1. INTRODUCTION

For a wide range of optical imaging applications, the requirements for optical performance, volume reduction, and cost minimization are steadily increasing. In these fields, significant improvements can be achieved by substituting conventional refractive or reflective components with elements of specially adapted characteristics and enhanced functionality. Among these elements, especially rotationally symmetric meso- and microscale optical elements such as phase rings, Fresnel zone plates (FZPs) or diffractive lenses are of particular interest, since a rotationally symmetric shape matches the symmetry of the vast majority of optical imaging systems. Thus, rotationally symmetric meso- and microscale optical elements are combined with refractive optical elements, forming hybrid systems with optimized performance and compactness [1]. Examples for hybrid systems, especially regarding the combination of refractive and diffractive lenses, are high-quality camera lenses, eyepieces or high-resolution microscopes with solid immersion lenses [1–3]. In order to use meso- and microscale rotationally symmetric structures in larger quantities and for individual applications, a process is required that provides fast, efficient, and flexible manufacturing. In this context, the independence from Cartesian coordinates is advantageous, as they are intrinsically suboptimal for the fabrication of rotationally symmetric structures. In order to find a suitable approach, it is useful to take a look at already established micro-optical manufacturing technologies. An established mastering technique of microscale structures is lithography, especially direct laser writing or electron beam lithography. In most of these processes, the beam scans and exposes a photoresist-coated substrate in Cartesian coordinates. The advantage is a high degree of flexibility regarding the geometric shape of the elements to be produced. Disadvantages are a long writing time for larger areas and problems attributed to the “stitching” that occurs due to a limited scan area of the respective beam. There are different approaches to increase the flexibility and efficiency of direct writing processes. An example is the ability to expose the substrate with multiple spots [4,5]. In order to reduce stitching effects connected to the fabrication of rotationally symmetric structures, Haefner et al. applied a direct laser writing system in combination with a rotating substrate [6]. A second example is the polar coordinate laser writing system, presented by Poleshchuk et al. [7]. As the substrate can be rotated and translated, arbitrary diffractive elements are producible that differ from rotational symmetry. However, there is potential concerning writing speed, since a single exposure spot is used for exposure. Another well-established technique to fabricate microscale structures is mask-based lithography. The decisive advantage is the short exposure time compared to direct laser writing, as the complete area is exposed in a single step. However, for each type of element to be manufactured, a corresponding mask must be produced beforehand, which leads to potentially high costs for the mask and severely restricted flexibility. An already existing approach to overcome the drawbacks of direct laser writing and conventional mask-based lithography is a hybrid lithography scheme presented in [8] that uses the large area patterning abilities of mask-based lithography and the high resolution of direct laser writing in a combined lithographic method. An alternative technique, which provides high resolution combined with a particularly high flexibility regarding the geometrical shape of the fabricated elements, is maskless lithography [9–11]. In this case, a certain area shape with a specific intensity distribution is exposed at one “exposure shot.” However, most of these established and approved systems used for structuring are complex and therefore expensive. Additionally, the problems attributed to the stitching in Cartesian coordinates are usually not solved.

In this contribution, we present a new straightforward, easily implementable, and cost-effective lithographic solution for the tailored fabrication of rotationally symmetric meso- and microscale optical elements. In particular, we describe for the first time a lithographic method based on a ring-shaped light distribution with a variable diameter that is used for the exposure of a photoresist-coated substrate. The presented method is fast, efficient, and suitable for extended areas without Cartesian stitching effects. Therefore, the required ring-shaped light distribution can be created using axicons [12]. To enable a variation of the ring diameter, a minimum of two axicons is required, of which one axicon has to be movable along the optical axis. A particularly simple and effective approach uses a combination of a plano–concave and a plano–convex axicon as key elements [13,14]. In recent years, a variety of applications for a ring-shaped light distribution has been presented, e.g., for laser material processing [15–18] or biomedicine [19,20]. To the best of our knowledge, lithographic methods [21] using ring-shaped light distributions are not known so far. In order to apply such a ring-shaped light distribution to expose photoresist, a compact laboratory demonstrator was realized. The presented setup is simple and aims primarily to demonstrate the capabilities of the lithographic exposure tool as a proof of concept. Its ability to fabricate tailored rotationally symmetric structures in different photoresists and on a variety of substrates guarantees a high degree of flexibility. In the first part of this paper, the optical design concept is presented, which is followed by the mechanical design, the systems characterization, and the demonstration of its working principle. Following this, initial exposure tests are carried out and exposure results of single-ring structures in photoresist are presented. Finally, we show the capabilities of the developed system by characterizing fabricated binary optical elements. The concept and the presented results pave the way for the fabrication of meso- and microscale optical elements.

