Experimental Design Applied to Spin Coating of 2D Colloidal Crystal

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Experimental Design Applied to Spin Coating of 2D Colloidal Crystal Masks: A Relevant Method? Pierre Colson,* Rudi Cloots,* and Catherine Henrist* Chemistry Department, Group of Research in Energy and Environment from Materials (GreentMAT), University of Liege, Allee de la Chimie 3, Building B6, 4000 Liege, Sart Tilman, Belgium ABSTRACT: Monolayers of colloidal spheres are used as masks in nanosphere lithography (NSL) for the selective deposition of nanostructured layers. Several methods exist for the formation of self-organized particle monolayers, among which spin coating appears to be very promising. However, a spin coating process is defined by several parameters like several ramps, rotation speeds, and durations. All parameters influence the spreading and drying of the droplet containing the particles. Moreover, scientists are confronted with the formation of numerous defects in spin coated layers, limiting well-ordered areas to a few micrometers squared. So far, empiricism has mainly ruled the world of nanoparticle self-organization by spin coating, and much of the literature is experimentally based. Therefore, the development of experimental protocols to control the ordering of particles is a major goal for further progress in NSL. We applied experimental design to spin coating, to evaluate the efficiency of this method to extract and model the relationships between the experimental parameters and the degree of ordering in the particles monolayers. A set of experiments was generated by the MODDE software and applied to the spin coating of latex suspension (diameter 490 nm). We calculated the ordering by a homemade image analysis tool. The results of partial least squares (PLS) modeling show that the proposed mathematical model only fits data from strictly monolayers but is not predictive for new sets of parameters. We submitted the data to principal component analysis (PCA) that was able to explain 91% of the results when based on strictly monolayered samples. PCA shows that the ordering was positively correlated to the ramp time and negatively correlated to the first rotation speed. We obtain large defect-free domains with the best set of parameters tested in this study. This protocol leads to areas of 200 μm2, which has never been reported so far.

’ INTRODUCTION Originally developed by Deckman et al.,1 nanosphere lithography (NSL) was further optimized by the Van Duyne group2 in the 1990s as a fast and inexpensive fabrication tool for producing regular arrays of nanoparticles and is becoming more and more popular.3,4 First, it consists of the preparation of a two-dimensional (2D) colloidal crystal5 mask (monolayer or double layer) made of monodisperse colloids (e.g., silica and polymer latex). These 2D patterns can then be used as a physical mask for subsequent additive deposition2,6,7 or subtractive etching processes.8,9 In a last step called lift-off, the mask is removed and the sputtered layer or substrate keeps the ordered patterning of the mask interstices. NSL is also known as colloidal lithography.7,10 Templated metallic nanodot arrays obtained by this technique have been used as surface enhanced Raman scattering (SERS) substrates for sensitive chemical and biological sensors, as well as catalysts for the growth of ordered one-dimensional (1D) nanostructures, such as nanowires11 or carbon nanotubes.12 The nanosphere lithography has also been employed to manufacture superhydrophobic coatings,13,14 microlens arrays,15 or ultrasmall organic light-emitting diodes.16 Besides, monolayers of dielectric spheres deposited on metallic substrates can strongly modify the emission of organic dyes contained in the spheres through coupling to hybrid plasmonic photonic modes of the structures.17 Moreover, three-dimensional (3D) colloidal crystals have also been extensively studied due to their potential applications as r 2011 American Chemical Society

diffractive optical devices,18 chemical and biosensors,19 or photonic crystals.20 24 In general, the preparation of these multilayered PS beads is much more facile than that of a uniform monolayer, but is not in the scope of this study. Several methods exist for the formation of self-organized particle monolayers such as the Langmuir Blodgett technique,6,25 controlled evaporation of solvent from a suspension containing latex particles,26 29 floating-transferring technique,30 convective self-assembly,31,32 dip coating,33,34 or spin coating.2 The first description of 2D array formation from colloid particles was reported by Perrin35 in his work on determining the Avogadro number. Hayahsi et al.36 investigated imaging by particles of polystyrene latexes. Those studies present observation of the final result of ordering, without considering the forces governing the ordering. Nagayama and co-workers37 39 performed pioneering work on the mechanism and stages of the process of ordering. They focused their research on the comprehension of interactions between colloidal nanospheres, which force them to organize into a 2D hexagonal close-packed array on a solid substrate or in thin films of liquids. The group of Scriven24,40 studied the mechanistic

