid-state dewetting. The simulations based on KMC models effectively incorporate parameters from original MD and DFT calculations, yet they still depend on some experimentally fitted parameters. This partially limits their a priori predictive capability beyond the qualitative level. Quantitative prediction with some fitting parameters basically meets the state of the art of such approaches (e.g., M. Trautmann et al., Appl. Phys. Lett. 110, 263105 (2017)) as well as other models. The demonstration related to the self-assembly of the thin-film transistor, as guided by simulation, appears somewhat limited. The simulated dynamics is relatively short, involve simple morphologies, and do not necessitate the use of KMC simulations (stable dewetting fronts, for example, could be anticipated through independent arguments or dewetting experiments). It is also noted that the formulation of hypotheses concerning the impact of different gas atmospheres appears reasonable but would benefit from clearer organization and presentation. These and other points are discussed in more detail below. Overall, the manuscript and the research presented therein provide some valuable insights into solid-state dewetting and thin film processing. However, I respectfully believe that, at its current stage, a stronger case is needed to justify the central claims for publication in Nature Communications.\nMore detailed aspects:\n- In the introduction, it is noted that one of the key reasons limiting the application of dewetting as a patterning method is the empirical nature of parameters used in KMC simulations, which is claimed to be addressed in this work. I agree that this is a major limitation in predicting the outcome of solid-state dewetting at a level that enables a priori design. Still, the approach presented here relies on an empirical fitting parameter (c) used to rescale T_KMC (see the Methods section). The authors transparently report that this is a fitting parameter used to match simulations with experiments, show the results obtained without this correction in the Supplementary Material (which indeed significantly differ from a quantitative point of view), and comment on the need for further research to clarify its origin and role. However, this is in contrast with the initial claim of having resolved the issue of reliance on empirical parameters for quantitative predictions.\n- In addition to the previous point, conclusions drawn on reported information show indeed they align with the state of the art and that the main claims are partially supported: i) At line 233, it is stated: \"Morphologies obtained without applying the fitting factor were also qualitatively consistent with experimental results ...\". Such a qualitative description is already the state of the art in simulating solid-state dewetting and would represent the actual situation before performing dedicated experiments. ii) line 304 - 308: the approach \"provide process guidelines for creating patterns ...\". This is true and useful. However, obtaining \"guidelines\" is again what is already known that can be achieved nowadays with numerical simulation in this context. iii) Lines 345-346: \"solid-state dewetting processes of pre-patterned single-crystal films can be predictably guided to create structures suitable for functional devices.\" This is a conclusion reached by other previous experimental studies (as mentioned in the first paragraphs above). The claim here is to introduce a better way based on simulation results, which is only partially true. iv) In the conclusions, \"We demonstrated that templated solid-state dewetting processes for single-crystal films can be designed and guided to deterministically create specific regular patterns on arbitrary substrates.\" This has been demonstrated before, except for the point of the arbitrary substrates. v) End of conclusions: \"This study demonstrates the feasibility of the predictable and precisely controllable fabrication of functional regular patterns on arbitrary substrates via the templated solid-state dewetting of single-crystal films.\" This is for all the aspects mentioned above, only partially supported by the presented evidence.\n– The initial shapes of the experimental patterns in Fig. 2(a) and 2(b), which form the basis for the main discussion, appear to differ slightly. While the inset in Fig. 2(a) is well approximated by a square patch with a central circular hole, the inset in Fig. 2(b) shows a patch featuring additional (small) facets at the corners. Why is this the case? Does it have any impact on the results? One would expect that using the same initial shape would be necessary to enable general parametrization and support broader conclusions.\n- In Fig. 2, the distinction between rings with regular and irregular shapes is made. While this can be followed qualitatively, quantification would be necessary (as the differences are relatively small anyway). Also, would a longer annealing time also cause these rings to break into islands? Especially the more irregular ones are expected to do so. This makes the discussion in terms of islands vs rings relative to transient phases, which need to be better presented.\n- The distinct facets observed at a 0.5 sccm H2 flow rate in 50 sccm of Ar (Fig. 2d) represent a rather specific case. Could a range of flow rates around this value (e.g., 0.5 ± ?) be estimated where this behavior is consistently observed? Additionally, does the stated consistency with multiple other patches refer to patches of identical shape and size, or does it also include variations in geometry?\n– The arguments used to explain the experiments (lines 136–181), presented before the multiscale modeling and simulation results, are not very clear and appear too speculative. Phrases such as “the results suggest,” “is attributable,” “could be,” and “consistent with the hypothesis” indicate a lack of clear evidence. This section would benefit from a concise summary of the key points, and rephrasing of critical sentences to clearly distinguish what is directly shown by the experiments and what remains a hypothesis. For instance:\ni) Line 144: It is unclear in what sense “These results suggest that oxygen and hydrogen chemisorption favored the formation of <011> in-plane facets in the Pd(100) films.” How are oxygen and hydrogen chemisorption linked to the previously mentioned observations? Should hydrogen chemisorption still be expected under conditions other than 3 sccm?\nii) Lines 146–155: It is not clear how this discussion explains the observations at an H2 flow rate of 0.3 sccm. In fact, the discussion seems to suggest that <011> in-plane facets are expected in all cases, which conflicts with the specificity of the observed behavior.\nAdditional minor comments:\n- One aspect that is not discussed is whether the different gas adsorption conditions also influence the dewetting dynamics. In certain cases, dynamical effects characteristic of surface attachment-detachment processes may emerge in addition to surface diffusion. Could the authors comment on this?\n– The interpretation of the results in terms of the surface energy anisotropy of Pd appropriately builds on the framework originally proposed in Ref. 23. Could this be more directly related to the classical Wulff construction/equilibrium shape description?", "reviewer_3": "In this paper, the authors have prepared the single crystalline Pd thin films and transferred on amorphous SiO2 substrate for the investigation of solid state dewetting behavior. They have also changed the annealing gas conditions with different Ar and H2 amounts and mixtures. Interesting structures evolutions have been observed. The authors have also tried to trace the dewetting process and behavior via numerical methods. As the authors mentioned, the dewetting of single crystalline metal films have been already studied, and the big difference in this paper is to use amorphous substrate instead of single crystalline MgO substrates. The Results are interesting, but the paper is not clearly formulated, and the novelty is also not high enough for NC. I would suggest to reject and transferred into another journal. Here are some comments:\n(1) It is confused in your statement that oxygen and hydrogen chemisorption favored the formation of <011> in-plane facets in the Pd(100) films. Because you have just described that formation of primary <001> in-plane facets only with small amount of H2.\n(2) In figure 3, you said there is no Si in the Pd structure confirmed by SAED. However, it is better to confirm it by investigation with EDX or similar method.\n(3) You study is about the investigation on dewetting of the single crystalline Pd on the amorphous SiO2 substrate, and suggests that surface energy anisotropy of films and gas adsorption are more important for the structure evolution than the film-substrate interface energy. But how about the influence of strain energy? The thermal extension coefficients between metals and oxides are large.