Annular Gray Tone Lithography for the Fabrication of Rotationally Symmetric Continuous Relief Meso- and Microscale Optical Elements

Abstract

Annular lithography is a recently introduced, flexible technique that has been tailored to the fabrication of rotationally symmetric optical structures in the meso and micro range. The optical concept for the exposure tool is based on a combination of axicons with movable components that create a ring-shaped light distribution with variable diameter in the image plane. This contribution demonstrates for the first time the use of gray tone exposure in annular lithography to fabricate continuous relief structures, overcoming the previous limitation using binary structures. For the controlled exposure of the continuous relief structures, the sensitivity curve of the resist, the exposure dose decreasing with increasing ring diameter, and the exposure time have to be considered. A control and simulation tool is introduced to provide radius-dependent exposure data and, furthermore, to control and iteratively improve the fabricated structures. To demonstrate the gray tone capabilities, various diffractive elements as well as refractive spherical and aspherical elements with a maximum diameter of ~6 mm and a maximum height of 4 µm are shown as examples. Profile shape measurements of fabricated elements show good agreement with the expectations.

1. Introduction

Gray tone lithography is an extremely important and certainly one of the most established processes for the fabrication of micro- and mesoscale optical elements. This technique enables the fabrication of almost arbitrarily shaped continuous relief structures with maximum flexibility in local variation, achieving structural resolutions down to the sub-µm range. Via suitable control of the exposure dose and selection of the appropriate photo-sensitive resist, diffractive, refractive, and hybrid 2.5D structures with depths of several 10 µm can be produced [1,2,3,4]. Here, the term “hybrid” refers to a combination of refractive and diffractive structures. In the original form of direct laser writing, a focused laser spot is directed point by point and line by line across the resist-coated substrate while the laser intensity is simultaneously varied. Disadvantages of this method include long writing times and the occurrence of stitching effects, i.e., inaccuracies in the aligned positioning of consecutively exposed areas of limited extension, making it difficult to structure large areas. Alternatives are mask-based lithographic gray tone processes, with halftoning, thin-film coatings, or HEBS glass-based approaches being examples of gray tone masks offering locally variable transparency [2,3,4,5,6,7,8]. The process of exposure is faster compared to direct laser writing, but the fabrication of the gray tone masks is demanding and in addition, the option of quickly modifying the structures to be exposed is eliminated. More flexibility is offered by so-called “maskless” methods, where the permanent mask is essentially replaced with switchable pixelated displays such as DMD (digital micro-mirror devices) or LCoS (liquid crystal on silicon) micro-displays [9,10,11,12,13,14,15]. Apart from specific disadvantages such as long writing times for the structuring of larger areas, complex mask production, or reduced flexibility, the above-mentioned established gray tone systems are not particularly well adapted to the manufacturing of rotationally symmetric elements, which make up the vast majority of optical elements. In fact, conventional gray tone lithography in Cartesian coordinates is inherently suboptimal for the fabrication of rotationally symmetric optical structures. In particular, the problem of stitching effects in the positioning of adjacent rectangular fields is usually not solved.

In recent articles, we have introduced variable annular lithography as a tailored solution for the manufacturing of rotationally symmetric meso- and microscale optical elements [16,17]. This method uses a ring-shaped focused light distribution with a variable diameter for exposure, which is created using axicons with an adjustable distance as key elements. The demonstrated variable annular exposure tool is fast and efficient, allows for exposure of ring diameters up to 6.5 mm in a single step, and completely avoids disturbing Cartesian stitching effects. So far, this structuring process has exclusively been used for the fabrication of binary optical elements.

In this contribution, we present an extension of this technology, introducing variable annular gray tone lithography and demonstrating the fabrication of rotationally symmetric structures with continuous relief, such as blazed diffractive optical elements (DOEs) and diffractive axicons as well as refractive aspherical-shaped phase elements. Thus, for the first time, the advantages of the basic concept of variable annular lithography are combined with the additional option of flexibly and continuously controlling profile shapes. This guarantees an even higher degree of flexibility regarding arbitrary rotationally symmetric element designs.

The first part of this contribution briefly reviews the basic optical design concept of the variable annular lithography system and explains specific adaptations. Subsequently, the method of data generation and the specific control of process parameters for the fabrication of continuous relief surface structures is introduced. Finally, the fabrication of various rotationally symmetric optical elements is presented and the performance achieved is discussed.

