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Polarity-Dependent Growth Rates of Selective Area Grown ZnO Nanorods by Chemical Bath Deposition Thomas Cossuet, Estelle Appert, Jean-Luc Thomassin, and Vincent Consonni Langmuir, Just Accepted Manuscript • Publication Date (Web): 30 May 2017 Downloaded from http://pubs.acs.org on May 31, 2017
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Polarity-Dependent Growth Rates of Selective Area Grown ZnO Nanorods by Chemical Bath Deposition Thomas Cossuet,1* Estelle Appert,1 Jean-Luc Thomassin,2 and Vincent Consonni.1* 1
Université Grenoble Alpes, CNRS, Grenoble INP, LMGP, F-38000 Grenoble, France
2
Université Grenoble-Alpes, CEA-Grenoble, INAC-PHELIQS-LATEQS, F-38000 Grenoble,
France
ABSTRACT
Polarity is known to affect the growth and properties of ZnO single crystals and epitaxial films, but its effects are mostly unknown in ZnO nanorods. To leave polarity as the only varying parameter, ZnO nanorods are grown by chemical bath deposition under identical conditions and during the same run on O- and Zn-polar ZnO single crystals patterned by electron beam lithography with the same pattern consisting of fifteen different domains. The resulting well-ordered O- and Zn-polar ZnO nanorod arrays with high structural uniformity are formed on all the domains. The comparison of their typical dimensions unambiguously reveals that Zn-polar ZnO nanorods have much higher growth rates than O-polar ZnO nanorods for all the hole diameter and period combinations. The distinct growth rates are explained in the framework of the surface reaction- / diffusive transport-limited elongation regime analysis, which yields a much larger surface reaction rate constant for Zn-polar ZnO NRs. The origin of the difference is attributed to polarity-dependent dangling bond 1 ACS Paragon Plus Environment
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configurations at the top polar c-faces of ZnO nanorods, which may further be affected by polarity-dependent interactions with the ionic species in aqueous solution. These findings show the relevance of considering polarity as an important quantity in ZnO nanorods.
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INTRODUCTION Zinc oxide (ZnO) has received increasing interest during the past decade as a promising IIVI semiconductor for applications in sensing, electronic, piezoelectric, and optoelectronic devices owing to its direct wide band gap energy (3.3 eV at 300 K), its large exciton binding energy (60 meV), its high electron mobility (200 cm2.V-1.s-1), and its strong piezoelectric properties (piezoelectric constants e33=1.34 C/m2 and e31=-0.57 C/m2).1 At ambient conditions, ZnO crystallizes into the hexagonal wurtzite structure belonging to the 6mm point group.1 This structure is formed of alternating planes of positively charged Zn atoms and negatively charged O atoms along the polar 〈0001〉 axis (i.e., c-axis), each O atom being tetrahedrally coordinated to four Zn atoms, and vice-versa. Owing to the non-centrosymmetric nature of the wurtzite structure, ZnO exhibits a non-zero dipole moment per unit volume, or spontaneous polarization, along the c-axis.2 Therefore, the 0001 and 0001 directions are not equivalent and the c-planes of ZnO are, by definition, polar. The polarity is defined by the Zn-O bond that is collinear to the c-axis of the wurtzite cell. The c-planes are by convention denoted as Zn-polar for the 0001 plane (i.e., when the vector goes from the Zn atom and plane (i.e., when the points towards the O atom) and reciprocally O-polar for the 0001 vector goes from the O atom and points toward the Zn atom), as represented in Figure 1.
Figure 1. Side view of the O- and Zn-polar ZnO faces with the coordination tetrahedron centered on the Zn atom.
