Tailoring the Anodic Hafnium Oxide Morphology Using Different Organic Solvent Electrolytes

Highly ordered anodic hafnium oxide (AHO) nanoporous or nanotubes were synthesized by electrochemical anodization of Hf foils. The growth of self-ordered AHO was investigated by optimizing a key electrochemical anodization parameter, the solvent-based electrolyte using: Ethylene glycol, dimethyl sulfoxide, formamide and N-methylformamide organic solvents. The electrolyte solvent is here shown to highly affect the morphological properties of the AHO, namely the self-ordering, growth rate and length. As a result, AHO nanoporous and nanotubes arrays were obtained, as well as other different shapes and morphologies, such as nanoneedles, nanoflakes and nanowires-agglomerations. The intrinsic chemical-physical properties of the electrolyte solvents (solvent type, dielectric constant and viscosity) are at the base of the properties that mainly affect the AHO morphology shape, growth rate, final thickness and porosity, for the same anodization voltage and time. We found that the interplay between the dielectric and viscosity constants of the solvent electrolyte is able to tailor the anodic oxide growth from continuous-to-nanoporous-to-nanotubes.


Introduction
Advances in nanoscience and nanotechnology are interconnected with the development of new platforms where the physical properties of materials/structures, like size, porosity, geometry and surface functionalization can be controlled at the nanoscale. In this way, the potential of applications is created for a large number of areas [1][2][3][4], and thus, are pushing fast the research on the topic. As an example, metal-oxide nanostructures, such as nanotube arrays, have been instigating great interest, due to their demand for optoelectronics, microelectronics, energy storage, solar cells, catalysis or biomedical applications [1][2][3][4][5][6].
Hafnium oxide (HfO 2 ) with its high thermal, chemical and mechanical stability, as well as its high refractive index and dielectric constant is remarkably appealing for new nanostructure architectures like nanoporous or nanotube (NT) arrays and a large range of applications [5][6][7][8][9][10][11][12]. Having into account the emerging application of anodic TiO 2 nanotubes in DSCs, the question arises about the applicability of self-ordered arrays of anodic HfO 2 for the same purpose. The truth is that the use of an HfO 2 Nanomaterials 2020, 10, x FOR PEER REVIEW 3 of 15 anodization was carried out in four different samples in freshly prepared electrolyte solutions containing NH4F (0.3 wt%) (to provide fluoride ions), H2O (2 wt%) and different organic solvents: Ethylene glycol (EG), formamide (FA), N-methylformamide (NMF) and dimethyl sulfoxide (DMSO). All the anodizations were performed under a constant potential of 60 V for 1 h, at room temperature with mechanical stirring [18,24]. After the anodization, the as-prepared samples were immediately cleaned with ethanol. From now on, the samples prepared with different electrolyte solvent will be referred to as EG, FA, NMF and DMSO. The NTs morphology was evaluated by an FEI Quanta 400FEG Field Emission (Hillsboro, United States) Scanning Electron Microscopy (SEM) using cross-sections (for the AHO length calculation) and surface top views.

Growth Mechanism: Anodization Curves with Different Organic Solvents
The main mechanisms responsible for the formation of NTs by an Hf anodization processes are: (i) The electric field-assisted oxidation at the metal/oxide interface, forming an HfO2 continuous layer; (ii) the field-assisted dissolution of the oxide layer (at the oxide/electrolyte interface); and (iii) the chemical dissolution of the oxide by F − ions at the metal/oxide and electrolyte/oxide interfaces ( Figure 1). The electrochemical equations for HfO2 formation are: and HfO2 + 6F − + 4H + → [HfF6] 2− + 2H2O (2) for the oxidation (1) and dissolution (2) reactions, respectively ( Figure 1). The reactions occurring at the anode are oxidation of the metal, that releases Hf 4+ ions and electrons: whereas, in the electrolyte one has the dissociation of water: OH − → O 2-+ H + (5) Differently from the Al metal anodization case [25,26], where a steady-state condition is achieved (oxidation rate is balanced with the dissolution rate), the Hf anodization case (as that of Ti anodization) consists in a non-steady state anodization process with higher oxidation than  Differently from the Al metal anodization case [25,26], where a steady-state condition is achieved (oxidation rate is balanced with the dissolution rate), the Hf anodization case (as that of Ti anodization) consists in a non-steady state anodization process with higher oxidation than dissolution rates [24]. Such effect severely compromises the HfO 2 NTs length and growth [24]. There are also additional chemical dissolution effects during the anodization that affect the oxidation/dissolution equilibrium and limit NTs growth.
