1. Introduction

Miniaturized lenses (microlenses, µ-lenses) and optical elements enable numerous applications, among them micro-optics, photonics, digital displays and imaging systems. The size of microlenses makes them compatible with microfluidic systems and allows direct integration into lab-on-chip devices as a part of an optical detection system [1–3]. Glass has been traditionally used as a material of choice for optical components due to its high transparency in a wide wavelength range, thermal and mechanical stability, chemical inertness and high refractive index. Due to the difficulty in miniaturization of glass optical elements, the materials of choice for microlenses are typically polymers. Polymer microlenses and microlens arrays can be made in a plethora of fabrication methods, such as photoresist melting, greyscale lithography, imprinting and replication and many others [4]. Some of the methods are low cost and suitable for large-scale production. Along this line, silicon-based polymer polydimethylsiloxane (PDMS) has been traditionally used to fabricate microfluidic devices due to its good biocompatibility, transparency and low cost.

While polymer microlenses were shown to have outstanding performance, glass microlenses have superior thermal and mechanical performance when compared with plastic lenses in many applications. In addition, glass shows significantly higher chemical resistance to many organic and inorganic solvents making them suitable for integration in devices designed to operate in harsh environments. As of today, fabrication methods, such as reactive ion etching [5], precision mechanical machining [6], laser ablation [7], compression moulding [8] and many others [4,9], can be used to produce glass microlenses. Unfortunately, it is difficult to control precisely parameters such as surface roughness and lens surface profile. Furthermore, most of the methods available are often tailored for fabrication of symmetrically shaped lenses (e.g. round or hexagonal) with a spherical or parabolic surface profile. In contrast, direct writing techniques offer a flexibility in the lens shape and profile. Focused ion beam (FIB) milling is a direct write technique that has been successfully applied for fabrication of a variety of optical elements [10,11] of complex shape in challenging substrates (e.g., the tip of an optical fiber [12,13]). In this method, a finely focused energetic ion beam (typically Ga + ) is scanned across a substrate. The ions impinging on the surface sputter away the substrate atoms. By controlling the beam path and the dwell time of the beam at every point, complex surface relief can be carved out in the substrate. Liquid metal (Ga) source FIB systems have been traditionally used in the semiconductor industry (e.g., mask repair) and in sample preparation for transmission electron microscopy (TEM). One of the strengths of FIB systems is their ability to modify a variety of hard materials. They are often used for nanofabrication in Si, but they were shown to successfully pattern high-quality structures in glass [14]. The disadvantages of FIB milling are its slow speed due to the serial nature of the pattern transfer and Ga implantation in the milled substrate. High concentrations of metallic Ga at the surface affect the material properties which may alter or degrade the performance of the fabricated optical components [15–18]. The advent of FIB systems based on inductively coupled plasma (ICP) sources [19,20] (plasma FIBs, P-FIBs) allows to significantly alleviate the optics fabrication problem associated with the above-mentioned disadvantages of Ga-FIBs. Thus, an ICP source allows a wide range of possible ion beams to be generated (e.g., N, O, Ar) with Xe being primarily used for milling due to its high mass and ease of plasma conditioning and handling. The use of Xe, heavy and noble gas, for milling eliminates the metallic Ga contamination and decreases the milling times due to the increased sputter yields by Xe ions compared to those of Ga. In addition, ICP sources are capable of delivering orders of magnitude higher currents (up to 2.5 µA versus 65 nA on traditional liquid metal Ga-FIB). Due to the broad and collimated ion beam from ICP sources, the size of the focused beam spot is considerably larger than the beam spot obtainable using a point-like Ga source. However, as the beam current exceeds several nA, the Ga beam spot deteriorates due to the spherical aberration of the ion optics, while the Xe beam spot of a P-FIB maintains its sub-µm size. This makes milling of multi-micron structures at high currents with Xe extremely attractive due to its relatively good resolution and more than an order of magnitude decrease in the milling times. Presumably, due to the relatively slow milling speed, most of the work on Ga milling in glass or quartz was focused on fabrication of lenses with dimensions of tens of µm [21,22], or shallow Fresnel zone plates with diameters up to or on the order of 100 µm [14,23].