Received: June 17, 2011 Revised: September 20, 2011 Published: September 20, 2011 12800

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Langmuir principles of 3D colloidal crystal growth by evaporation-induced convective steering. Deegan et al.41 examined the formation of ring-stain deposits in drying drops containing dispersed solids. They ascribed the characteristic pattern of the deposition to a form of capillary flow in which pinning of the contact line of the drying drop ensures that liquid evaporating from the edge is replenished by liquid from the interior. Parameters such as temperature31 or concentration42 have been proven to have a significant impact on the evaporation rate for a given colloidal deposition process. The evaporation of solvent can be accelerated by carefully spin coating the colloidal suspension onto a solid substrate. Time scales that characterize spin coating of colloidal suspensions are shown to be quite different from those that characterize spin coating of polymer suspensions.43 Thanks to its rapid implementation and its compatibility with wafer-scale processes, the spin coating appears to be a technique of choice. Spin coating is a well-established technique in microfabrication to form highly uniform thin films with adjustable thickness over large area.23,44 A spin coating process consists of several distinct stages. In the first one, a drop of colloidal suspension is deposited onto a fixed substrate. The substrate is then accelerated to a certain rotational speed in the second step and the liquid droplet spreads out to cover the whole substrate. In the next stage, the film thins due to equilibrium between centrifugal force and viscous shear force. Finally, evaporation dominates in the last stage, where the film thickness reduces to the same order as particle size, at which capillary forces have a significant impact on particle aggregation. The transition between the different stages depends notably on the volatility of the solvent. Traditional spin coating is based on the use of volatile solvents (e.g., water or alcohol) to disperse colloidal particles, which may result in a rapid freezing of the system. In order to give enough time to the particles to organize into energetically favorable states, Jiang et al.23,45 recently reported the use of nonvolatile solvents (i.e., monomer), which led to a nonclose-packed colloidal crystal embedded in a polymer matrix. The selective removal of the matrix can be performed by dry etching, without affecting the colloidal crystal. However, the non-closepacked structure of the mask is not suitable for the synthesis of isolated nanodot arrays. Most spin coaters allow the setting of 1 to 3 successive cycles of acceleration ramps (RAMPi) to a rotation plateau (RPMi) during a defined time (TIMEi). All those experimental parameters exert an influence of the evaporation and spreading of the liquid, and it is highly difficult to discriminate among them. A number of computational and theoretical studies exist for nonparticulate films46,47 of precise thickness during spin coating, starting with the classic work of Emslie et al.48 However, for the spin coating of colloidal suspensions, so far empiricism has mainly ruled the world of nanoparticle self-organization and much of the literature is experimentally based. Even if recent papers are more detailed,49 spin coating protocols described in the literature are various and most of the time imprecise.50 52 Most researchers give a rough idea of the size of the monolayer areas, ignoring most of the time the presence of small defects and usually emphasizing a perfect structure rather than deviation. Moreover, the wide diversity of the size of particles does not facilitate comparisons. For example, Spada et al.53 announced homogeneous bidimensional colloidal mask (496-nm-diameter PS nanospheres) reaching areas up to 0.5 cm2. However, many defects were present in the monolayer, and we estimated the

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defect-free area to ∼80 μm2. For their part, Brown et al.3 hardly reached defect-free areas of ∼30 μm2 for particles of similar sizes. The development of experimental protocols to control the ordering of particles on solid substrates and to get large wellordered structures is therefore a major goal for further progress in NSL. This is why we focused on the preparation of the mask and applied experimental design to the spin coating process. Comprehensive theoretical description of self-assembly mechanisms can be found in specialized literature such as very good publications by Zhao et al.54 and Regh et al.43 The aim of this study is to extract by an original experimental approach the influence of each parameter on the degree of ordering of the nanospheres layers. Therefore, it does not aim at giving new insights in colloidalscale forces or transport effects in fluids. The ordering will be considered from a macroscopic point of view. The experimental design allows the simultaneous variation of several experimental parameters, therefore reducing the total number of experiments. We used two different statistical analysis tools to study the masks, in an attempt to identify the most influential spin coating parameter(s) and investigate the relationships between them. This statistical analysis aims at developing a mathematical model able to predict the ordering degree from the spin coating parameters. To our knowledge, no experiment of this type has yet been reported in the literature.

