In the past centuries, the creation of smaller features is of paramount importance in nanofabrication to explore unique opportunities to achieve new applications in material sciences¹, nano-photonics², and nano-biotechnology³. The development of nano-fabrication technology is driven by the need to increase the density of components and performance, which requires high accuracy in material processing and the capability of manufacturing in an atmospheric environment. Nevertheless, large area nano-creation toward higher resolution has proven to be increasingly challenging as feature sizes keep decreasing by using traditional methods, including extreme ultraviolet lithography⁴, electron beam lithography⁵, and reactive ion etching⁶. Compared to other advanced processing methods, laser precision engineering has been recognized as one of the most extensively used tools for micro/nano-structuring in the past centuries^7-11. Owing to the feature of low heat affected zone (HAZ), ultrafast laser processing is well adapted to the high-quality micro-fabrication of soft materials, such as biological tissues¹² and hard or brittle materials¹³. The suppression of heat diffusion to the surroundings improves the spatial resolution of nano-creations. Non-linear absorption is another important benefit of ultrafast laser processing^{14, 15}. When processing transparent materials, such as glass and wide bandgap materials, with ultrafast laser pulses, the excitation of electrons from valence band (VB) to conduction band (CB) is initiated by non-linear absorptions, including multi-photon absorption or tunnel ionization^{16, 17}. Using ultrafast lasers in materials processing can substantially reduce the fluctuation associated with optical breakdown threshold and improve reproducibility by tuning the laser processing parameters.

Complicated structures can be precisely made through ultrafast laser direct writing^{18, 19}. However, the key challenge of the ultrafast laser processing to produce extremely small features is the optical diffraction limit. To overcome such difficulty, various laser-based techniques have emerged for sub-diffraction processing, such as near-field scanning optical microscope patterning²⁰, interference lithography^{21, 22}, and stimulated emission depletion microscopy²³, as well as multi-photons absorption lithography²⁴. Sub-50 nm nanostructures have been also achieved by multiple femtosecond laser overlapping irradiation in far-field. However, the HAZ via these techniques is still much larger than the nano-structures, which mostly exhibit >300 nm melting zone ^{25, 26}. Using a dielectric microsphere as a near-field lens for super-resolution nano-imaging and nano-fabrication has attracted great research interest^{27, 28}. The optical phenomenon known as photonic nano-jet can also contribute to laser beam focusing to overcome the diffraction limit. To increase the microsphere ultrafast laser processing throughput, the self-assembly method²⁹ and micro-lens arrays lithography³⁰ have been developed to fabricate surface patterns at a fast speed and low cost. In addition to nano-hole structures achieved by contact mode, the microsphere femtosecond laser fabrication can also realize arbitrary structures on sample surfaces in non-contact mode. By lifting the microsphere up to form a gap between sample and microsphere, the working distance (WD) can be increased to several micrometers. This strategy leads to the microsphere working in far field. In this case, the feature size of surface structures can only be reduced to ~300 nm by the 405 nm lamp³¹, 512 nm, and 800 nm femtosecond laser irradiation^{32, 33}, which is still far from the optical diffraction limit. Thus, how to achieve a good balance between the WD and feature size is a vital issue for the microsphere laser fabrication.

In this paper, the nano-structuring with feature size <50 nm is achieved on Sb ₂S₃ thin films by non-contact microsphere femtosecond laser irradiation in far field and in ambient air. The surface nano-ablation is attributed to the extreme focus ability of the microsphere, the femtosecond laser high-repetition-rate incubation effect, and the non-linear effect associated with the femtosecond laser irradiation. The ablation depth and width of surface nano-structures are well tuned by laser fluence and scanning speed, while the achieved maximum depth and minimum width are ~40 nm and ~30 nm, respectively. The ablation results at different thicknesses, and the related linear fitting analyses predict that the feature size can be down ~15 nm at the film thickness of ~10 nm. Arbitrary surface nano-structures are realized, and the fabricated grating structures perform desirable optical properties, which reveals that this novel approach is a promising and feasible way to achieve surface nano-creation with excellent performance.