\n(4) As you mentioned that the interface energy is not important for the structure evolution due to the amorphous nature, but it is strange that in figure 4b, the structures are clearly different with different tilt angles. Why? Influence of gas flow direction?\n(5) The whole arguments about the influence of anisotropy of surface energy and gas adsorption are also not clear enough. By anisotropy of surface energy you mean the orientation dependent aspect. But surface energy is the energy associated with two phases (solid and gas), and this means if you have different gas or gas mixture, then the interface energy is different, and this can also lead to different anisotropy of surface energy."}, "author_response": "Responses to reviewer comments\nWe sincerely appreciate the reviewers’ insightful comments.\nOur detailed, point-by-point responses are provided below.\nRevisions of the manuscript made in response to the comments are marked in blue in the revised\nmanuscript.\nAuthor’s Note to Reviewers\nThis note is to inform reviewers that one new figure has been added (now Fig. 6) and several\nfigures have been modified during the revision. The major changes are summarized below.\n- Figure 6: A new figure has been added to address the reviewer’s request for quantitative\nanalyses regarding the consistency between the experimental results and the KMC simulations.\n- All figures including the KMC simulation results: The original images showing the KMC\nsimulation results were saved with gamma correction, which is the default setting in the\nOpenDX software. For the revised manuscript, all images were saved without gamma\ncorrection. Only the color schemes were affected by this change.\n- Figure 2: The two OM images in the bottom row of Fig. 2(b) were replaced because the\noriginal images were taken from patches with holes slightly smaller than those in the top row.\nWe found this during the quantitative analyses and the images were replaced although the\nresulting patterns exhibit no appreciable differences. The OM images in Figs. 2(c) and 2(d)\nwere retaken because the original images exhibited a green tint due to a temporary microscope\nsetting at that time. The images have now been replaced to ensure consistent background color\nand improved clarity. Some panels were additionally updated using newly prepared samples\ndue to additional XPS measurements and hole-shape observations performed during the\nrevision.\nThe Pd 3d XPS spectra were also remeasured because extending the acquisition range beyond\n~347 eV allows more reliable determination of the Shirley background in the presence of\nplasmon-loss and oxide-satellite features. We therefore extended the measurement range to 355\neV and performed new deconvolutions (the full-range data are not shown in the figure for space\nlimitations but are provided in the source data file). We also added the O 1s spectra (Fig. 2(g))\nas suggested by the reviewer.\n- Figure 7 (previously Figure 6): The KMC simulation results and OM images in panels (a) and\n(b) have been replaced due to low resolution. The replacement images were obtained from a\ndifferent sample fabricated under the same process conditions, and the KMC simulation was\nreperformed to match its slightly different initial shape. In panel (d), the electrode-pattern\nimages have also been replaced. The previous submission inadvertently included images\nobtained from 30-nm-thick samples; in the revision, these have been replaced with images from\n50-nm-thick samples. 50-nm-thick patterns were used in the device fabrication and\ncharacterization as stated in the original manuscript.\n1\n- In accordance with the journal’s style guidelines, we have made minor adjustments to the\nfigure subpanel labels.\nReviewer #1 (Remarks to the Author):\nThe experiments presented in this paper shed new basic insights into the dewetting of metal\nfilms. For example, they show very clearly how the initial orientation of the edges of the films\naffects dewetting mechanisms . They also demonstrate that edge orientation can dominate the\neffects of substrate epitaxy. I found the experimental design to be clever and novel. I thus\nhave no hesitation in recommending publication in Nature Communications. I do, however, have\nsome comments that the authors might want to address before publication:\nResponse: We appreciate the reviewer’s positive and encouraging assessment of our work. We\nare grateful for the insightful comments, which have helped us substantially improve the clarity\nand rigor of the manuscript. Our detailed responses to each comment are provided below.\n1) The annealing that induces dewetting is performed at 800˚C. At that temperature I would\nexpect that surface concentrations of relatively weakly adsorbed species such as H (and maybe\nO) to be very low. The authors could estimate these concentrations from their DFT calculations\nof adsorption energies. Are the expected concentrations high enough to changes the orientation\ndependent surface energies enough to support their hypothesis about how surface energy affect\ndewetting?\nResponse: We estimated the O and H surface coverages at 800˚C based on Langmuir adsorption\ntheory, assuming dissociative chemisorption of O and H molecules. The O coverage was\n2 2\ncalculated using the following equation:\n√𝑒𝑥𝑝(𝜇 −𝐸 )/𝑘𝑇⁡\n𝑂2 𝑂\n𝑓 =\n𝑂\n1+√𝑒𝑥𝑝(𝜇 −𝐸 )/𝑘𝑇⁡\n𝑂2 𝑂\nwhere 𝜇 is the chemical potential of O , 𝐸 is the O binding energy, and k and T are the\n𝑂2 2 𝑂\nBoltzmann constant and temperature. The same formulation was used for hydrogen. The gas-\nphase chemical potentials at 800 ℃ were obtained from the NIST-JANAF thermochemical data\nvia regression analysis, assuming that they are ideal gases. The resulting O and H coverages\non Pd(111) and Pd(100) as a function of partial pressure are provided in Fig. S14 in the\nSupplementary Information.\nIn the manuscript, we showed that KMC simulation results matched the experimental results\nin 2000 sccm Ar when ζ was increased to 7.5. This ζ value corresponds to an oxygen partial\npressure of ~2.91 3 atm at 800 ℃. Under these conditions, the calculated O coverages\nwere ~0.056 ML on Pd(111) and ~0.023 ML on Pd(100), as now included in the manuscript\nand Note S2 in the Supplementary Information.\nSuch low coverages cannot be precisely quantified by ex-situ measurements because native\n2\nsurface oxides form before and after annealing. Furthermore, the equilibrium partial pressure\nof oxygen changes with the temperature during the heating and cooling. A definitive\nquantitative comparison would therefore require fully in-situ dewetting and surface\nspectroscopy under UHV conditions, which are not currently available to us. Nonetheless, the\nlow O coverages are physically reasonable given the strong purging effect of the high Ar flow\nrate.\nFor hydrogen, the calculated coverages at the same partial pressure were substantially lower\ndue to their weaker binding energies, consistent with the reviewer’s expectation. Assuming that\nthe tube ambient consists of only argon and hydrogen, increasing the H₂ flow rate to 3 and 5\nsccm corresponds to partial pressures of 0.057 and 0.091 atm, which yield ζ values of 2.50 and\n2.57, respectively. These increases are significantly smaller compared to the O adsorption case\n(see Results section: DFT-calculated adsorption energetics and their implications for\ndewetting).\nAs shown in Fig. S20(a), hydrogen adsorption lowers the vacancy formation energy on Pd(100),\nsimilar to oxygen. This reduction suggests that hydrogen may also influence the dynamic\nanisotropy by modifying the rates of vacancy-mediated exchange diffusion along the <001>\ndirections. Nevertheless, the reemergence of the dominant <011> in-plane facets cannot be\nexplained by H adsorption because the magnitude of this effect is also expected to be modest.\n2) Small concentrations of adsorbed species can however have dramatic effects on surface\ndynamics (by changing defect formation energies) and thus Have the authors considered this\npossibility? Can they rule it out?\nResponse: We agree that the effect raised by the reviewer cannot be fully ruled out within the\nscope of the present study. We addressed this possibility by calculating the vacancy formation\nenergies on the Pd(100) surface using DFT, considering multiple vacancy–adsorbate\nconfigurations with 4 × 2 × 4 slabs (see Methods). The configurations examined in the\ncalculations are shown in Fig. 6(c) of the main text and Fig. S20 in the Supplementary\nInformation.\nAs shown in Figs. 6(c) and S20, both O and H adsorption reduce the vacancy formation energy\non Pd(100). For the nearest-neighbor configuration, the vacancy formation energy decreases\nfrom 0.573 eV to 0.321 eV for O adsorption and to 0.529 eV for H adsorption, with smaller\nreductions for more distant configurations (0.566 and 0.565 eV). Because exchange-mediated\ndiffusion along the <001> directions on fcc(100) proceeds through vacancy formation, these\nreductions indicate that adsorbates can enhance surface diffusion rates along the <001>\ndirections. The effect is expected to be stronger for oxygen due to the larger reduction in\nvacancy formation energy.