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Abstract
Due to digital micromirrors device (DMD) digital lithography limited by non-integer pixel errors, the edge smoothness of the exposed image is low and the sawtooth defects are obvious. To improve the image edge smoothness, an optimized pixel overlay method was proposed, which called the DMD digital lithography based on dynamic blur effect matching pixel overlay technology. The core of this method is that motion blur effect is cleverly introduced in the process of pixel overlap to carry out the lithography optimization experiment. The simulation and experimental results showed that the sawtooth edge was reduced from 1.666 µm to 0.27 µm by adopting the 1/2 dynamic blur effect to match pixel displacement superposition, which is far less than half of the sawtooth edge before optimization. The results indicated that the proposed method can efficiently improve the edge smoothness of lithographic patterns. We believe that the proposed optimization method can provide great help for high fidelity and efficient DMD digital lithography microfabrication.
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1. Introduction
Digital micromirrors device (DMD) digital lithography technology utilizes the principles of photochemical reactions and chemical/physical etching methods to transfer patterns from a digital mask template to a wafer in the semiconductor manufacturing process [1–4]. Due to its low cost, high efficiency, and lightweight characteristics [5–7], DMD digital lithography technology has been widely applied in various fields [8–10]. For example, in the preparation of photonic devices, DMD digital lithography technology can be used for maskless projection exposure, which enables rapid and convenient preparation of such devices. In biomedical and cell biology research, the three-dimensional structure can be decomposed layer by layer, and all cross-sections of the structure can be input into the DMD exposure system for layer-by-layer printing from bottom to top to manufacture the three-dimensional target structure [11–14]. Some specially designed 3D printed sensors are applied in the fields of biology and chemistry [15,16]. However, in the process of generating dynamic mask patterns, DMD digital lithography technology produces a non-integer pixel error, known as DMD pixel quantization error, which results in the contour edges of the pattern after lithography exhibiting a sawtooth structure [17–20]. The most common method is to reduce the magnification of the projection lens and improve the optical resolution, but this approach greatly reduces the exposure area and thus lowers production efficiency [21].
To solve the above problem, scholars at home and abroad have carried out relevant scientific research work. K Kim et al. [22] proposed a sub-pattern oscillation superposition exposure method, but the smooth surface roughness is limited. Liu Hua et al. [23] proposed a time-space coordinated exposure technology, which fills the exposure pattern with continuously overlapped sub-patterns, increasing pattern smoothness. However, the creation of numerous sub-patterns creates a cumbersome process, thereby reducing efficiency. The core idea of many processes is pixel overlap [24]. The DMD-based oblique scanning exposure mode can also effectively reduce edge aliasing, thereby improving the fidelity of the pattern, but the linkage of its multi-axis high-precision moving platform has high requirements for focusing, especially in high-precision lithography, the depth of focus is very small, and focusing during motion is more difficult [25–28]. Dynamic blur effect is also an effective method for image processing, and combining it with pixel overlap can effectively smooth image edges [29–32].
This study proposed an optimized pixel overlay method based on dynamic blur effect matching pixel overlay technology, which aims to improve the smoothness of lithography patterns at the edges. Firstly, the basic principle of pixel overlapping technology is discussed. By analyzing the exposure pattern, a predetermined experimental sequence is programmed into a three-dimensional moving platform. Through nano-scale movement, the jagged edges of the image are overlapped with pixels, thereby enhancing the smoothness of the graphic edges. Inspired by Chen’s research, this study incorporates dynamic motion blur technology into DMD digital lithography. Motion blur is one of the main causes of image defects, resulting from the relative movement between the image and the imaging device during the exposure process. Conversely, the motion blur effect can be utilized to further fill the gaps between jagged pixels caused by relative motion during image formation. A comparison of the smoothness of lithography patterns demonstrates the feasibility and correctness of the DMD pixel overlapping technology based on motion blur. In summary, we have proposed an effective method to improve the smoothness of lithography patterns in DMD digital lithography by combining pixel overlapping technology and dynamic motion blur technology, which can provide new insights for improving the precision and quality of lithography.
