Atomic-Layer Deposition into 2- versus 3-Dimensionally Ordered

Subscriber access provided by - Access paid by the | UCSB Libraries

Article

On the Atomic Layer Deposition into 2- versus 3- Dimensionally Ordered Nanoporous Media: Pore Size or Connectivity? Changdeuck Bae, Hyunchul Kim, Eunsoo Kim, Hyung Gyu Park, and Hyunjung Shin Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.8b01615 • Publication Date (Web): 27 Jun 2018 Downloaded from http://pubs.acs.org on June 28, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Chemistry of Materials

On the Atomic Layer Deposition into 2- versus 3Dimensionally Ordered Nanoporous Media: Pore Size or Connectivity? Changdeuck Bae,1* Hyunchul Kim,1 Eunsoo Kim,1 Hyung Gyu Park2 and Hyunjung Shin1* 1

Department of Energy Science, Sungkyunkwan University, Suwon 440-746, South Korea

2

Department of Mechanical and Process Engineering, Eidgenössische Technische Hochschule (ETH)

Zurich, Zurich 8092, Switzerland *

To whom the correspondence should be addressed. C.B. ([email protected]), and H.S.

([email protected])

ACS Paragon Plus Environment

Chemistry of Materials 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 21

ABSTRACT Atomic layer deposition (ALD) is now being recognized as a powerful, general tool for modifying the surfaces of nanomaterials in applications for many energy conversion devices. However, ALD involves slow processes particularly when it is subjected to nanoporous media with high-aspect ratios. Predicting the exact experimental conditions of desired reactions for coating inside deep pores by ALD is not available because of the lack of complete understanding of diffusion in nanoporous media. Here, we report a comparative study of the ALD coating onto two distinctive templates having nanopores, i.e., two- and three-dimensionally ordered media (DOM), of similar porosity and pore dimension. Selfsupporting, crack-free templates were carefully prepared in centimeters for both 2- and 3-DOM, and thus avoid any possible sources of uncontrollable diffusion of precursor gas molecules through unwanted microvoids and cracks. Comparison of the ALD coating profiles across the thickness of both templates reveals fundamentally distinct coating mechanism; while a uniform growth zone develops along the pores of the 2-DOM (i.e., 1-D diffusion path), a gradual decrease in the deposition is observed in those of the 3-DOM (i.e., 3-D diffusion path) as ALD pulse time increases. This observation suggests an essential role of the pore connectivity, rather than individual pore sizes, in the gas diffusion dynamics inside nanoporous media. The present model can universally predict the ALD behaviors into nanoporous media even with different types of pore connectivity.


2

Page 3 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


MAIN TEXT Diffusion in nanoporous media is of paramount importance in biophysics,1 batteries,2 fuel cells,3 catalysts,4 separation membranes,5 and many other reaction-diffusion processes.6 Although materials containing pores are traditionally categorized into microporous (< 2 nm), mesoporous (2 - 50 nm), and macroporous (> 50 nm) materials,7 a term, “nanoporous,” is becoming popular with increasing research activities in nanoscience and technology.8 Conventionally, the nanopores refer to 100 nm in diameter or smaller because they originate from nanomaterials having sub-100-nm dimension.9 Nanoporous materials often bear a mixture of micro-, meso- and/or macropores within their pore network. Defining the physical dimension of the nanoscale pores (e.g., diameter, 2r) is critical in that the types of diffusion are determined by the mean free path (λ) of the moving particles inside. Most of the studies on describing the diffusion phenomena in nanoporous materials assume two distinctive cases: Knudsen diffusion for relatively long λ in comparison to 2r (i.e., mesoporous systems) where the molecules frequently collide with the pore walls;10 and molecular diffusion (λ ≪ 2r) where intermolecular collision dominates the momentum and energy exchange.11 Knudsen diffusion is described by the EinsteinSmoluchowski relation as follows:12 () = lim→