The evaluation of the mechanisms that lead to the formation and growth of self-ordered HfO 2 nanoporous/nanotubes, can be studied using current density [j(t)] curves ( Figure 2) [23][24][25][26][27]. The evolution of the HfO 2 barrier layer thickness (δ b ) at the bottom of the NTs (Figure 1) was also estimated from the j(t) curves ( Figure 3) [27]. According to the high-field conduction theory [28], the current density (j) is related to the voltage (V) drop across the barrier layer as follows: where α and β are electrolyte and material-dependent constants and the (V/δ b ) ratio is the effective electric-field across δ b [27,28]. From Equation (6) we obtain, during the anodization [24,27]. It was considered the material constants, α = 2.4 × 10 −9 mA·cm −2 and β = 27.98 nm·V −1 (at room temperature), determined previously for TiO 2 [27], and due to the physical similarities between these oxides here are also considered. Figure 3 shows the evolutions of δ b along the anodization time calculated from the Equation (7).
Nanomaterials 2020, 10, x FOR PEER REVIEW 5 of 15 [24] with fairly smaller j(t) values over such region [indicating a thinner δb ( Figure 3)] when comparing with other samples (FA or EG) [24,27]. Additionally, Figure 3 shows that by changing the electrolyte medium, we obtain different final δb. Furthermore, for each sample, the capacitance density (C) at the oxide barrier was also calculated from the j(t) curves [Supporting Information (SI) - Figure S3 and Table S1. At the end of the anodization (1 h), we can extract the final δb and C for each sample (SI -Table S1). It shows that the FA/EG samples led to thicker δb (and lower C) and DMSO/NMF led to thinner δb (and higher C).
Moreover, we perform additional anodizations with the same conditions as for the samples EG, FA, NMF and DMSO during 17 h (SI - Figure S1). In this case, j(t) of the sample NMF rapidly decays after 444 min. This corresponds that a complete conversion on the Hf foil into HfO2 has occurred at this time (444 min), as observed by SEM cross-section images. (SI - Figure S2)      Figure 2 and corresponding inset) present the transient anodization characteristic of the successful formation of nanopore/nanotube arrays (as in the Al or Ti cases [23][24][25][26][27]). After applying 60 V, a continuous HfO 2 layer is rapidly formed that leads to a resistance increase [rapid j decrease (inset of Figure 2) and δ b increase (Figure 3)]. The following slight j decrease marks the initiation of pore nucleation, likely on the surface valley-type irregularities where the electric field enhances the oxide dissolution and promotes hole formation (i.e., the dissolution promoted by F − ions in favorable spots of the HfO 2 surface) [21,24]. Consequently, the HfO 2 layer thickness starts to increase, while the pores/tubes formation accelerates. This is evidenced by the increase of j until a maximum is reached. A barrier layer, with thickness δ b , forms at the pores/tubes bottom (Figures 1 and 3). Afterwards, the emerging porous structure will mechanically adjust and compete with each other in a self-organization process.
The differences between j(t) transient periods of each sample (inset of Figure 2) clearly reveals the decisive importance of the electrolyte solvent in promoting effective nucleation spots. In fact, comparing the j(t) transient period of each sample, we can observe three main aspects: (i) The lower j(t) values; (ii) the earlier emergence of NT nucleation; and (iii) the smaller nucleation time are attributed to samples FA, NMF, EG and DMSO, respectively.
As the anodization process evolves, j(t) of samples FA and EG present similar trends with the typical j(t)-decay of Ti anodization in fluoride-based electrolytes with EG [23][24][25][26][27]. This behavior arises from the non-equilibrium in the oxidation/dissolution processes, being the HfO 2 dissolution lower than its formation, resulting in a slow decay of j(t) during the anodization. As a result, a progressive increase of δ b of the NTs' occurs, as shown in Figure 3. Consequently, the ionic migration path along the oxide barrier [27,29] significantly extends, inhibiting the transport of F − , Hf 4+ and O 2− ions across δ b (Hf 4+ and O 2− for oxidation, F − for dissolution) which subsequently limits a further NTs growth ( Figure 1). Additionally, chemical effects, such as local pH decrease, occur throughout the anodization leading to the chemical dissolution of the NTs wall preferentially at the NTs tops (V-shape NTs) [17,18,27,29,30]. The NMF j(t) curve presents a large decay up to 8 min, similar to EG and FA, but then an overall constant j(t) emerges, although with some singularities during the anodization.