’ EXPERIMENTAL SECTION Monodisperse PS nanospheres with a mean diameter of 490 nm (polydispersity less than 5%) were purchased from Bangs Laboratory as suspensions in water (concentration of about 10 wt %). We checked their diameter by dynamic light scattering. The suspension was filtered and diluted in surfactant Triton X-100/methanol mixture (1:400 by volume) to improve wettability. Prior to sphere deposition, circular quartz substrates (Crystal Gmbh) were cleaned following the procedure described in many papers.55,56 The aim is to obtain a hydrophilic surface. Each substrate was separately cleaned by immersing in a piranha solution (1:3 30% H2O2/H2SO4) and sonicated for 1 h. We rinsed the substrates repeatedly with ultrapure water (18.2 MΩ, Milli-Q) and then sonicated for 1 h in 5:1:1 H2O (Milli-Q)/NH4OH/30% H2O2. Finally, the substrates were copiously rinsed with water and stored in water (no longer than one week) until use. Before deposition of the colloidal suspension, the substrates were flash-airdried at room temperature. We performed the spin coating of the bead suspension onto the substrate with a Spin-coater P-6708 (SCS) following a three-step scheme: RAMPi stands for the time to reach the required speed RPMi, with i = 1 to 3. Those parameters are interdependent and have to be set according to the conditions RPM3 g RPM2 g RPM1 and in the ranges RPM1 e 2000 rpm, RPM2 e 4000 rpm, and RPM3 e 8000 rpm. A set of twenty experiments was generated by MODDE software (Umetrics), which is commonly used for experimental design. In this study, all ramp times (RAMPi) were taken equal to each other within an experiment, and spinning rates RPMi were maintained for 2 s. All manipulations were performed in a Class-100 clean room at constant temperature and humidity (50% RH) so as to minimize external contaminations or physical perturbation. The twenty samples were synthesized in the same day. Repetitions were carried out on other days with freshly prepared suspensions to check repeatability. We also used the software (MODDE) to build a mathematical model of the relationships between the spin coating parameters. To do so, we analyzed the samples by scanning electron microscopy (SEM) analyses on a FEG-ESEM XL30 (FEI) with an accelerating voltage of 15 kV under high vacuum. All samples were submitted to an O2-plasma etching 12801

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Langmuir (50 sccm O2 flow, 300 W, 30 s) and gold-coated (60 s) before observation. To improve sampling, fourteen SEM pictures were taken on each sample, starting from center and moving toward the edge of the substrate. The SEM pictures were taken at 4000 magnification. Thanks to a homemade program (designed in MatLab), we then quantified the order in the colloidal masks. As a quantification index of order in a hexagonal close-packed (HCP) arrangement, the image analysis consisted of measuring the percentage of beads in contact with six close neighboring beads. This digital output value is unambiguously the rate of HCP order in the nanospheres layer. The HCP percentage output data was subsequently used to perform a statistical study. The MODDE package offers several statistical analysis tools such as simple linear regression (LR), multiLinear regression (MLR), and partial least squares (PLS). In parallel, we used principal component analysis (PCA, available from Statistica) to investigate the correlation between the spin coating parameters and the ordering degree (percentage of nanospheres in HCP coordination).