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It is worth noticing that polarity is a bulk crystallographic property and differs from surface termination, namely the O- and Zn-polar c-planes can both be O- or Zn-terminated.3,4 The polarity in wurtzite semiconducting compounds such as ZnO and GaN has extensively been investigated.5–38 It is known to greatly affect surface stability and configuration,2,13,14,16– 18,20,30,32,37
chemical reactivity,15,21 etching behavior,38,10 growth rate,15,22,24,36 morphology,10,22
dopant incorporation,23 as well as electrical28 and optical properties.23,34 These polarity dependent properties have so far been almost exclusively determined in the case of ZnO single crystals and epitaxial films. They are still open to a very large extent in the case of ZnO nanostructures including NRs. These nano-objects offer unique chemical and physical properties as compared to planar films39 thanks to their high surface-to-volume ratio at nanoscale dimensions. They are considered as promising building blocks for a wide variety of devices such as piezoelectric nanogenerators,40 LEDs,41 UV-photodetectors,42–44 and solar cells.45,46 As ZnO NRs grow along the polar c-axis, they exhibit a c-plane face at their top,
0 plane (i.e., either O- or Zn-polar depending on the growth direction, and six non-polar 101 m-plane) sidewalls. Their formation are typically achieved by various physical and chemical deposition techniques,47,48 including the low-cost, low-temperature, and easily implemented chemical bath deposition (CBD).49 This technique is based on the heterogeneous formation of ZnO NRs on top of a ZnO nucleation surface in aqueous solution containing a zinc salt with a source of hydroxide ions and complexing agents. However, the integration of ZnO NR arrays still remains a challenge and requires a precise control of their growth and of their properties in terms of diameter, period, vertical alignment, doping, and polarity.50 Overall, the issue of polarity in the field of ZnO nanostructures have been reported depending on the polarity of the ZnO nucleation surface15,24,27,35,51–54 and investigated regarding their polarity itself. The physical and chemical vapor deposition techniques typically results in the formation of Zn-polar ZnO NRs25,26,37,55–60 or nanostructures following 4 ACS Paragon Plus Environment
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the catalyst-free or self-induced approaches,15,29 regardless of the polarity of the nucleation surface. Even on O-polar ZnO nucleation surfaces, extended defects like inversion domain boundaries are commonly formed to reverse the polarity of ZnO NRs in favor of the Znpolarity, owing to aluminum surfactant effects.26,59 In contrast, Consonni et al. have recently shown that O-polar ZnO NRs can be formed by using CBD and that their structural uniformity can thoroughly be controlled on patterned ZnO single crystals by electron beam lithography (EBL).31 The polarity of ZnO NRs grown by CBD is thus tunable by transferring the polarity from the nucleation surface, which was later on reported also by Wu et al.35 on Ga- and N-polar GaN single crystals. This opens the way for more deeply analyzing the effects of polarity on the nucleation and growth of ZnO NRs by CBD as well as on their overall physical properties, which are still critical open questions. However, the major issue is that the nucleation and growth mechanisms of ZnO NRs by CBD depend on a large number of parameters including the morphology of the ZnO nucleation surface (i.e., grain/domain size, grain/domain texture and mosaicity, roughness, porosity)61–69 and the conditions used in aqueous solution (i.e., volume, temperature, pH, nature and concentration of chemical precursors).70–74 In other words, fixing all these parameters is needed to accurately disentangle and investigate the effects of polarity. This requires the development of thorough experimental procedures in which the selective area growth (SAG) using patterned ZnO nucleation surfaces must be used. In this work, well-ordered ZnO NR arrays were grown by CBD on O- and Zn-polar ZnO single crystals to investigate their polarity dependent nucleation and growth. The O- and Znpolar ZnO single crystals were both patterned by EBL to form fifteen domains of 100 x 100 µm2 with various hole diameter and period combinations. The same number of domains with the same combinations were used to leave the polarity as the only varying parameter. The growth by CBD was subsequently achieved under identical conditions and during the same 5 ACS Paragon Plus Environment
