Optical-force-directed single-particle-based track etching in polystyrene films

To investigate the system, we drop-cast Au NPs (80 nm) on PS films (120 nm)/Si substrate. The scattering spectrum of Au NPs shows a plasmonic resonance at ∼560 nm. After irradiation with a 635 nm CW laser (4 mW) for 100 s, the plasmon peak redshifts to ∼620 nm (figure 1(a)) with a yellowish scattering colour (figure 1(b)). The SEM images in figures 1(c) and (d) reveal that the Au NP develops a cavity (Φ = 120 nm) in the PS film which is much smaller than the diffraction limit of 635 nm light (480 nm). Because the refractive index of the surrounding medium increases from 1 (air) to 1.6 (PS) with Si underneath after the irradiation, it is reasonable to expect a redshift of the plasmon peak as shown in figure 1(a). However, it is not obvious why the Au NP concaves the PS film, as the maximum surface temperature (from simulation) of a Au NP when irradiating at this power (4 mW) is 460 K (figure 1(e) and figure S2 available online at stacks.iop.org/NANO/30/305304/mmedia), which is not sufficient to degrade the underlying PS films (T_d = ∼550K). This etching process is not likely due to the near-field-enhanced photochemical degradation as PS does not absorb 635 nm light and no cavities are generated if the irradiated region contains no Au NPs.

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Although the surface temperature of the Au NP is not high enough for thermal degradation of the polymers, it is sufficient to melt the PS films locally if the laser power is above 3 mW (figure 1(e)). In addition, the focused laser beam can exert radiation pressure (${F}_{{\rm{rp}}}$) on the Au NP, which pushes it into the PS films if the viscous resistance (F_v) is small. To rationalise this process, we use the dipole approximation to calculate the radiation pressure using the formula [19]

$$\begin{eqnarray}&&{F}_{{\rm{rp}}}={\sigma }_{{\rm{ext}}}\displaystyle \frac{n}{c}I\left(r\right),\end{eqnarray} \tag{ 1 }$$

where ${\sigma }_{{\rm{ext}}}$ is the extinction cross-section of the Au NPs (figure S1), $I\left(r\right)$ is the intensity of the laser beam, n is the refractive index of the environment and c is the speed of light. This dipole approximation is qualitatively fine in this system.

As for the calculation of the viscous resistance, F_v, of the PS films, we apply the Stokes equation [20]

$$\begin{eqnarray}&&{F}_{v}=6\pi \eta rv,\end{eqnarray} \tag{ 2 }$$

where r is the radius of Au NP, v is the speed with which the Au NP moves in the molten PS film and $\eta$ is the viscosity of the PS, which is dependent on temperature (blue line in figure 1(f)) [21].

For 4 mW laser irradiation, the calculated results (see the online supporting information for detailed calculations) show that the radiation pressure acting on the Au NP gradually increases from 0.2 pN to 1.6 pN (figures 2(a) and (b)) when it enters into the PS film, which is sufficient to overcome the viscous resistance (0.1 pN) at this temperature (red line in figure 1(f)). Therefore, it is plausible that the Au NP can be pushed into the PS film by radiation pressure even if we ignore the gravitational force on the Au NP.

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What is intriguing, however, is that the Au NPs appear to deviate from the centre of the cavities, which is independent of polarisation (figures 1(d) and S4). Such deviation is proportional to the irradiation time with distance up to 50 nm (figure S5). Thus, this deviation is not likely to be due to microscope stage vibration or drifting as these artifacts will only result in much larger deviation without any trend. We interpret that some forces push on the Au NPs horizontally so that they stick to the walls of the cavities rather than staying at the bottom. The possible forces that may take effect in this scenario are optical forces and photophoretic forces, which are commonly observed in plasmonic systems and have been applied to manipulate micron-sized particles [22]. Photophoretic forces, which arise from the thermal gradient within the particle, are negligible in this case as the Au NP (80 nm) is much smaller than the laser beam spot size. Therefore, the main contribution of the forces that move the Au NPs seems to be the radial component of radiation pressure (${F}_{{\rm{rad}}}$) and optical gradient force (${F}_{{\rm{grad}}}$), which can be calculated using the formulae [23]

$$\begin{eqnarray}&&{F}_{{\rm{rad}}}=\,\sin \,\theta \cdot {F}_{{\rm{rp}}}\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{F}_{{\rm{grad}}}=-\displaystyle \frac{z}{2}{\rm{Re}}\left\{\alpha \right\}{\rm{\nabla }}I(r),\end{eqnarray} \tag{ 4 }$$