2. Optical Design Concept

The basic concept of the exposure tool, which is described in detail in [16], is shown in Figure 1. The divergent light bundle emitted by the fiber output of a fiber-coupled laser diode is collimated by the first lens and focused by the second lens to the image plane. Within the focal length of the second lens, a plano-concave axicon and an axially movable plano-convex axicon are inserted. The plano-concave axicon splits the ray bundle and creates an annular light distribution. By moving the plano-convex axicon along the optical axis, the ring diameter can be changed. With increasing axicon distance, the ring diameter expands [18,19]. In principle, different base angles for the axicons are possible. They have a direct influence on the value of the ring diameter [17]. For implementation, we chose a configuration with equal base angles for the plano-convex and plano-concave axicon. This combination yields the largest zoom range, since the difference between the smallest and largest possible diameter is the greatest. Thus, the distance between both axicons can theoretically be reduced to zero, creating a point image. However, it is recommended that physical contact of the optical elements be avoided, as it might cause damage.

In the following, the selected optical components of the system are described in more detail, focusing on the modifications that were made specifically to improve the suitability of the setup for exposures in gray tone resist. For all optical elements and for the light source, commercially available components were selected. Their significant specifications are summarized in

Table 1. Essential specifications of the optical components.

Component	Optical Specifications and Characteristics
Laser light source SM Fiber-pigtailed laser diode LP405-SF10 (Thorlabs GmbH, Bergkirchen, Germany) [20]	-Wavelength: 405 nm -Mode field diameter: 3.3 ± 0.5 µm at 405 nm -Numerical Aperture (NA): 0.12; used NA: 0.05 (aperture stop) -Max. optical output power: 10 mW
Plano-convex lenses, AR- coated (2x) 48-286 (Edmund Optics GmbH, Mainz, Germany) [21]	-Diameter: 25 mm -Focal length: 100 mm -Material: fused silica -Surface quality (S/D): 40-20 -Wavelength range (AR coating): 250–425 nm
Plano-concave axicon (VM-TIM GmbH, Jena, Germany) and Plano-convex axicon (Thorlabs GmbH) [22]	-Base angle: 5° -Diameter: 25.4 mm -Material: fused silica (AR coated)

. When these optical components are used, a maximum ring radius R₀ of about 3.7 mm is obtained at a theoretical maximum distance d of approximately 84 mm between both axicons. However, the axial dimension of the mountings, especially for the two axicons, limits their minimum and maximum distance (Figure 1), resulting in a minimum diameter (approximately 1.8 mm) and a maximum diameter (approximately 6 mm) of the ring.

To increase the resolution of the structures to be fabricated, the previously used fiber-coupled LED (fiber core diameter of 50 µm) was replaced with a fiber-coupled laser diode [17,20]. The new laser light source has a mode field diameter of 3.3 ± 0.5 µm, which serves as the entrance pinhole of the optical system. This leads to a significantly reduced total ring width in the image plane. A further advantage of the new laser light source is its high optical power, which guarantees a high degree of flexibility concerning the definition of exposure dose. The high optical power allows for shorter exposure times, which is useful especially for the exposure of gray tone resists with an increased thickness.

Due to their optimized contrast, gray tone resists react more sensitively to inhomogeneities of the incoming light than binary resists. For ring-shaped exposure setups, the homogeneity of the light distribution along the ring circumference and the shape of the Gaussian profile (in the cross-sectional view of the annular light distribution) in particular are critical parameters. Thus, further adaptations were made to the optical design: For collimation and focusing of the beam, spherical glass lenses were chosen instead of pressed acrylic aspheres, since the spherical lenses have an improved surface quality (Table 1). The most critical system parameter is the ring width, since it defines the maximum resolution of the structures to be fabricated. To determine its theoretical size, an optical simulation was carried out using the software OpticStudio^®. The ring width is influenced by the size of the entrance pinhole, aberrations, and diffraction effects. To reduce imaging errors such as spherical aberration, the numerical aperture (NA) of the system was decreased from 0.12 to 0.05 by minimizing the aperture stop size (Figure 1). The resulting RMS spot radius is used to characterize optical aberrations and has a value below 10 µm for all ring diameters. This value includes the influence of the fiber diameter (field size). The reduction of the NA results in increased diffraction effects and a substantial light loss, which is acceptable due to the high laser power. The influence of diffraction is inversely proportional to the NA of the partial ray bundle (0.025) and is assumed to increase the ring width to a value of approximately 20 µm. Thus, the resulting ring width is estimated to be approximately 20 µm.

