## 3 Results
### Size and Geometrical Analysis  
The analysis of the size of the 3D-RMS displayed in Figure 4b was obtained from the micrograph in Figure 4a in an area of 2200 \(\upmu\)m\({}^{2}\), where a total of 1200 domains were counted and the minimum and maximum diameter are 0.3 and 3.3 \(\upmu\)m respectively. As a  
Figure 3: Scanning (**a**,**b**,**b**,**b**,**b**,**2**,**c**,**c**.1**) and transmission (inset in (**b.2**)) electron microscopy images of the Ni/Al multilayers deposited on Si needles (the images were taken at the following tilt angles: (**b**,**b**,**2**) at 36\({}^{\circ}\) and (**c**) at 52\({}^{\circ}\)). The schematic representation of the made shape on the left side illustrates the approximate region from which the samples were taken via FIB for subsequent SEM analysis of the cross-section and top-section view. result, the distribution graph of the top radius of the mac structures depicted in Figure 4b has been fitted with a log-normal distribution curve, where the calculated mean diameter is 1.4 \(\upmu\)m with a standard deviation of 0.44 \(\upmu\)m. The log-normal size distribution of cluster or grain sizes is frequently observed as a result of crystallite size distributions of solids; this distribution has been attributed to time-dependent growth and nucleation kinetics [27,28]. In this work, the distribution of diameter size can also be influenced by the variation in the size and diameter of the silicon needles, preferential growth, and coalescence of domains. Figure 3b,1,b,2 reveals a change of the curvature of the deposited layer due to the topography of the nanoneedles (\(k_{i}\) and \(k_{f}\)), where \(k_{i}\) is assigned to the smallest structures near the substrate surface and \(k_{f}\) to those above. To quantify the curvature of the layers, the following relationship is used:  
\[k=\frac{1}{R} \tag{1}\]  
where \(k\) represents the curvature of the multilayer and \(R\) is the radius of the arc; \(k\) is calculated at different points, as shown in Figure 5a,b. This analysis was carried out for the domains that grew on the silicon needles and reached the surface without presenting interruptions during their growth. The domains that did not reach the surface or those that coalesced with each other were affected by other variables. Figure 4: (**a**) Size of the multilayer domain structure in top-view, analyzed by a watershed filter in MountainsMap software [22], used to obtain the domain size log-normal distribution shown in (**b**). Figure 5: (**a**) Schematic illustration of the morphology of the 3D-RMS on top of the black Si needles displaying the different parameters taken for evaluation of the normalized curvature. (**b**) Normalized curvature as a function of distance to the first layer after evaluation of 4 different domains. The initial curvature \(k_{i}\) was obtained at about 170 nm from the tip of silicon needle where the growth of the structure originates (Figure 3b.2), \(k_{f}\) was taken at different points in relation to the distance \(d\) up to the last layer of the system, as seen in the Figure 5a schematic illustration. Subsequently, the normalized curvature \(k_{v}\) was calculated using the following relation for variable distances \(d\):  
\[k_{v}=\frac{k_{f}}{k_{i}} \tag{2}\]  
where \(k_{v}\) was calculated in eight points for four domains, randomly chosen from Figure 3b, with \(k_{f}\) at different distances \(d\) from the tip of the needle. The values obtained for \(k\) and \(k_{v}\) are shown in Table 1.  
As represented in Figure 5b, the data in Table 1 was fitted with the following exponential decay function:  
\[k_{v}=\exp\biggl{(}c_{1}+\frac{c_{2}}{d+c_{3}}\biggr{)} \tag{3}\]  
where constants \(c_{1}=1.89\); \(c_{2}=2.38\)\(\upmu\)m, and \(c_{3}=0.71\)\(\upmu\)m fit the equation for the resulting curve. The growth of the nanostructures starts on the top of the needles. Owing to this, the multilayers present a curvature that reduces by 90% for the layer that is farthest from the first layer \(k_{i}\). This trend can be seen in Figure 5b.