Plasma-FIBs were designed originally for high speed milling cross-sectioning with a lower than Ga-FIB resolution. In this study, we verify the feasibility of milling various refractive microlenses with large diameters (50-250 µm) with parabolic profile directly in glass using a relatively low-resolution, but high-speed P-FIB with high current Xe focused beams (>60 nA). Such large microlenses are currently not straightforward to fabricate using a Ga-FIB. For instance, a microlens optically characterized in this study with a 230 µm diameter and a sag height of 9 µm requires ~1 h or ~3 h of milling at 200 nA or a more moderate 60 nA of Xe beam current, respectively. For a corresponding beam current and beamspot size from a Ga-FIB (15-50 nA), the required time to mill a single lens can be as high as 5-30 h or more. Such long milling times can be acceptable for fabrication of molds, but are prohibitively long for quick prototyping. While high-resolution Ga-FIBs are more appropriate for fabrication of <100-µm lenses, P-FIBs are more suited for fabrication of larger >200-µm lenses. In this study, we fabricate a series of microlenses with diameters >200 µm, characterize their profiles and demonstrate diffraction-limited optical performance thus demonstrating the feasibility of rapid microlens direct writing with high-current focused Xe beams.

2. Microlens fabrication

We milled microlenses of varying diameter (50-250 µm) and different sag height (down to 13 µm) in quartz microscope slides 76.5 × 25.4 × 1 mm in size. Prior to milling, the substrates were coated with 5 nm of Ti to remove charging effects and avoid the consequent artefacts. A focused 30 keV beam of Xe + ions at currents between 60 and 500 nA from a ThermoFisher Helios P-FIB Ux-G4 system was raster-scanned across the substrate to mill parabolically shaped structures. The desired lens profiles were translated into digital 8-bit images, where the pixel coordinates defined the beam position in the pattern and the pixel value (0-255) defined the beam dwell time. In this way, we could control the local sputtering rate and hence the amount of material removed, see Fig. 1. In order to maximize the smoothness of the lens surface, the raster-scan pattern was digitized to have a sufficient number of pixels to ensure 80% beam spot overlap between the neighbouring points. Furthermore, to reduce surface roughness associated with the digitalization error of the dose map, the patterns were written serially in the vertical direction with next milling orientation rotated by 120° compared to the raster scan direction of the previous mill [Fig. 1(b)]. We noticed that this strategy considerably improved the surface smoothness and reduced digitalization artefacts (e.g. rings [10]). The pattern quality can be potentially further improved by optimizing the milling parameters [24], such as beam dwell time and scanning direction (e.g., spiralling). The patterns were designed to contain a brim that received the maximum dose during the milling. The brim around the lens that was milled together with the lens provided an escape path for the sputtered atoms (especially those milled from the deep depressions at the lens edges), reduced the re-deposition effects and helped realize the required profile shape and curvature all the way until the lens’ full diameter. The brim width was typically 5-10% of the full lens diameter.

 

Fig. 1 Pattern for milling microlens in glass with P-FIB is a) a parabolic profile where lateral pixels represent the position of the beam and the value of the pixels is proportional to the amount of material to be milled away. b) The patterns are 8-bit bitmap images. To reduce digitalization errors, the pattern is raster-scanned in three steps with each step the pattern rotated by 120°. The procedure is repeated until the desired mill depth is achieved.

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Figure 2(a) shows microlenses of different diameter and sag height (up to 13 µm) milled into the glass substrate. Larger microlenses (150 and 180 µm in diameter) were milled using 200 nA beam current, while the smaller lenses (75 and 100 µm in diameter) were milled using 60 nA beam current. In order to assess the lens curvature, we coated the milled surface of selected microlenses with a thin Pt layer using e-beam deposition. Next, we milled cross-sections through the centre of the lenses. The profile of the lenses was digitized using ImageJ package and the curvature was fitted. The example shown in Figs. 2(b) and 2(c) represent a lens with 45 µm diameter (50 µm including the brim). The maximum depth was 8.1 µm, however, the lens sag height is 6.7 µm as measured from the interface between the brim and lens edge. This results in a 40.7-µm radius of curvature and a nominal focal distance of ~50 µm at 500 nm wavelength. Apart from the brim width, the curvature of the lens is perfectly parabolic and matches the designed shape [Fig. 2(c)]. This result indicates the importance of the brim in order to realize the full diameter of the lens with the required sag height. Sputtered material is not able to efficiently escape from deep troughs which would degrade the edge quality of the lens.

 

Fig. 2 Scanning electron microscopy (SEM) images of a) overview of different microlenses milled into the glass substrate using P-FIB at 60 and 200 nA of Xe beam current and b) cross-section view revealing the profile of a 55-µm microlens. SEM stage tilt is 52°. c) Parabolic fit to the measured profile of the lens from (b).

