Supplementary Figure 1.

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1 Supplementary Figure 1. Supplementary Figure 1. Effects of the unlimited current. (a) Photograph of a AAO formed by pulsed anodization in the following conditions: V MA=25 V, t MA=180 s; V HA,N =36 V, t HA= 2 s, current density was limited to 50 ma/cm 2. (b and c) Cross sectional SEM images of the of the AAO regions indicated in (a). 1

2 Supplementary Figure 2. a Top surface b Bottom surface c MA layers between pulses Supplementary Figure 2. Order of the longitudinal nanopores. (a) SEM images of the free surface of the 3D-AAO. (b) SEM image of the underside of the 3D-AAO after selective removal of the underlying Al substrate with an acidic CuCl 2 solution, and the etching of the barrier layer with 10 wt % H 3PO 4, at 35 C for 8 min. (c) Artificially colored surface view of two MA layers corresponding to the AAO formed before (red) and after (blue) a HA step. Green colored AAO bits are broken pieces. Scales bars correspond to 500 nm. 2

3 Supplementary Figure 3 Supplementary Figure 3. Order of transversal nanochannels. Schematic illustration of the porous network structure and SEM images SEM micrograph of fractures of a 3D-AAO showing a MA terrace after the detachment of the upper layers 3

4 Supplementary Figure 4 a b c c2 c2 Supplementary Figure 4. Geometry of the transversal nanochannel network. (a) SEM images of the cross section of the 3D-AAO showing three regions with transversal pores. (b) Enlarged view of the area marked in (a) with a rectangle, in which the hexagonal geometry of the transversal nanochannel structure can be deduced. Red arrows indicate the transversal channels (denoted as c#), while green arrows point the pillars surrounding the transversal channels and are identified as p#. Scale bars correspond to 100 nm. (c) shows the schematic illustration of the transversal channels of a HA region in the plane of the section of the longitudinal pores. Longitudinal pores appear as black circles. The fracture plane of the SEM image in (b) is also indicated. Likewise, the transversal channels and pillars formed as a consequence of the collapse of longitudinal pores are indicated in the illustration 4

5 Supplementary Figure nm 60 nm 210 nm 1 mm 20 nm Supplementary Figure 5. Schematic illustration of the material used for ellipsometry experiments. The sample contained a single transversal nanochannel plane sandwiched between two MA layers 5

6 Supplementary Figure 6 Al 20 nm Barrier layer 1 mm Psi Delta Psi (50) Simulated Psi (50) Psi (60) Simulated Psi (60) Psi (70) Simulated Psi (70) Delta (50) Simulated Delta (50) Delta (60) Simulated Delta (60) Delta (70) Simulated Delta (70) Result: % porosity in the AAO Psi (70) Simulated Psi (70) Al 1000 nm AAO 20 nm Barrier layer 1 mm Psi Delta Delta (70) Simulated Delta (70) Result: 80% porosity in the broadened AAO Psi (70) Simulated Psi (70) nm «broadened» AAO 500 nm AAO Psi Delta Al 20 nm Barrier layer 1 mm Delta (70) Simulated Delta (70) Result: 75% porosity in the broadened AAO 55 Psi (70) Simulated Psi (70) Delta (70) Simulated Delta (70) Psi 45 Delta Supplementary Figure 6. Porosity analysis by ellipsometry measurements. 6

7 Supplementary Figure 7 a b Transmitance (%) Reflectance (%) AAO-3D wavenlength (nm) c Transmitance (%) AAO wavelength (nm) Supplementary Figure 7. Optical properties of the 3D nanostructures. Transmittance (a) and reflectance (b) spectra obtained from an empty three-dimensional nanopores template ( 3D-AAO ). (c) Transmittance spectrum of a porous alumina template without transversal nanochannels ( normal AAO ) 7

8 Supplementary Notes Supplementary Note 1. Current limitation The fact of carrying out the pulses at controlled current is a key issue for the homogeneity of the 3D template along the cross plane direction. Firstly, because in this way we avoid the decrease of the current of pulses as the pores becomes longer and longer (which is probably related to ion diffusion through longitudinal pores). Hence, in this way, every single pulse in our method is equal to the previous pulses. Secondly, because we experimentally observed that if a voltage-controlled pulse is applied, the reached current is quite high, which induces the periodic heating up of the system, which end up in a slight widening of pores as a consequence of each pulse. This widening of the pores is almost imperceptible if only a few pulses are applied but becomes significant when a large number of pulses are applied (for example 60 pulses), which is absolutely required to produce a real 3D nanostructure with macroscopic dimensions in the cross plane direction. As a consequence of this, longitudinal nanopores become interconnected in the upper region of the AAO (so transversal nanochannels are already created), while in the lower region, longitudinal nanopores are still non-mutually-connected. Obviously, this leads to the impossibility of producing uniform and homogeneous nanostructures in the cross plane direction of the template. Supplementary Figure 1 shows this issue in a porous alumina prepared by pulse anodization in the following conditions: VMA=25 V, tma=180 s; VHA,N =36 V, tha= 2 s, while the current density was limited to 50 ma/cm 2. Note that VHA,N and current density value during pulses are is higher than those of the optimized procedure. The number of HA pulses was 60 and the chemical etching with phosphoric acid that leads to the formation of transversal nanochannels was not carried out to this sample. Firstly, it can be clearly observed that the template it is not uniform in the in-plane directions. The area of the template in the upper part of the photograph (Supplementary Figure 1a) present the structural color associated to the periodic alternation of layers of different refractive indexes, while the area in the lower part of the picture has no color at all. The reason behind the different coloring of the template is fairly observed in the SEM images (Supplementary Figure 1b and Supplementary Figure 1c). Supplementary Figure 1b shows a SEM image of the cross section of the colored AAO area. As can be seen, 8