\nThese changes in exchange-mediated diffusion suggest that adsorbates may increase the\nrelative surface diffusivity and edge-retraction rates along the <001> directions compared to\nthe <011> directions, with oxygen having a stronger effect.\na fully quantitative assessment would require incorporating adsorbate-specific diffusion\nbarriers and vacancy energetics on various facets into the KMC model—extensions that are\nbeyond the scope of the present study. Nonetheless, the DFT results indicate that small\nconcentrations of adsorbates can modify defect formation energies, providing a physically\ngrounded basis for their potential influence on surface dynamics.\n3) The presentation of the XPS results were a bit incomplete. What were the surface\nconcentrations of impurities such as C, S and O? Carbon is a very common contaminate in Pd\nand it would be important to know how much carbon was detected and how it varied with\nannealing recipe. (And as I mentioned above, trace amounts of O and S can have dramatic\neffects on surface diffusion.)\nResponse: We performed additional XPS measurements and analyses for samples annealed\nunder the ambient conditions used in Fig. 2. The corresponding O 1s, C 1s, and S 2p spectra\nare now provided in Fig. 2(g) (O 1s) of the main text and Fig. S4 (C 1s and S 2p) in the\nSupplementary Information. As shown in Fig. 2(g), the relative intensity of the O 1s peak\nassociated with Pd surface oxides and oxygen adsorbates increases as the Ar flow rate decreases,\nconsistent with the increasing fractions of the corresponding components in the revised Pd 3d\nspectra in Figs. 2(e) and 2(f).\nAll C 1s spectra exhibit typical signatures of adventitious carbon (Fig. S4), indicating that the\ndetected carbon originates primarily from ambient contamination. The S 2p spectra were fitted\nusing three doublets corresponding to terminal S in polysulfides, central S in polysulfides, and\nsulfates. The sulfur atomic concentration generally ranged from 0 to 2 at% in survey scans.\nSince most sulfur species were identified as polysulfides, the number of S atoms directly\nbonded to the Pd surface should be smaller than the total atomic percent.\nAlthough these impurity levels are not negligible, we found no evidence that sulfur affected\nthe hole morphology. These contaminants can shift the Pd 3d peak to a higher-binding-energy\nregion, potentially increasing the Pdδ+ peak intensity. We mentioned in the manuscript that the\nPd2+ (PdO) peak is therefore a better indicator of oxidation (see Results section: Effects of Pd\nsurface energy anisotropy and oxygen adsorption).\nTo further examine whether S or C adsorption could influence surface energy anisotropy or\ndynamic anisotropy, we performed additional DFT calculations. As shown in Figs. S16(a–c),\nthe binding energies of S and C are the weakest on Pd(111) and strongest on Pd(100), opposite\nto the trend for O and H. This implies that S and C adsorption would modify the surface energy\nanisotropy in the opposite direction and would not promote the formation of the prominent\n(111) facets observed in Fig. 3. Therefore, neither the orientation-dependent hole shape nor the\nring stability in Fig. 2 can be explained by S or C adsorption.\nFigure S20 shows that, unlike O and H, S and C adsorption increase the vacancy formation\nenergy on Pd(100) (to 0.877 and 0.778 eV for the nearest configurations, with smaller increases\nof 0.595 and 0.599 eV for farther ones). Such increases would reduce, rather than enhance,\n4\nvacancy-mediated diffusion on Pd(100).\nReviewer #2 (Remarks to the Author):\nThis manuscript presents a study on the dewetting of patterned Pd films transferred onto\namorphous SiO₂ substrates. Selected configurations are investigated to understand the impact\nof anisotropies under varying gas-adsorption conditions. A multiscale simulation framework is\nemployed to reproduce experimental observations and provide insights into spontaneous\npatterning. While the overall process and techniques are well-established in the literature, some\nelements of novelty may lie in the proposed predictive multiscale framework, which is based\non different simulations, and in the approach of transferring Pd films onto amorphous SiO2,\npotentially enabling new applications.\nThe main claim of this work, entering both experiments and simulations, is the achievement of\n\"predictive patterning\" via solid-state dewetting. From an experimental standpoint, this claim\nhas been explored in earlier studies (e.g., Ye et al., Advanced Materials 23, 1567–1571 (2011)),\nwhich demonstrated deterministic outcomes in patterned solid-state dewetting. The simulations\nbased on KMC models effectively incorporate parameters from original MD and DFT\ncalculations, yet they still depend on some experimentally fitted parameters. This partially\nlimits their a priori predictive capability beyond the qualitative level. Quantitative prediction\nwith some fitting parameters basically meets the state of the art of such approaches (e.g., M.\nTrautmann et al., Appl. Phys. Lett. 110, 263105 (2017)) as well as other models. The\ndemonstration related to the self-assembly of the thin-film transistor, as guided by simulation,\nappears somewhat limited. The simulated dynamics is relatively short, involve simple\nmorphologies, and do not necessitate the use of KMC simulations (stable dewetting fronts, for\nexample, could be anticipated through independent arguments or dewetting experiments). It is\nalso noted that the formulation of hypotheses concerning the impact of different gas\natmospheres appears reasonable but would benefit from clearer organization and presentation.\nThese and other points are discussed in more detail below. Overall, the manuscript and the\nresearch presented therein provide some valuable insights into solid-state dewetting and thin\nfilm processing. However, I respectfully believe that, at its current stage, a stronger case is\nneeded to justify the central claims for publication in Nature Communications.\nWe appreciate the reviewer’s thoughtful assessment and constructive comments, which have\nhelped us improve the clarity of the manuscript. Before addressing the specific points, we\nbriefly clarify how this work extends previous studies on patterned solid-state dewetting.\nAs the reviewer mentioned, the formation of deterministic patterns through the solid-state\ndewetting of single-crystal films has been previously demonstrated (e.g., Ye et al., Adv. Mater.\n2011), where the role of surface energy anisotropy was effectively established. However, those\napproaches relied exclusively on single-crystal MgO substrates, which require long preheating\n5\nfor epitaxial growth and are sensitive to vacuum conditions. These practical constraints have\nlimited the broader use of the method for device-relevant structures.\nIn this work, we eliminate these constraints by using Si substrates for room-temperature\nepitaxial growth of Cu and Pd, followed by transfer onto amorphous SiO₂. This removes the\nneed for substrate preheating and makes the process compatible with commonly available e-\nbeam evaporation systems. We believe this substantially improves the accessibility of\nanisotropy-guided dewetting for functional device fabrication.\nFrom a scientific perspective, a central contribution of this study is the identification of the\nchemical origin of ambient-dependent morphological changes. To our knowledge, previous\nsolid-state dewetting studies did not incorporate DFT calculations of adsorbate binding\nenergies. These calculations enable us to quantify how gas adsorption modifies the surface\nenergy anisotropy, and they provide the necessary energetic input for our multiscale simulation\nframework.\nOur KMC simulations incorporate MD simulations and DFT calculations, allowing for\nvariations in the surface energy anisotropy. Earlier KMC frameworks did not explicitly include\nsuch anisotropy-modifying effects, which limited their applicability across different film\nmaterials and processing conditions. While we acknowledge that the fitting parameter 𝑐\nprevents fully quantitative predictions, the integration of DFT-based energetic trends represents\na step toward a more predictive modeling framework.\nFinally, the use of amorphous substrates allows us to exclude interfacial anisotropy effects and\nisolate the contributions from surface energy anisotropy and gas adsorption. We agree with the\nreviewer that some aspects of the presentation required clarification, and we have revised the\nmanuscript accordingly in response to the detailed comments listed below.