〈| () − (0)| 〉

(1)

where Ds is the self-diffusion coefficient as a function of the concentration, c, t is time, N is the number of particles, and ri is the position vector of the i-th particle. The real-world applications involve more complex reaction-diffusion processes in the presence of concentration/pressure gradients, with varying the collision probability. It implies that Knudsen number (Kn = λ/2r) goes far below the unity in the region of interest, and gas transport within the system is governed by Fick’s law (i.e., driving force in the concentration):13


3


= − () ∙ ∇

Page 4 of 21

(2)

where j is the mass flux, Dt is the transport diffusion coefficient, and ∇c is the concentration gradient. Therefore, the fact that the pore dimensions of nanoporous materials span across mesopores and macropores and that the presence of the concentration/pressure gradients in reaction-diffusion processes imply complexity in the analysis of diffusion dynamics in nanostructured materials. Furthermore, nanoporous media have not only morphological effects on surface roughness of the material itself but also topological ones on the connectivity of pore networks. Indeed, Roy et al. have shown that the presence of pore trapping zones could further lead to diminution of Ds.14 Atomic layer deposition (ALD) is a variant of chemical vapor deposition (CVD) for it brings chemical reactions of desire onto surfaces through chemical design using precursor molecules.15 It differs from CVD in that the thermal decomposition of precursors that might be involved in the target reactions does not take place, resulting in the overall surface reactions in a sequential, self-limiting manner.16 As a result, ALD is capable of controlling the resulting layers of materials down to sub-unitcell thicknesses and suitable for the conformal coating of nanostructures of very high aspect ratio.17 Combined with the recent progresses in the chemical synthesis of precursor molecules, ALD is actively seeking a wide range of applications by applying its capability to nanoporous materials/systems. Materials systems available in the literature range from diverse oxides through compound semiconductors to noble metals.18 When applied to nanostructured devices/systems, the discrete and/or continuous ALD layers should produce synergetic effects on the performance with the large specific surface area by the unconventional junction interfaces difficult to create by other methods. Recent studies report that the resulting topologies of the ALD-grown materials pertain the charge transport properties.19,20 ALD on nano/micro powders also offer a great deal of potential for many applications in the fabrication of novel core/sheath and composite particles.21,22 Even in this case, the particles before


4

Page 5 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


and after coating could form large agglomerates during reactions, and estimating the exquisite experimental conditions is the key. Despite the great promise of this strategy, the lack of understanding of the transport phenomenon in nanoporous media currently hampers the prediction of the reliable experimental conditions for desired ALD processes in depth.23,24 Gordon and co-workers have developed a kinetic model to describe the ALD coating on the hole/trench surfaces.25 The key idea is based on the transmission probability with a nonlinear function along pore length when molecules enter the pore.26 The exposure condition on planar surfaces is given by Eq. 3. " = #√2π'()

(3)

where P is the partial pressure of the precursor near the surface (Pa), m is the molecular mass (kg), k is the Boltzmann constant (1.38 × 10−23 J·K−1), T is the temperature (K), t is the time required for the vapor to supply a saturation dose, S. In Eq. 3, a non-SI (International System of Units) unit, Langmuir = 10−6 torr·s, was intendedly used to directly produce the exposure time, t by Pt. This value allows an idea on the typical experimental conditions of ALD in a more intuitive manner. The exposure in ALD on the narrow hole/trench surfaces is given in Eq. 4: " = #√2π'() *1 + where / is the aspect ratio,

2

3

.