2. Dynamic motion blur effect matching pixel overlapping technology based on DMD
Figure 1 illustrates the DMD digital lithography experimental system, which includes the light source, uniformity elements, DMD chip, reflector, projection lens, 3D motion platform, DMD controller, piezoelectric ceramic platform, and a computer. The DMD lithography system is configured and calibrated to its operational state, where ultraviolet light from the light source passes through the uniformity element, the DMD chip, the reflector, and the projection lens to accurately expose the desired pattern onto the workpiece placed on the 3D motion platform. In the experiments, a UV light source with a wavelength of 405 nm was chosen. The model of DLP 6500 DMD controller (Texas Instruments, Texas, USA) was used with a DMD resolution of 1920 × 1080. The photosensitive resin (Water Washable Resin, eSUN, Shen Zhen, China) used in the experiment is cured by the polymerization reaction under the influence of UV light. The 3D motion platform (Coremorrow, XYZ100, E70.D3S closed loop piezoelectric controller) was adopted, which can effectively ensure the accuracy of exposure.
Compared with the traditional per-pixel exposure lithography system, the proposed lithography system adopts a high-precision 3D motion platform, which can realize high-precision 3D micro-motion. Maximum displacement range is 100 microns, and positioning accuracy is 3 nm. This precise movement allows for more precise pixel overlap, making better use of motion blur effects.
The DMD consists of multiple micromirrors with small gaps in both vertical and horizontal directions. Since it is a non-reflective region that cannot produce light aggregation, the input graphics displayed are two-dimensional quantized patterns that form a network of patterns, with each micromirror representing a pixel. This is also why overlapping pixels can improve the edge smoothness of an exposed image. In the above DMD lithography system, when the magnification of the image projection lens is 1, the DMD pixel size in the 1920 × 1080 micromirror array is 7.56 µm. Due to the 4X magnification of the system’s projection lens, the actual minimum projection exposure pixel size is 1.89 µm. The following is a series of process operations carried out to improve the smoothness of the edge of the lithography image in this study. Firstly, the whole DMD digital lithography system was checked to ensure that the system can work normally. Secondly, the image was identified that needs to be exposed and analyzed the edges that need to be optimized. Then, the position relationship between the image edge and the 3D moving platform was determined, the displacement trajectory of the 3D moving platform was set, and the entire exposure time was determined. Finally, the experiment was performed as shown in Fig. 2.
This study used isosceles right triangles to test the proposed idea, with the size of each small grid corresponding to the size of the DMD micromirror divided by the magnification of the projected lens (1.89 µm). During the study, the positioning relationship between the platform and the experimental pattern was determined to ensure that the two right-angle sides of the exposed triangle were parallel to the X and Y axes of the 3D platform, as shown in Fig. 3.
The process of pixel superposition is shown in Fig. 4. It should be noted that the size of each grid corresponds to 1.89 µm, and the exposure method used in this method is continuous moving exposure. The pattern shown is the end of the exposure in one direction and the start of the next displacement. Since the purpose of this paper is to study the method of combining motion blur and pixel superposition to smooth the image, the sub-pattern is not used for superposition, and only the hypotenuse that needs to be studied is processed. From the exposure in the original position, the platform begins to move up half a pixel distance until it reaches the position shown in Fig. 4(b). The platform then begins to move half a pixel distance to the left until it reaches the position shown in Fig. 4(c). At this point, the platform can return, moving half a pixel distance to the right to the position shown in Fig. 4(d), and then half a pixel distance up again to the position shown in Fig. 4(e). At this point, it returns to the original 3d relative position between the moving platform and the projected lens, and completes one cycle. During the entire exposure process, the displacement trajectory of the 3D platform is repeatedly cycled to complete the pixel superposition.
Fig. 4. Schematic diagram of a moving pixel overlay on a 3D moving platform. (a) Original exposure position, (b) Displacement position 1, (c) Displacement position 2, (d) Displacement position 3, (e) End position (coincides with Original position).