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run of experiment. Using the precise experimental procedure, well-ordered O- and Zn-polar ZnO NRs with high structural uniformity are grown on the different domains patterned on Oand Zn-polar ZnO single crystals, respectively, and their typical dimensions are directly compared. It is unambiguously shown that the O- and Zn-polar ZnO NRs have distinct growth rates. The possible origins of the polarity-dependent nucleation and growth of ZnO NRs by CBD are discussed. EXPERIMENTAL AND THEORETICAL SECTION ZnO single crystals patterned by EBL C-plane O- and Zn-polar ZnO single crystals from CrysTec were used as substrates to control the crystal orientation and polarity of the nucleation surface. A 90-100 nm thin PMMA layer was first spin coated on both ZnO single crystals and subsequently patterned identically by EBL with fifteen different domains presenting a unique combination of hole diameters and periods. Three hole diameters of 125 ± 21, 194 ± 21, and 254 ± 22 nm were used, each of them being combined with five different hole periods of 0.6, 0.8, 1.0, 1.2, and 1.4 µm. The size of the fifteen patterned domains was 100 x 100 µm2 and the domains were separated by a distance of about 500 µm for increasing hole periods and 1000 µm for increasing hole diameters. A schematic representation of the c-plane ZnO single crystals with the fifteen patterned domains is given in Figure 2a. The patterned ZnO single crystals were eventually etched with an Evactron RF plasma cleaning system using an O2 plasma with a pressure of 0.4 Torr and a RF power of 12 W in order to remove the residual PMMA layer inside the holes. ZnO NRs grown by CBD O- and Zn-polar ZnO NRs were respectively grown using the SAG approach on top of these patterned O- and Zn-polar ZnO single crystals by CBD under identical conditions and during the same run of experiment. The solution consisted of a 0.03 M equimolar ratio of zinc 6 ACS Paragon Plus Environment
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nitrate hexahydrate Zn(NO3)2 and hexamethylenetetramine (C6H12N4) from Sigma-Aldrich, dissolved and mixed in deionized water. Each ZnO single crystal was placed face down in separate beakers containing the solution and at the same height (i.e., at approximately half the distance between its base and the waterline). They are finally heated up to 90°C for 3 h in a regular oven. The samples were eventually removed from the beakers, rinsed with deionized water, and dried with nitrogen. Electron microscopy characterizations The structural morphology of the patterned O- and Zn-polar ZnO single crystals and of the corresponding O- and Zn-polar ZnO NR arrays grown on top of them was characterized by top-view and tilted-view (30°) filed-emission scanning electron microscopy (FESEM) images using a FEI Quanta 250 FEG-SEM. To compare the radial and axial growth rates of ZnO NRs with both O- and Zn-polarity, their mean diameter and length were systematically measured for the fifteen different patterned domains on both O- and Zn-polar ZnO single crystals by FESEM image analysis using Image-J software. The apparent length of ZnO NRs was measured on the tilted-view FESEM images taken at the edge of the domains. The real length was then calculated by dividing the apparent length by sin(30°) to take into account the 30° tilt angle. As the diameter of ZnO NRs varies with their height, it was calculated at a constant height of 1 µm in order to be able to compare it between the different patterned domains. The diameter was first measured at the top of ZnO NRs using top-view FESEM images. The inclination angle was then measured on tilted-view FESEM images and used to calculate the diameter at the height of 1 µm. Thermodynamic calculations Thermodynamic computations at 90°C were achieved with Visual MINTEQ software, by considering Zn2+ ions as the single metallic cations and HO- ions and NH3 as the ligands to
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form Zn(II) hydroxide and amine complexes. The following nine soluble Zn(II) species were considered in aqueous solution: Zn2+ ions, ZnOH , ZnOH aq , ZnOH , ZnOH , ZnNH , ZnNH , ZnNH , and ZnNH . The simplified chemical mechanism is given by: Zn2+ + iL ↔ ZnL with β
! "
, !
in which L is the ligand (i.e., HO- ions or
NH3), ZnL is the complex considered, i is the coordination number, and β is the stability
constant. The stability constants β were initially taken at 25°C from NIST, and, subsequently, deduced at 90°C by using Kelley’s equation.75 The in situ pH measurements were performed with a Mettler-Toledo Seven Compact pH/Ion S220 pH meter, which was further equipped with a temperature probe.
Figure 2. (a) Schematic representation of the c-plane ZnO single crystal (in yellow) with the fifteen patterned domains (in blue), each having a different hole period/diameter combination. The hole periods are (from left to right) 0.6, 0.8, 1.0, 1.2, and 1.4 µm and the hole diameters (from top to bottom) are 125, 194 and 254 nm. (b) Top-view FESEM images of the fifteen patterned domains on the Zn-polar ZnO single crystal. The scale bar of 3 µm is valid for the whole FESEM images in (b). RESULTS
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The fifteen different patterned domains on the Zn-polar ZnO single crystal are shown by the FESEM images in Figure 2b. The hole periods used are 0.6, 0.8, 1.0, 1.2, and 1.4 µm and the measured hole diameters are 125 ± 21, 194 ± 21, and 254 ± 22 nm. The same hole diameters and periods are employed for the O-polar ZnO single crystal. Structural morphology and uniformity of ZnO nanorods The subsequent growth by CBD on both O- and Zn-polar ZnO single crystals and the structural morphology of the resulting ZnO NRs depending on the hole periods and diameters of the pattern is shown in Figure 3 by tilted- and top-view FESEM images.