The experimental setup of non-contact microsphere femtosecond laser irradiation is shown in Fig. 1(a). The femtosecond laser (Mira 900 of Coherent, Inc., 800 nm, 76 MHz) is focused by a microsphere via an objective lens (10×, 0.26 NA). The laser fluence is controlled by a half-wave plate and an isolator. The 470 nm light source is combined with the 800 nm femtosecond laser in the same optical path via two beamsplitters (BS), while the average ratios of reflectance and transmission are approximately 50∶50 at 470 nm and 40∶60 at 800 nm. The soda-lime glass microsphere of ~54 μm diameter (SLGMS, Cospheric) is fixed by a lens holder and aligned into a microscope system. The distance between the objective lens and the microsphere is equal to the focus length of the objective lens (~20 mm). The sample is put on a three-dimension (3D, XYZ) nano-stage with a minimum moving accuracy of 10 nm, a maximum speed of 5 mm/s, and a travel range of 20 mm (FS-3200P-WE2 series, OptoSigma). The nano-stage moving is automatically undertaken through an in-house programming code. The samples are amorphous Sb₂S₃ films at different thicknesses from 10 to 50 nm (prepared by magnetron sputtering deposition on silicon surfaces). Two charge-coupled devices (CCD) and a long WD objective lens are employed for the observation of focus position and working distance from top and side views. The related side view of the setup is shown in Fig. 1(b). It can be observed that the WD is ~8 μm, which means the focus length is ~35 μm (27 μm+8 μm). The focal length is about 44 times of the laser wavelength of λ=800 nm. Therefore, the microsphere femtosecond laser irradiation works in an optical far field. Near-field femtosecond laser fabrication mostly requires a smooth target surface due to its short working distance. Since the sub-50 nm ablation based on near-field effect is due to the generation of evanescent waves, the ablated depths are shallow and mostly <10 nm ^{20, 34}. For the microsphere femtosecond laser irradiation working in far field, the length of photonic nanojet is normally over several micrometers^{32, 35}. Thus, it is feasible to achieve a considerable ablation depth. By lifting the microsphere up, arbitrary surface patterning can be realized via the programming movement of the nano-stage.

The surface nano-creation is fabricated by the microsphere femtosecond laser irradiation in far field, as shown in Fig. 2(a), ~43 nm (λ/18) wide nano-lines with ~150 nm (λ/5) period are directly created on 30 nm thick Sb₂S₃ films at the laser fluence of 0.38 mJ/cm² and the scanning speed of 100 μm/s. The nano-lines have a sharp boundary and smooth edge. For the previously reported microsphere laser working in near field, the melting zone is obvious after laser irradiation^{31, 36}. In our experiments, the localized heating of the Sb₂S₃ thin films via the microsphere focusing drastically increases the temperature on the irradiated area. There is no apparent surface melting or damage on the ablated edge of the Sb₂S₃ film surface, which means the thermal diffusion to the surrounding around the femtosecond laser irradiation area is very small. Thus, the femtosecond laser irradiation via microsphere can create sub-50 nm nano-structures with high quality on the Sb₂S₃ thin films. The AFM image as well as the cross-sectional profile in Fig. 2(b, c) confirm that the ablation depth is ~30 nm, which indicates the Sb₂S₃ film is completely removed for the nano-lines with a depth-to-width ratio of 3∶4. It illustrates the capability far-beyond the diffraction limit fabrication by the microsphere femtosecond laser irradiation. Nano-structures with this feature size can be applied to fabricate different opto-electronics devices. Especially for the Sb₂S₃ thin films, which can exhibit tunable large bandgap (1.72~2.05 eV) and optical properties in the visible wavelength via the phase change³⁷, the high refractive index and low phonon frequency make Sb₂S₃ thin film attractive for applications that require high transmission from the visible to the mid-infrared region. The surface nano-creations on phase change materials are mostly realized via traditional methods, such as focused ion beam or electron beam lithographies^{38, 39}. Nevertheless, the low efficiency and high system cost inhibit large-area processing by these methods. Therefore, the microsphere femtosecond laser irradiation, which can realize sub-50 nm surface nano-creation in far field and in ambient air with high efficiency, is a feasible way to realize Sb₂S₃-based visible opto-electronics devices.

The formation of such nano-structures relies on the co-effect of the microsphere focusing, high-repetition-rate femtosecond laser induced incubation effect, and the non-linear absorption of femtosecond laser irradiation. According to the experimental results and the physics behind laser interaction with materials, the formation mechanism of such nano-features can be divided into three processes, as illustrated in Fig. 3.