\nMore detailed aspects:\n- In the introduction, it is noted that one of the key reasons limiting the application of dewetting\nas a patterning method is the empirical nature of parameters used in KMC simulations, which\nis claimed to be addressed in this work. I agree that this is a major limitation in predicting the\noutcome of solid-state dewetting at a level that enables a priori design. Still, the approach\npresented here relies on an empirical fitting parameter (c) used to rescale T_KMC (see the\nMethods section). The authors transparently report that this is a fitting parameter used to match\nsimulations with experiments, show the results obtained without this correction in the\nSupplementary Material (which indeed significantly differ from a quantitative point of view),\nand comment on the need for further research to clarify its origin and role. However, this is in\ncontrast with the initial claim of having resolved the issue of reliance on empirical parameters\nfor quantitative predictions.\nResponse: We agree with the reviewer that our approach does not fully enable quantitative a\npriori prediction because the fitting parameter 𝑐 is still required, as clearly noted in the\nmanuscript. Although we could not eliminate this parameter, we discussed its possible origins\nin the main text and have revised our claims in the introduction to avoid implying that this issue\nhas been completely resolved.\nwere not included when determining the roughening temperature used to normalize the\nexperimental temperature. In Fig. 4(c), the fitted value of 𝑐 = 0.772 indicates that T was\nKMC\noverestimated. This is likely because the experimental temperature (800 °C) was normalized\nusing the roughening temperature at 𝜁=0.266, which was obtained from total-energy\ncalculations of Pd(1811) slabs containing a single-kink pair of one- and two-atom height. In\nthese calculations, the effect of adsorption was not considered. As shown in Fig. 4(e), the BE\nof oxygen was calculated to be stronger on (100) than on (210) and (110) surfaces, suggesting\nthat oxygen adsorption could increase the roughening temperature of (100) surfaces. Taking\nthis effect into account when normalizing the experimental temperature could make the value\nof c closer to unity.\nIn contrast, the fitted value of 𝑐 =1.267 in the left panel of Fig. 3(a) indicates that T was\nKMC\nunderestimated. Absorbed hydrogen is known to significantly increase the vacancy\nconcentration, implying a reduced cohesive energy and, consequently, a lower roughening\ntemperature. It is also known that compressive stress lowers the roughening temperature.\nConsidering these effects in the estimation of the roughening temperature would again tend to\nmove the fitted value of 𝑐 closer to unity.\nThese potential origins of the fitting parameter are discussed in both the main text and the\nSupplementary Information of the revised manuscript. Incorporating adsorption- and\nabsorption-dependent effects, as well as stress effects, into the multiscale framework would\nrequire developing new force fields for MD simulations and extending the KMC algorithm,\nwhich is substantial future work. To reflect these limitations more accurately, we have revised\nthe introduction to state that this work improves the limitations of previous simulation\nframeworks rather than fully resolving the reliance on empirical parameters (see Results\nsection: Multiscale KMC simulations and DFT-calculated adsorption energetics and their\nimplications for dewetting).\n- In addition to the previous point, conclusions drawn on reported information show indeed\nthey align with the state of the art and that the main claims are partially supported: i) At line\n233, it is stated: \"Morphologies obtained without applying the fitting factor were also\nqualitatively consistent with experimental results ...\". Such a qualitative description is already\nthe state of the art in simulating solid-state dewetting and would represent the actual situation\nbefore performing dedicated experiments. ii) line 304 - 308: the approach \"provide process\nguidelines for creating patterns ...\". This is true and useful. However, obtaining \"guidelines\"\nis again what is already known that can be achieved nowadays with numerical simulation in this\ncontext. iii) Lines 345-346: \"solid-state dewetting processes of pre-patterned single-crystal\nfilms can be predictably guided to create structures suitable for functional devices.\" This is a\nconclusion reached by other previous experimental studies (as mentioned in the first paragraphs\nabove). The claim here is to introduce a better way based on simulation results, which is\nonly partially true. iv) In the conclusions, \"We demonstrated that templated solid-state dewetting\nprocesses for single-crystal films can be designed and guided to deterministically create\nspecific regular patterns on arbitrary substrates.\" This has been demonstrated before, except for\nthe point of the arbitrary substrates. v) End of conclusions: \"This study demonstrates the\n7\nfeasibility of the predictable and precisely controllable fabrication of functional regular patterns\non arbitrary substrates via the templated solid-state dewetting of single-crystal films.\" This is\nfor all the aspects mentioned above, only partially supported by the presented evidence.\nResponse: We respond to each point below.\ni) We agree that qualitative trends obtained without the fitting parameter can already be\nreproduced using the state of the art. However, in previous approaches—including the work\nmentioned by the reviewer (Appl. Phys. Lett. 110, 263105 (2017))—all key parameters such\nas J and E were empirically determined, and no theoretical component accounting for the\nS\nsurface energy anisotropy was implemented. This limits their applicability to different film\nmaterials and processing conditions.\nA recent work has introduced 𝜁 to reproduce a wide range of experimental hole morphologies.\nOur work further shows that the effects of gas adsorption on surface energy anisotropy can be\nincorporated by using 𝜁 within a multiscale calculation framework, and that 𝜁 can be linked to\nadsorbate properties using DFT. In the above-mentioned recent theoretical work (ref. 15), the\nvalue of 𝜁 was chosen arbitrarily. In contrast, our multiscale framework incorporates the\nchemical properties of the film materials and gas species, allowing it to be applied to different\nmaterials and annealing conditions.\nWe agree that the fitting parameter must ultimately be removed for fully quantitative\npredictions. Instead of removing it, we discussed the potential origins of the parameter 𝑐 in\neach case. Accordingly, we have revised our introduction to emphasize the implementation of\ngas-adsorption effects on the surface energy anisotropy within the multiscale framework, rather\nthan suggesting that all empirical parameters were eliminated.\nii) State-of-the-art numerical approaches cannot provide correct guidelines on the effect of\nannealing ambient because they do not incorporate material-dependent adsorbate binding\nenergies. The orientation-dependence of binding energies vary strongly with the film material.\nFor instance, O binding energies strengthen in the order of Ag(110), Ag(100) and Ag(111) as\npreviously reported by the corresponding author—opposite to the Pd case shown in this work.\nAs demonstrated in ref. 35, Ag(100) and Ag(111) islands annealed in air became more isotropic,\nconsistent with the relative binding strengths (with O binding being stronger on atomically\nrough surfaces for Ag) (see Discussion section).\nWe are currently extending our multiscale approach to other materials such as nickel and gold.\nFor Ni films on MgO, previous studies suggested that oxygen adsorption increases the relative\nwidth of the (110) facet. We think this may also be explained by stronger O binding energies\non (110) than on (100) and (111).\nWhile more systematic calculations and experiments are needed to generalize this point, we\nbelieve that incorporating DFT-calculated adsorbate binding energies into the multiscale\nframework is essential for providing accurate guidelines. In this sense, we respectfully disagree\nthat our guidelines correspond to what can already be obtained by existing numerical\nsimulations.\n8\niii) We have revised the sentence as suggested by the reviewer to clarify the contribution of this\nwork, specifically the ability to perform predictable patterning on arbitrary substrates:\n(original) solid-state dewetting processes of pre-patterned single-crystal films can be\npredictably guided to create structures suitable for functional devices\n(revised) solid-state dewetting processes of pre-patterned single-crystal films can be transferred\nand predictably guided to create structures suitable for functional devices on arbitrary\nsubstrates.\nThis reflects the fact that previous studies were limited to substrates that enabled epitaxial\ngrowth, whereas our transfer-based approach removes this constraint.