Figure 3. Tilted-view FESEM images of ZnO NRs grown by CBD on patterned Zn- and Opolar ZnO single crystals for the fifteen different domains. The top and bottom triangles correspond to the growth on O- and Zn-polar ZnO single crystals, respectively. The insets are the corresponding top-view FESEM images. Except the ZnO NRs grown at the smallest period of 0.6 µm, a very well-ordered ZnO NR array is formed on the fifteen different patterned domains on both O- and Zn-polar ZnO single
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crystals. The ZnO NRs typically nucleate inside the holes in the PMMA layer and therefore grow with the same period as the pattern. Neither parasitic nanostructures nor ZnO NRs are found to grow on the PMMA layer, which inhibits their formation and thus acts as an efficient mask. The diameter of ZnO NRs appears to be larger than the hole diameter due to their radial growth out of the mask.31 For hole periods ranging from 0.8 to 1.4 µm, ZnO NRs are thus highly vertical and exhibit a very high uniformity in their structural morphology. The alignment of the m-plane sidewalls of ZnO NRs also shows a strong in-plane orientation, indicating that they have homoepitaxially nucleated on the ZnO single crystals. For the 0.6 µm hole period, where the distance between ZnO NRs is the smallest one, compact structures composed of several coalesced NRs in contact with each other occur. This phenomenon is particularly pronounced for the 125 nm hole diameter on the Zn-polar ZnO single crystal and can be ascribed to the mean diameter of ZnO NRs as large as 575 ± 42 nm, at a height of 1 µm, which is very close to the 0.6 µm distance separating adjacent NRs. It is also worth noticing that capillary forces occurring during rinsing and drying, as described in Refs. 76 and 77, might lead to these types of compact structures. A low magnification top-view FESEM image of ZnO NRs grown on the patterned Zn-polar ZnO single crystal with a 1.2 µm hole period and 194 nm hole diameter, as shown in Figure 4a, confirms that the ZnO NR array is uniform over the entire 100 x 100 µm2 patterned domain. The combination of CBD and EBL using the SAG approach is therefore suitable to control the typical dimensions in a broad range and the structural uniformity of well-ordered ZnO NR arrays over relatively large surface areas. Typical for the synthesis of ZnO NRs by CBD, a non-uniform growth occurs at the domain boundaries as seen from the tilted-view FESEM images taken at the edge of the domain patterned with a 0.6 µm hole period and a 194 nm hole diameter for ZnO NRs grown on the Zn- and O-polar ZnO single crystals in Figure 4b and 4d, respectively. The ZnO NRs at the 10 ACS Paragon Plus Environment
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edges are slightly longer and larger than the rest of the NRs, which also leads to their coalescence. This phenomenon results from the growth regime operating in aqueous solution and especially from the higher local concentration of reactants at the domain boundary.78,79 The related drastic reduction of the density of ZnO NRs at the domain boundary hence leads to larger and longer NRs than inside the patterned domains. Tilted-view FESEM images taken at the edge of the domain patterned with a 1.4 µm hole period and 194 nm hole diameter for ZnO NRs grown on patterned Zn- and O-polar ZnO single crystals as shown in Figure 4c and 4e, respectively, reveal another important feature. On both ZnO single crystals, the diameter of ZnO NRs varies with their height and is significantly smaller at their top than at their bottom (about 63 ± 6 and 52 ± 6 % smaller on average for ZnO NRs grown on the O- and Znpolar ZnO single crystals, respectively). The sidewalls of ZnO NRs are correlatively not perfectly aligned vertically and a 2-3° inclination angle is typically observed. The reduction of the diameter of ZnO NRs with their height is attributed to the layer-by-layer growth mechanism of ZnO crystal along the c-axis.72,80,81 The high axial to radial growth rate ratio is expected to result in the nucleation of a new layer before the underlying layer radial growth is completed, leading to a stack of ZnO hexagonal layers with progressively decreasing surface area.82 The local depletion of reactants has also been proposed as an additional explanation to this effect.83