’ THEORETICAL BASIS: STATISTICAL ANALYSIS PLS regression replaces the initial space of the (many) regressors by a low-dimensionality space spanned by a small number of variables called factors. The factors will then be the new regressors of classical linear regression model. Factors are orthogonal (uncorrelated) and are linear combinations of the original regressors. In this respect, they are therefore similar to principal components (PC) of principal component analysis (PCA). PCA is based on a mathematical process that aims to reduce the dimensionality of a problem while trying to minimize the loss of information (maximize the explained variance). The analysis seeks to replace a family of variables by new variables (principal components) of maximum variance, which are linear combinations of original variables. The number of components extracted in a principal component analysis is equal to the number of observed variables being analyzed. The first component extracted in a PCA accounts for a maximal amount of total variance in the observed variables. Under typical conditions, this means that the first component will be correlated with at least some of the observed variables. It may be correlated with many. The second component extracted will account for a maximal amount of variance in the data set that was not accounted for by the first component. Again, under typical conditions, this means that the second component will be correlated with some of the observed variables that did not display strong correlations with component 1. In general, only the first few components will account for meaningful amounts of variance, and the later components will tend to account for only trivial variance. The choice to retain only the first two components is based on the Kaiser criterion.57 An eigenvalue represents the amount of variance that is accounted for by a given component. The rationale for this criterion is straightforward. Each observed variable contributes one unit of variance to the total variance in the data set. Any component that displays an eigenvalue greater than 1.00 is accounting for a greater amount of variance than had been contributed by one variable. Such a component is therefore accounting for a meaningful amount of variance, and is worthy of being retained. ’ RESULTS AND DISCUSSION The spin coating parameters of each experiment and the corresponding output values (% HCP) calculated with our program are summarized in Table 1. We tested the repeatability

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Table 1. Spin Coating Parameters of the Experiments Generated by the Experimental Design Program and the Corresponding HCP and Substrate Coverage Percentages Given by Homemade Image Analysis Program no RAMP/s

RPM1/ RPM2/ RPM3/ % multi-/ % substrate rpm rpm rpm HCP monolayer ? coverage

1

21

510

700

4400

52

Multi

90

2

3

1930

2500

6900

73

Mono

62

3

17

380

3000

6400

46

Mono

88

4

8

630

3300

5200

60

Mono

91

5

23

740

800

2500

28

Multi

88

6 7

12 30

360 760

3300 2500

4000 5400

47 56

Multi Multi

88 89

8

14

1710

2400

2800

47

Multi

91

9

30

970

4000

4500

31

Mono

75

10

3

1940

2300

5200

73

Mono

48

11

8

1640

2700

4200

57

Multi

94

12

11

850

2300

2300

55

Multi

33

13

22

240

2300

3300

57

Multi

91

14 15

12 11

580 610

2500 1800

2500 6900

10 32

Multi Multi

80 87

16

24

1070

1300

1300

46

Mono

89

17

10

1120

3500

4500

27

Multi

85

18

30

1400

3600

3700

49

Multi

97

19

28

830

900

3600

31

Multi

85

20

28

1760

3600

5200

50

Multi

88

of our process twice, and obtained less than one percent deviation on the percentage of hexacoordinated nanospheres. We obtained variable results such as multilayers or monolayers with small or large HCP well-ordered domain sizes. Typical SEM pictures are presented in Figure 1. Only six samples show strictly monolayer film (Table 1, illustrated by Figure 1a), while all the other samples presented multilayers in which square lattices (Figure 1c) were systematically observed.

’ QUALITATIVE DESCRIPTION According to Prevo et al.,32,42 the packing of the PS nanospheres in a hexagonal or square lattice is due to a balance between thermodynamics (which aims to reduce the surface energy by packing the beads in a way to maximize the contacts between them) and the geometric arrangement of PS beads in the drying liquid film. Square lattices, considered metastable transition states to the hexagonal lattices, could result from a quick-drying step.58 The highest percentage of HCP order (73%) was observed for experiments 2 and 10. In these experiments, we obtained large, totally defect-free HCP areas of ∼200 μm2, which is very high compared with literature. So far, we never reached higher percentage of HCP with other spin coating parameters. Looking closer at Table 1, all parameters are similar except the rotation speed of the third step (RPM3). Ramp time and RPM1 have a respectively low (3 s) and high (∼2000 rpm) value, which means that the high rotation speed is reached in a short time. The RPM2 value is slightly higher than RPM1. On the opposite, the smallest percentage of HCP (10%) is obtained for experiment 14, characterized by a median value of ramp time (12 s), a rather low value of RPM1 (580 rpm) and an equal value of RPM2 and RPM3 (2500 rpm). From this point of view, it is tempting to conclude 12802

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parameters. For example, Prevo et al.42 report monolayers of nanospheres obtained by convective assembly from highly concentrated suspensions, up to 30 vol %. However, micrographs show a high occurrence of structural defects that can be incompatible with some applications of nanospshere lithography, like those relying on perfectly isolated nanodots (i.e., magnetic nanodots for data storage6).