0

/ + / 1

(4)

, of a hole with the radius, r, and the pore length, L. Note that Eq. 4 has

been proven experimentally in describing the ALD of HfO2 and ZrO2 layers for both of trench and hole pores.27,28 Although Eq. 4 is universal and is practically valid when 2r ≪ λ, in the literature, the difficulties in conformally coating other types of nanoporous templates such as sintered nanopowders and opals are often found.21,22 Note that both types of media (trench/hole versus powder/opal) have


5


Page 6 of 21

similar physical dimension of pores (i.e., 2r ≪ λ). The origin of such controversial observations remains elusive to date. Here, we clarify the significance of the configuration of pore network in diffusion in nanoporous media by comparatively studying the ALD of TiO2 as a model functional material onto two different kinds of nanoporous templates. Crack-free templates were carefully prepared in centimeters for both 2and 3-DOM to eliminate possible sources of uncontrollable gas-phase diffusion of precursor molecules through micropores. By monitoring the thickness profiles in depth upon ALD on both templates, we found out that even under the identical experimental conditions, the resulting thickness profiles differ fundamentally from each other. While the uniform growth zones were observed along 2-DOM pores, a gradual decrease in thickness was observed in 3-DOM. Remarkably, Eq. 4 failed when the pore configuration deviates from that of the 1D cylinder, indicating that the way how pores are connected is essential in diffusion in nanoporous media. The fact that this discrepancy of diffusion can be modeled simply by introducing tortuosity suggests that the primary effect of the pore connectivity in nanoporous diffusion lies in the effective residence time of the molecules diffusing across the porous media. The study began by carefully considering the conditions of two model templates. Three key prerequisites include: (i) similar porosities; (ii) distinctive pore connectivities; (iii) crack- or void-free media. We chose anodic alumina membranes (AAMs) and silica synthetic opals (SSOs) as model 2and 3-DOM, respectively. Note that AAMs represent 1D cylindrical pores, and SSOs, 3D pores in view of the diffusion paths (Fig. 1A and D). While the porosity of as-grown opals has a fixed value of 26 % (for close-packed lattices), that of AAMs is tunable in between 13 to 74 % (assuming the triangular 2D lattice) via so-called pore-widening processes with aqueous phosphoric acid. AAM samples we used here were prepared with well-known two-step anodization methods to have 25-30 % in porosity in oxalic acid (Fig. 1C).29,30 The physical dimensions of the pore cross-section were also selected carefully


6

Page 7 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


at a cross-over point between AAMs and SSOs. The depth of pores in AAMs is tailorable by controlling the charge currents during anodization, and the resulting AAMs are free-standing and crack-free in a centimeter scale after removal of aluminum (Fig. 1B, after removing the back-side Al mostly). Preparing crack-free opals is essential in that the cracks should incur uncontrollable gas-phase diffusion of precursor molecules. In SSOs, the formation of microcracks has been known to be inevitable because silica beads prepared by the sol-gel Stöber process contain substantial amounts of water within their surfaces. Upon self-assembly and subsequent drying of SSOs, such cracks additionally make them not self-suspending and intact mechanically although SSOs can be grown on various substrates. Chabanov et al. have reported that the heat treatment of silica beads prior to self-assembly can effectively avoid the crack formation.31 Following this method, we successfully prepared crack-free SSOs in a centimeter scale, and the resulting SSOs upon released from glass vials (Fig. 1E) show only stacking faults and vacancies at their surfaces (Fig. 1F, also see Fig. S1 for more details). Indeed, without any supporting substrates, our single-crystalline SSOs are freestanding (Fig. 1E), indicative of the presence of no macroscopic cracks.


7


Page 8 of 21

Fig. 1. Preparation of the self-suspending and crack-free two- and three-dimensional ordered media (2and 3-DOM) as model templates. Schematic illustrations of diffusion dynamics in (A) anodic alumina membranes (AAMs), and (D) silica synthetic opals (SSOs). Photographs of (B) the resulting AAMs and (E) SSOs. The representative SEM micrographs of (C) the cross-sectional AAMs, (inset, plan view), and (F) the SSOs, (inset, a magnified photo).