On the other hand, in the case of the DMSO, the j(t) curve remains approximately constant throughout the anodization, indicating a more optimized anodization for NTS growth, with balanced oxidation/dissolution processes that lead to a constant oxide growth rate (similar with Al nanoporous Nanomaterials 2020, 10, 382 6 of 15 anodization were no limit in length is imposed [25,26]). Additionally, the DMSO j(t) transient curve shows an extended nucleation period of time (indication of low-rate pore nucleation) [24] with fairly smaller j(t) values over such region [indicating a thinner δ b (Figure 3)] when comparing with other samples (FA or EG) [24,27].
Additionally, Figure 3 shows that by changing the electrolyte medium, we obtain different final δ b . Furthermore, for each sample, the capacitance density (C) at the oxide barrier was also calculated from the j(t) curves [Supporting Information (SI) - Figure S3 and Table S1]. At the end of the anodization (1 h), we can extract the final δ b and C for each sample (SI -Table S1). It shows that the FA/EG samples led to thicker δ b (and lower C) and DMSO/NMF led to thinner δ b (and higher C).
Moreover, we perform additional anodizations with the same conditions as for the samples EG, FA, NMF and DMSO during 17 h (SI - Figure S1). In this case, j(t) of the sample NMF rapidly decays after 444 min. This corresponds that a complete conversion on the Hf foil into HfO 2 has occurred at this time (444 min), as observed by SEM cross-section images (SI - Figure S2). Figure 4 shows the charge curves Q(t) obtained from the integration of the j(t) data. The Q(t) curves describe the growth rate along the anodization [24]. Until the first 13 min both Q(t) slopes of NMF and FA samples are higher than those of the DMSO and EG. Although the NMF sample presents a higher charge over time for the entire anodization period (comparing to the rest of the samples), Q(t) of the DMSO sample overcomes that of the FA sample at the end of the anodization period (close to 50 min). Higher Q(t) curve indicates higher charge transfer, leading to a higher growth rate. The charge transferred during the anodization process can then be related to the solvent characteristics and Q(t) values. Additionally, the Q(t) curves present different slope's trend: Whereas, in NMF and DMSO samples the slope is fairly linear, providing an almost constant AHO growth rate, that is not the case for the EG and FA samples, where Q(t) has a non-linear slope and presents two distinct growth rate regimes. After 11 min and 13 min of anodization time, for EG and FA, respectively, the growth rate slows down. With these electrolytes, the δ b increases during the anodization, leading to a constant Q(t) over time [and significantly lower final Q(t) values]. As discussed before, the δ b increase is related to the unbalanced oxidation-dissolution rate reactions, being the HfO 2 dissolution smaller than its formation, ultimately limiting the NTs growth and length [24,27]. δ b (t) curves ( Figure 3) of NMF/DMSO samples present thinner δ b , while EG/FA samples shows thicker δ b . One can observe the similar Q(t) trend of the two groups of samples EG/FA and NMF/DMSO. EG and FA presents the transition of two regimes at 11 min and 13 min, respectively. After these anodization times, δ b greatly increases ( Figure 3) and the growth rate slows down. On the other hand, NMF/DMSO samples show a Q(t) linear slope, corresponding to a constant δ b over time (Figure 3). At the end, EG/FA samples presents thicker δ b than NMF/DMSM samples.

Morphology and Layer Thickness
Figures 5-8 shows SEM cross-section, and top view images of the AHO templates for all samples after 1 h of anodization. Comparing the different samples, one sees that the electrolyte solvent has a critical impact on the AHO morphology, growth rate and layer thickness. From the top view images, we can see that FA leads to a self-ordered nanoporous template ( Figure 5), while EG and DMSO lead to highly self-ordered NT arrays with hexagonal closely packed distribution ( Figures 6 and 7, respectively). For the NMF samples ( being the HfO2 dissolution smaller than its formation, ultimately limiting the NTs growth and length [24,27]. δb(t) curves ( Figure 3) of NMF/DMSO samples present thinner δb, while EG/FA samples shows thicker δb. One can observe the similar Q(t) trend of the two groups of samples EG/FA and NMF/DMSO. EG and FA presents the transition of two regimes at 11 min and 13 min, respectively. After these anodization times, δb greatly increases ( Figure 3) and the growth rate slows down. On the other hand, NMF/DMSO samples show a Q(t) linear slope, corresponding to a constant δb over time (Figure 3). At the end, EG/FA samples presents thicker δb than NMF/DMSM samples.