2. OPTICAL DESIGN CONCEPT AND DISCUSSION OF PRELIMINARY EXPOSURE STUDIES

In this section, the basic concept and the optical design model of the exposure tool for variable ring-shaped lithography are presented, and key parameters of the system are discussed in detail. Within this concept, we pursue an approach published in [13] that combines two identical lenses and two axicons from which one is plano–concave and the other one is plano–convex (Fig. 1). Light is emitted by an idealized point light source and enters the optical system, forming a divergent light cone. The first lens forms a collimated ray bundle that propagates to a second lens, where the light is focused onto the image plane. Between the focusing lens and the image plane a fixed plano–concave axicon and an axially movable plano–convex axicon are inserted. Both axicons exhibit equal base angles $\alpha$, which is the condition for an ideal annular ring zoom system [14]. The principle of ring creation in the image plane can be explained in a two-dimensional cross-sectional view (Fig. 1): the convergent ray bundle coming from the second lens passes the fixed plano–concave axicon and is divided into two convergent partial ray bundles. Each partial ray bundle is characterized by a chief ray that is deflected in dependency of base angle $\alpha$ and refractive index ${{n}}$ of the axicon. The deflected convergent partial ray bundles are symmetric with respect to the optical axis. The second axicon causes a deflection of the partial rays into the original direction. The variation of the ring radius is achieved by continuously changing the distance ${{d}}$ between both axicons. In particular, the axial position of the convex axicon determines the distance between both convergent partial ray bundles before they experience the second change of direction, which finally results in the distance between the two spots in the image plane. In a three-dimensional view, a ring is created in the image plane. When the distance between the axicons is decreasing to zero, the ring is reduced to a point image. With increasing distance, the ring radius extends. It should be noted that the combination of axicons slightly influences the imaging properties of the system: in particular, the axicons in direct contact act as a plane-parallel plate with a small focus shift. As the distance between the axicons increases, the value of this shift varies slightly. The linear correlation between the radius of the ring ${{{R}}_0}$ and the distance $d$ between the two axicons with refractive index ${{n}}$ can be described by the following Eq. (1) [13], which is only valid for small and equal axicon base angles $\alpha$ and an idealized, aberration-free system:

 

Fig. 1. Optical design concept: The plano–convex axicon is moved along the optical axis to realize (a) shorter or (b) longer distances. This results in a variation of the ring diameter in the (c) image plane.

Download Full Size | PDF

In order to prepare an experimental implementation of the concept (Section 3), ray-trace simulation and optimization steps were carried out using an appropriate software tool (OpticStudio). To keep the implementation simple, commercially available components for all optical elements and also for the light source were selected. As a light source for the optical system a fiber-coupled LED (Thorlabs GmbH) with a wavelength of ${{405}}\;{{\pm}}\;{{7}}\;{\rm{nm}}$ was used. For the optical design, monochromatic light with a wavelength of 405 nm was assumed. The fiber core diameter, which measures 50 µm, defines the entrance pinhole of the optical system. The numerical aperture (NA) of the system has a value of 0.11. All optical elements have a diameter of one inch (25.4 mm). Aspheres are chosen instead of spherical lenses to reduce imaging errors like spherical aberration. Both aspheres (Edmund Optics, 48184) have a focal length $f$ of 100 mm. The base angles $\alpha$ of the plano–concave axicon (VM-TIM GmbH) and the axially movable plano–convex axicon (Thorlabs GmbH) have a value of 0.0873 rad (5°). The axicons are made of fused silica with a refractive index $n$ of approximately 1.46 at 405 nm. Using Eq. (1), a maximum ring radius ${{{R}}_0}$ of about 3.7 mm is obtained at a theoretical maximum distance $d$ of approximately 84 mm between both axicons. The actual system layout also affects the achievable cross-sectional ring width: the fiber output located in the focal point of the first asphere and the same focal length for both aspheres results in an image scale of ${-}{{1}}$. Consequently, a simple geometric optical consideration results in a ring width ${{w}}$ of 50 µm in the image plane. However, optical aberrations and diffraction effects increase the width of the ring. The contribution of diffraction is inversely proportional to the NA of the partial ray bundle (0.055), which is half of the aspheres’ NA. Therefore, diffraction contributes a broadening of ${\sim}{{10}}\;{{\unicode{x00B5}{\rm m}}}$. The aberrations can be characterized using the rms spot radius resulting from the optical design, which varies slightly for different ring diameters and has a maximum value of ${\sim}{{10}}\;{{\unicode{x00B5}{\rm m}}}$. Following these aspects, the final total ring width can be estimated to be ${\sim}{{70}}\;{{\unicode{x00B5}{\rm m}}}$. It stays nearly constant for all ring diameters. Figure 2(a) shows a simulated spot diagram for different ring diameters. To properly control the lithography process, it is necessary to know the exposure intensity for each ring diameter. In order to take the ring width into account, we choose the peak diameter ${{{d}}_{{\rm peak}}}$ as a reference that describes the distance between the respective intensity maxima. Assuming a symmetric Gaussian intensity profile of the ring width cross section, which remains constant for different ring diameters, the peak position is located in the center of the ring width. Additionally, taking Guldinus’s theorem for revolution-generated objects into account, it follows that the local intensity (total power per area segment) used for the exposure is inversely proportional to the ring diameter (Eq. 2), which changes linearly by the axicon movement (cf. Eq. 1),