8

Page 9 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Once the crack-free, self-supporting 2- and 3-DOM are prepared with very similar porosity values, TiO2 layers were grown onto both porous media under the identical ALD conditions (except for pulse time, tp). Titanium (IV) isopropoxide (TTIP, UP Chemical, South Korea) and water were used as precursors, and argon (5N) as purging gas. The ALD process was carried out in a shower-head type reactor (Ozone, Forall, South Korea) under a so-called flow-through mode (i.e., maximal concentration gradient by continuous evacuation when precursor molecules are exposed), which is suitable in such a study. A full cycle consists of tp of 1-30 s for both precursors, followed by purging for 5-150 s. The pore surfaces have an equal distance with respect to the shower head. Then, the resulting thicknesses, d, were measured in depth with the micrographs taken by both transmission electron microscopy (TEM) and scanning electron microscopy (SEM) upon thermal annealing at 400 °C for ~1 hr (see Fig. 2 and Fig. 3). The annealing leads to the phase transformation from amorphous to anatase TiO2, further rendering its chemical resistance during wet etching of the templates in KOH.32 First of all, the length of nanotubes obtained by ALD of 2-DOM was a function of tp, as expected in Eq. 4 (also see Fig. S3). The separation between the saturation and under-saturation regions along the pore was clearly visible in the thickness profiles (Fig. 2C, 2D). Note that in the uniform growth zone, the variation in dAAM must come from the Wulff construction of anatase TiO2 in the confined geometry, rather than non-uniformity in the resulting thicknesses.33


9


Page 10 of 21

Fig. 2. Results of the diffusion through 1D nanopores (2-DOM) by observing the thicknesses of ALDgrown layers along the pores. (A) SEM and (B) TEM of the TiO2 nanotubes released from AAMs by wet-chemical etching. (C) The representative thickness profiles from selected tp, measured with TEM mosaics such as panel (D). The uniform thickness zones were highlighted by colored areas.

dSSO was also measured in the same way upon thermal annealing at 400 °C for ~1 hr, followed by wet etching of SSOs in diluted HF. The large-area inverse opals of TiO2 remained intact in structure (Fig. 3A-E, also see Fig. S2 for more data with different experimental conditions). The difference in dSSO between the structures near the distal pores (Fig. 3D) and around the deep pores (Fig. 3E) is unambiguously seen by the self-collapsed hollows. Remarkably, while dAAM in the saturation zone was uniform up to about 3 micrometers only at tp = 1 s, the overall dSSO was gradually decreased in depth inside SSOs even for tp = 10 s. Such a trend was similar in control experiments with different diameters of silica beads (Fig. 3F). The depths of ALD coating between AAM by tp = 1 s and SSO by tp = 10 s were comparable each other, indicative of the strong suppression of precursor diffusion along the


10

Page 11 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


nanopores of SSOs. Reported for the first time in this study with carefully prepared and reliable model templates, this observation is understood intuitively by the unique nature of 3D pores (Fig. 1D). Considering λ ≈ several micrometers, connectivity of the pores inside 2- and 3-DOM should be critical because the characteristics of scattering events differ between each other as expected (schematically illustrated in Fig. 1A and 1D). The present observation should be beneficial for fabricating inverse opals having gradient-index on a large scale. Fig. 3G exhibits the photonic band gaps of TiO2 inverse opals when prepared with different tp. The optical shifts could be understood in the context of systematic changes in effective refractive indices.34 Briefly, the optical spectra at about 600 through 800 nm do not correspond any materials absorption because the present TiO2 structures have anatase form to be a bandgap of 3.2 eV (ca. 387.5 nm). The resulting spectral patterns at longer wavelengths come from the titania inverse opals that had been originally close-packed via self-assembly of monodisperse silica beads. They correspond to the pseudogap between the second and third bands at the L point of the first Brillouin zone, as confirmed with the modified Bragg law, λmax = 2D ε eff where D is the distance between the crystal planes and εeff is the volume-averaged effective dielectric constant;