Morphology and Layer Thickness
Figures 5-8 shows SEM cross-section, and top view images of the AHO templates for all samples after 1 h of anodization. Comparing the different samples, one sees that the electrolyte solvent has a critical impact on the AHO morphology, growth rate and layer thickness. From the top view images, we can see that FA leads to a self-ordered nanoporous template ( Figure 5), while EG and DMSO lead to highly self-ordered NT arrays with hexagonal closely packed distribution ( Figures 6 and 7, respectively). For the NMF samples ( EDS analyses showed (SI- Figure S5) that the anodic as-grown nanoporous (FA) nanotubes (DMSO/EG) presents significant amounts of F, which is typical of anodic HfO2 or TiO2 structures [14,18]. Literature associates the F presence with the formation of hafnium oxyfluoride in the AHO. For the sample NMF the same the F presence was obtained (SI - Figure S5d). Additionally, in NMF sample we perform separated EDS analyses for bulk oxide (SI - Figure S5e

Morphology and Layer Thickness
Figures 5-8 shows SEM cross-section, and top view images of the AHO templates for all samples after 1 h of anodization. Comparing the different samples, one sees that the electrolyte solvent has a critical impact on the AHO morphology, growth rate and layer thickness. From the top view images, we can see that FA leads to a self-ordered nanoporous template ( Figure 5), while EG and DMSO lead to highly self-ordered NT arrays with hexagonal closely packed distribution (Figures 6 and 7, respectively). For the NMF samples ( EDS analyses showed (SI- Figure S5) that the anodic as-grown nanoporous (FA) nanotubes (DMSO/EG) presents significant amounts of F, which is typical of anodic HfO2 or TiO2 structures [14,18]. Literature associates the F presence with the formation of hafnium oxyfluoride in the AHO. For the sample NMF the same the F presence was obtained (SI - Figure S5d). Additionally, in NMF sample we perform separated EDS analyses for bulk oxide (SI - Figure S5e      The pore diameter (Dp), and interpore distance (Dint) geometrical parameters were extracted from the SEM image (100 pores analyzed) for the EG, FA and DMSO samples as shown in Table 1. The average Dp and Dint (and standard deviation SD) were estimated from the histogram of the size distribution, which were then fitted to a normal distribution (Figure 9).    The pore diameter (Dp), and interpore distance (Dint) geometrical parameters were extracted from the SEM image (100 pores analyzed) for the EG, FA and DMSO samples as shown in Table 1. The average Dp and Dint (and standard deviation SD) were estimated from the histogram of the size distribution, which were then fitted to a normal distribution (Figure 9).  EDS analyses showed (SI- Figure S5) that the anodic as-grown nanoporous (FA) nanotubes (DMSO/EG) presents significant amounts of F, which is typical of anodic HfO 2 or TiO 2 structures [14,18]. Literature associates the F presence with the formation of hafnium oxyfluoride in the AHO. For the sample NMF the same the F presence was obtained (SI - Figure S5d). Additionally, in NMF sample we perform separated EDS analyses for bulk oxide (SI - Figure S5e: Z1 area), and surface top nanostructures (flakes/needles; SI - Figure S5f: Z2 area) identifying the same chemical elements in both areas and are in accordance with the other anodic hafnium oxide samples.
The pore diameter (D p ), and interpore distance (D int ) geometrical parameters were extracted from the SEM image (100 pores analyzed) for the EG, FA and DMSO samples as shown in Table 1. The average D p and D int (and standard deviation SD) were estimated from the histogram of the size distribution, which were then fitted to a normal distribution (Figure 9).  Usually, the regularity of the geometrical patterns in self-ordered nanoporous/nanotubes of anodic TiO2, Al2O3 or HfO2 is analyzed by a typical parameter-the porosity (P). For the well-defined hexagonal porous structures, P of the anodic oxide layer is given by the equation proposed by Nielsch et al.: where r is the pore radius (r = Dp/2) [31]. For the hexagonal self-ordered nanoporous Al2O3, or TiO2 NT arrays the obtained porosities are close to 10% (10% porosity rule) when mild anodizations are implemented (low anodization potentials). This rule assumes that a perfect hexagonal structure shows a P of 10% and deviations from these values results in the imperfect ordering of the structures. Qiu et al. presented a study of porosity for anodic HfO2 NTs (electrolyte with ethylene glycol as solvent) and obtained porosity values of 10% when the anodizations were performed within the range of 10 to 40 V [14]. In this work, P was calculated for the samples FA, EG and DMSO, as shown in Table 1. For the FA and DMSO samples, porosities closer to 10% (of~9.3 and 14.2%, respectively) were obtained, consistent with the 10% rule. However, for the EG sample P clearly deviates from the 10% rule (P~18.1%). The resulting AHO layer thicknesses are shown in Table 2. The EG, FA and DMSO samples have a mean AHO layer thickness (L) of approximately 8.0; 23.6 and 37.3 µm, respectively. On the other hand, the NFM sample shows a rapid AHO growth rate with L = 94.8 µm, much larger than the Usually, the regularity of the geometrical patterns in self-ordered