9 the AAO region located in the upper side of the image, which corresponds to the firstly formed alumina, already has the transversal pores created even if the chemical etching was not performed over this sample. In contrast, the transversal nanopores were not formed in the AAO region shown in lower side of the image. In fact, the color observed in Supplementary Figure 1a is comes from the transversal nanopores already formed. On the other side, the AAO template is fully destroyed in the area without any color shown in Supplementary Figure 1a, as can be deduced from the SEM image in Figure 1c. Again, the collapse of the structure is increases with the distance from the upper template surface, in such a way that formerly synthesized aluminum oxide shows higher levels of etching than the aluminum oxide formed later. This means that the structure gets damaged as the anodization advances. 9

10 Supplementary Note 2. Order of the 3D structure Longitudinal pores are orderly fashioned as can be observed in the SEM micrographs of the top surface (Supplementary Figure 2) due to the fact that both the first anodization and the MA steps of the pulse anodization were carried out in self-ordering conditions (25V, 0 C, 0.3 M H2SO4). To analyze the bottom surface, the underlying Al substrate and the barrier layer were removed. The hexagonal distribution of the longitudinal nanopores at the bottom surface of the template can be also observed in Supplementary Figure 2. This hexagonal pore distribution of pores is not disturbed by the HA steps. Supplementary Figure 2 shows the surface view of two strata/layers corresponding to the AAO formed before (right part, colored in red) and after (left part, colored in blue) a HA step. Green colored AAO bits are broken pieces. As it can be observed in the image, the pore ordering is not disturbed from one layer to the next, which means that the HA pulse does not perturb significantly (if any) the ordering achieved in the MA regime. These results thus suggest that longitudinal nanopores are completely parallel along the whole thickness of the template. On the other side, the geometry of the transversal nanochannel network can be deduced from the morphology of an internal MA terrace after the detachment of the upper, as shown in Supplementary Figure 3. A close view of its reveals that the transversal nanochannels conforms a 2D porous network of hexagonal symmetry like that illustrated in the cartoon. Moreover, we have tried to confirm the geometry/ordering of the transversal nanochannel from look at the junctions between longitudinal nanopores and transversal nanochannels. Supplementary Figure 4 shows the cross sectional SEM images employed for this. (a) Shows a SEM image of the cross section of the 3D-AAO showing three regions with transversal pores. (b) Enlarged view of the area marked in (a) with a rectangle, in which the hexagonal geometry of the transversal nanochannel structure can be deduced. Red arrows indicate the transversal channels (denoted as c#), while green arrows point the pillars surrounding the transversal channels and are identified as p#. Form this image we also deduce the hehagonal symmetry of the transversal nanochannel network as schematically explained in Supplementary Figure 4c. Supplementary Figure 4c represents the transversal channels of a HA region in the 10

11 plane of the section of the longitudinal pores. Longitudinal pores appear as black circles. The fracture plane of the SEM image in (b) is also indicated. Likewise, the transversal channels and pillars formed as a consequence of the collapse of longitudinal pores are indicated in the illustration. 11

12 Supplementary Note 3 Spectroscopic ellipsometry The optical constants of four different samples have been extracted by means of spectroscopic ellipsometry. The final aim of the measurements was to obtain the porosity of the HA layer as well as the porosity of MA layers once the transversal nanochannels were already formed. Therefore, a set of samples was prepared specifically for this experiment, consisting of the different layers that form the final 3D AAO. The first one was an aluminum substrate in which only a non-porous alumina barrier layer was grown. This was achieved by a common two-step anodization process [20] in which the second anodization step was interrupted exactly when the currenttime curve reached the minimum value. The obtained data was fitted to a two-layer model and the optical parameters of both the substrate and the barrier layer were thus fixed. Then, a second sample with longitudinal pores was fabricated (the 2 nd anodization time was 15 min). These longitudinal nanopores were then widened up to nm in diameter. The structure was simulated with the same aluminium substrate and barrier layer used before, plus a new layer simulated with an effective medium theory that consisted of a certain percentage of alumina and a certain percentage of air. From the fitting of the data we obtained a porosity of this region of % and a length of 0.78 μm. The third sample consisted of the same aluminium substrate, barrier layer and longitudinal pores of around 0.5 μm length, plus a HA layer of around 60 nm in thickness, see Supplementary Figure 5 for a sketch. The data was fixed with a four-layer model, which consisted of the same substrate, barrier layer, the % porosity layer obtained before of 515 nm thickness and a new layer with a porosity of 80% and 60 nm length. The last sample was fabricated in such a way that the broadened layer was located in the middle of the porous alumina, and the ellipsometric data was fixed with a five-layer model that took the fundamental parameters from the previous fittings. Then, the obtained porosity for the normal porous alumina was of % and the broadened layer was fixed with a 75% porosity, see data a fitting in Supplementary Figure 6. 12

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