ε eff = ( n1 ) 2 f + ( n2 ) 2 (1 − f ) where f is the crystal filling fraction and n is the refractive index. That is, the peaks at 650 - 700 nm (Fig. 3G) could be assigned to the positions of the (111) stop gaps of 360 nm titania (n2 = 2.49) inverse opals. The detailed calculation results with the uniform d could be found in Supporting Information (Table S1). Although the present structures have gradients in the thickness (i.e., dSSO) along L and, estimating the exact prediction of εeff is not easy. Nonetheless, the observed positions well correspond to the pseudogaps assuming d = 10~15 nm. Moreover, the detected blue shifts could be understood by the increasement of εeff with increasing tp, indicative of the capability of fine-tuning the desired optical properties.


11


Page 12 of 21

Fig. 3. Results of the nanopore diffusion through 3D networks (3-DOM) by observing the thicknesses of ALD-grown layers along the pores. (A-D) SEM images of the TiO2 inverse opals liberated from SSOs upon etching at different magnifications. (F) The representative thickness profiles (tp = 10 s, 600 cycles) measured with SEM mosaics such as panel (E), (insets, TEM results). The uniform thickness zones were not clearly defined. (G) Optical reflectance spectra of TiO2 inverse opals (2Rsso = 360 nm) with different tp.


12

Page 13 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The experiments have shown that the pore connectivity is critical in performing ALD of nanoporous materials even in the similar, meso-to-microporous pore size regimes. The estimation of diffusion behaviors would fail by this quasi-1D diffusion/heat equations only. To fill this gap for the tendency in d, we propose that the introduction of tortuosity can result in a good estimation of the thickness profiles of ALD-layers, in general, into diffusion within nanoporous media. The tortuosity, τ, represents the actual paths through the porous media, defined by the arc-chord ratio: 5

τ = 6

(5)

where M is the length of the curve to the distance (C) between the two points. By substituting Eq. 5 to Eq. 4, consequently, we obtain a tortuosity-correlated form of Gordon’s equation:

" 7 =

=> ?

A B

√89:;*< @< @B 1 C

(6)

where 7 is time for the revised tp. For a straight line that implies the 1D path as in our AAMs, τ equals to one and does not affect the original Gordon equation. As for 3-DOM, however, the curved path results in increasing the denominator, leading to the estimation of the prolonged tp. We also have proven the present solution, by performing numerical calculations on the thickness profiles of TiO2 layers by solving differential equations on the basis of Fick’s law.35 Uniform zones were visible as functions of both tp and 2rAAM as expected and in the previous reports by others23 (Fig. 4, dotted lines). Additionally, we applied the τ correction to ALD of 3-DOM (also see Fig. S4). As seen in the results (Fig. 4, solid lines), the overall uniform zones were reduced with respect to pore depth, L. This observation strongly suggests that the pore connectivity affects the residence time of the diffusing precursor molecules and that the simple correlation by τ is truly practical in the experimental design of ALD into nanoporous media.


13


Page 14 of 21


14

Page 15 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 4. Calculation results on the thicknesses of the ALD-grown TiO2 layers by solving differential equations upon the correction by tortuosity (τ) of 3-DOM. By comparing the results at tp = 1 s and 10 s (panels A and B, respectively), the simulations fit well with our experiments, indicative of the feasibility of the utility of τ -correction when ALD is applied for nanoporous media. The inset illustrations represent the approximated diffusion paths (dotted blue lines) in order to apply τ -correction (dotted black lines). The open hexagons and closed circles represent experimentally measured dAAM and dSSO (d = thickness of TiO2), respectively. The vertical and dotted sky blue lines were used for comparison between the top and bottom lines.