nanoporous/nanotubes of anodic TiO 2 , Al 2 O 3 or HfO 2 is analyzed by a typical parameter-the porosity (P). For the well-defined hexagonal porous structures, P of the anodic oxide layer is given by the equation proposed by Nielsch et al.: where r is the pore radius (r = D p /2) [31]. For the hexagonal self-ordered nanoporous Al 2 O 3 , or TiO 2 NT arrays the obtained porosities are close to 10% (10% porosity rule) when mild anodizations are implemented (low anodization potentials). This rule assumes that a perfect hexagonal structure shows a P of 10% and deviations from these values results in the imperfect ordering of the structures. Qiu et al. presented a study of porosity for anodic HfO 2 NTs (electrolyte with ethylene glycol as solvent) and obtained porosity values of 10% when the anodizations were performed within the range of 10 to 40 V [14]. In this work, P was calculated for the samples FA, EG and DMSO, as shown in Table 1. For the FA and DMSO samples, porosities closer to 10% (of~9.3 and 14.2%, respectively) were obtained, consistent with the 10% rule. However, for the EG sample P clearly deviates from the 10% rule (P~18.1%). The resulting AHO layer thicknesses are shown in Table 2. The EG, FA and DMSO samples have a mean AHO layer thickness (L) of approximately 8.0; 23.6 and 37.3 µm, respectively. On the other hand, the NFM sample shows a rapid AHO growth rate with L = 94.8 µm, much larger than the other samples. Notice that while previously discussing the Q(t) curves (Figure 3), the higher final Q(t) was indicative of thicker L: L(NMF) > L(DMSO) > L(FA) > L(EG), as obtained [24].

Electrolyte Solvent as the Driven Factor behind AHO Morphology, Porosity and Growth
In this study, there are two relevant parameters in the electrolyte solvent: The viscosity (η) and dielectric constant (κ) ( Table 2). The Stokes-Einstein equation relates the diffusion constant (D) of a macroscopic particle of radius r, undergoing a Brownian motion, to the viscosity η of the fluid in which it is immersed [32]. Thus, at a constant temperature, the individual ions [O 2− ] or [F − ] diffusion constant will be inversely dependent on solvent η, limiting both oxidation and dissolution rates. On the other hand, a high-κ solvent draws a higher electrolyte capacitance (for a constant potential) inducing the formation of more charges at the oxide layer, thus, improving the extraction of the Hf 4+ ions and ultimately leading to a high oxidation rate [17,18]. Therefore, κ will be intimately related to the rate of the oxidation processes [Equation (1)] at the oxide/metal interface (higher κ, higher oxidation rate).  (Figure 10b) (deviating from the optimized 10% rule for optimized self-ordered regularity). On the other hand, by decreasing κ [or the solvent conductivity (σ) SI: Table S1], P increases, also leading to deviations of 10% rule).

Electrolyte Solvent as the Driven Factor behind AHO Morphology, Porosity and Growth
In this study, there are two relevant parameters in the electrolyte solvent: The viscosity (η) and dielectric constant (κ) ( Table 2). The Stokes-Einstein equation relates the diffusion constant (D) of a macroscopic particle of radius r, undergoing a Brownian motion, to the viscosity η of the fluid in which it is immersed [32]. Thus, at a constant temperature, the individual ions [O 2− ] or [F − ] diffusion constant will be inversely dependent on solvent η, limiting both oxidation and dissolution rates. On the other hand, a high-κ solvent draws a higher electrolyte capacitance (for a constant potential) inducing the formation of more charges at the oxide layer, thus, improving the extraction of the Hf 4+ ions and ultimately leading to a high oxidation rate [17,18]. Therefore, κ will be intimately related to the rate of the oxidation processes [Equation (1)] at the oxide/metal interface (higher κ, higher oxidation rate).  Figure 10b] (deviating from the optimized 10% rule for optimized self-ordered regularity). On the other hand, by decreasing κ [or the solvent conductivity (σ) SI: Table S1], P increases, also leading to deviations of 10% rule).  Figure 11a,b displays the counterplots (color-maps) of the AHO L and P as a function of the solvent physical parameters η and κ. We used the parameters for each sample, (η, κ, L) from Table 2 and (η, κ, P) from Tables 1 and 2, to perform a numerical estimation of 20 new data points by the interpolation method of cubic Spline. By this interpolating method, we are able to create an estimation of new values of L and P with certain conditions of the electrolyte (varying η and κ). The  Figure 11a,b displays the counterplots (color-maps) of the AHO L and P as a function of the solvent physical parameters η and κ. We used the parameters for each sample, (η, κ, L) from Table 2 and (η, κ, P) from Tables 1 and 2, to perform a numerical estimation of 20 new data points by the interpolation method of cubic Spline. By this interpolating method, we are able to create an estimation of new values of L and P with certain conditions of the electrolyte (varying η and κ). The obtained (η, κ, L) and (η, κ, P) arrays were then plotted in 3D counterplot in Figure 11a,b, respectively. One can observe that thicker AHO is obtained for high κ and low η values. These anodization conditions led to extremely fast