\niv) We have cited previous works and clarified the contributions of this study. The main\ncontributions are (1) implementing the multiscale calculation scheme and (2) forming single-\ncrystal patterns on amorphous substrates. We revised the sentence accordingly:\n(original) We demonstrated that templated solid-state dewetting processes for single-crystal\nfilms can be designed and guided to deterministically create specific regular patterns on\narbitrary substrates\n(revised) We demonstrated that templated solid-state dewetting processes for single-crystal\nfilms can be designed and guided to deterministically create specific regular patterns on\namorphous substrates, overcoming the substrate limitations of previous studies.\nv) We revised the concluding statement to more accurately reflect the contributions of this work:\n(original) This study demonstrates the feasibility of the predictable and precisely controllable\nfabrication of functional regular patterns on arbitrary substrates via the templated solid-state\ndewetting of single-crystal films\n(revised) This study demonstrates the feasibility of predictable and precisely controllable\nfabrication of functional regular patterns on arbitrary substrates through the integration of\nmultiscale calculation schemes and film transfer techniques with templated solid-state\ndewetting of single-crystal films\n– The initial shapes of the experimental patterns in Fig. 2(a) and 2(b), which form the basis for\nthe main discussion, appear to differ slightly. While the inset in Fig. 2(a) is well approximated\nby a square patch with a central circular hole, the inset in Fig. 2(b) shows a patch featuring\nadditional (small) facets at the corners. Why is this the case? Does it have any impact on the\nresults? One would expect that using the same initial shape would be necessary to enable\ngeneral parametrization and support broader conclusions.\nResponse: The slight differences in the initial shapes of the patches in Figs. 2(a) and 2(b) arose\nfrom minor variations in the photoresist exposure, development, or wet-etching steps. Such\nvariations are common at these feature sizes (6–8 μm edge length and 2–5 μm hole diameter).\nAs the reviewer noted, the precise initial geometry can influence the details of the\n9\nmorphological evolution during dewetting.\nDespite these small geometric differences, our main conclusions rely on two key findings that\nare robust across different initial shapes:\n(1) In 2000 sccm Ar, the ring stability is strongly direction-dependent. Uniform rings appear\nonly along the <011> direction, and patches aligned along <011> and its adjacent directions\nshow higher stability than those aligned along <001> and its adjacent directions.\n(2) In 0.5 sccm H₂ and 50 sccm Ar, the dewetting also remains direction-dependent, but the\nstability contrast between the two direction groups is much smaller, and both <001>- and\n<011>-aligned patches are relatively stable under these conditions.\nTo test whether the initial shape affects these conclusions, we examined patches whose initial\ngeometries were intentionally or unintentionally varied from those in Figs. 2(a) and 2(b).\nThe results (Fig. S2) were consistent with the two key findings above. This indicates that the\nslight geometric deviations do not alter the fundamental physics underlying the direction-dependent\nring stability (see Results section: Ambient-dependent dewetting behaviors of transferred\nPd(100) films).\nWe also repeated the KMC simulations in Fig. 4 after swapping the initial patch geometries\n(Figs. S12(a) and S12(b)). The simulated results remained consistent with our main conclusions.\nIn Fig. S12(b), only the part of the second key finding related to the relatively higher stability\nof the <001> and <011> directions cannot be observed, because all patches decay into particles\nunder that condition. Nevertheless, the reduction in the stability contrast between the two\ndirection groups—which is the main implication of the second key finding—is still reproduced.\nThis behavior is consistent with the experimental observation that patches annealed in 0.5 sccm\nH₂ and 50 sccm Ar decay into particles (Fig. S2) and with the corresponding KMC results in\nFig. S12(c) (see Results section: Multiscale KMC simulations).\nTherefore, both the experimental data and the simulation results confirm that the slight\ndifferences in initial patch shape do not compromise the generality of our conclusions. We\nretained the patches in Fig. 2 because they most clearly highlight the two key findings and\nprovided the additional cases in Fig. S2 for completeness. This clarification is now included in\nthe revised manuscript (see the two Results subsections referenced above).\n- In Fig. 2, the distinction between rings with regular and irregular shapes is made. While this\ncan be followed qualitatively, quantification would be necessary (as the differences are\nrelatively small anyway). Also, would a longer annealing time also cause these rings to break\ninto islands? Especially the more irregular ones are expected to do so. This makes the\ndiscussion in terms of islands vs rings relative to transient phases, which need to be better\npresented.\nResponse: We agree that quantitative analysis is necessary. Figure 6 presents quantitative\nmeasurements of feature sizes and geometric characteristics for the patterns in Fig. 2(b), Fig.\n4(c), Fig. 5, and Fig. S18. As shown in Fig. 6, the deviations between the simulated and\n10\nexperimental values are mostly within 10%. These results were obtained using the same\nsimulation conditions as in Figs. 4(c) and 5, including the fitting factor. As noted earlier,\nachieving comparable quantitative accuracy without the fitting factor will require an improved\nmethod for determining the roughening temperature.\nSome features exhibit relatively larger deviations. We suggested that incorporating dynamic\nanisotropy into the KMC algorithm could reduce these discrepancies. To support this, we\nprovided DFT results in Fig. 6(c), showing that oxygen adsorption lowers the vacancy\nformation energy on Pd(100). Because exchange diffusion on fcc(100) surfaces requires\nvacancy formation whereas hopping diffusion does not, this reduction indicates a relative\nenhancement of exchange diffusion along the <001> directions. Accounting for adsorbate-\ninduced diffusivity changes across multiple facets in the KMC model may improve quantitative\naccuracy.\nRegarding transient versus later-stage morphologies, we added additional experimental data\nfor ring patterns in Fig. S2. Certain aspects of the orientation-dependent evolution can indeed\nbe illustrated more clearly in later-stage patterns—for example, misaligned patches with larger\ninitial holes ultimately break, as shown in Figs. S2. However, the transient-stage patterns in\nFig. 2 most clearly reveal the contrast between the two misaligned directions. Under 2000 sccm\nAr, the misaligned direction closer to <011> is significantly more stable, whereas this\nanisotropic behavior is not observed under 0.5 sccm H₂ and 50 sccm Ar.\nThese quantitative results and explanations have been incorporated into the revised manuscript\n(see Results section: Quantitative comparison between experiments and KMC simulations).\n- The distinct facets observed at a 0.5 sccm H2 flow rate in 50 sccm of Ar (Fig. 2d) represent a\nrather specific case. Could a range of flow rates around this value (e.g., 0.5 ± ?) be estimated\nwhere this behavior is consistently observed? Additionally, does the stated consistency with\nmultiple other patches refer to patches of identical shape and size, or does it also include\nvariations in geometry?\nResponse: We performed thermal annealing under various H flow rates with 50 sccm of Ar.\nTheir relative lengths gradually decreased as the flow rate increased from 0.5 to 2 sccm, and\nbecame negligible at 3 sccm and above. This is mentioned in the revised manuscript (see\nResults section: Effects of Pd surface energy anisotropy and oxygen adsorption).\nRegarding the consistency across multiple patches, this refers to patches with minor variations\nin initial geometry (as noted in our earlier response concerning photolithography and wet-\netching fluctuations). Despite these small geometric differences, the fundamental relationship\nbetween patch orientation and ring stability remained the same.\n– The arguments used to explain the experiments (lines 136–181), presented before the\nmultiscale modeling and simulation results, are not very clear and appear too speculative.\nPhrases such as “the results suggest,” “is attributable,” “could be,” and “consistent with the\n11\nhypothesis” indicate a lack of clear evidence. This section would benefit from a concise\nsummary of the key points, and rephrasing of critical sentences to clearly distinguish what is\ndirectly shown by the experiments and what remains a hypothesis. For instance:\ni) Line 144: It is unclear in what sense “These results suggest that oxygen and hydrogen\nchemisorption favored the formation of <011> in-plane facets in the Pd(100) films.” How are\noxygen and hydrogen chemisorption linked to the previously mentioned observations? Should\nhydrogen chemisorption still be expected under conditions other than 3 sccm?