Figure 1. 2D or 3D organization of PS nanospheres. Typical SEM micrographs of organized PS nanospheres showing in (a) large HCP area, (b) small HCP area, and (c) multilayers. Scale bars are 5 μm.

that an increase of ramp time and a small value of RPM1 lead to a decrease in the order. However, regarding experiment 7 with a high ramp time (30 s) and low value of RPM1 (760 rpm), the percentage of HCP is not that bad (56%). Therefore, a combination of a small ramp time and high RPM1 is not sufficient to explain a high percentage of HCP order in the sample. The samples with the highest hcp order (2 and 10) are characterized by low covering percentage. According to Zhao et al.,54 this could be due to the strong adhesive force between the particles and the substrate, which therefore remain trapped to the substrate after they touched it. It is tempting to consider the selected spin coating parameters applied to suspensions with higher concentrations to increase coverage. However, as described by Prevo et al.42 the evaporation rate must be increased accordingly to avoid the formation of multilayers. Moreover, the modification of suspension composition is known to impact significantly the wetting of the substrate, which is a key point in the early stages of the process.59,60 Consequently, such a modification of solution would imply a complete revision of spin coating

’ STATISTICAL ANALYSIS First, we tried to identify separately any linear correlation between the % HCP and each factor (RAMP, RPM1, RPM2, and RPM3). We did not evidence any obvious correlation between the output value and any of the inputs. Traditionally, multiple linear regression (MLR) is used to predict some response properties from a set of independent variables, but the multiple linear regression methodology yields imprecise predictions when the independent variables are correlated, which is the case with our spin coater programmer. We therefore selected the partly least squares (PLS) method, which can overcome some of these numeric problems, since it first extracts uncorrelated factors and works from there. On the basis of the PLS regression on all experiments, the program generated predicted values for the parameters of our twenty experiments. Unfortunately, the measured (observed) % HCP values did not agree with the predicted ones (Figure 2a) and a large deviation was observed. We concluded that the presence of multilayered samples in the twenty experiments could disrupt the modeling procedure. Hence, we performed another PLS regression analysis only on the monolayered samples. This time, the predicted and measured values did agree (Figure 2b). In order to judge the predictive power of our model, we generated five new experiments (with equal ramp times) and asked the model the expected % HCP values. Although all samples were composed of monolayers, a quite large deviation (up to 20%) was observed between predicted and measured values. This could be due to the fact that our model is based on a very small number of experiments. In order to improve the model, we would suggest making many more experiments and directly removing the multilayered samples from the regression. Moreover, the acquisition of highresolution micrographs could also allow an increase of the size of the analyzed area. The fact that the RPM values are in a way linked to each due to the inherent constraints of the apparatus may eliminate any chance of modeling their impact on the organization of the nanospheres. Finally, we submitted the results to the principal component analysis (PCA).61 PCA is recommended as an exploratory tool to uncover unknown trends in the data. First, we performed PCA on all the experiments and then we repeated the operation on the monolayered samples. The different parameters are projected in the plane of the first two components (Figure 3a,b). The angle between two variables, measured by its cosine, is equal to the linear correlation coefficient between two variables. Therefore, the variables that are pointing in the same (opposite) direction are correlated positively (negatively), while perpendicular oriented variables are uncorrelated. Moreover, the closer a variable is to the circle of correlations, the more weight it has to explain the variability described by the first two PCs. As expected, the cumulated variance explained by the two first components is higher when the analysis is performed on the monolayered samples (∼91%) than on all samples (∼60%). 12803

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Figure 2. Comparison between measured (observed) % HCP values ad the values predicted by the partial least squares (PLS) regression. (a) PLS regression on all experiments. (b) PLS regression on monolayered samples.