oxidation rates as in the case of the NFM sample and demonstrated by the Q(t) curve (Figure 4). The NFM sample shows a faulty structure without self-ordered nanoporous or tubes [only small areas revealed a nanoporous structure; Figure 7c]. Indeed, much faster oxidation than field-enhanced dissolution occurred during the anodization, being the process out of the steady-state anodization conditions, which is mandatory for nanoporous/tubes upraise. We believe that, at the initial anodization stages, already nanoporous/NTs formation occurred [see initial j(t) transient in Figure 2 and SEM image in Figure 8c], but the NMF solvent high-κ ( Table 2) led to a much faster Hf 4+ extraction, and thus, leaving no time to maintain the nanostructures self-organization regime, i.e., to have a proper dissolution rate that would counter-balance the high oxidation rate. Additionally, the NMF j(t) singularities observed during the anodization (Figure 2) can be related to the different nanostructures morphologies obtained (Figure 8).
Nanomaterials 2020, 10, x FOR PEER REVIEW 11 of 15 anodization conditions led to extremely fast oxidation rates as in the case of the NFM sample and demonstrated by the Q(t) curve (Figure 4). The NFM sample shows a faulty structure without self-ordered nanoporous or tubes [only small areas revealed a nanoporous structure; Figure 7c]. Indeed, much faster oxidation than field-enhanced dissolution occurred during the anodization, being the process out of the steady-state anodization conditions, which is mandatory for nanoporous/tubes upraise. We believe that, at the initial anodization stages, already nanoporous/NTs formation occurred [see initial j(t) transient in Figure 2 and SEM image in Figure  8c], but the NMF solvent high-κ (Table 2) led to a much faster Hf 4+ extraction, and thus, leaving no time to maintain the nanostructures self-organization regime, i.e., to have a proper dissolution rate that would counter-balance the high oxidation rate. Additionally, the NMF j(t) singularities observed during the anodization (Figure 2) can be related to the different nanostructures morphologies obtained (Figure 8). Figure 11b shows the counterplot of P as a function of the solvent parameters η and κ. With this analysis, we establish a range of P tunability. We can observe that porosities closer to the 10% rule can be obtained for higher κ and lower η. However, it is also observed that the porosity clearly deviates from the 10% rule for lower values of κ and higher η. Notice that moderate values of P (closer to 10%) can be obtained with higher η values, but κ has to be at the higher value range. Contrarily to what is usually presented in literature, that P depends exclusively on anodization parameters such, voltage, (Dp, Dint) or water content, we demonstrate for the first time that the porosity also critically depends on physical properties of the solvent (η, κ). These new results bring the possibility to mix the solvents in order to tune the anodic oxides with a perfect hexagonal arrangement. The anodization conditions mandatory for the self-ordered nanoporous/tubes morphology to arise are obtained decreasing κ, either with low or high η. The FA solvent has a relatively lower κ, but a slightly higher η than those of NMF. This seems to be enough to establish the necessary conditions of a more equilibrated oxidation/dissolution balance for the formation of structures with self-organization (nanoporous structure; Figure 5). Additionally, under these conditions, moderate L is obtained, as shown in the counterplot map [ Figure 11a]. On the other hand, the NT structure arises when decreasing even more κ, either in low or high η regimes, although with thinner or thicker thicknesses, respectively. Both DMSO and EG samples showed an NT structure, but the DMSO sample presented a higher L. Both own a similar κ value, albeit much smaller than the one from the previously discussed samples. EG much higher viscosity, making Fions more difficult to be replaced by new ones at the NTs bottom. As a result, oxidation is faster than dissolution, leading to a j(t) decrease during the anodization, indicating the progressive increase of δb. Thus, the ionic migration path along the oxide barrier [29] significantly extends, inhibiting the transport of F − , Hf 4+ and O 2− ions across δb (Hf 4+ and O 2− for oxidation, F − for dissolution) which subsequently limits a  Figure 11b shows the counterplot of P as a function of the solvent parameters η and κ. With this analysis, we establish a range of P tunability. We can observe that porosities closer to the 10% rule can be obtained for higher κ and lower η. However, it is also observed that the porosity clearly deviates from the 10% rule for lower values of κ and higher η. Notice that moderate values of P (closer to 10%) can be obtained with higher η values, but κ has to be at the higher value range. Contrarily to what is usually presented in literature, that P depends exclusively on anodization parameters such, voltage, (D p , D int ) or water content, we demonstrate for the first time that the porosity also critically depends on physical properties of the solvent (η, κ). These new results bring the possibility to mix the solvents in order to tune the anodic oxides with a perfect hexagonal arrangement.