where $\theta$ is the angle between the axial component of radiation pressure (${F}_{{\rm{ax}}}$) and ${F}_{{\rm{rp}}}$, $\alpha$ is the polarizability of Au NPs, z is the wave impedance in a vacuum and ${\rm{\nabla }}I\left(r\right)$ is the intensity gradient. These two forces are opposite to each other but because ${F}_{{\rm{grad}}}$ (∼0.1–0.2 pN) is slightly larger than ${F}_{{\rm{rad}}}$ (∼0.02–0.14 pN) (figures 2(c), (d)), the net force direction on the particle is towards the beam centre. As a result, the Au NP is pulled to the beam centre when it develops a cavity in the PS film, leading to anisotropic etching (figure 2(e)).

During the optical pushing, the surface temperature of the Au NP increases up to 569 K (figure 3), which is due to the increased intensity of the electric near field as the Au NP moves into the PS film (figure S3). As a result, it starts to degrade the PS at the stage when it is fully embedded, causing a cavity to form around the Au NP. The temperature drops dramatically to 330 K if the Au NP touches the Si substrate (figure 3(e)), which is due to the good thermal conductivity of Si (∼150 W K^–1 m^–1). Therefore, it is likely that a thin layer of PS exists between the bottom of the cavities and the Si substrate as the lowered temperature of the surrounding PS significantly increases the resistance against the Au NPs, which stops them from moving downwards. Therefore, the distance moved by Au NPs in PS films, besides the magnitude of optical forces, is also dictated by the thickness of the PS film.

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To verify this, we used a 532 nm laser for the particle irradiation, which is close to the plasmon resonance (red line in figure 1(a)). Thus, this optical heating is more prominent, which increases the temperature of Au NPs up to 566 K with only 1 mW power (figure S6). However, due to the cooling effect of the Si substrate, as mentioned above, the Au NPs only travel a limited length of ∼50 nm for a thin PS film (120 nm), irrespective of the irradiation time and irradiation wavelength (figures 1(d) and 4(a), (b)). If the thickness of the PS film is increased to 200 nm, the Au NP travels with much larger distance (up to ∼300 nm), and embeds itself into the PS film (figure 4(c)). As such, the distance that the Au NPs travel is determined by the PS film thickness due to the cooling effect of the substrate (figure 4(d)).

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Based on the etching mechanism mentioned above, the formation of cavities in PS films is affected by irradiation time, laser power, wavelength and the shape of Au NPs as these factors influence how much heat is generated around a Au NP. For a 4 mW CW laser (635 nm), the irradiation time needs to be above 60 s to clearly observe a cavity around the Au NP (figure 5(a)). However, if a 3 mW laser is applied, a longer irradiation time (100 s) is required for clear cavity formation (figures 5(b), (c)). A 2 mW laser does not seem to be capable of generating cavities for the irradiation time we have applied (figure 5(d)) as the temperature is below the viscous flow temperature of PS (figure 1(e)). The etching diagram of irradiation conditions (figure 5(h)) suggests there is a certain threshold of time and power above which nanoparticle-assisted photolithography can occur. Moreover, using Au NPs with a smaller size (60 nm) also makes etching of PS films difficult even after irradiation for 120 s (figure 5(e)). This is mainly because of the lowered surface temperature of Au NPs with smaller absorbance cross-section. But for a Au prism with the same effective diameter (∼60 nm), etching can be observed (figure 5(g)) (4 mW, 120 s) as the field is more concentrated around the corners, which produces a much larger absorbance cross-section than with its spherical counterpart, leading to a higher surface temperature for thermal degradation. The size of the particle used for etching can be even smaller as long as it produces sufficient heat for photothermal degradation. But it will be challenging to locate the particles less than 50 nm under dark field optical microscope. All of this evidence again suggests that it is the plasmon-assisted photothermal effect that degrades the polymers locally, forming the concave etching.

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As the shape of the nanoparticle determines the shape of the cavity, we can engineer the shape of the cavity by using different shaped plasmonic nanoparticles and their assemblies. For instance, ellipsoidal cavities can be formed either with a Au NR (figures 6(a), (b)) or Au dimer (figures 6(d)–(f)) as the heating particles. The aspect ratio of the cavity can be increased by using a Au NR dimer as the heating nanoparticle (figure 6(c)). These Au NPs can be removed by wet etching, leaving an empty hole in the PS film (figure S7). As such, the combination of differently shaped NPs and their assemblies significantly enriches the etching morphology of the cavities, making it tailorable for different applications.

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