The analysis of the first component in Figure 3a shows that the weight is well-distributed on all variables. We noticed that the variable RAMP is diametrically opposed to the % HCP, which means that a low value of RAMP is required to achieve high values of HCP organization. As the percentage of HCP and RPM1 are pointing in the same direction (with a cosine near from 1), we conclude that they are strongly positively correlated, which means that a high value of RPM1 leads to a high percentage of organization. The fact that the parameter RPM2 is orthogonally oriented relative to % HCP suggests that it has no impact on the HCP order. In the PCA performed on monolayered samples (Figure 3b), the first component is mainly composed of contributions due to RPM1 and RAMP variables, while most of the weight in the second PC is distributed on RPM2 and RPM3. The strong positive (respectively negative) correlation between RPM1 (respectively, RAMP), already suspected in Figure 3a, is confirmed here. These

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Figure 3. Projection of spin coating parameters in the plane of the two first components. (a) Principal component analysis (PCA) performed on all samples. The two first principal components explain 60% of the total variance. (b) PCA performed on strict monolayered samples. The first two principal components explain 91% of the total variance.

results agree with studies on spin coating of colloidal suspensions43,45 and are highly valuable as the conclusion here is reached through a statistical analysis. The onset of ordering process coincides with the moment when the thickness of the liquid layer becomes smaller than the particle diameter.37 As theoretically shown by Kralchevsky et al.,62 interparticle capillary forces arise between spherical particles, which are partially immersed in a liquid on a horizontal solid substrate. As the liquid becomes thinner, the liquid surface deformation increases giving rise to increased capillary forces. The next step begins with the motion of more colloids that are driven toward the nucleus and is attributed to a convective flux, which compensates the evaporated solvent in the already ordered array, hence dragging particles suspended in the thicker layers toward the thinner regions. The newcomers remain attached to the 12804

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Langmuir domains, pressed by a hydrodynamic pressure and captured by capillary forces. The ordering is therefore highly related to the thickness of the evaporating film. The film thickness has been demonstrated to be inversely proportional to the spin speed,45,63 which corroborates our results. Moroever, Rehg et al.43 and Dushkin et al.39 both concluded that rapid evaporation rates is better at assembling more uniform monolayers and colloidal crystals.

’ CONCLUSION In an attempt to model the influence of the various spin coating parameters (RAMP, RPM1, RPM2, and RPM3) on the 2D HCP order, twenty experiments were generated by experimental design. Thanks to our homemade image analysis program, we calculated the percentage of hexacoordinated nanospheres with very small deviation (1%) in the repetition experiments. As no direct linear correlation was found between the % HCP and the spin coating parameters, we proceeded to a partial least square (PLS) regression on all results. However, the predicted % HCP values did not agree with the measured ones (deviation up to 20%). We therefore ran another PLS regression only based on monolayers (6 out of the 20). Predicted and measured did agree. Unfortunately, the predictability of our model proved to be unsatisfactory. We then performed a principal component analysis (PCA) on the results. The explained variance reached 91% (respectively 60%) when the analysis was performed on the monolayered samples (respectively on all samples). In both cases, PCA highlighted that the percentage of HCP order was respectively positively and negatively correlated to the ramp time and RPM1. That means that, to get large HCP well-ordered areas, we had to quickly spin coat the suspension at high rotation speed. Finally, we identified adequate spin coating parameters to synthesize large HCP domains. We obtained large, defect-free areas reaching up to 200 μm2, which is the highest value ever reported for samples prepared by spin coating. Further studies will focus on designing a new set of parameters suitable for higher concentration of suspension, in an attempt to increase coverage of the substrate. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected], [email protected], catherine. [email protected].

’ ACKNOWLEDGMENT P. Colson acknowledges Dr. K. Fleury-Frenette from the CSLLiege (Liege Space Center) for the O2-plasma etching performed on colloidal crystal masks of polystyrene nanospheres. The authors are also obliged to Drs. S. Blacher and C. Gommes (Department of Chemical Engineering, Chemistry Institute, University of Liege) for their help and advice during image processing with Matlab. Part of this work was supported by the Belgian Science Policy (Belgian State) under the Interuniversity Attraction Poles program (INANOMAT - P6/17). ’ REFERENCES (1) Deckman, H. W.; Dunsmuir, J. H. Appl. Phys. Lett. 1982, 41, 377–379. (2) Hulteen, J. C.; Van Duyne, R. P. J. Vac. Sci. Technol., A 1995, 13, 1553–1558.

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