The anodization conditions mandatory for the self-ordered nanoporous/tubes morphology to arise are obtained decreasing κ, either with low or high η. The FA solvent has a relatively lower κ, but a slightly higher η than those of NMF. This seems to be enough to establish the necessary conditions of a more equilibrated oxidation/dissolution balance for the formation of structures with self-organization (nanoporous structure; Figure 5). Additionally, under these conditions, moderate L is obtained, as shown in the counterplot map (Figure 11a). On the other hand, the NT structure arises when decreasing even more κ, either in low or high η regimes, although with thinner or thicker thicknesses, respectively. Both DMSO and EG samples showed an NT structure, but the DMSO sample presented a higher L. Both own a similar κ value, albeit much smaller than the one from the previously discussed samples. EG much higher viscosity, making F − ions more difficult to be replaced by new ones at the NTs bottom. As a result, oxidation is faster than dissolution, leading to a j(t) decrease during the anodization, indicating the progressive increase of δ b . Thus, the ionic migration path along the oxide barrier [29] significantly extends, inhibiting the transport of F − , Hf 4+ and O 2− ions across δ b (Hf 4+ and O 2− for oxidation, F − for dissolution) which subsequently limits a further NT growth (Figure 1). On the other hand, from the dissolution reaction [Equation (2)] one can see that the failure of F − leads to H + excess, and thus, to additional chemical dissolution effects that also result in limited NTs growth. DMSO showed a perfect balance between oxidation and dissolution, j(t) constant during the anodization, just as in the Al anodization case [23,25,26]. The increased NT-array length when using a DMSO electrolyte can also be attributed to the controlled chemical dissolution process effect. Thus, the route to successfully obtain long NT arrays is to minimize the pH decrease promoted by H + additional etching. The DMSO aprotic photophilic solvent accepts an H + ion from NH 4 F and reduces its activity, decreasing the chemical etching. Thus, allowing the DMSO NTs to grow deep into the hafnium foil without any significant loss at the tube tops. The presence of DMSO modifies the space charge region in the pores, thereby also avoiding the lateral etching and leading to a steady-state pore growth and low chemical etching of the NT walls.
As expected, the same conclusions were obtained for the counterplots with the solvent conductivity (σ) instead of using κ (SI - Figure S6).
In summary, the electrolyte solvent affects the morphology and length of anodic HfO 2 ( Figure 12). Different nanostructures with different shapes of morphologies are obtained by changing the electrolyte solvent physical characteristics. For instance, we can tailor the anodic oxide morphology from NTs (EG and DMSO) to nanoporous (NPs; FA) to a thick oxide layer (NMF), by increasing the electrolyte κ, since the oxidation rate is higher (Figure 11a (easier Hf 4+ extraction). Additionally, with the κ increase the porosity decreases (Figure 11a). On the other hand, increasing η, the L severally decreases (Figure 11b), since the dissolution rate decreases because the ionic diffusion is limited. Overall, an accurate balance between the electrolyte solvents' κ and η is needed to obtain the desired morphology, porosity and length. further NT growth (Figure 1). On the other hand, from the dissolution reaction [Equation (2)] one can see that the failure of F − leads to H + excess, and thus, to additional chemical dissolution effects that also result in limited NTs growth. DMSO showed a perfect balance between oxidation and dissolution, j(t) constant during the anodization, just as in the Al anodization case [23,25,26]. The increased NT-array length when using a DMSO electrolyte can also be attributed to the controlled chemical dissolution process effect. Thus, the route to successfully obtain long NT arrays is to minimize the pH decrease promoted by H + additional etching. The DMSO aprotic photophilic solvent accepts an H + ion from NH4F and reduces its activity, decreasing the chemical etching. Thus, allowing the DMSO NTs to grow deep into the hafnium foil without any significant loss at the tube tops. The presence of DMSO modifies the space charge region in the pores, thereby also avoiding the lateral etching and leading to a steady-state pore growth and low chemical etching of the NT walls. As expected, the same conclusions were obtained for the counterplots with the solvent conductivity (σ) instead of using κ (SI - Figure S6).