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Figure 4. (a) Low magnification top-view FESEM image of ZnO NRs grown by CBD on patterned Zn-polar ZnO single crystal with P = 1.2 µm and D = 194 nm. (b-e) Tilted-view FESEM images of ZnO NRs at the edges of the domains grown on patterned (b-c) Zn- and (de) O-polar ZnO single crystals for D = 194 nm as well as P = 0.6 µm and 1.4 µm, respectively. The scale bar of 1 µm is valid for the whole FESEM images in (b-e). Polarity-dependent radial and axial growth rates of ZnO nanorods The evolution of the mean diameter and length of ratio is ZnO NRs versus the hole period and diameter is presented in Figure 5. Their ratio is given in Figure S1 in Supporting Information. First, the mean diameter and length of ZnO NRs for both polarities significantly increase respectively from 785 ± 50 to 1152 ± 52 nm and 4.17 ± 0.30 to 6.99 ± 0.30 µm for Zn-polar ZnO NRs (and from 613 ± 61 to 927 ± 76 and 3.08 ± 0.30 to 4.77 ± 0.30 for O-polar ZnO NRs) as the hole period increases from 0.8 to 1.4 µm, as shown in Figure 5a. Second, the mean diameter of ZnO NRs for both polarities is apparently independent upon the hole 12 ACS Paragon Plus Environment
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diameter, while a distinct evolution of the mean length of O- and Zn-polar ZnO NRs is revealed by increasing the hole diameter, as shown in Figure 5b. The mean length of Znpolar ZnO NRs linearly decreases for all the periods ranging from 0.8 to 1.4 µm when the hole diameter increases from 125 to 194 and 254 nm. In contrast, the mean length of O-polar ZnO NRs versus the hole diameter remains fairly constant within the error bar for all the periods considered. The Zn-/O-polar NR mean length ratio versus the hole diameter as plotted in Figure 6b correlatively decreases from 1.5 ± 0.2 to 1.1 ± 0.2 µm as the hole diameter is increased for all the periods larger or equal to 0.8 µm. A lower decrease is revealed for the smallest 0.6 µm period owing to coalescence occurring at small hole diameters.
Figure 5. (a) Evolution of the mean diameter and length of ZnO NRs as a function of the hole period for the given Zn- and O-polarity. (b) Evolution of the mean diameter and length of ZnO NRs as a function of the hole diameter for the given Zn- and O-polarity. The solid (resp.
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dashed) lines with the full (resp. open) symbols corresponds to the Zn- (resp. O-) polar ZnO NRs. Importantly and as observed in Figure 5a and 5b, the crystal polarity of ZnO NRs clearly affects their growth rate. For all possible combinations of hole periods and diameters, the mean diameter and length are larger for the Zn-polar ZnO NRs than for the O-polar ZnO NRs. The measured difference of the mean diameter of O- and Zn-polar ZnO NRs can be relatively low for the smallest hole period due to the coalescence at the edges of the patterned domain. For all the other hole periods, the difference is much larger and significant. For a hole period of 1.2 µm and a minimum hole diameter of 125 nm, a 6.99 ± 0.30 and 4.43 ± 0.30 µm mean length is measured for Zn- and O-polar ZnO NRs, respectively, which corresponds to a maximum length difference of about 34 ± 11 %. The polarity dependence of the dimensions of ZnO NRs on the hole period is highlighted by plotting the evolution of the Zn-/O-polar NR mean diameter and length ratios as a function of the hole period, as shown in Figure 6a. It is revealed, for hole periods equal or larger than 0.8 µm, that the mean length ratio of about 1.5 ± 0.2, 1.3 ± 0.2, and 1.1 ± 0.2 is reached for hole diameters of 125, 194, and 254 nm, respectively. Regarding the mean diameter of ZnO NRs, no clear trend can be drawn for the 0.6 µm hole period and 254 nm hole diameter by considering the significant error bar (i.e., 420 ± 36 nm and 429 ± 22 nm for the O- and Zn-polar ZnO NRs, respectively). However, for all the other possible hole periods equal or larger than 0.8 µm and their combinations with the hole diameter, the mean diameter is larger for Zn-polar ZnO NRs than for O-polar ZnO NRs, with a ratio ranging from 1.1 ± 0.2 to 1.3 ± 0.2 as shown in Figure 6a, which correlates with the larger mean length of Zn-polar ZnO NRs. These experimental observations unambiguously indicate higher radial and axial growth rates of Zn-polar ZnO NRs than of Opolar ZnO NRs when grown by CBD.