\nii) Lines 146–155: It is not clear how this discussion explains the observations at an H2 flow\nrate of 0.3 sccm. In fact, the discussion seems to suggest that <011> in-plane facets are expected\nin all cases, which conflicts with the specificity of the observed behavior.\nResponse: We appreciate the reviewer’s comment regarding the clarity of this section.\ni) We agree that the earlier paragraph was unclear because it preceded the discussion where the\nevidence for adsorbate-induced faceting is presented. We have therefore revised this paragraph\nto remove statements implying that oxygen and hydrogen chemisorption directly promote\nspecific in-plane facet orientations at this stage of the paper. Instead, we now separate the\nexperimentally supported observations from the hypotheses. The experimental results are\npresented as they are, and any interpretation involving adsorbate coverage or adsorbate-\ninduced surface energy anisotropy is explicitly stated as a hypothesis that requires further\nevidence.\nThe earlier ambiguity also arose from the insufficient explanation of hydrogen’s dual roles:\n(1) acting as a reducing agent that removes surface oxides, and\n(2) acting as an adsorbate that may influence surface energy and surface diffusion anisotropy.\nThis distinction has now been clarified in the revised manuscript.\nii) We also agree that the explanation of the behavior at 0.5 sccm H₂ required clarification.\n(We assume the reviewer’s reference to 0.3 sccm was meant to refer to 0.5 sccm.) At such a low\nflow rate, most of the supplied hydrogen is consumed in reducing residual surface oxides,\nleaving only a small fraction available for adsorption. As a result, the effect of hydrogen\nadsorption on the surface energy anisotropy becomes limited, and <001> edges remain primary\nunder these conditions. When the H₂ flow rate is sufficiently increased, oxide reduction\nbecomes complete and excess hydrogen remains available for adsorption, at which point\nadsorption-induced changes in anisotropy can emerge. This distinction has been clarified in the\nrevised paragraph, with hypotheses clearly separated from experimental evidence.\nWe also found that the low BE of H leads to a very low surface coverage at 800 °C in the\ncalculation suggested by another reviewer. Our revised XPS analyses also indicate that there is\nno evidence that hydrogen adsorption plays a critical role at higher H flow rates. Hence, we\n2\nrevised our claim to state that the origin of the reemergence of the <011> facets needs to be\nfurther investigated using in-situ surface measurements (see Results section: Effects of Pd\nsurface energy anisotropy and oxygen adsorption and DFT-calculated adsorption energetics\n12\nand their implications for dewetting).\nAdditional minor comments:\n- One aspect that is not discussed is whether the different gas adsorption conditions also\ninfluence the dewetting dynamics. In certain cases, dynamical effects characteristic of surface\nattachment-detachment processes may emerge in addition to surface diffusion. Could the\nauthors comment on this?\nResponse: We agree that gas adsorption can influence the dewetting dynamics. As shown in\nFig. 6(c) and Fig. S20, gas adsorption modifies the vacancy formation energy on Pd(100).\nThis affects the rate and possibly the dominant mechanism of surface self-diffusion. Oxygen and\nhydrogen adsorption decrease the vacancy formation energy, suggesting that exchange self-\ndiffusion could be facilitated, whereas sulfur and carbon adsorption increase it, implying a\nreduction in the exchange-diffusion rate. We have discussed the potential implications of these\nadsorbate-induced changes on pattern evolution in the main text and in earlier responses (see\nResults section: Quantitative comparison between experiments and KMC simulations).\nAt this stage, we cannot determine how strongly these dynamical effects influence the rim\nmorphology. Although both oxygen and hydrogen lower the vacancy formation energy, a\ndefinitive identification of the dominant mass-transport mechanism would require a more\ndetailed comparison of the possible kinetic pathways. In our experiments, the rim morphologies\ndeveloped in a consistent manner across all ambient conditions, suggesting that surface\ndiffusion remained the primary mechanism under our processing conditions. This clarification\nhas been added to the revised manuscript (see Results section: Effects of Pd surface energy\nanisotropy and oxygen adsorption).\n– The interpretation of the results in terms of the surface energy anisotropy of Pd appropriately\nbuilds on the framework originally proposed in Ref. 23. Could this be more directly related to\nthe classical Wulff construction/equilibrium shape description?\nResponse: We have revised the discussion to briefly relate the weighted-curvature description\nto the Winterbottom construction, which is the supported-film counterpart of the classical Wulff\nconstruction. This addition provides a clearer conceptual connection without altering our\noriginal analysis (see Results section: Effects of Pd surface energy anisotropy and oxygen\nadsorption).\nReviewer #3 (Remarks to the Author):\nIn this paper, the authors have prepared the single crystalline Pd thin films and transferred on\namorphous SiO2 substrate for the investigation of solid state dewetting behavior. They have\nalso changed the annealing gas conditions with different Ar and H2 amounts and mixtures.\nInteresting structures evolutions have been observed. The authors have also tried to trace the\ndewetting process and behavior via numerical methods. As the authors mentioned, the\n13\ndewetting of single crystalline metal films have been already studied, and the big difference in\nthis paper is to use amorphous substrate instead of single crystalline MgO substrates. The\nResults are interesting, but the paper is not clearly formulated, and the novelty is also not high\nenough for NC. I would suggest to reject and transferred into another journal. Here are some\ncomments:\nResponse: We appreciate the reviewer’s careful consideration.\nFirst, we would like to clarify the primary advances of this work.\nAs noted by the reviewer, patterned solid-state dewetting of single-crystal metal films has been\npreviously studied, primarily on single-crystal MgO substrates. A central contribution of the\npresent study is that we enable deterministic and orientation-dependent pattern formation on\namorphous substrates by combining multilayer epitaxial growth with a film-transfer process.\nThis removes the dependence on MgO substrates, whose use is limited by the need for long-\nduration preheating and highly sensitive growth conditions. In contrast, our method allows\nepitaxial Pd films to be grown at room temperature on Si using a standard e-beam evaporator\nand subsequently transferred onto amorphous SiO₂, greatly expanding the accessibility of this\npatterning approach.\nA second contribution is the systematic identification of the physical and chemical origins\ngoverning the ambient-dependent pattern morphologies through a multiscale approach that\nintegrates MD and DFT calculations with KMC simulations. Prior studies did not incorporate\nadsorbate binding energies or vacancy formation energies and therefore could not account for\nthe effects of annealing ambient or adsorbate-induced anisotropy. By including these\ncomponents, we provide mechanistic explanations for both the orientation dependence and the\nambient dependence of the observed pattern formation—features that were not addressed in\nearlier works.\nWe have revised the manuscript for clarity and organization following the reviewer’s comments,\nand detailed responses to individual points are provided below.\n(1) It is confused in your statement that oxygen and hydrogen chemisorption favored the\nformation of <011> in-plane facets in the Pd(100) films. Because you have just described that\nformation of primary <001> in-plane facets only with small amount of H2.\nResponse: We agree that the earlier description may have caused confusion, and we have\nclarified this point in the revised manuscript. Since thermal annealing was carried out at\natmospheric pressure, the Pd surface becomes oxidized in the absence of a reducing gas.\nHydrogen was introduced primarily to prevent oxidation or to reduce the surface oxide. At a\nlow flow rate such as 0.5 sccm, a substantial fraction of the supplied hydrogen is consumed\nduring oxide reduction, leaving only a limited amount available for adsorption. Under these\nconditions, adsorbate-induced changes in surface energy anisotropy are insufficient, and the\nprimary in-plane facets remain aligned along the <001> directions.