Theoretical studies34,35 have demonstrated that interparticle capillary forces are the driving force for the ordering of nanospheres on the substrate. Such forces occur as a result of increasing curvature of the liquid surface between the particles as the solvent evaporates. As a result of the action of capillary forces, the nanospheres are assembled into a hexagonal close-packed structure due to the fact that the system tends to the configuration with the lowest energy, and hence, to the maximum contact with neighboring particles. Thus, the evaporation rate of the solvent, consisting in our case of isopropyl alcohol and propylene glycol, is one of the main factors, which affects capillary forces and, as a result, the process of self-assembly of nanospheres36. In turn, the evaporation rate of the solvent is influenced by parameters such as rotation rate (N) and time (T), as well as the viscosity of the solution, which depends on the relative concentrations of each component in solution (V1—isopropyl volume, V2—propylene glycol volume, V3—volume of aqueous solution of nanospheres). In this regard, the nature of the influence of the above technological parameters on the area of the substrate covered by mono- and bilayer of nanospheres was studied in order to determine the optimal technological parameters for creating a monolayer close-packed nanosphere coating.
The content of each component in the solution applied to the substrate was considered as a percentage of the volume of one component to the total volumes of the other two components. This was done for the convenience of information perception, since in a series of experiments to determine the optimal contents of nanospheres, alcohol and propylene glycol in the solution, the total volume of the solution applied to the substrate varied according to the varying volume of the component under consideration, while the volumes of the other two components were unchanged.
The initial volume ratio of all solution components was determined during a preliminary series of experiments aimed at optimizing the parameters of the nanosphere lithography process based on the Taguchi matrix method37. The best result in terms of substrate coverage area was shown by the V1/V2/V3 = 80/56/50 μl solution, which was chosen as starting solution for further basic experiments. The influence of the time and temperature of ultrasonic mixing of the solution on the quality of the coating was also investigated, during which the best quality coatings were obtained at 15 min and 50 ℃, respectively. The ultrasonic treatment parameters were constant in all subsequent series of experiments.
The first series of experiments was aimed at determining the nature of the influence of the spin speed on the quality of the coating, while other process parameters remained unchanged. It is known that the spin speed affect both the solvent evaporation rate and the centrifugal force, which moves the suspension to the edge of the substrate20. As can be seen from the plot (Fig. 3a), at a rotation speed below 3300 rpm, a significant number of bilayer clusters are formed, shown in the microphotograph in Fig. 3b. This double-layered areas are not acceptable for the fabrication of nanosphere coatings used as masks for subsequent etching. This is probably due to the fact that at low spin speeds the balance of forces acting on the nanospheres is disturbed. Due to the low centrifugal force, the flow of nanospheres toward the edge of the substrate is not sufficient to compensate the capillary flow of the suspension into the central region. On the contrary, the high spin speed (> 3500 rpm), which facilitates the evaporation process and increases the centrifugal force, creates a large number of voids in the array (Fig. 3d), because most of the suspension is thrown away from the substrate surface. In addition, the solvent evaporates faster than the nanospheres have time to self-assemble into a hexagonal array22. The optimal spin speed of 3300 rpm was found experimentally, at which the coverage area was 98.6%, and there were almost no bilayers (0.7%) (Fig. 3c). With further increase of the spin speed, the bilayers completely disappear, but the total coverage area of the substrate decreases sharply.
In the next series of experiments, we determined the optimal amount of aqueous solution of nanospheres, which was taken from a purchased solution and centrifuged. Then the water was removed from it, and finally the dry spheres were mixed with solvent in the form of isopropyl alcohol and propylene glycol.
As can be seen from the plot (Fig. 4a), a good coverage area close to 100% is achieved at nanosphere content (in this case the percentage ratio of the volume of the aqueous nanosphere solution discussed above to the total volume of isopropyl and propylene glycol) starting from 29%. Smaller content values produce a large number of empty spaces on the substrate, as can be seen in Fig. 4b. However, the number of bilayers begins to increase sharply at nanosphere content of 37% and higher. This indicates that at the selected technological parameters of the spin speed and time, a larger amount of polystyrene remains on the substrate than is necessary for the close-packed monolayer coating (Fig. 4d). Therefore, a nanosphere content of 29% was selected for further experiments, corresponding to the volume of the initially sampled aqueous nanosphere solution of 40 µl. At this chosen value, the coverage area was equal to 95.3%, and there were no bilayers (Fig. 4c).