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Figure 6. (a) Evolution of the Zn-/O-polar ZnO NR mean diameter and length ratios as a function of the hole period. (b) Evolution of the Zn-/O-polar ZnO NR mean diameter and length ratios as a function of the hole diameter. DISCUSSION Preferential growth regime in aqueous solution In our growth conditions, it is revealed by in situ pH measurements that the pH lies in the range of 5.57 at 90°C after 40 min to 5.42 at 90°C after 180 min, as presented in Figure 7a. The Zn(II) ion complex distribution in aqueous solution as determined by thermodynamic simulations in Figure 7b is strongly dominated by the Zn2+ ions, while the #$%& and
#$'& ion complexes are formed in a much lesser extent.74
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Figure 7. (a) Evolution of the pH during the growth as a function of time for the Zn(NO3)2 and HMTA equimolar concentration of 0.03 M. The growth temperature of 90°C is reached after 40 min as shown by the vertical dashed line. (b) Speciation diagram of Zn(II) species at 90°C as a function of pH ranging from 0 to 14 as computed with Visual MINTEQ Software for the Zn(NO3)2 and NH3 equimolar concentration of 0.03 M. The orange filled rectangle represents the pH range in our growth conditions. Basically, the growth of ZnO NRs is limited either by the surface reaction for small c-plane top surface area or by the diffusive transport of reactants for larger c-plane top surface area.79 The transition between both growth regimes is mainly dependent upon the c-plane top surface area ratio, which typically lies in the broad range of 0.14 to 0.54 for the fifteen patterned domains, and upon the bulk solution concentration of Zn2+ ions. In the framework of the surface reaction- / diffusive transport-limited regime analysis considering the serial processes 16 ACS Paragon Plus Environment
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of the consumption of Zn2+ ions at the ZnO crystal growth front and of their diffusive transport from the bulk solution, the c-plane growth rate Rc-plane is given by the following relation: ( )*+,-./0
1 23 45
+
17 23 8
9
Eq. (1)
where ρ is the ZnO molar density, C∞ is the bulk solution concentration of Zn2+ ions, k1 is the surface reaction rate constant for crystallizing ZnO, δ is the stagnant layer thickness (i.e. the thickness of fluid adjacent to the substrate surface with only diffusive transport), D is the diffusion coefficient of Zn2+ ions in aqueous solution, and S is the c-plane top surface area ratio. In the present configuration, the main assumption to use the present theoretical modelling is that each domain independently works from the nearby domain, which is particularly relevant owing to their significant separation distance. The experimental growth rates are deduced from Figure 5 by dividing the length of ZnO NRs by the elongation time, which is assumed to be 140 min by considering the time of 40 min required to reach the growth temperature of 90 °C.
The two linear fits of the experimental results for both
polarities to Eq.(1) are very good, as presented in Figure 8. By taking C∞ = 30 mM, ρ = 4.20 x 1028 m-3, and D = 2.91 x 10-9 m2/s, the slope basically gives the values of the stagnant layer thickness δ while the intercept to the ordinate axis provides the values of the surface reaction rate constant k1, as summarized in Table 1. Interestingly, δ is found to be about 3.8 mm, which is in agreement with Ref. 79 and expectedly similar for both polarities. In contrast, k1 is found to be 1.83 ± 0.13 µm/s for O-polar ZnO NRs and increases to 2.95 ± 0.42 µm/s for Znpolar ZnO NRs. Accordingly, the surface reaction rate constant k1 is about sixty percent larger for Zn-polar NRs than for O-polar ZnO NRs. The Thiele modulus, measuring the degree to which the growth is limited by the surface reaction or by the diffusive transport of Zn2+ ions, is given by the following expression: 17 ACS Paragon Plus Environment
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:
45 7 8
9
Eq. (2)
By solving Eq.(2) with Φ =1, the critical c-plane surface area ratio Sc, reporting the value at which the growth switches from a surface reaction-limited regime to a diffusive transportlimited regime is deduced and gathered in Table 1. Interestingly, Sc is found to be 0.42 ± 0.07 for O-polar ZnO NRs and decreases to 0.26 ± 0.07 for Zn-polar ZnO NRs. In other words, the growth of the O-polar ZnO NRs takes place in the surface-reaction limited regime for thirteen patterned domains, as indicated in Figure 8. The present elongation regime supports the fact that the length of O-polar ZnO NRs does not depend on the hole diameter, as shown in Figure 5b. In contrast, the growth of the Zn-polar ZnO NRs proceeds in the surface reaction-limited or diffusive transport-limited regimes for half of the fifteen patterned domains each. Owing to the fact that the surface reaction rate constant k1 of Zn-polar ZnO NRs is larger, their growth rate is limited by the diffusive transport of Zn2+ ions for larger c-plane surface area ratios. By considering the error bar over Sc and its potential overestimation, the present elongation regime may to some extent account for the specific decrease in the length of Zn-polar ZnO NRs as the hole diameter is increased.