1) The first process is the small focusing capability of microsphere. The focusing behavior of microsphere can be calculated by finite-different time-domain (FDTD) method. Since the lime soda glass microsphere in our experiments have a size deviation of 10%, the diameter of the microsphere for the numerical calculation is set as 50 µm. As shown in Fig. 3(a), a plane wave (800 nm, x-polarized) propagates (along z axis) through a 50 µm lime soda glass microsphere (n_g=1.5172 at 800 nm). The microsphere diameter is much larger than the incident laser wavelength of 800 nm. The calculated focus length is ~31.4 μm with a ~4 μm depth of focus (radius: 25 μm, WD: 6.4 μm, see details in Fig. S1, Supplementary information), which is consistent with the measured WD shown in Fig. 1(b). The electric field intensity squared |E|2 distribution along z axis shows that the energy of the light field increases rapidly and is the highest at a distance of 6.4 µm from the exit facet of microsphere, where the |E|2 is approximately 1500 times of the incident electric field intensity squared ( |E0|2=1), as shown inFig. S1(b). As described above, the required laser fluence for creating sub-50 nm nano-lines is only 0.38 mJ/cm² at the high repetition rate of 76 MHz. The intensity enhancement by the microsphere leads to the surface ablation. Then the intensity decreases rapidly with the distance in z direction and the length of the photonic nanojet is ~5 μm. This photonic nanojet is long enough to achieve the dozens of nanometers of ablation depth on the Sb₂S₃ thin films. The intensity profile of |Ex|2 (x-polarized) and |Ez|2 (z-polarized) along x axis at the maximum intensity position (z=6.4 μm) is plotted inFig. S1(c), at which the calculated FWHM of the photonic nanojet is ~678 nm. This FWHM of intensity profile is much larger than the ablated feature size in Fig. 2. Thus, the microsphere focusing is not the only reason to create the sub-50 nm structures. However, the enhancement of electric field intensity via microsphere can localize the laser energy within a narrow area to achieve a high laser fluence at the focus position, which is an important factor for the subsequent non-linear effect. Meanwhile, considering the tight focusing condition, the distribution of Ez component surrounds the focus point, which leads to less debris and suppresses the laser-induced periodic surface structures (LIPSS) effect^{40, 41}.

2) The second process is the two photons absorption (TPA) of the Sb₂S₃ films under the femtosecond laser irradiation. When the photon energy of incident beam is larger than the bandgap of irradiated material, an electron can be excited from VB to CB by the single-photon absorption. In the case of photon energy lower than the bandgap of the irradiated target, the excitation of an electron to a high energy state may require the absorption of two or more photons, which leads to the TPA or multi-photons absorption^{42, 43}. In our experiment, the photon energy of the 800 nm femtosecond laser (1.55 eV) is smaller than the bandgap of amorphous Sb₂S₃ thin film (2.05 eV)³⁷. It requires at least two photons absorption for the excitation of an electron from VB to CB, as shown in Fig. 3(b). Due to the quadratic dependence of TPA on the laser fluence, the effective intensity profile becomes narrower by the absorption of two photons^{44, 45}. Through numerical calculation, the FWHM of the effective focal spot size for TPA is further reduced to ~500 nm. Although it is still ~10 times of the FWHM of the ablation area achieved in our experiments, the narrow effective intensity profile due to the TPA also brings about the top threshold ablation effect, which can further reduce the ablation feature size.

3) The third process is the co-effect of the top threshold and high-repetition-rate heat incubation of the femtosecond laser irradiation. Because of the threshold effect of TPA, the laser fluence could be precisely controlled so that only a small portion of the focus spot exceeds the ablation threshold of target materials, resulting in feature size beyond the optical diffraction limit⁴⁶. The threshold effect performs a highly non-linear dependence on femtosecond laser fluence, especially when the laser fluence is approaching the threshold. Since the resolution can always be improved if one keeps reducing the difference between the laser fluence and threshold value, in principle, there is no limit to the fabrication resolution when taking advantage of the threshold effect. So far, there is no theoretical description to define the exact feature size of surface nano-ablation, which results from the threshold effect. The reported studies have described that the feature size is mostly reduced to two-fifths of the original beam width due to the TPA¹⁶. By controlling the laser fluence and material properties, the effective feature size due to the top threshold can be <10% of the focusing beam width of the TPA absorption ^{47, 48}. In our experiments, as shown in Fig. 3(c), through precisely tuning laser fluence and scanning speed, the top threshold effect of femtosecond laser irradiation keeps reducing the effective ablation area, and the ~45 nm line is achieved, which is only 9% of the calculated beam profile of the TPA absorption. Considering the sub-50 nm ablation is realized under the high-repetition-rate femtosecond laser irradiation, the multi-pulses incubation effect should be another critical factor for the surface nano-creation. At the laser fluence of 0.38 mJ/cm² and the repetition rate of 76 MHz, the single pulse energy is only ~0.3 nJ. It is not high enough for the surface ablation of Sb₂S₃ thin films by single-pulse irradiation at such low pulse energy. At the repetition rate of 76 MHz, the interval between two individual laser pulses is ~12 ns. The femtosecond laser can increase the electron temperature rapidly due to its short duration, and then transfer the energy from electrons to lattices for the heating of lattices within several picoseconds. However, for the temperature decrease of lattice, the required time is normally on a scale of ~100 ns⁴⁹. For the high-repetition-rate femtosecond laser irradiation, the heat accumulation is considerable at the multi-pulse irradiation with a short interval (12 ns) between pulses. The reported study has demonstrated that the absorption of Sb₂S₃ thin film at 800 nm is dependent on the temperature, while the absorption changes from <1% to >10% while the temperature increases from 200 to 250 °C ⁵⁰. During the high-repetition-rate femtosecond laser irradiation, the absorption of Sb₂S₃ thin film keeps increasing with temperature. This non-linear absorption change can lead to the incubation effect. Therefore, the sub-50 nm surface nano-structures on the Sb₂S₃ thin films are attributed to the co-effect of the microsphere focusing, non-linear absorption, and the high-repetition-rate incubation effect associated with the femtosecond laser irradiation.