3. Preliminary Exposure Studies and Determination of Exposure Recipes

In order to facilitate an efficient lithographic fabrication, it is necessary to convert the desired element design into suitable exposure data. Therefore, a simulation tool was developed to generate look-up tables (LUTs) consisting of axicon positions and corresponding exposure times, with the important steps being described in this section.

The diameter of the ring in the image plane is linearly related to the distance between the axicons, and each axial position of the plano-convex axicons corresponds to a specific radial position of the exposure. Single exposures can be superimposed by subsequently exposing several rings using only small changes in the axial position of the axicon. The creation of a continuous profile shape by overlapping individual Gaussian ring profiles with variable profile depths in radial direction is schematically shown in Figure 2.

In order to find suitable input parameters for the ring width and for the value of ring overlap intended for simulation, test exposures were carried out for individual rings and for ring structures with different overlap values. The measured values for the full width–half maximum (FWHM) of the exposed ring profiles were approximately 15 µm. A continuous profile shape was achieved by overlapping these profiles at equal distances of FWHM/2, corresponding to a change of the axicon position (step size) of 0.18 mm. Thus, these values were implemented in the simulation tool. Due to the overlap of the individual Gaussian profiles, there is a systematic overexposure along the entire exposure profile (blue line in Figure 2). The larger the overlap of the Gaussian profiles, the more significant this effect. To take this into account during the simulation, all exposure times were corrected by a constant factor. For the distance of FWHM/2 between the Gaussian profiles, the correction factor has a value of approximately 0.5. The depth of the Gaussian profiles after the wet-chemical development process is directly related to the exposure dose, which was calculated by multiplying the incident intensity by the exposure time. For simplicity, the output power of the light source was kept constant during the exposure process, which results in decreasing exposure doses for increasing ring diameters. This information in combination with the sensitivity curve of the resist and the desired local structure height was used to create a LUT that contained the positions of the axicon and the corresponding exposure times required to expose the respective selected ring-shaped structure. For the simulation, two dependencies for the required exposure dose had to be taken into account: First, it must be noted that the incident intensity (power per area segment) decreases with increasing ring diameter, since the optical power of the laser diode was kept at a constant value of approximately 20 µW (measured in the image plane). Thus, constant exposure times resulted in a decreasing profile depth with increasing diameter (Figure 2). To achieve equal profile depths with increasing diameter, the exposure dose must be held constant by applying longer exposure times. Second, the exposure dose had to be varied depending on the exposure time according to the desired profile depth for the respective element design.

Figure 3a presents a flow chart of the procedure steps, starting from element design to the LUTs, which were implemented in MATLAB^® R2021b, and finally to the manufactured structures. The exemplary element design consists of four saw teeth of a diffractive lens, whose period decreases with increasing radius (Box A). In the following, the procedure steps were applied exemplarily to this element design to be fabricated. Essential conditions and input variables of the subsequent exposures had to be included in the simulation. Examples are the FWHM of the Gaussian profile and the value for their overlap, the achievable ring radii, the linear correlation between ring radius and axicon position, the laser power and the resist characteristics (Box B). For exposure, the positive resist AZ^®4562 (Merck KGaA, Darmstadt, Germany) with a maximum thickness of approximately 7 µm was used. The details of resist preparation are described in Section 4. To characterize the sensitivity of the resist at different depths, individual ring structures of various diameters were exposed. For each ring diameter, the exposure times varied. The exposed samples were developed for 1 min, and the profile depths were subsequently measured. As shown in Figure 3b, there was a nonlinear correlation between exposure times and resulting profile depths. For structures up to 3.5 µm, a significantly higher exposure dose and thus extended exposure times were necessary. In future investigations, a longer development time could reduce this effect. Additionally, the slope of the curve was much steeper for smaller diameters (red curve with square symbols) than for larger diameters (blue curve with triangular symbols). The resulting sensitivity curves of the photoresist determined the exposure times required for the exposed ring diameters in various depths of the resist and were included in the simulation tool as well.