Finally, we discuss other effects on the coating of nanoporous media by ALD. We also observed a higher growth rate (0.45 Å/cycle) of TiO2 on the pore-entering surfaces (i.e., L ≈ 0) in the case of SSOs than that on both planar and AAM substrates (0.40 Å/cycle). This observation could not be understood in the context of the ideal ALD growth because we assume that the precursor molecules on surfaces is saturated at equilibrium distance. However, the ideal mode deviates chemistry by chemistry in practice, except for the ALD of trimethylaluminium and water for Al2O3. The authors claim that the enhanced collision near the entering pores might affect the molecular saturation. Similar behaviors have been reported in the ALD of WN into opals.36 Therefore, it could be understood by the increased normal-mode diffusion (a type of diffusion modes where mutual inter-transports of particles take place along the pore). This is because the back-side diffusion was boosted near the molecular entrance (with the nature of 3D pore connectivity) although diffusion in forward direction is originally expected from the pore entrance to the deep pores as a result of concentration gradients. Therefore, the reaction probability of the precursor molecules was enhanced accordingly. Capillary condensation would be another trapping source of water (if used) at around the contact or sintering points when ALD is applied


15


Page 16 of 21

for 3-DOM. Considering the slow kinetics of capillary condensation (~ hours),37 however, we could rule out this possibility during typical ALD processes having tp of ~ seconds. We also highlight that the present approach can generally describe the diffusion behaviors of 3D media with other pore structures. Porous media consisting of irregular particles could be first approximated into spherical ones, and by introducing a structural factor, n (see Fig. 5), we obtain the corresponding τ values. This further explains why the coating by ALD in micropores is difficult as a result of very limited transmission probability.

Fig. 5. Generalization of τ -correction with different pore sizes (A and B) by introducing a structural factor, n.


16

Page 17 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


In conclusion, we presented a comparative study of the ALD coating onto two distinctive nanoporous templates (2- versus 3-DOM). Crack-free templates were carefully prepared in centimeters and possible sources of uncontrollable gas-phase diffusion were ruled out. With the resulting thickness profiles, we found out that even under the identical experimental conditions, the resulting profiles fundamentally differ from each other. The pore connectivity was the key in the gas-phase diffusion dynamics inside nanoporous media. A corrected model in the estimation of ALD procedures was proposed by considering tortuosity. The present model study helps universally describe the ALD coating of nanoporous media even with different types of pore connectivity.

ASSOCIATED CONTENT AUTHOR INFORMATION Corresponding Author * To whom correspondence should be addressed. C.B. ([email protected]) and H.S. ([email protected]) Author Contributions C.B. and H.S. conceived the project. C.B. and H.K. prepared the samples, and analyzed the structures. C.B. and E.K. carried out the calculation. C.B., H.G.P., and H.S. wrote the manuscript. All authors reviewed the paper. Notes The authors declare no competing ﬁnancial interest. ACKNOWLEDGMENT


17


Page 18 of 21

This research was supported by National R&D Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (2018R1D1A1B07051059; 2017R1A4A1015770; 2018K1A3A1A32055268). Supporting Information The estimation of photonic bandgaps; additional SEM micrographs of silica opals; cross-sectional SEM images of TiO2 inverse opals obtained under various experimental conditions; tp-dependent results on dAAM; calculation results without and with tortuosity.


18

Page 19 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TOC graphic

REFERENCES

1

Retan, N. K.; Juthajan, A.; Lindmo, T.; de Lange Davies, C. Macromolecular Diffusion in the Extracellular Matrix Measured by Fluorescence Correlation Spectroscopy, J. Biomed. Opt. 2008, 13, 054040 2

C. Zhu, R. E. Usiskin, Y. Yu, J. Maier, The nanoscale circuitry of battery electrodes, Science 2017, 358, eaao2808 3

Shao, Z.; Haile, S. A High-Performance Cathode for the Next Generation of Solid Oxide Fuel Cells, Nature 2004, 431, 170–173 4

C. Costentin, C. D. Giovanni, M. Giraud, J.-M. Savéant, C. Tard, Nanodiffusion in electrocatalytic films, Nat. Mater. 2017, 16, 1016–1021 5

Striemer, C. C.; Gaborski, T. R.; McGrath, J. L.; Fauchet, P. Charge- and Size-Based Separation of Macromolecules Using Ultrathin Silicon Membranes, Nature 2007, 445, 749–753 6

Ghosh, PK.; Hänggi, P.; Marchesoni, F.; Martens, S.; Nori, F.; Schimansky-Geier, L.; Schmid, G. Driven Brownian transport through arrays of symmetric obstacles, Phys Rev E 2012, 85, 011101 7

IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997).