To demonstrate the capability of arbitrary fabrication, more surface nano-structures are fabricated, as shown in Fig. 4. Nano-dot structures are created on ~30 nm thick Sb₂S₃ thin films at 7.6 ×10⁵ pulse number (exposure time: 1 ms) and different laser fluences, as shown in Fig. 4(a–c). By changing laser fluence from 0.26 to 0.46 mJ/cm², the feature size of the nano-dots can be tuned from 35 to 80 nm (λ/26~λ/10) as well as ablation depth increases from 17 nm to 30 nm (see details AFM cross-section profiles in Fig. S2, Supplementary information). The flat bottoms shown in Fig. 4(b, c) indicate the 30 nm Sb₂S₃ thin films are removed completely at the laser fluence >0.42 mJ/cm ². These nano-dots fabricated at different laser fluences reveal strong dependence between the ablation feature size and laser fluence. Depending on the laser parameters, nano-lines can be fabricated by tuning the scanning speed and laser fluence. At the scanning speed of 100 μm/s and laser fluence of 0.38 mJ/cm², the Sb₂S₃ thin film is ablated obviously, and a ~39 nm nano-line is created, as shown in Fig. 4(d). The edge of the ablated area is sharp, and no obvious damage is observed. In this case, the laser fluence is slightly higher than the threshold. Thus, the top threshold effect leads to the ablation of a feature size much smaller than the optical diffraction limit. Furthermore, as shown in Fig. 4(e), the width of the nano-line is increased to ~52 nm at a laser fluence of 0.42 mJ/cm², as well as the HAZ at the edge becomes obvious and the width of HAZ is ~30 nm. In Fig. 4(f), the width of nano-line and HAZ keep enlarging while the laser fluence increases to 0.46 mJ/cm². The melting becomes obvious around the ablated nano-line. It is attributed to the heat accumulation caused by the multi-pulse irradiation. The corresponding AFM image and cross-sectional profile shown in Fig. S3(a, b) show that the ablation depth is 30 nm, as well as the FWHM is ~80 nm, respectively. The formation and evolution of nano-lines are similar to the nano-dots in Fig. 4(a–c), which indicates the surface nano-structures of the Sb₂S₃ thin films can be well tuned by changing the scanning speed and laser fluence. More ablation results of nano-dots and nano-lines fabricated at different laser parameters are shown in Fig. S4. These nano-structures also show the non-linear and the incubation effects of the high-repetition-rate femtosecond laser irradiation play key roles in the surface nano-creation.

The microsphere femtosecond laser irradiation allows the free writing of arbitrary planar patterns with a controllable length, separation, and trajectory. In Fig. 4(g), triple nano-lines are fabricated at the linewidth of ~30 nm, and the spaces are from 100 to 300 nm. The creation of these nano-lines indicates the microsphere femtosecond laser irradiation is able to realize desirable nano-structures and make high-performance optical devices. As shown in Fig. 4(h), a wavy line of sub-100 nm width is fabricated at a laser fluence of 0.6 mJ/cm² and a scanning speed of 100 μm/s. The corresponding AFM image of the wavy nano-line is characterized in Fig. S3(c, d), while the ablation depth and the FWHM are ~30 nm and ~88 nm, respectively. There is no crack or damage on the corner of the curve. Double sub-50 nm wavy lines are also made at a laser fluence of 0.38 mJ/cm², as shown in Fig. 4(i). The minimum space between two nano-curves can be reduced to ~50 nm (λ/16). The successful creation of these complex nano-structures indicates that the microsphere femtosecond laser irradiation is suitable for the construction of arbitrary nano-patternings with high resolution and smoothness, which can be used for the nano-fabrication of opto-electronics devices. The relationship between the minimum FWHM and the depth is evaluated via surface nano-creation at different thick Sb₂S₃ thin films (25, 35, and 42 nm), as shown in Fig. 5. All these nano-structures are fabricated at a scanning speed of 100 μm/s. By the microsphere femtosecond laser irradiation, the minimum FWHM changes from 30 to 50 nm with the increase of thickness from 25 to 42 nm, as shown in Fig. 5(a–i). Depending on the ablation results at different thicknesses, the fitting analyses of the curve between the ablation depth and FWHM is plotted in Fig. 5(j). The distribution of the experimental results is approximately linear, and the FWHM increases with ablation depth, as well as the ratio of ablation depth and FWHM is ~0.7. According to the linear fitting analyses, the minimum ablation width can be evaluated at different thicknesses. As shown in Fig. 5(j), by extending the fitting line to the smaller or larger ablation depth (the dashed area), the corresponding FWHM can be tuned widely. At the ablation depth of 10 nm, the minimum FWHM can be reduced to ~15 nm (~λ/53).