The viscosity of the solution also has a significant effect on solvent evaporation and self-assembly of the nanospheres, and hence on the coverage area and the number of bilayers. Solution viscosity can be controlled by changing the relative concentrations of isopropyl alcohol and propylene glycol in the solution. Nanospheres without solvent are not capable to self-assemble into a dense hexagonal package, because there are electrostatic repulsive forces between them, which are overcome by surface tension forces arising from solvent carriers in the colloidal solution38. In addition, propylene glycol, which has two O–H groups and a small hydrophobic chain, wets the polystyrene surface more strongly than water and isopropyl alcohol, so it reduces the hydrophobic interactions of nanospheres in the solvent, which prevent the processes of reorientation and compaction of particles39. As can be seen from the plot (Fig. 5a), increasing the content of isopropyl alcohol (in this case the percentage ratio of the alcohol volume to the total volume of nanospheres and propylene glycol) from 23 to 103% leads to decreasing the total coverage area of the substrate, while the number of bilayer regions also decreases and is close to 0 at the content of isopropyl more than 83%. This is probably due to the fact that the small volume of isopropyl, which has a viscosity slightly higher than a viscosity of water, evaporates very quickly. Consequently, only propylene glycol with much higher viscosity remains in the solution, and it becomes more difficult for the nanospheres to move across the substrate surface with such excessive solution viscosity. As a result, more than one monolayer remains on the substrate (Fig. 5b). Increasing the content of isopropyl in the solution leads to a more rarefied and non-uniform coating (Fig. 5d). Due to decreasing the relative concentration of propylene glycol, the compaction forces are not capable to overcome the barrier of hydrophobic interactions to order the particles, as a result of which the nanospheres are randomly fixed on the substrate. Thus, the optimal value of the isopropyl content in the solution was found to be 83%, corresponding to the alcohol volume of 80 µl. At this chosen value, the substrate is filled with a close-packed array by 97.6%, and there are approximately 0.6% bilayer areas (Fig. 5c).
It is worth noting that a purchased solution of nanospheres of a given size, although in small quantities, initially contains large polystyrene spheres. Therefore, in some cases, such as shown in the inset in Fig. 5c, this single large sphere can act as a nucleation center for multilayered areas of small spheres around it. Such areas have also been included in the total percentage of bilayer coverage of the substrate for a more objective study.
It follows from the plot in Fig. 6a that the total lack of propylene glycol in the solution leads to a low total coverage area of the substrate (≈ 78%), with the formation of a completely non-monolayer coating. This is probably related to the impossibility of self-assembly of nanospheres due to their poor wettability by isopropyl and the strong effect of hydrophobic interactions between the nanospheres in the solvent without adding propylene glycol to the solution. This assumption is confirmed by the microphotograph (Fig. 6b) demonstrating the formation of multilayer disordered regions of nanospheres in the absence of propylene glycol in the solution. It can also be seen from the plot (Fig. 6a) that with increasing the propylene glycol content (in this case the percentage ratio of the propylene glycol volume to the total volume of nanospheres and alcohol) from 16 to 33%, there is a slight decreasing coverage area of the substrate by a monolayer of nanospheres and almost complete disappearance of bilayer areas. In this regard, the content of 33% was chosen as the optimal value of the propylene glycol content in the solution, corresponding to the propylene glycol volume of 40 µl, at which the coverage area of the substrate with a close-packed monolayer of nanospheres is 98.5%, and there are approximately 0.8% of bilayer areas (Fig. 6c). As the propylene glycol content is further increased, solution viscosity probably becomes too high for the normal self-assembly process, and a significant number of voids appear, as shown in Fig. 6d.
The final series of experiments was aimed at determining the nature of the influence of spin-coating time on the coverage area of the substrate with mono- and bilayer of nanospheres. According to the obtained plot shown in Fig. 7a, when the rotation time is less than 10 s, a significant number of bilayer areas are formed, demonstrated in Fig. 7b. This is due to the fact that the bulk of the suspension still remains on the substrate, and the solvent does not have time to evaporate. Moreover, in addition to the bilayers, a short rotation time during the spin-coating process formed a thickening on the periphery of the substrate, which flowed over a large area of the substrate and reduced its working area. On the contrary, at spin-coating times longer than 10 s, as follows from the plot (Fig. 7a) and the microphotograph (Fig. 7d), the formation of voids was observed, because by this time, probably, too many nanospheres leave the substrate. Using the obtained dependences, the optimal spin-coating time was chosen to be 10 s (Fig. 7c).
The optimal technological parameters of the nanosphere lithography process for obtaining the close-packed hexagonal array of polystyrene nanospheres with a diameter of 300 nm were determined on the basis of analyzing the obtained experimental data (Table 1). To check the reproducibility of the results, five experiments with the selected optimal parameters were conducted, and the coverage area with mono- and bilayer was estimated for each (Table 2). As a result, the average coverage area of the substrate with monolayer of the nanospheres (diameter 300 nm) was 97.8%, with a small number of bilayer regions (0.5%).