 

Fig. 2. Simulation with OpticStudio. (a) Top view (spot diagram); (b) intensity distribution for different ring sizes at constant power of light source.

Download Full Size | PDF

To validate these assumptions, the intensity distribution for different ring diameters was calculated using OpticStudio [cf. Fig. 2(b)]. Figure 2(a) represents the top view and Fig. 2(b) the cross section of the intensity distribution. Within this simulation, a constant light source power of 10 µW was assumed, which correlates with the subsequent exposure tests (Section 3.C).

 

Fig. 3. Optomechanical setup of the implemented system. (1) Light source; (2) aperture stop; (3) combination of two aspheres; (4) plano–concave axicon; (5) plano–convex axicon; (6) motorized stage; (7) substrate holder (in image plane); (8) CCD camera (out of image plane); (9) dovetail guide.

Download Full Size | PDF

3. IMPLEMENTATION AND PROOF OF CONCEPT

Based on the optical design, a laboratory demonstrator has been developed that was subsequently used to expose single-ring structures with constant ring widths and varying diameters in photoresist. The reproducible exposure of these structures facilitates the lithographic fabrication of application-specific binary optical elements (Section 4).

A. Optomechanical Setup

In the following, an overview of the setup is given and essential optomechanical details are presented. The complete system is shown in Fig. 3. For practical reasons, the entire system is oriented horizontally, offering the advantages that the individual elements are easy to mount and conveniently accessible for alignment. In order to guarantee high mechanical stability and accuracy, a basic cage system (Thorlabs GmbH) was chosen, in which all components except for the plano–convex axicon were successively mounted on cage rods. The plano–convex axicon was mounted on the carriage of a motorized precision linear stage (OWIS GmbH, LTM 60-100 [22]). The motorized stage guarantees an accurate positioning of the positive axicon along the optical axis with a positioning error ${\lt}\;{{35}}\;\unicode{x00B5} {\rm{m/100}}\;{\rm{mm}}$, which is associated with an uncertainty of ${\sim}{2.9}\;{{\unicode{x00B5}{\rm m}}}$ for the ring diameter. The possibility for precise lateral position correction of the light source and both axicons is given by fixing these elements in laterally alignable mounts. Starting with the light source, the elements of the system were mounted along the optical axis. Following the initial system setup, the resulting illumination spot created at the focal point of the second asphere was checked regarding its centric lateral position. Subsequently, the two axicons were inserted and laterally aligned. In order to evaluate the homogeneity of the annular light distribution in the image plane, the substrate holder can be replaced by a CCD camera (Allied Vision GE2040 [23]). Therefore, the camera and the substrate holder are individually mounted on a movable carriage fixed to a dovetail guide, allowing a manual shift without tilting. A scale on the guide facilitates a reproducible repositioning of the camera or the substrate holder.