After defining the element design and capturing essential input parameters, the resist depth at each radial position of the element design was converted into a corresponding exposure time. Both the structure depth and the exposure time are functions of the ring radius r. The resulting design (Figure 3a, Box C) shows the expected increase of exposure time with increasing ring radius. In addition, the influence of the resist characteristic can be identified: Deeper structures in the resist required disproportionately longer exposure times, noticeable from the curved shapes. Following the conversion, the simulation was carried out. Thus, the required exposure times at each radial position were reconstructed with Gaussian functions in equal distances. Finally, the individual radii were mapped back to the axis positions. The result is a LUT (Box D in Figure 3a) consisting of axis positions and corresponding exposure times, which is used to control the linear axis in the subsequent exposure.

Another important aspect which has to be discussed is the theoretical limit of the achievable profile shape of the design element. Discrete convolutions were performed (MATLAB^® R2021b) with the element design as the input signal and both an ideal Gaussian kernel and a kernel of the real exposure profile as impulse responses, respectively. The shape of the real exposure profile was obtained from test exposures of single rings in photoresist (red profile in Figure 4a). The measured FWHM of 18.8 µm of the real exposure profile confirms the value for the FWHM of the ideal Gaussian profile used in the simulation (15 µm) and is also in the order of magnitude of the theoretical ring width determined in the optical design (Section 2). To perform the convolution, each kernel (Figure 4a) was normalized such that its sum equaled unity. Additionally, all discrete sampling frequencies were adapted to the same value. The resulting theoretical output signals of the exemplary structure compared to the original design are shown in Figure 4b.

4. Exposure of Gray Tone Elements

In this section, diffractive and refractive continuous relief surface profiles that have been exposed in gray tone resist are presented. Based on the representative example of a diffractive lens, the simulation method was verified by comparing and evaluating theoretical and experimental results. In addition, another diffractive lens with different parameters and a diffractive axicon as well as refractive structures (spherical and aspherical surface profiles) for various applications are presented and characterized.

For structuring, fused silica wafers (700 µm thickness) were chosen as substrates. The photoresist was deposited on the substrate using spin coating with a maximum speed of 2000 rpm. Afterwards, a softbake was performed in the oven at a maximum temperature of 90 °C. Following the exposure of the samples (described separately below), the samples were developed for 1 min to dissolve the exposed areas. For the topographical measurements of the generated resist structures, a white light interferometer was used (Zygo^®, Middlefield, CT, USA, NewView9000).

Prior to all exposures, the substrate holder with the photoresist coated substrate had to be axially aligned with an adjustment screw to guarantee the correct position of the substrate surface in the image plane of the optical system. At the beginning of each exposure, the optical power of the ring-shaped light distribution was set to a constant value (see Section 3) and checked with a power meter in the image plane. For the exposure of a defined surface structure, the exposure dose had to be controlled precisely by adjusting the exposure time. Thus, exposure times had to be applied that were not too short for implementation (control electronics), but also not too long in terms of limiting the total exposure time for one element design. For these reasons, and additionally to guarantee working in the sensitivity range of the photoresist, the optical power in the image plane had to be reduced to the constant value of 20 µW. This was achieved by operating the laser in the low power range of its linear characteristic and additionally by using the pulse-width modulation mode (PWM) of the laser. For instance, a profile depth of 1 µm was obtained by exposing a single ring (small diameter, Figure 3b) with a time of ~3.8 s. During the axicon movement, the laser was automatically switched off and thus used as an optical shutter. Consequently, unwanted exposures between the individual positions of the LUT could be avoided. The exposure result of the element design that is introduced in Section 3 is presented in Figure 5. The exposure time for the whole element was approximately 10 min.

The measurement was taken with both an objective with a 10× magnification (Figure 5a on left side) and a 50× magnification (Figure 5a right side). The cross-section in Figure 5b shows the desired radial profile of four saw teeth. The structure had a maximum depth of 1.5 µm. The minimum and maximum lateral extension of the saw teeth were 320 µm and 460 µm, respectively. Note that there were still inhomogeneities of the light distribution and of the Gaussian shape along the ring circumference (left side in cross-section). This can be explained by residual adjustment errors of the laser light source and the optical elements within the optomechanical setup, which can cause a slightly inhomogeneous light distribution transferred to the photoresist during exposure.

In the following, the described exposure result (radial cross-section, marked in Figure 6a) will be compared with the theoretical profile of the corresponding convolution depicted in Figure 4b. For a detailed evaluation, both profiles are compared in Figure 6b.