To estimate the accuracy characterizing the reproducibility of the results, the relative root-mean-square was calculated according to the formula (1)
$$\nu =\sqrt\frac\sum_i^n(x_i-\overlinex )^2\overlinex ^2\cdot (n-1)\cdot 100\%$$
where \(x_i\) is the monolayer coverage area of the substrate in each experiment, \(\overlinex \) is the average value of the monolayer coverage area of the substrate, and n is the number of experiments, equal to 5. Thus, the relative root-mean-square error was 1.37%, which can be considered quite acceptable result.
It is well known that self-assembled arrays are characterized by individual domains, or as they are called, grains, which can be differently oriented, but within which spheres are strictly ordered into a hexagonal lattice with one orientation. In order to estimate the degree of ordering of the resulting coatings, a Fourier transform of SEM images covering different areas was performed. The corresponding 2D Fourier images of the arrays are shown in the insets in Fig. 8a–c. The maximum covered area, where a hexagonal ordered domain with one orientation was obtained, was found to be 1535 μm2, as confirmed by the peaks in the Fourier image located at the vertices of the regular hexagon (Fig. 8a). However, despite the ordering, dislocations can also be present in one domain and are clearly visible in SEM images at high magnification (Fig. 8b,c). Using the HEXI software, the percentage of defective areas in each image was calculated. Close-packed nanospheres are marked with green circles and nanospheres entering dislocation areas are marked with red circles (Fig. 8d–f). The resulting percentage of dislocations was 22% in an area of 1535 µm2 (Fig. 8d), 24% in an area of 175 µm2 (Fig. 8e) and 25% in an area of 45 µm2 (Fig. 8f).
The next step to obtain an array of silicon nanostructures of a certain geometry is the process of reducing the size of polystyrene nanospheres in inductively coupled oxygen plasma, to form an ordered, not close-packed array with gaps between nanospheres. For controlled reduction of nanosphere size in oxygen plasma, it is necessary to study physicochemical regularities of polystyrene etching process, as well as processes occurring in plasma during etching. In this regard, the nature of the influence of the main process technological parameters (high-frequency (HF) power, etching time, bias voltage on the substrate holder, pressure in the chamber, and oxygen flow rate) on the etching rate and the diameter of nanospheres was determined.
The etching of polystyrene in oxygen plasma occurs by breaking the aromatic ring, formation of oxygen-containing functional groups on the surface, and subsequent formation of volatile products such as carbon monoxide and carbon dioxide40. Figures 9c–h show how the size of nanospheres etched at different HF power for 1 min changes. From the plot (Fig. 9a) it can be observed that the polystyrene etching rate increases monotonically from 83 to 175 nm/min when the applied power is increased from 250 to 500 W. Such nature of the dependence is related to the fact that with increasing absorbed power, the concentration and average energy of electrons in plasma grows, therefore, the intensity of inelastic collisions of electrons with oxygen molecules increases. As a result, it leads to more efficient formation of such active particles as radicals and ions which react with polystyrene41. This is confirmed by the increasing concentration of atomic oxygen in plasma when the applied power is increased (Fig. 9b).
Next, the reduction in the size of the nanospheres at different etching times was studied, while the other technological parameters remained constant. As can be seen from the plot (Fig. 10a), the diameter of the nanospheres decreases from 240 to 15 nm when the etching time is increased from 1 to 5 min, while the etching rate changes insignificantly. When the nanospheres are still large enough, during the first 2 min of etching, bridges with a length of about 50 nm are formed between them, thanks to which the nanospheres are well stabilized in their initial positions (Fig. 10b). The formation of such bridges is caused by the tendency of the nanospheres to reduce the surface energy42 With further increasing the etching time, these bridges, like the spheres, are etched in oxygen plasma and disappear (Fig. 10c). After that the nanospheres can start moving along the substrate surface, because their size by this time strongly decreases, therefore, the contact area with the substrate also decreases43. In addition, as can be seen from Fig. 10d–f, when the etching time reached 3 min, the nanospheres deformed, taking an irregular shape. In this regard, for further experiments the optimal etching time of 2 min was chosen, at which the nanospheres are still well stabilized in their places, are circular in shape and are ≈ 210 nm in diameter (Fig. 10c).