 

Fig. 4. Focus alignment: CCD camera (shifted to the image plane using a dovetail guide) is continuously moved in axial direction by (1) an adjustment screw to find the exact focus position. The axial position is checked with (2) a dial gauge.

Download Full Size | PDF

The size of the camera chip is ${15.1}\;{\rm{mm}} \times {15.2}\;{\rm{mm}}$, so the maximum diameter of the exposure ring can be recorded in a single shot. The size of the mountings for the two axicons is limiting their minimum axial distance to ${\sim}{19.4}\;{\rm{mm}}$, which results in a minimum ring diameter of 1.6 mm. The axial dimension of the mountings also limits the minimum distance between the plano–convex axicon and the substrate holder, which leads to a maximum ring diameter of 6.5 mm within the setup. The substrate holder is also arranged independently of the cage system. Its position can be aligned in both lateral directions and along the optical axis. The axial alignment of the substrate holder ensures the exact positioning of the substrate surface in the image plane of the optical system, i.e., the focus of the annular light distribution.

B. Experimental Verification of the Setup

To prepare the lithography process, it is necessary to experimentally determine the resulting ring-shaped light distributions in the target plane. In particular, the shape of the radial intensity cross section of the ring width and the homogeneity of the intensity along the ring circumference have to be characterized. For this purpose, the substrate holder was replaced by the camera, and the camera chip was placed in proximity to the image plane. The camera was mounted axially alignable (Fig. 4) and moved in an axial direction through the focus of the system in steps of 200 µm while pictures were subsequently taken. To verify the correct axial displacements, the respective axial camera position was checked with a dial gauge.

 

Fig. 5. Camera recordings of a single ring. (a) Top view with locations of cross sections (dashed lines); (b) exemplary cross section, showing the symmetric intensity distributions recorded in the image plane; (c) single radial intensity cross section with Gaussian fit (red curve) and FWHM, recorded at camera position of 600 µm defocus.

Download Full Size | PDF

The captured images were processed and analyzed using MATLAB (R2018b). In particular, cross sections were placed through the ring images at different positions [see dashed lines in Fig. 5(a)] and their radial intensity distributions were plotted and evaluated. Figure 5(b) shows an exemplary cross section. The characteristic beam profile emitted by the light source can be assumed to be a Gaussian distribution. If the camera chip is exactly located in the image plane, the Gaussian profile shape should also appear in the recorded cross sections. In Fig. 5(c), an exemplary ring profile cross section is shown (black dotted line), located in the focus of the optical system. The comparison with a mathematical Gaussian curve (fitted red line) shows only a very small deviation.

By recording the intensity distribution in different axial detector positions, it can be found that both criteria, full width at half-maximum (FWHM) and symmetry of the cross-sectional profile, change and, therefore, are useable for the definition of the image plane.

Hereby, it should be noted that both criteria slightly depend on the ring diameter: The FWHM of the smaller ring diameters is generally larger than the FWHM of the larger ring diameters. For a smaller distance between both axicons (small ring diameter) the area of the convex axicon sectioned by the entering ray bundle is larger than for a large distance (Fig. 1). This larger transmitted area may lead to a higher impact of surface aberrations and an enlargement of the FWHM at small diameters. Figure 6(a) shows the FWHM as a function of the axial position, where the origin of the scale was set to correlate with the smallest measured FWHM. The two curves show the dependency of the FWHM for a larger ring diameter (${\sim}{4.9}\;{\rm{mm}}$, red dotted line) and, respectively, for a small ring diameter (${\sim}{1.6}\;{\rm{mm}}$, black dotted line). Both curves show the same shape with minima at approximately the same axial position. The average of the measured FWHM at the minimum position was found to be ${\sim}{{64}}\;{{\unicode{x00B5}{\rm m}}}$ for the larger ring diameter and ${\sim}{{70}}\;{{\unicode{x00B5}{\rm m}}}$ for the smaller ring diameter. It has to be mentioned that the value of the ring diameter is also slightly dependent on the axial position of the camera, as the system does not fulfil the condition of telecentricity. As a second criterion, the shape variation of the cross section of the ring width is dependent on the axial position of the detector and was used to find the appropriate image plane. A symmetric profile shape is expected for the axial position close to the image plane. The symmetry behavior is evaluated in a range of about ${{\pm 1}}\;{\rm{mm}}$ around the assumed target position. For the axial position with the narrowest FWHM, it is found that the measured cross section does not show a symmetric profile shape [Fig. 6(b)]. The reason for the symmetry loss might be also connected to the lack of the system to fulfil the condition of telecentricity. By shifting the axial position by 600 µm, the observed cross-sectional profile changes to a symmetric shape [Fig. 5(c)]. With a further increasing distance, the symmetric profile form is preserved, and only the FWHM is enlarged drastically [Fig. 6(c)].