The black profile shows the radial cross-section of the exposure result. The red profile presents the theoretical result of the discrete convolution with a real exposure profile. To compare the two profiles in terms of their shape, the profile of the exposure result was scaled in height by a factor of 0.6. This scaling corresponds to a shorter development time and is therefore justifiable. The profiles of the exposure cross-section and the convolution with the real exposure profile show a good agreement in terms of shape accuracy. Comparing the periods of both profiles, a small lateral deviation of approximately 25 µm on a radius difference of approximately 1.6 mm is noticeable. This value was obtained by measuring the maximum difference between the values of the left-most and the right-most vertical edges. Thus, the maximum deviation in a lateral direction is approximately 1.6%. Again, reasons for this may be small remaining adjustment errors in the optomechanical setup as well as a slight deviation of the axicon position–radius relation. Note that the agreement of the theoretical and the experimental results is very good considering the simplicity of the setup. In the following, further exposure results are shown to emphasize the flexibility of the exposure tool with respect to arbitrary element designs. It has to be noted that all elements have a minimum diameter of approximately 1.8 mm and a maximum diameter of approximately 6 mm (Section 2).

Figure 7 shows a diffractive lens consisting of nine saw tooth structures. The minimum and maximum lateral extension of the saw teeth are 150 µm and 260 µm, respectively. The maximum diameter of the exposed element is approximately 6 mm; the depth in the resist is approximately 1.35 µm.

Figure 8 presents an example of the combination of two blazed diffractive axicons, composed of laterally alternating sawtooth structures with two different depths. The maximum depths vary between the values of approximately 1.25 µm and 2 µm (for small diameters). All saw teeth have a constant lateral extension of 200 µm regardless to their depths.

Figure 5, Figure 7 and Figure 8 reveal a height difference between the top of the sawtooth pattern and the zero level of the resist at the unexposed edges. This can be explained by the employed overlapping Gaussian profiles (FWHM/2), which slightly expose the edges of the saw teeth.

In addition to diffractive structures, refractive structures with continuous profile shapes and increased structure depths can be fabricated with the exposure tool, as well. Figure 9a shows an example of a fabrication result of a spherical lens. The measured profile shape is shown in the cross-section (black line in Figure 9b) and was fitted with a spherical function (red dotted line). Thus, a radius with a curvature of approximately 740 mm was determined. Compared to the exposure results of the diffractive elements, the spherical lens has an increased structure depth of approximately 4 µm.

Figure 10 shows the exposure result of an aspherical element. An inflection point in the profile geometry was achieved, which is visible in the 3D view as well as in the cross-section. A typical application of this exposure profile is a Schmidt corrector plate, which serves as a negative lens at the edge and as a positive lens in its center. It is applied to compensate for spherical aberrations in telescopes [23]. The maximum depth of the resist structure measures approximately 2 µm. By performing a fit (red dotted line) on the measured profile shape (black line), values for the radius and the asphere coefficients a4 and a6 (standard asphere equation) were obtained.

5. Conclusions

This paper presents a new approach to perform ring-shaped gray tone lithography using a tailored exposure tool. The presented technique offers new opportunities concerning a fast and efficient fabrication of annular continuous relief structures without disturbing stitching effects in Cartesian coordinates. The optical concept combines two lenses and an axicon combination of a plano-concave and an axially movable plano-convex axicon, which create a ring with an adjustable diameter in the image plane. Considering the optical design and its specific adaptations, single ring structures are obtained with a ring width (FWHM) of ~18 µm, which determines the resolution of the fabricated structures. The rotationally symmetric surface profiles were exposed by changing the ring diameter and controlling the exposure dose simultaneously. Therefore, a simulation tool was developed to generate the exposure recipes (LUTs), consisting of axicon positions and corresponding exposure times. The presented exposure results prove the successful fabrication of diffractive and refractive meso- and microscale continuous relief optical elements, using the introduced ring-shaped exposure tool. The profile heights of the fabricated structures ranged from less than 1 µm up to 4 µm. However, structures with heights of several 10 µm can be produced with appropriately coated substrates using an adapted exposure dose. There are various fields of application for the fabricated elements; for example, in medical technology, diffractive elements are commonly used as bi- or multifocal interocular lenses (IOLs) or contact lenses. The fabricated continuous relief optical elements are still limited in terms of resolution and achievable diameter. Improvements of the successfully implemented exposure tool could be achieved by an advanced optical design using a higher NA, combined with an extended zoom range for smaller and larger ring diameters. These improvements might also include typical approaches to increase lithographic resolution such as shorter exposure wavelengths, immersion technology, or two-photon-absorption.