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3. Microlens characterization

In order to characterize the optical performance of glass microlenses milled with the P-FIB and establish design rules for their fabrication, we produced a series of 230-µm microlenses with the sag height of up to 13-µm using 200 nA of Xe current. Their surface quality and profile were characterized using a white light interferometer. The measurements reveal very smooth profiles of the lenses [Figs. 3(a)-3(d)] with the RMS roughness not exceeding 25 nm and 60 nm for the central and outer region of the lenses, respectively [Figs. 3(e)-3(g)]. The surface roughness is larger for the lenses that were milled deeper (~10 nm roughness for the central region of the lens with sag height of 7.3 µm compared to ~25 nm surface roughness for the lens with a 13.2 µm sag height). Generally, shallower profiles exhibit better match with a parabolic profile, see Fig. 3(d). The increasing deviation of the profile from a perfect sphere for deeper milled lenses is associated with the increased sputter yield for the ions impinging on the sloped profiles of the lens edges. The increased sputter yield results in more material removed from the periphery of the lens and hence divergence of the resultant shape from the designed (in this case parabolic). This can be remedied by adjusting the beam dwell time on the further-off-center pixels during the milling to account for the change in the milling rate as the beam angle of incidence on each pixel changes with the emerging three-dimensional surface profile [25].

 

Fig. 3 The surface profile of 230-µm microlenses with a) 7.3 µm, b) 9 µm and c) 13.2 µm sag height, respectively. The lenses were milled at 200 nA current of 30 keV Xe ions. The profiles were measured with a white light optical profilometer. d) Comparison of profile curves measured with the optical profilometer for the microlenses in a), b) and c). Parabolas were fitted to the profiles to estimate the radius of curvature on the lenses’ profiles. (e,f,g) Surface roughness map of the lenses shown in a), b) and c), respectively.

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The focusing performance of the milled microlenses was characterized by illuminating them with a laser (λ = 485 nm) through an aperture and mapping the transmitted intensity with a 2-µm pinhole. The light was incident normally on the flat unpatterned backside of the glass slide and focused into the air after exiting from the patterned frontside, effectively resulting in a planar-convex lens configuration. The pinhole was raster-scanned at various positions from the lens to map the beam at various planes before and after the focal spot [Figs. 4(a)-4(g)]. The cross-sectional views through the beam propagation for microlenses with both short (1.4-2.0 mm) and long (6.9 mm) focal distances are shown in Figs. 4(d)-4(g), respectively, while the intensity profiles through the foci of the lenses are depicted in Fig. 4(h). While Figs. 4(d)-4(e) show spherical wavefronts (amplitude) shaped by the microlenses L01 and L02 as they converge into the diffraction-limited spots at the focus, Fig. 4(f) reveals minor distortions in the beam propagation, which is expected as the profile of this lens departs more from the purely parabolic shape compared to the shallower L01 and L02. Nevertheless, Figs. 4(d)-4(f) and the corresponding cross-sections in Fig. 4(h) with Airy-function fits show very good optical performance and focusing properties of the lenses achieving the diffraction-limited performance.

 

Fig. 4 Focusing properties characterization of microlenses by mapping the intensity at different planes around the focus (a-c, a microlens with a sag height 7.3 µm) (d,e,f,g). Cross-sectional view through the focused beam for microlenses with 7.3 µm, 9 µm, 13.2 µm and 1.8 µm sag height, respectively. Some misalignments in the figures are due to the mechanical drift and vibrations. h) Comparison of intensity profiles at the focus of the microlenses with the corresponding Airy function fit.

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A summary of the measurements is presented in Table 1. The designed and measured focal distances are in good agreement (95%) for the lens with a shallow profile and hence the long focal distance (6.9 mm). The agreement decreases with the increase of the sag height (7.28 µm – 84%, 9.01 µm – 74%, and 13.21 µm – 65%). Similarly, the discrepancy between the measured beam spot full width at half maximum (FWHM) and diffraction-limited expected beam spot (Abbe limit) follows the same trend. The deviation of the measured beam spot from the diffraction-limited size is, therefore, fully accounted by the increase of the apparent focal distance from the designed values, and as a result, increased numerical aperture (NA) of the microlenses that were milled deeper into the glass. As we have not observed changes in the material (e.g., transparency) subjected to prolonged Xe beam treatment, we attribute this to the departure of the lens profile from the parabolic shape as the milling depth is increased [Fig. 3(d)]. The larger mismatch between the expected and measured beamspot for the lens with the long focal distance, however, cannot be fully explained by the increase of the focal distance from the design value. The discrepancy is mainly due to the small NA of this lens (0.016) and hence a large depth of focus (DOF) of ± λ/(2NA²) = ± 873 µm (see Fig. 4(b) showing the extent of the focal spot along the beam axis). The large DOF introduces an additional uncertainty into the measured focal distance and hence an increased discrepancy between the expected and measured values.