 

Fig. 6. (a) Value of FWHM for different focus positions of CCD sensor, shown for two exemplary ring diameters; (b) asymmetric intensity distribution of ring recorded at sensor position of 0 mm (smallest FWHM); (c) almost symmetric intensity distribution of ring recorded at sensor position of 1.0 mm (strongly increased FWHM).

Download Full Size | PDF

As the symmetry of the intensity profile is essential for the exposure process, a compromise between both criteria—small FWHM and symmetric intensity profile—was selected. In particular, the axial position of 600 µm distance to the minimum FWHM criterion was chosen as the reference plane for the following exposure processes. At this position, the intensity profile has a symmetrical Gaussian shape and the FWHM measures ${{75}}\;{{\pm}}\;{{5}}\;{{\unicode{x00B5}{\rm m}}}$. After fixing the focus position of the camera, the homogeneity of the intensity distribution along the circumference of the ring was analyzed. The degree of homogeneity is used as an alignment criterion for the lateral position optimization of both the plano–concave and the plano–convex axicon. As a result, a maximum intensity variation of approximately 5%–10% along the ring circumference was measured. This precision is considered to be sufficient to perform the intended exposure processes.

C. Exposure Preparation and Test Exposure Performance

This section describes the preparation of the samples for the lithography process and initial exposure studies. The results serve as a basis for the following fabrication of the specific meso- and microscale optical elements (Section 4). For all exposure tests, fused silica wafers with a thickness of 700 µm are used as substrates and the positive photoresist AZ1505 (Merck KGaA) is chosen for structuring [21]. A photoresist layer with a thickness in the range between 360 and 430 nm is deposited on the substrate by means of spin coating. Subsequently, a soft-bake step at 90 $^\circ$C is performed for 25 min in a convection oven. Finally, the samples are exposed using the presented setup. This process is described separately below. Following the exposure process, the samples are developed for approx. 20 s to dissolve the exposed areas. For the topographical measurements of the generated ring structures, a white light interferometer is used (Zygo NewView9000). Prior to each exposure test, the optical power of the fiber-coupled LED was set to a value of 10 µW using an appropriate LED driver. For verification of this value, the power was checked before each exposure procedure with a power meter temporarily located in the target plane. If necessary, the power was readjusted by the driver so that possible deviations remain in a single-digit percentage range. The substrate holder has to be aligned properly to guarantee the correct axial position of the substrate surface with respect to the target plane of the optical system. For this purpose, a procedure was used that is analogous to the previously presented camera positioning (Section 3.B). In detail, several test exposures were made at different axial positions of the substrate surface. After evaluating the resulting profile shapes in the photoresist with respect to their symmetry, the optimal focus position of the substrate was found. In our case, this procedure had to be done only once for all subsequent exposures, as the substrate thickness remained constant for all exposures. However, the alignment of the substrate holder could be repeated for different substrate thicknesses. Within the focus position of the substrate, the incident intensity distribution is reproduced in the resist, forming a profile cross section in the shape of a negative Gaussian curve. This transfer is possible because real binary resists naturally have a nonideal contrast curve (contrast below infinity). In order to fabricate defined binary ring structures, the photoresist has to be fully exposed to the substrate surface. Additionally, it is necessary to achieve constant ring widths on the substrate surface for all exposed ring diameters and over the entire extension of each ring. For binary structures, the ring width is determined by the radial extent of the uncovered substrate surface. Figure 7 shows an exemplary exposure profile cross section exhibiting a flat ring width at the substrate surface (black line), where the photoresist layer is completely removed.

 

Fig. 7. Single radial exposure cross section with corresponding ring width (black curve) and fitted Gaussian distribution (red curve); substrate is positioned in the focus of the optical system.