8

R. E. Morris, P. S. Wheatley, Gas Storage in Nanoporous Materials, Angew. Chem. Int. Ed. 2008, 47, 4966–4981 9

Y. Xia, P. Yang, Y. Sun, Y. Wu, B. Mayers, B. Gates, Y. Yin, F. Kim, H. Yan, One-Dimensional Nanostructures: Synthesis, Characterization, and Applications, Adv. Mater. 2003, 15, 353–389 10

Welty, James R.; Wicks, Charles E.; Wilson, Robert E.; Rorrer, Gregory L. (2008). Fundamentals of Momentum, Heat and Mass Transfer (5th ed.). Hoboken: John Wiley and Sons.


19


Page 20 of 21

11

B. Hosticka, P.M Norris, J.S Brenizer, C.E Daitch, Gas flow through aerogels, J. Non-Cryst. Solids 1998, 225, 293-297 12

K. Malek, M.-O. Coppens, Knudsen self- and Fickian diffusion in rough nanoporous media, J. Chem. Phys. 2003, 119, 2801-2811 13

Fick, A. On liquid diffusion, Poggendorffs Annalen. 1855, 94, 59

14

S. Roy, R. Raju, Modeling gas flow through microchannels and nanopores, J. App. Phys. 2003, 93, 4870-4879 15

S. M. George, Atomic Layer Deposition: An Overview, Chem. Rev. 2010, 110, 111–131

16

T. A. Ho, C. Bae, S. Lee, M. Kim, J. M. Montero-Moreno, J. H. Park, H. Shin, Edge-On MoS2 Thin Films by Atomic Layer Deposition for Understanding the Interplay between the Active Area and Hydrogen Evolution Reaction, Chem. Mater. 2017, 29, 7604–7614

17

C. Bae, H. Shin, K. Nielsch, Surface modification and fabrication of 3D nanostructures by atomic layer deposition, MRS Bull. 2011, 36, 887-897 18

V. Miikkulainen, M. Leskelä, M. Ritala, R. L. Puurunen, Crystallinity of inorganic films grown by atomic layer deposition: Overview and general trends, J. Appl. Phys. 2013, 113, 021301

19

N. Yazdani, D. Bozyigit, I. Utke, J. Buchheim, S. K. Youn, J. Patscheider, V. Wood, H. G. Park, Enhanced Charge Transport Kinetics in Anisotropic, Stratified Photoanodes, ACS Appl. Mater. Interfaces, 2014, 6, 1389–1393 20

M. Kim, C. Bae, H. Kim, H. Yoo, J. M. M. Moreno, H. S. Jung, J. Bachmann, K. Nielsch, H. Shin, Confined Crystallization of Anatase TiO2 Nanotubes and Its Implications on the Transport Properties, J. Mater. Chem. A 2013, 1, 14080-14088 21

J. A. McCormick, B. L. Cloutier, A. W. Weimer, S. M. George, Rotary reactor for atomic layer deposition on large quantities of nanoparticles, J. Vac. Sci. Technol. A 2007, 25, 67-74

22

C.L. Duan, X. Liu, B. Shan, R. Chen, Fluidized bed coupled rotary reactor for nanoparticles coating via atomic layer deposition, Rev. Sci. Instrum. 2015, 86, 075101