\nWhen the hydrogen flow rate is increased to 3–5 sccm, additional hydrogen remains available\nafter the reduction step, which may allow hydrogen adsorption to influence the surface energy\n14\nanisotropy. In this regime, primary <011> in-plane facets can appear. This clarification has\nbeen added to the revised manuscript\nIn the calculation suggested by another reviewer, however, the H coverage at 800°C was found\nto be too small to solely account for the reemergence of the dominant <011> facets. Hence, we\nnoted that further investigation (e.g., in-situ surface characterization) is needed to clarify the\norigin underlying the reemergence at high H flow rates (see Results section: Effects of Pd\n2\nsurface energy anisotropy and oxygen adsorption and DFT-calculated adsorption energetics\nand their implications for dewetting).\n(2) In figure 3, you said there is no Si in the Pd structure confirmed by SAED. However, it is\nbetter to confirm it by investigation with EDX or similar method.\nResponse: We agree that confirming the absence of Si using EDS is appropriate. We performed\nEDS analyses on one of the patterns shown in Fig. 3(d). The results, including two line scans\nacquired at different positions of the pattern, are now provided in the Supplementary\nInformation (Fig. S6). As shown in Fig. S6, the Si signal within the Pd pattern is\nindistinguishable from the background, indicating that Si is not incorporated into the Pd\nstructure (see Results section: Effects of Pd surface energy anisotropy and oxygen adsorption).\n(3) You study is about the investigation on dewetting of the single crystalline Pd on the\namorphous SiO2 substrate, and suggests that surface energy anisotropy of films and gas\nadsorption are more important for the structure evolution than the film-substrate interface\nenergy. But how about the influence of strain energy? The thermal extension coefficients\nbetween metals and oxides are large.\nResponse: We compared the reductions of surface/interfacial energy and strain energy\nfollowing the approach used in previous studies (ref. 2 in the Supplementary Information). The\ndetailed analysis is provided in Note S3 of the Supplementary Information.\nAs the reviewer pointed out, the thermal expansion mismatch between Pd and SiO₂ generates\nthermal stress. The purely elastic thermal stress at 800 °C is approximately 1.72 GPa; however,\nsince the samples were heated to 800 °C over ~22 min, the actual stress at the onset of dewetting\nis expected to be significantly lower than this theoretical value. For this reason, we used the\nyield stress of Pd as the relevant stress to estimate the strain-energy reduction.\nThe yield stress of Pd depends strongly on microstructure, and values reported in the literature\nvary widely across different specimen types. To cover a broad and conservative range, we\nevaluated the strain energy using several reported yield-stress values measured at room\ntemperature for different Pd specimens, including nanocrystalline Pd films (~500 MPa), cold-\nworked Pd (~250 MPa), and annealed Pd (~40 MPa). Among these, nanocrystalline Pd films\nshow the highest reported value (~500 MPa), which we used as a conservative upper bound.\nBecause this value (~500 MPa) corresponds to nanocrystalline Pd, it represents a conservative\nupper bound. Epitaxial Pd(100) films—lacking grain-boundary strengthening—and the\nelevated annealing temperature are both expected to substantially reduce the actual yield stress\nrelative to this upper-bound estimate. Using this upper-bound stress together with a particle-\n15\nradius-to-film-thickness ratio of ~4 (estimated from ref. 1 in the manuscript), the reduction in\nsurface/interfacial energy was calculated to exceed that of strain energy by a factor of\napproximately 12.5. When lower yield-stress values reported for cold-worked and annealed Pd\nare used, the dominance of surface/interfacial energy becomes even more pronounced (ratios\nof ~50 and ~1960, respectively).\nThese results show that surface and interfacial energies dominate the driving force for\ndewetting under our experimental conditions. Nonetheless, we acknowledge that stress may\nstill influence certain aspects of the evolution—for example, by lowering the hole-nucleation\nbarrier or affecting the roughening temperature. These points are noted in Note S3 of the\nSupplementary Information.\n(4) As you mentioned that the interface energy is not important for the structure evolution due\nto the amorphous nature, but it is strange that in figure 4b, the structures are clearly different\nwith different tilt angles. Why? Influence of gas flow direction?\nThe reviewer’s confusion likely arises from distinguishing the role of the substrate from the\nrole of the initial in-plane crystallographic orientation of the Pd pattern. Because the SiO₂\nsubstrate is amorphous, the film–substrate interface does not impose any preferred in-plane\nalignment. Thus, the interface energy does not vary with the in-plane rotation of the pattern.\nHowever, the film itself is single-crystalline, and therefore its surface energy anisotropy\ndepends on the crystallographic orientation of the initial edges. Dewetting proceeds by edge\nretraction processes that depend on the relative stability of <001> and <011>–type edges,\nwhich is why patches with different in-plane orientations evolve into different morphologies\neven on an amorphous substrate.\nThe patterns in Figs. 4(b) and 4(c) correspond directly to the experimental cases in Figs. 2(a)\nand 2(b), where only the initial crystallographic edge orientations differ. The differences in the\nresulting morphologies therefore originate from the intrinsic surface energy anisotropy of Pd\nand are not related to the substrate or the gas-flow direction.\n(5) The whole arguments about the influence of anisotropy of surface energy and gas adsorption\nare also not clear enough. By anisotropy of surface energy you mean the orientation dependent\naspect. But surface energy is the energy associated with two phases (solid and gas), and this\nmeans if you have different gas or gas mixture, then the interface energy is different, and this\ncan also lead to different anisotropy of surface energy.\nWe agree that different gas environments can influence the solid–gas interfacial energy, and\nthis is one of the central points addressed in our work. In our study, the ambient-dependent\nmorphological evolution was interpreted in terms of facet-dependent chemisorption, where\nadsorbates bind with different strengths to Pd surfaces of different crystallographic orientations.\nThese facet-specific binding energies modify the relative surface energies of the facets and\ntherefore alter the effective surface-energy anisotropy.\nThis concept has already been discussed in the manuscript, where the DFT-calculated binding\nenergies for each facet were used to explain the experimentally observed changes in facet\n16\nstability and pattern evolution (see Results section: Effects of Pd surface energy anisotropy and\noxygen adsorption and DFT-calculated adsorption energetics and their implications for\ndewetting).\n17"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have thoroughly addressed all of my concerns, and I still recommend publication in Nature Communications. I read the other reviewers concern that the results are not convincing enough for publication in Nature Communications. I think it is true that any computational attempt at predicting the behaviour of surface energies and kinetics is fraught. Surfaces are complex and one can (and should!) always worry that something has been left out (as I stated in my review). But that does not diminish the importance of work such as presented here that makes a serious attempt using all the tools available to account for complex experimental observations. If the presented model of dewetting turns out to still be incomplete, it will be for an interesting reason.", "reviewer_2": "The authors carefully revised their manuscript, addressing most of the comments raised in my previous report, clarifying crucial points, and providing additional evidence. The \"stronger case\" I was referring to has now been made.\nI acknowledge the relevance of making the self-assembly of nanostructures exploiting dewetting compatible with relatively standard processes (room-temperature epitaxial growth, avoiding state-of-the-art vacuum conditions). The proposed analysis of chemical effects in the gas phase, which is deeper than what has been reported in the literature so far, is also a relevant aspect.\nI believe the authors have appropriately downplayed the claim of a fully predictive modeling framework, and I agree that this work represents \"a step toward a more predictive modeling framework,\" although further efforts and understanding (now also discussed in the manuscript) are still needed. It remains, however, that the title points to \"predictive patterning of ...