Download Full Size | PDF

Its Gaussian shape in its peripheral areas is proven by the comparison with a mathematical Gaussian curve (fitted red line). As shown in Fig. 7, the photoresist has a thickness of ${\sim}{{420}}\;{\rm{nm}}$, which stays constant for the exposures presented in this section. The resulting ring width is directly related to the exposure dose ${{D}}$, which depends on the incident intensity ${{I}}$ and exposure time ${{t}}$,

As the power of the light source is kept constant for each exposure step, the adjustment of the exposure dose is accomplished by varying the exposure time. In order to create a specific ring width at the substrate surface, the appropriate exposure time for one single reference ring diameter has to be determined. To achieve this, the exposure time was varied, and the corresponding ring width at the substrate surface was determined for the smallest ring diameter of 1.6 mm. Figure 8 shows a diagram in which the measured ring width at the substrate surface is displayed as a function of the exposure time. The diagram demonstrates that the experimentally determined ring widths follow the expected curve of the reverse function of the Gaussian exposure profile. The smallest change of the ring width occurs at values between 70 and 80 µm, where the photoresist is exposed with an exposure time of approximately $({{25}}\;{{\pm}}\;{{2}})\;{\rm{s}}$. These values correlate with the extension of the ring width in the region slightly above and below the FWHM (${\sim}{{75}}\;{\rm{\unicode{x00B5}{\rm m}}}$) of the Gaussian profile, where the rising edges are steepest (cf. Section 3.B and Fig. 7). Therefore, the choice of an exposure time of 25 s is advantageous, as in this case the value of the ring width at the substrate surface is least sensitive to external influences such as inaccuracy in timing the exposure and deviations of the LED power or photoresist thickness.

 

Fig. 8. Dependency of ring width values on exposure time variations; experimental determination of the exposure time $t$ of 25 s for a ring diameter of 1.6 mm to expose a ring width of ${\sim}{{75}}\;{\rm{\unicode{x00B5}{\rm m}}}$ at the substrate surface.

Download Full Size | PDF

 

Fig. 9. White-light interferometric measurement (Zygo NewView9000) of eight ring structures exposed subsequently in photoresist. (a) Top view on the fabricated ring structures, which have diameters in the range from 1.6 up to 6.24 mm; (b) the cross section reveals symmetric profiles with constant ring widths of $({{75}}\;{{\pm}}\;{{5}})\;{\rm{\unicode{x00B5}{\rm m}}}$ for all ring diameters.

Download Full Size | PDF

Table 1. Values of Exposure Preparation and Performance at Constant LED Power of 10 µW and Constant Exposure Dose ${{D}}$

View Table

To keep the selected ring width at the substrate surface independent of the ring diameters, a constant exposure dose is essential. Assuming a constant ring width of the light distribution for different ring diameters, the irradiated intensity changes inversely proportional to the increasing diameter, as mentioned before (cf. relation 2). Starting with the exposure time of 25 s for the smallest ring diameter, the exposure time for larger ring diameters can be calculated simply by multiplying the initial exposure time by a factor corresponding to the ratio of the new ring diameters to the reference value. Figure 9(a) shows a measurement of eight concentric rings with different diameters, which were fabricated in photoresist with a constant ring width of (${{75}}\;{{\pm}}\;{{5}}$) µm. The cross section [Fig. 9(b)] shows a uniform and symmetric profile shape for all ring structures (cf. Fig. 7). This proves that the adjustment of the exposure time results in a constant exposure dose for different ring diameters. The distance between all subsequent ring diameters is ${\sim}{0.66}\;{\rm{mm}}$. For all eight uniform ring structures depicted in Fig. 9, the corresponding parameters of relative axicon position, ring diameter, and exposure time are summarized in Table 1. These numbers can be used as reference values to derive the setting parameters for any subsequent exposure process.

4. FABRICATION OF BINARY MESO- AND MICROSCALE OPTICAL ELEMENTS

In this section, various meso- and microscale optical elements are presented, which were fabricated with the introduced lithography setup. All elements are photoresist structures that can be used directly as phase elements or can be further processed (e.g.,  by subsequent etching steps). The sample preparation (spin coating, preprocessing) was conducted in the same way as described in Section 3.C.

 

Fig. 10. Measured resist surface topography (Zygo NewView9000). (a) Top view and (b) profile cross-sectional view on a diffractive axicon with 12 zones; (c) top view and (d) profile cross-sectional view on a diffractive axicon with 15 zones; (e) single phase ring with (f) cross-sectional view of the profile; (g) combination of two phase rings with different sizes (3D view).