23

S. O. Kucheyev, J. Biener,T. F. Baumann,Y. M. Wang, and A. V. Hamza, Z. Li, D. K. Lee, R. G. Gordon, Mechanisms of Atomic Layer Deposition on Substrates with Ultrahigh Aspect Ratios, Langmuir, 2008, 24, 943–948 24

J. W. Elam, D. Routkevitch, P. P. Mardilovich, and S. M. George, Conformal Coating on UltrahighAspect-Ratio Nanopores of Anodic Alumina by Atomic Layer Deposition, Chem. Mater. 2003, 15, 3507–3517

25

R.G. Gordon, D. Hausmann, E. Kim, J. Shepard, A Kinetic Model for Step Coverage by Atomic Layer Deposition in Narrow Holes or Trenches, Chem. Vap. Dep. 2003, 9, 73–78

26

P. Clausing, Ann. Phys. (Leipzig) 1930, 5F, 567


20

Page 21 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


27

Perez, I.; Robertson, E.; Banerjee, P.; Henn-Lecordier, L.; Son, SJ.; Lee, SB.; Rubloff, GW. TEMbased metrology for HfO2 layers and nanotubes formed in anodic aluminum oxide nanopore structures, Small 2008, 4, 1223-1232 28

H. Kim, M. Kim, C. Bae, E. Kim, S. Lee, J.M. Montero-Moreno, H.S. Jung, and H. Shin, Enhanced Stabilization of Tetragonal (t) – ZrO2 in the Controlled Nanotubular Geometry”, RSC Adv. 2015, 5, 80472 – 80479 29

M. Kim, H. Kim, C. Bae, J. Lee, H. Yoo, J. M. Montero Moreno, H. Shin, Initial Self-Ordering of Porous Anodic Alumina: Transition from Polydispersity to Monodispersity, J. Phys. Chem. C 2014, 118, 26789–26795

30

H. Yoo, C. Bae, Y. Yang, S. Lee, M. Kim, H. Kim, Y. Kim, H. Shin, Spatial Charge Separation in Asymmetric Structure of Au Nanoparticle on TiO2 Nanotube by Light-Induced Surface Potential Imaging, Nano Lett. 2014, 14, 4413–4417 31

A. A. Chabanov, Y. Jun, D. J. Norris, Avoiding cracks in self-assembled photonic band-gap crystals, Appl. Phys. Lett. 2004, 84, 3573 32

C. Bae, Y. Yoon, W.-S. Yoon, J. Moon, J. Kim, H. Shin, Hierarchical Titania Nanotubes with SelfBranched Crystalline Nanorods, ACS Appl. Mater. Interfaces. 2010, 2, 1581–1587

33

H. Yoo, M. Kim, C. Bae, S. Lee, H. Kim, T. K. Ahn, H. Shin, Understanding Photoluminescence of Monodispersed Crystalline Anatase TiO2 Nanotube Arrays, J. Phys. Chem. C 2014, 118, 9726–9732 34

C. Bae, J. Moon, H. Shin, J. Kim, M. M. Sung, Fabrication of Monodisperse Asymmetric Colloidal Clusters by Using Contact Area Lithography (CAL), J. Am. Chem. Soc., 2007, 129, 14232–14239 35

N. Yazdani, V. Chawla, E. Edwards, V. Wood, H. G. Park, I. Utke, Modeling and optimization of atomic layer deposition processes on vertically aligned carbon nanotubes, Beilstein J. Nanotechnol. 2014, 5, 234–244 36

A. Rugge, J.S. Becker, R. G. Gordon, S. H. Tolbert, Tungsten Nitride Inverse Opals by Atomic Layer Deposition, Nano Lett. 2003, 3, 1293–1297 37

Restagno, F.; Bocquet, L.; Biben, T. Metastability and nucleation in capillary condensation, Phys. Rev. Lett. 2000, 84, 2433-2436


21

Atomic-Layer Deposition into 2- versus 3-Dimensionally Ordered

Recommend Documents