Table 1. Summary of the microlenses optical characterization. The designed

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Finally, to demonstrate the microscopy application of glass microlenses, we performed imaging experiments on a reference sample (Fig. 5(a), Cu TEM grid, 25 µm wide bars, 85 µm pitch, 15 µm height). Using the focused beam spot, the sample was raster scanned across the beam and images were formed by collecting the transmitted intensity. Figures 5(b)-5(c) compare the scanning transmission images obtained using L01 and L03 lenses (Table 1), respectively. As expected, the microlens with a higher NA provides a sharper image [Fig. 5(c)]. The patterns observed on the non-transparent Cu bars in the images are attributed to the scattering from the surface contamination and particles adhering to the grid [Fig. 5(a)]. In the projection imaging experiments, the grid was illuminated via a 200-µm aperture matching the diameter of the microlenses (230 µm) and imaged with an objective [Fig. 5(d)]. The same area was imaged through microlenses L01 and L03 were inserted right after the grid [Figs. 5(f) and 5(g)]. The corresponding magnifications are 1.7 × and 3.3 × , respectively. These values match well with magnifying powers expected (1.95 × and 3.5 × ) from the focal distances of the lenses and the distance between the object and the lenses. This distance (~1 mm) is the thickness of the glass slide when the grid is in contact with the glass face with the milled lenses being on the opposite face. The origin of the rings artefacts in the projection images is not fully understood given the great smoothness of the lens surfaces [Figs. 3(e)-3(g)]. With the lateral pitch of the rings (~10 µm and ~20 µm for L01 and L03 lenses, respectively) and their central alignment with the lens axis, the diffraction from circular apertures with diameters of ~48 µm and ~17 µm is most likely to generate such ring patterns. Upon inspection of the roughness map of the lens profiles, minor ring artefacts at the vertex of the lens can be observed. These are associated with the digitalization error of the lens profile at the centre of the pattern. While the incremental dose increase between the bitmap levels is relatively small, the proportional increase of the delivered dose can be substantial especially at the center of the lens with assigned low bitmap level values (e.g., the discontinuity of the dose between the neighboring pixels with the bitmap dose levels with values 1/256 and 2/256 is 100%). These defect can potentially be mitigated by choice of a different milling strategy (e.g., along a spiralling path), averaging milling patterns with different pixelization, and optimizing beam parameters, such as dwell time and de-focus to smoothen the pattern artefacts [24]. The minute variations in the surface profile were revealed due to the use of highly coherent laser source. This was needed in order to verify the diffraction-limited performance of the fabricated lenses. Using an incoherent light source (LED) results in lower resolution of the imaging, however, the artefacts due to the diffraction and interference could no longer be observed [Figs. 5(g)-5(i)].

 

Fig. 5 Imaging characterization of the glass microlenses using a Cu TEM grid (a) as a reference sample (the insert shows a tilted (45°) image of Cu bars). (b and c) The image was formed by raster scanning a beam focused by L01 and L03 lenses from Table 1, respectively, across selected regions in the reference sample. d) The object was illuminated with a coherent laser beam through a 200-µm aperture and imaged using an objective. (e and f) Microlenses L01 and L03 (Table 1), respectively, were inserted to form a magnified image of the sample. (g,h,i) are similar to (d,e,f) respectively, with the images formed using incoherent light source (LED) and not using the aperture.

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4. Conclusion

Smooth microlenses were fabricated in quartz substrates by direct milling using focused Xe beam. Surface characterization of selected lenses with a diameter of 230 µm and sag height up to 13 µm revealed smooth profiles. The profile of the lenses is parabolic as designed, however, it tends to deviate from the perfect parabolic shape as the sag height (milling depth) of the lens is increased. The deviation of the surface profile from the designed curvature and shape is responsible for the departure of the focal distance from the designed values as the lens sag is increased. The focusing properties of the selected lenses were characterized by mapping the transmitted intensity. The results indicate diffraction-limited focusing with the smallest beam spot of 2.8 µm at FWHM observed. The lenses were used in transmission scanning microscopy to test their optical performance. As expected, the lens with the higher NA produced a sharper image of the resolution sample. The same resolution sample was used in projection imaging showing good match of the magnifying power of the microlenses with the expected values. The rings artefacts observed in the projection images are attributed to the digitalization errors of the lens profiles and discontinuity of the height mapping, especially in the central lens region. The rings artefacts could not be observed when using incoherent illumination in image formation. The results indicate the feasibility of the P-FIB for the rapid writing of micro-optical components of high quality and diffraction-limited performance directly in glass.