Download Full Size | PDF

With continuous reduction of the radial distance between neighboring single-ring structures, the mutual influence of their Gaussian profiles increases and finally leads to a complete overlap at the substrate surface. Thus, an exposed zone is created, whose width depends on the amount of single-exposure profiles overlapping at the substrate surface. The measured respective widths of exposed zones and unexposed areas are always referred to the substrate surface. The adjustment of their amount and widths enables the fabrication of specific meso- and microscale optical elements. In the first example of fabricated elements, the aim was to create two binary diffractive axicons with comparable diameters and different spatial periodicities. In both cases, the widths of the exposed zones were supposed to remain constant, while the widths of the unexposed areas were varied. Therefore, the different periodicities were achieved by changing the fill factor, which represents the ratio between exposed zones and unexposed areas. Each zone width was chosen to be as small as possible and therefore has the width of a single-ring structure itself. For exposure, a photoresist with a thickness of ${\sim}{{360}}\;{\rm{nm}}$ was chosen. Since it is thinner than the photoresist used for exposure preparation, the width of the single-ring profiles at the substrate surface was expected to be slightly larger than the FWHM of the Gaussian profile (cf. Fig. 7 in Section 3.C). Figures 10(a)–10(d) present the surface topography measured by white-light interferometry of both binary diffractive axicon elements. Each element has a constant spatial periodicity, and the ring structures appear highly uniform across the entire element. The maximum outer diameter of the largest exposed zone is almost identical for both cases (6.2 and 6.3 mm). The different number of exposed zones [12 zones versus 15 zones, cf. Fig. 10(a) versus Fig. 10(c)] results in different spatial periodicities for both elements. Quantitatively, the width of exposed areas measures ${\sim}{{90}}\;{\rm{\unicode{x00B5}{\rm m}}}$, and the widths of the unexposed areas (“footprint”) have values of ${\sim}{{115}}$ and ${\sim}{{80}}\;{{\unicode{x00B5}{\rm m}}}$, respectively. The comparison of both diffractive axicons shows that the element with the smaller spatial period measures a slightly lower value for the vertical dimension of the remaining photoresist in the unexposed areas (300 versus 280 nm). This difference originates from the specific exposure settings: for the generation of the element with the smaller spatial periods, the adjacent exposure steps have to be set in a closer radial distance to each other, so that an increasing overlap between the subsequent Gaussian exposure profiles occurs. For most applications, this effect can be tolerated for the fabrication of binary elements because the ring width at the substrate surface is the crucial parameter for subsequent processing steps. The exposure times for the diffractive axicons are ${\sim}{{11}}\;{\min}$ (12 zones) and ${\sim}{{15}}\;{\min}$ (15 zones).

Next, the results for fabricated binary phase rings are presented. Such phase rings are key components for phase contrast microscopy, usually inducing a 90° phase difference between the unchanged direct light and the contribution affected by the sample structure. Figure 10(e) shows the topography of a single phase ring fabricated as a circular zone in the photoresist. The phase ring has an inner diameter of ${\sim}{5.5}\;{\rm{mm}}$, an outer diameter of ${\sim}{6.5}\;{\rm{mm}}$, and a zone width of ${\sim}{{500}}\;{{\unicode{x00B5}{\rm m}}}$. In the lower part of Fig. 10(f), the cross section of the ring structure is presented. The depth of the zone is ${\sim}{{400}}\;{\rm{nm}}$. To obtain a homogeneous, flat structure at the bottom surface of the zone, the distances of the subsequent exposure rings have to be adjusted in close proximity to each other. Similarly, also a set of several concentric phase rings can be fabricated. As an example, Fig. 10(g) shows an element combining a first smaller phase ring with an inner diameter of ${\sim}{3.6}\;{\rm{mm}}$ and a width of ${\sim}{{290}}\;{{\unicode{x00B5}{\rm m}}}$ with a larger phase ring exhibiting the same dimensions as the ring mentioned above and presented in Fig. 10(e). The exposure of the smaller phase ring lasts ${\sim}{{4}}\;{\min}$.