In summary, the electrolyte solvent affects the morphology and length of anodic HfO2 ( Figure  12). Different nanostructures with different shapes of morphologies are obtained by changing the electrolyte solvent physical characteristics. For instance, we can tailor the anodic oxide morphology from NTs (EG and DMSO) to nanoporous (NPs; FA) to a thick oxide layer (NMF), by increasing the electrolyte κ, since the oxidation rate is higher (Figure 11a(easier Hf 4+ extraction). Additionally, with the κ increase the porosity decreases (Figure 11a). On the other hand, increasing η, the L severally decreases (Figure 11b), since the dissolution rate decreases because the ionic diffusion is limited. Overall, an accurate balance between the electrolyte solvents' κ and η is needed to obtain the desired morphology, porosity and length. Figure 12. Scheme of (a) AHO morphology transition from bulk-to-nanoporous (NPs)-to-nanotubes (NTs) with the electrolyte solvent constant dielectric constant (κ) increase (as the porosity (P) decreases); and (b) the AHO layer thickness (L) increase with the viscosity (η) decrease.

Conclusions
We investigated the growth of self-ordered anodic hafnium oxide (AHO) by using different solvent base electrolytes: EG, FA, NMF and DMSO. We found that the solvents are a key factor for tunning the possible morphology of the nanostructures of the AHO. EG and DMSO allow vertically oriented growth in self-ordered NT arrays, due to low κ and high η (in the case of EG), and because Figure 12. Scheme of (a) AHO morphology transition from bulk-to-nanoporous (NPs)-to-nanotubes (NTs) with the electrolyte solvent constant dielectric constant (κ) increase (as the porosity (P) decreases); and (b) the AHO layer thickness (L) increase with the viscosity (η) decrease.

Conclusions
We investigated the growth of self-ordered anodic hafnium oxide (AHO) by using different solvent base electrolytes: EG, FA, NMF and DMSO. We found that the solvents are a key factor for tunning the possible morphology of the nanostructures of the AHO. EG and DMSO allow vertically oriented growth in self-ordered NT arrays, due to low κ and high η (in the case of EG), and because the photophilic character (in the case of DMSO) of the solvent. On the other hand, FA and NMF lead to nanoporous AHO (for FA), due to their much higher κ, and to diverse nano-shapes (for NMF), including nanoflakes, nanoneedles, nanotube-agglomerations and thick continuous oxide. Furthermore, the final layer thickness of the AHO was also correlated with the electrolyte solvent type, and particular its κ and η values. While κ determines a higher oxidation rate (out of the steady state regime), leading to thicker HfO 2 oxide layer (NMF) out of the self-organization anodization regime (nanoporous or nanotubes), a lower κ combined with lower η lead to higher lengths, but in the self-ordered regime, and thus, to hexagonally distributed NTs (DMSO). Additionally, porosities within the 10% self-ordered regime were obtained for high κ and low η.
The detailed analyses of j(t), δ b (t) and Q(t) anodization curves combined with morphology analyses demonstrate that an accurate balance between the oxidation and dissolution rates during the anodization is mandatory to obtain optimized self-ordered nanostructures. The anodization curves j(t) and Q(t) for the different solvent electrolytes revealed different growth mechanism and growth rates of AHO.
Overall, the κ and η constants from the solvent electrolyte directly affects the transition from thick oxide-to-nanoporous-to-nanotubes (as κ decreases), the porosities and the growth of oxide layer thickness, (as η increase). This study clearly reveals that the organic solvent is the main factor affecting the transition from pores to tubes and the regularity of the structures, as well as the anodization growth rates.
Supplementary Materials: The following are available online at http://www.mdpi.com/2079-4991/10/2/382/s1, Figure S1: Current density anodization curves during 17 h, Figure S2: SEM images of the NMF sample for 17 h of anodization, Figure S3: Capacitance Calculation Estimative -Capacitance density as a function of the anodization time (60min), Figure S4: Barrier layer thickness (δ b ) and capacitance density (C), at the AHO nanotubes/nanoporous bottom, as a function of the electrolyte viscosity (η), Table S1: Summary of electrolyte physical parameters (κ, η and σ) and the AHO experimental parameters extracted from the anodization curves (δ b and C) and from the SEM images (L and P), Figure S5: EDS Spectroscopy-Chemical Characterization -EDS spectra for all the samples, Figure S6: Counterplots of L and P as a function of the solvent parameters η and conductivity (σ).