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Langmuir
Figure 8. Reciprocal c-plane growth rates of O- and Zn-polar ZnO NRs vs their c-plane top surface area ratio. The blue solid lines correspond to the linear fit to Eq.(1) with C∞ = 30 mM, ρ = 4.20 x 1028 m-3, and D = 2.91 x 10-9 m2/s. The vertical dark dashed lines delimit the transition between the surface reaction- and diffusive transport-limited elongation regimes for both polarities. The present analysis considering surface reaction- and diffusive transport-limited elongation regimes is in very good agreement with the experimental results, but has some limitations to account for all the chemical processes involved as nucleation and growth proceeds. In particular, the local conditions in terms of temperature and concentration of Zn2+ ions are expected to dynamically vary with time while the c-plane top surface area ratio is not constant either as ZnO NRs develop. The characteristics of the nucleation phase are also likely dependent upon the polarity and the correlated surface structural quality. Zn-polar ZnO single crystals have a higher density of surface defects and steps for instance, which should affect the nucleation rate of ZnO NRs.2,13,17,70,84,85 The different contributions to the overall growth time (including the incubation, nucleation, and elongation times) may also depend on the polarity,86 but their variation is here expected to be small with respect to the selected overall growth time of 180 min. As a consequence, the higher growth rate of Zn-polar ZnO NRs and, correlatively, the larger surface reaction rate constant k1 are expected to result from two contributions, namely i) the dangling bond configuration at the growing interface that is related to the surface termination of both O- and Zn-polar ZnO single crystals during the nucleation phase and that is inherent to the alternate stack of O and Zn atom planes at the top c-faces of ZnO NRs during the growth phase, as the main contribution, and ii) the interactions (e.g., electrostatic interactions) between these charged polar c-faces and the ionic species in aqueous solution
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Langmuir
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such as Zn2+ and HO- ions. A schematic representation of the possible mechanisms accounting for the polarity dependent growth of ZnO NRs is presented in Figure 9. k (µm/s) δ (mm) Sc O-polar 1.83 ± 0.13 3.81 ± 0.36 0.42 ± 0.07 ZnO NRs Znpolar 2.95 ± 0.42 3.78 ± 0.46 0.26 ± 0.07 ZnO NRs Table 1. Extracted k, δ and Sc values for O- and Zn-polar ZnO NRs. Polarity-dependent dangling bond configurations The polarity dependent growth rate of wurtzite ZnO has been reported for thin films and NRs grown by vapor phase techniques.22,24,36 The faster growth rate of Zn-polar ZnO thin films as compared to the O-polar ones is commonly explained by the different dangling bond configuration at the growing interface.36 Under O-rich conditions, both O- and Zn-polar ZnO surfaces are O-terminated and each O atom of the Zn-polar ZnO surface have three dangling bonds along the c-axis, in contrast to the O-polar ZnO surface where only one dangling bond per O atom is left. This configuration is expected to promote the more efficient incorporation of Zn atoms on the Zn-polar ZnO surface in comparison with the O-polar ZnO surface and typically results in the different growth rates observed. In the case of the hydrothermal growth of ZnO crystals at high temperature, a preferential growth along the Zn-polar c-axis has also been reported.11,35,37 It has been stated that the hydrothermal growth of ZnO crystals is obtained by the formation of growth units, typically #$%& ions, which are incorporated at the ZnO growing crystal interface. The growth rate is accordingly tailored by the orientation of the #$ − %