As a third example, anFZP was manufactured. In this case, the widths of exposed zones and unexposed areas are both varied within one element. Starting in the center of the element, the subsequent radii ${{{R}}_n}$ follow the square root of the zone number ${{n}}$ (${R_n} = \sqrt {{n}} {R_1}$, with ${{{R}}_1}$ presenting the radius of the innermost zone) [24]. According to this formula, the aim was to fabricate a zone plate consisting of as many zones as possible within the given diameter range. The presented FZP consists of nine exposed and eight unexposed zones [Fig. 11(a)]. From the center to the edge of the FZP, the topographic image shows the known decreasing distances between the individual zones. The smallest possible radius of the first zone, which is limited by the implemented optomechanical setup (Section 3.A), measures 1.53 mm, and the outer diameter of the FZP is 6.4 mm. Also in this case, each individual zone of the FZP is highly uniform. The resolution of the FZP towards the outer diameter is limited by the width of a single-ring structure. Furthermore, the decreasing zone width with increasing radius leads to a stronger overlap of adjacent exposure profiles during the lithography process. This also affects the vertical dimensions of the unexposed zones, which decrease slightly with increasing radius [Fig. 11(b)]. This variation in structure height within one element is not observed at the previously presented elements, since the exposed areas there have a constant radial distance within one element [cf. Figs. 10(b) and 10(d)] and therefore exhibit constant vertical dimensions of the unexposed zones. Nevertheless, this effect does not influence the fabrication of binary amplitude FZPs. In this case, an opaque layer (e.g.,  chromium) located below the resist is structured, which is also possible with slightly varying structure heights. For phase FZPs, the height variation has to be considered. Since the diffraction angles increase to the outer part of the FZP, the decreasing structure height may even be advantageous.

 

Fig. 11. Resist structure of an FZP with nine zones. (a) Top view and (b) cross-sectional view.

Download Full Size | PDF

In addition to single elements, the presented lithography process also allows the fabrication of arrays of elements. This possibility further increases the application range of the introduced method. For this purpose, it is only necessary to align the individual structures precisely with respect to each other. This is realized by using a substrate holder that can be moved accurately in two lateral axes (Section 3.A). Figure 12 shows an array consisting of ${{2}} \times {{3}}$ FZPs with five and seven zones, alternately arranged. The image was taken with a conventional microscope (Zeiss Axio Zoom V16) using reflected light. In the image, the individual exposed zones are bright, while the unexposed zones (photoresist) appear dark.

 

Fig. 12. Microscopic image of an FZP array consisting of ${{2}} \times {{3}}$ FZPs with five or seven zones, alternately arranged.

Download Full Size | PDF

5. CONCLUSION

In this contribution, the basic concept, the optical design, and the implementation of a novel lithographic exposure tool for the fabrication of ring-shaped structures are presented. The optical design concept combines two aspheres with a fixed plano–concave and an axially movable plano–convex axicon to create a ring of variable diameter in the image plane. Basic characteristics of the optical design include a Gaussian intensity distribution of the ring profiles with an almost constant FWHM of approx. 75 µm for all ring diameters. The implemented laboratory demonstrator has a compact, straightforward setup and is used for lithographic fabrication of circular structures. Its basic capabilities are demonstrated by the fabrication of exemplary meso- and microscale structures such as diffractive axicon elements, phase rings, and FZPs. Beyond the ability to fabricate tailored rotationally symmetric elements in photoresist, the system allows one to structure an expanded area without disturbing stitching effects. As the substrate holder can be moved precisely in both lateral directions, the exposure tool also enables the fabrication of element arrays. Furthermore, the approach has the potential to reach comparatively short exposure times, because in principle the area of one “exposure shot” is larger compared to conventional direct-writing lithography. In the future, the geometric dimensions of the manufactured meso- and microscale optical elements can be further varied within the range determined by the specific optomechanical setup and thus tailored to different applications. There is still potential to improve the existing optical design model and its implementation, e.g.,  concerning the size of the entrance pinhole, the NA, or the working distance. Thus, the presented elements are limited in terms of resolution and achievable diameter. Additionally, the use of a light source with higher optical power would result in shorter exposure times. However, these limits are not fundamental and can be improved further. In particular, an advanced optical design will allow a higher NA in combination with fewer aberrations and a larger diameter zoom range. In order to decrease the entrance pinhole diameter while maintaining sufficient light for the exposure steps, a laser light source can be used. These future improvements will lead to a total ring width of approximately 5 µm, which further paves the way to microscale optical elements.