As the entire process involves intermittent movement, the overlapping portion of the exposed image receives less exposure energy. Therefore, the exposure time based on this method needs to be greater than or equal to the normal exposure time. In general, in practical experiments, an additional 1∼2 seconds of exposure time is added. Specifically, the exposure time ($T$) based on the three-dimensional DMD digital lithography technology can be obtained by adding a fixed value to the normal DMD digital lithography technology’s exposure time ($t$), as follows.
For the exposure time of one cycle ($tn$), it can be calculated by dividing the total exposure time ($T$) by the number of back-and-forth cycles ($n$), as follows.
Due to the constant relative motion of our 3D motion platform and projection lens during exposure, the resulting effect is more than just a simple superposition of pixels. At this point, it needs to consider the effect of motion blur. In fact, the exposure is the process of receiving a certain amount of light, creating a chemical reaction on a photosensitive material, and eventually curing or producing other effects. If there is a relative change between the exposure beam and the position of the object during this process, it will cause a change in the incident light, resulting in blurred exposure results. Therefore, the motion blur kernel function was introduced, also known as the motion blur filter or motion blur matrix. It is a two-dimensional function used to simulate the motion blur effect of an image.
The blur direction and distance are represented as two-dimensional vectors. The magnitude, length of this vector $({x,y} )$, representing the length of the ambiguity, can be calculated as follows.
Then, a matrix [kernel_size, kernel_size] was constructed and the elements in the length range around the center of the matrix was set. each element in the matrix $M[i,j]$ is at the center of the matrix and is less than or equal to the length from the center. The mathematical formula can be expressed as the following.
Finally, the normalized matrix ${M_N}$ can be expressed as the following.
where, M is the blur kernel matrix, i and j are the indices of elements in the matrix, length is the length of the motion blur, and $\textrm{sum(}M\textrm{)}$ is the sum of all elements in the matrix.In this case, the kernel_size was set to 2. It is important to note that when using this motion blur kernel function, adjust the kernel_size according to the size of the length. Otherwise, if some elements are not within the effective range of the kernel matrix, it will affect the generation of the blur effect.
The creation of this motion blur kernel function is also known as the creation of a convolution kernel or filter. Using this original negative effect, the edge effect of exposure images in DMD digital lithography can be further optimized. Using the motion blur kernel function and the continuous displacement shown above to simulate motion blur, the actual exposure effect after the exposure is completed should be as shown in Fig. 5.
Fig. 5. Schematic diagram of the motion blur effect. (a) Schematic diagram of the motion blur effect. (b) Schematic diagram of motion blur effect matching pixel overlap technology.
It can be seen that the exposure mode based on the motion blur effect has better edge smoothness than the exposure mode with a simple overlapping half pixel. Since the main purpose of this article is to demonstrate the feasibility of dynamic blur technology combined with subpixel overlap, the two right-angle edges are not optimized or blurred. If all edges need to be processed, the subpixel overlay matching dynamic blur technique can be used.
3. Simulation of DMD digital lithography technology based on isosceles right-angled triangle image
Without any optimization, the edges of the exposure generated image are also composed of ordinary the sawtooth edges. However, in our exposure method, the dynamic blur effect of the exposed image is caused by the constant movement of the 3D mobile platform. Based on the motion blur kernel function created before, the motion exposure is simulated by Python. Since the minimum resolution of the image in Python code is only 1 pixel, the result of moving half a pixel distance cannot be displayed. So, we magnify the entire exposed image by a factor of 10, with the edge reaching a distance of 10 pixels, and move it in the way described above, moving the distance by 5 pixels. Simulation diagram of motion blur effect is shown in Fig. 6.
Fig. 6. Simulation diagram of motion blur effect. (a) Original image. (b) Simulation of the dynamic blur effect.
The triangle image after the motion blur effect is overlapped by Python, and the triangle mask mapping based on the motion blur effect matching pixel overlap technology is obtained as shown in Fig. 7. A Python code utilizing Hopkins optical functions. The python exposure simulation was used to expose ordinary triangle mask and triangle mask based on dynamic blur effect matching pixel overlap technology, respectively. And the simulation diagram is shown in Fig. 8. It can be seen from the final simulation results that the edge smoothness of the graphics exposed by DMD digital lithography based on 3D motion is better than that of the graphics exposed by simple superposition of 1/2 pixels.