\" rather than to the aspects mentioned above (\"transferred\" is relatively unclear at first reading), and that the predictive and reproducible character of dewetting exploiting pre-patterning has already been discussed extensively in the literature (as properly acknowledged by the authors). I therefore suggest making the actual relevant element of novelty more clearly evident from the very beginning (e.g., in the title).\nI thank the authors for the extensive explanations concerning KMC simulations and appreciate the effort made to clarify their claims, also through additional discussion in the manuscript. The point raised regarding the proposed \"guidelines\" is now fully clarified as they indeed refer to the specific process considered here (including ambient conditions) rather than to controlled solid-state dewetting in general. The same applies to remarks on the relevance of the transfer step.\nImportantly, quantitative analyses have been added (new Fig. 6). Moreover, the extended simulation campaign, which increases the reliability of the claims, is definitely a plus and demonstrates the robustness of the process, which was not clearly conveyed in the previous draft.\nI believe the manuscript can now be accepted for publication, while noting that further tailoring the visibility of the key messages to better convey the actual points of novelty could further increase the work's impact and accessibility.", "reviewer_3": "it is great that the authors have made big efforts to revise the manuscript, and the revisions are properly done. I suggest to accept it for publication. But the language should be polished again. For example, the sentence in the abstract is hard to understand: “The anisotropies of Pd surface energy and gas adsorption strength were found to cause the <001> and <011> in-plane facets to form and favor the latter as oxygen adsorption increases or hydrogen flow rate is sufficiently high.”"}, "author_response": "Responses to reviewer comments\nWe sincerely appreciate the reviewers’ comments and recommendations for publication.\nOur responses are provided below.\nAuthor’s Note to Editor and Reviewers\nThere were typographical errors in the equation used to estimate the adsorbate coverage. The\nE has been corrected to 2E , and the notation was further revised to 2BE(O*) for consistency\nO O\nwith the other equations in the manuscript. The coverage values reported in the manuscript\nwere originally calculated using this formulation.\n√exp(𝜇 −2BE(O∗))/𝑘𝑇⁡\nO2\n𝑓 =\nO\n1+√exp(𝜇 −2BE(O∗))/𝑘𝑇⁡\nO2\nMinor numerical adjustments to the adsorption coverage data were also made following a\nrefined treatment of the gas-phase enthalpic contribution to the gas-phase chemical potential.\nAs a result, three numerical values in the following sentences have been updated. However,\nthese changes do not affect the discussion and conclusions of the manuscript.\n(original)\nThe surface-energy ratio between the (100) and (111) surfaces was calculated to be ~1.119,\nwhich corresponds to 𝜁 = 7.5, as the O coverages were ~0.0227 and ~0.0561 ML on (100)\nand (111) surfaces at an oxygen partial pressure of ~2.9110-3 atm at 800 ℃, respectively.\n(revised)\nThe surface-energy ratio between the (100) and (111) surfaces was calculated to be ~1.119,\nwhich corresponds to 𝜁 = 7.5, as the O coverages were ~0.0227 and ~0.0561 ML on (100)\nand (111) surfaces at an oxygen partial pressure of ~1.1010-3 atm at 800 ℃, respectively.\n(original)\nUsing an upper-bound estimate based on an Ar–H ambient, increasing the H₂ flow rate to 3\n2\nand 5 sccm in 50 sccm Ar corresponds to partial pressures of ~0.0566 and ~0.0909 atm, which\nyield ζ values of ~2.50 and ~2.57, respectively.\n(revised)\nUsing an upper-bound estimate based on an Ar–H ambient, increasing the H₂ flow rate to 3\n2\nand 5 sccm in 50 sccm Ar corresponds to partial pressures of ~0.0566 and ~0.0909 atm, which\nyield ζ values of ~2.668 and ~2.798, respectively.\nThe authors have thoroughly addressed all of my concerns, and I still recommend publication\nin Nature Communications. I read the other reviewers concern that the results are not\nconvincing enough for publication in Nature Communications. I think it is true that any\ncomputational attempt at predicting the behaviour of surface energies and kinetics is fraught.\nSurfaces are complex and one can (and should!) always worry that something has been left out\n(as I stated in my review). But that does not diminish the importance of work such as presented\nhere that makes a serious attempt using all the tools available to account for complex\nexperimental observations. If the presented model of dewetting turns out to still be incomplete,\nit will be for an interesting reason.\nResponse: We thank the reviewer for the support of our work and recommendation for\npublication.\nReviewer #2 (Remarks to the Author):\nThe authors carefully revised their manuscript, addressing most of the comments raised in my\nprevious report, clarifying crucial points, and providing additional evidence. The \"stronger\ncase\" I was referring to has now been made.\nI acknowledge the relevance of making the self-assembly of nanostructures exploiting\ndewetting compatible with relatively standard processes (room-temperature epitaxial growth,\navoiding state-of-the-art vacuum conditions). The proposed analysis of chemical effects in\nthe gas phase, which is deeper than what has been reported in the literature so far, is also a relevant\naspect.\nI believe the authors have appropriately downplayed the claim of a fully predictive modeling\nframework, and I agree that this work represents \"a step toward a more predictive modeling\nframework,\" although further efforts and understanding (now also discussed in the manuscript)\nare still needed. It remains, however, that the title points to \"predictive patterning of ...\"\nrather than to the aspects mentioned above (\"transferred\" is relatively unclear at first reading),\nand that the predictive and reproducible character of dewetting exploiting pre-patterning has\nalready been discussed extensively in the literature (as properly acknowledged by the authors).\nI therefore suggest making the actual relevant element of novelty more clearly evident from\nthe very beginning (e.g., in the title).\nI thank the authors for the extensive explanations concerning KMC simulations and appreciate\nthe effort made to clarify their claims, also through additional discussion in the manuscript.\nThe point raised regarding the proposed \"guidelines\" is now fully clarified as they indeed refer\nto the specific process considered here (including ambient conditions) rather than to\ncontrolled solid-state dewetting in general. The same applies to remarks on the relevance of the\ntransfer step.\nImportantly, quantitative analyses have been added (new Fig. 6). Moreover, the extended\nsimulation campaign, which increases the reliability of the claims, is definitely a plus and\n2\ndemonstrates the robustness of the process, which was not clearly conveyed in the previous\ndraft.\nI believe the manuscript can now be accepted for publication, while noting that further tailoring\nthe visibility of the key messages to better convey the actual points of novelty could further\nincrease the work's impact and accessibility.\nResponse: We thank the reviewer for the positive evaluation of the revised manuscript and the\nsuggestion. We revised the first sentence of the Abstract to clarify that, although specific\ndewetting patterns have been demonstrated previously, extending them toward the fabrication\nof functional structures requires improved predictability and extensibility. We also added a\nsentence in the Introduction explaining that film transfer removes the need for single-crystal\noxide substrates and associated process constraints.\nReviewer #3 (Remarks to the Author):\nit is great that the authors have made big efforts to revise the manuscript, and the revisions are\nproperly done. I suggest to accept it for publication. But the language should be polished again.\nFor example, the sentence in the abstract is hard to understand: “The anisotropies of Pd surface\nenergy and gas adsorption strength were found to cause the <001> and <011> in-plane facets\nto form and favor the latter as oxygen adsorption increases or hydrogen flow rate is sufficiently\nhigh.”\nResponse: We thank the reviewer for the recommendation for publication and the suggestion\nregarding language polishing. We have revised several sentences to improve clarity.\nFor example, the sentence mentioned by the reviewer has been revised as follows:\n(original) The anisotropies of Pd surface energy and gas adsorption strength were found to\ncause the <001> and <011> in-plane facets to form and favor the latter as oxygen adsorption\nincreases or hydrogen flow rate is sufficiently high.\n(revised) The anisotropies of Pd surface energy and gas adsorption strength lead to <001> and\n<011> in-plane facets, favoring the latter as oxygen adsorption increases or the hydrogen flow\nrate is sufficiently high.\n3"}]

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