The pressure in the reaction chamber determines both the energy distribution of electrons and ions and the number of chemical reactions occurring on the surface of the treated material. So, as the gas pressure increases, the energy of ions bombarding the surface decreases due to decreasing the mean free path of the particles. In addition, the average energy of electrons, which determines the rate of generation of active oxygen particles, also decreases44. As can be seen from the plot (Fig. 11a) and microphotographs (Fig. 11c–g), the etching rate of polystyrene nanospheres decreased from 115 to 47 nm/min when the pressure in the chamber was increased from 0.4 to 1.25 Pa. However, the dependence of the concentration of oxygen atoms on pressure shown in Fig. 11b demonstrates only a slight increasing atomic oxygen with increasing pressure. Thus, we assume that the contribution of the physical component (i.e., ion bombardment) to the polystyrene etching process prevails in this case over the contribution of the chemical component (i.e., chemical reaction).
In addition, decreasing the intensity of ion bombardment of the surface with increasing pressure is confirmed by the fact that at low pressure (< 1 Pa) and higher ion energy the nanospheres become irregularly shaped (Fig. 11c–e). The intensity of ion bombardment is primarily determined by the magnitude of the negative bias potential on the substrate, which also has a great influence on the etching rate and the morphology of the nanospheres45. As can be seen from the plot (Fig. 12a), a higher bias voltage leads to a more efficient bombardment of the material, therefore, a higher etching rate. Namely, as the modulus of the bias voltage on the substrate holder increases from 12 to 100 V, the diameter of the plasma-treated nanospheres decreases from 207 to 14 nm (Fig. 12b–f).
The final series of experiments was aimed at determining the nature of the influence of oxygen flow rate on the etching rate of polystyrene nanospheres. Despite the fact that the concentration of atomic oxygen increases by approximately two times when the oxygen flow rate is increased from 9 to 15 sccm (Fig. 13b), the polystyrene etching rate does not show significant changes and remains at an average level of 82 nm/min (Fig. 13a,c–g). Probably, in the selected range of technological parameters, the weak variation of the etching rate depending on the oxygen flow rate is related to the fact that there is a certain amount of oxygen sufficient to saturate the chemical etching process27. In other words, we assume that in our case the flow rate of 9 sccm is sufficient to saturate the polystyrene surface with functional groups, and a further slight increasing the flow rate to 15 sccm does not significantly affect the probability of interaction of oxygen atoms with carbon atoms in polystyrene.
As a result, silicon nanostructures in the form of nanoneedles of various sizes were fabricated using the developed nanosphere lithography technology. For this purpose, at the first stage, ordered close-packed nanosphere masks were formed using spin-coating technique. Then, by PCE in oxygen plasma, the sizes of nanospheres were reduced to different values (220, 175, and 115 nm), as shown in Fig. 14aI–III. Finally, plasma-chemical etching of silicon on the formed mask was conducted in SF6/C4F8 gas mixture, resulting in arrays of nanoneedles with base diameters ranging from 70 to 125 nm, with needle diameters ranging from 10 nm (aspect ratio over 90) to 50 nm, and heights ranging from 170 to 1000 nm depending on the initial size of the nanospheres (Fig. 14bI–III). It should be noted that the dimensions of the nanostructures were estimated as average values from measurements of several needles.
After silicon etching, polystyrene residues still remained on the tops of the nanoneedles (Fig. 14cI–III), which were removed by treatment in oxygen plasma. The optimal time of plasma etching for complete removal of polystyrene nanospheres was controlled in real time using the method of optical emission spectroscopy by changes in the polystyrene-specific spectral lines. Figure 15 shows the plasma emission spectrum during the etching process. We can identify the oxygen lines (844 and 777 nm) and the line belonging to carbon or hydrogen, which have very close values of the emission wavelength (656.28 and 656.87 nm, respectively) and cannot be identified exactly. However, both carbon and hydrogen are formed as a result of polymer chain splitting and atom detachment by active oxygen particles in plasma, therefore, this line can be used to determine the end point of the polystyrene etching process. The time variation of the intensity of the H/C emission line can be clearly seen in the enlarged view in Fig. 15. It can be observed that as the oxygen plasma cleaning time increases, the intensity of the H/C line gradually decreases and approaches 0 when plasma etching reaches 30 min. This indicates the disappearance of reaction byproducts by this time, therefore, the removal of polystyrene nanospheres from the surface of silicon nanostructures (Fig. 14d).
Thus, after the formation of the nanosphere mask, the process of fabricating silicon nanoneedles, which includes reduction of nanosphere size in oxygen plasma, silicon etching and removal of polystyrene residues from the surface of nanostructures, can be conducted in a single technological cycle without additional stages of sample unloading to the atmosphere. In addition, it is possible to use the OES method as in situ control of the end point of polystyrene etching to determine the time of complete removal of polystyrene nanospheres from the sample surface.