Fig. 7. Motion blur matches the exposure mask of overlapping pixels. (a) Simulation of the dynamic blur effect. (b) Motion blur effect matching pixel overlap technique mask map.
Fig. 8. Exposure simulation based on motion blur effect matching pixel overlap. (a) Raw image exposure simulation. (b) Optimized exposure simulation image.
4. Experimental results and evaluation
In our experiment, a UV light source with a wavelength of 405 nm was used as the light source, and a projection objective with a 4x magnification was used as the projector. The experiment initially fine-tunes the entire system to ensure normal exposure of experimental images. Using the experimental method of reverse exposure, the exposure material is placed on a three-dimensional moving platform. The light source and the platform are synchronously controlled on a computer. When the light source is activated, the platform begins to move synchronously, moving up half a pixel and then moving left half a pixel. Once it reaches the desired position, it is reset to zero. The reset process includes moving right half a pixel, then moving left half a pixel, and repeating the entire process. When the light intensity is set to 8.11 mw/cm2, the entire process takes approximately 5∼6 seconds, which can be appropriately adjusted according to the intensity of the light source. Once the exposure is complete, the platform stops moving, processes the exposed substrate, and places it under a microscope to observe its edges, then comparing it with the unoptimized exposure image. The photosensitive material used is resin. The normal exposure results observed by the light microscope and the DMD lithography results based on three-dimensional motion are shown below. Since the minimum size of the actual exposed pixels in the experimental system is 1.89 µm, it is difficult to observe any difference using an optical microscope at low magnification. Therefore, the lithographic pattern of the partially observed edge is observed using a 40X magnification, as shown in Fig. 9.
At the lowest point of the triangle’s edge, a straight line parallel to the hypotenuse was drawn and 5 points on this line was chosen to measure the smoothness of the edge. The average value of the five unoptimized points is 1.666 µm, and the average value after optimization is 0.27 µm, which is significantly lower than the edge smoothness of the unoptimized points. This phenomenon has been observed in many experiments and measurements. In theory, when the subpixel superposition displacement is halved, the roughness of the edge smoothness should be reduced by half. However, in the actual experiment, the decrease of edge smoothness roughness is only slightly more than half. The edge roughness of the exposed image by DMD digital lithography based on dynamic blur effect of pixel superposition is obviously less than half of the edge roughness of the ordinary exposed image. The experimental results are highly consistent with the above simulation results, which also proves the effectiveness and feasibility of the proposed method.
5. Conclusion
We proposed an edge smoothing optimization method based on dynamic blur matching pixel overlap technique for DMD digital lithography. This study proves the feasibility and correctness of DMD digital lithography based on dynamic blur effect matching pixel superposition from both theoretical simulation and experimental verification. The simulation results of DMD digital lithography based on dynamic blur effect matching pixel overlap technology showed that DMD lithography based on dynamic blur effect matching pixel overlap technology has better smoothness than ordinary exposure. The experiment results proved that without reducing the size of the DMD micromirror or the magnification of the projection lens, applying the technique of matching pixel overlap based on dynamic blur effect to DMD scanning lithography can significantly improve the edge smoothness of the lithography pattern, which can efficiently reduce the sawtooth edge from 1.666 µm to 0.27 µm. We believe that the edge smoothness could be more effective and efficient improved if the sub-graphs moving path algorithm was optimized further.
Funding
National Natural Science Foundation of China (62305001); Key Research and Development Program of Anhui Province (2022a05020008); Natural Science Foundation of Anhui Province (2008085QE258, 2308085MF210); Major Project of Natural Science Study in Universities of Anhui Province (2022AH040138); China Postdoctoral Science Foundation (2022M710175); Open Project of Special Display and Imaging Technology Innovation Center of Anhui Province (2022AJ05002); Research Activities of Postdoctoral Researchers in Anhui Province (2023B707); Anhui Province College Young and Middle-aged Teachers Training Action Project; Anhui Polytechnic University Graduate Education Innovation Fund; New Era Education Quality Project (Postgraduate Education).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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