The applications of surface nano-structures created by the microsphere femtosecond laser irradiation are demonstrated via the fabrication of diffractive gratings. Reflective gratings at a period of 1, 2, and 4 μm are designed and fabricated. The size of each diffractive grating structure is 1×1 mm². Uniform reflective grating structures of Sb₂S₃ thin films are fabricated on silicon surfaces. For a high diffraction efficiency of the grating at 532 nm incident light, the feature size of each unit is ~500 nm. The uniformity of the reflective gratings can be found in Fig. 6(a, c, e). The fabricated nano-structures are smooth. All the experimental and calculated values of diffraction angles at different grating structures are listed in Supplementary Table S1. The diffraction angles can be theoretically estimated by Eq. (1):

where m refers to the diffraction order, λ the wavelength of incident light, Λ the period width of the grating, θi the incident angle and θm the diffraction angle at different orders. The 532 nm laser at an incident angle of θi=15∘ irradiates on the grating structures and the charge coupled device captures the reflection laser spots. The diffraction results of the grating at a period of 1, 2, and 4 μm are shown in Fig. 6(b, d, g), respectively. In response to the 532 nm laser illumination, the grating at a period of 1 μm results in the first order at 15.8° (m=1) and −52.6° (m=−1), which agrees well with the theoretical value of 16.1° (m=1) and −53.2° (m=−1). As the period of the grating changes to 2 μm, the laser diffraction beam spots increase with the first, second, third, and fourth orders (m>0) at 0.4°, 15.8°, 32.6°, and 53.61°, respectively. As for the period of 4 μm, the diffracted laser beam spots up to the 4th order with the diffraction angles from −7.2° to 32.6°, while the 5th order diffraction spot intensity is too weak to be recognized. When the period decreases, the number of the supported orders also reduces, and each supported order covers a larger diffraction angle. The deviation of the diffractive angel between the experimental results and theoretical calculation is less than 1°. The slight deviation between the experimental and simulation results is attributed to the fabrication quality of the gratings. Further reducing the feature size to sub-50 nm makes it possible to fabricate more functional opto-electronics devices, especially for the realization of tunable visible metasurfaces. This strategy can be further improved. First of all, the optimal combination between the focus spot and working distance should be further tuned. The focus spot of microspheres can be reduced by using smaller microspheres^{31, 32, 35}. However, the smaller microsphere means a shorter working distance. Thus, a balance between the focus spot size and working distance should be considered. The microsphere can also work in different conditions to increase the effective numerical aperture for a smaller focus spot. Furthermore, the optical property of microspheres can be adjusted by the engineered microsphere. Different focusing characteristics based on the engineered microspheres are reported, including spatial modulation⁵¹ and multi-focusing⁵², which can be used for the arbitrary surface nano-patterning directly. Therefore, the microsphere femtosecond laser irradiation has a great potential for the nano-fabrication of functional devices.

In this study, sub-50 nm nano-structures are successfully fabricated on Sb₂S₃ thin films via the microsphere femtosecond laser irradiation in far field and in ambient air. The feature size can be tuned flexibly by laser fluence, scanning speed, and thin film thickness. The fitting results based on the ablation width at different thicknesses predict that the feature size can be reduced down to ~15 nm at the film thickness of ~10 nm. The arbitrary surface structuring indicates the flexible patterning capability of the microsphere femtosecond laser irradiation. The fabrication and the excellent performance of surface grating structures show the large area processing ability and high uniformity of this strategy, which is significant for the nano-fabrication of functional devices.