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Abstract
Maskless lithography technologies have been developed and played an important role in the fabrication of functional micronano devices for microelectronics, biochips and photonics. Optical projection lithography based on digital micromirror device (DMD) is an efficient maskless lithography technology that can rapidly fabricate complex structures. The precise modulation of gap width by DMD maskless optical projection lithography (MOPL) using femtosecond laser becomes important for achieving micronano structures. Herein, we have investigated the relationship between the structure morphology and the light intensity distribution at the image plane by multi-slit diffraction model and Abbe imaging principle, and optimized the gap width more accurately by modulating exposure energy. The aperture diameter of the objective lens has a substantial effect on the pattern consistency. The continuously adjustable structural gap widths of 2144 nm, 2158 nm and 1703 nm corresponding to 6, 12, 24 pixels are obtained by varying the exposure energy in the home-built MOPL system. However, the ideal gap structure cannot be obtained only by adjusting the exposure energy when the gap width is small, such as 1 or 2 pixels. Furthermore, we have proposed an alternative way to achieve fine gap structures through the structural decomposition design and precise control of exposure energy in different regions without changing the MOPL optical system. This study would provide a promising protocol for fabricating gap microstructures with controllable configuration using MOPL technique.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Maskless lithography technologies such as electron-beam lithography [1–3], ion-beam lithography [4–6], femtosecond laser direct writing [7–15], multi-beam interference [16–18], digital projection lithography [19–22] have been developed and played significant roles in the micronano scale patterning for fabricating devices in the fields of microelectronics, biochips, photonics and so on. Among them, the digital projection lithography using digital micromirror device (DMD) can quickly realize the fabrication of complex structures, and its resolution has reached to sub-micron level with the optimization of light source and zoom ratio of objective lens [23–27]. A large number of functional structures such as photonics devices [27,28], three-dimensional (3D) biological scaffolds [29,30], bionic robotic arms [31], etc. have been designed and fabricated.
The resolution of DMD lithography has played an important role in achieving diverse devices with high precision. S. K. Saha et al. and Y. H. Liu et al. have achieved 3D photonic crystal structures and the multi-scale structures by DMD two-photon lithography [32,33], in which the minimum linewidths reached to 175 nm and 32 nm, respectively. Algorithm for selecting appropriate light wavelength for micromirrors of different sizes and adjusting the optimal mirror incident angle [34], aberration compensation method [35], and light intensity modulation technique [36] have been used to improve the imaging accuracy of DMD lithography. These studies indicate that this technology would have high potential in wide applications.
With the improvement of the resolution in DMD lithography, the consistency of pattern printing between 2D designed pattern and the patterned structure becomes more important. We have comprehensively investigated the relationship between the structure morphology and the light intensity distribution at the image plane by multi-slit diffraction model and Abbe imaging principle in the maskless optical projection lithography (MOPL) system. The aperture diameter of the objective lens has an obvious impact on the light intensity distribution. The continuously adjustable structural gap widths are obtained by varying the exposure energy in the home-built MOPL system. However, the desirable gap structure cannot be obtained only by adjusting the exposure energy when the gap width is as small as 1 or 2 pixels. Furthermore, we propose a protocol for optimizing the precise exposure of MOPL technique by the structural decomposition design and precise control of exposure energy in different regions of the patterned structure.
2. MOPL optical system
The schematic diagram of the MOPL system is shown in Fig. 1. Femtosecond laser (MaiTai HP+ Inspire AUTO100, Newport) of 400 nm is used as the light source. The laser beam is expanded to 10 cm diameter by extender lens composed of objective lens (10 ×, N.A. 0.25, Thorlabs, LMU-10X-NUV) and the convex lens with a long focal length of 1000 mm. A pinhole with aperture size of 5 µm is used to filter sharp high-frequency components in the light source. Then, the laser beam with an area of 10 × 14 mm2 is taken by the beam interception method and incidents to the DMD chip (2xLVDS, 0.7 inches 1024 × 768 pixels, 13.68 µm, Texas Instruments) at an angle of 24 degrees with the projected optical axis. The uniformity of the light intensity is characterized by using the Camera Beam Profiler (Thorlabs, BC106N-VIS/M). The homogeneity value is better than 90%. Finally, the reflected light is projected onto the focal plane of the projection lens composed of tube lens (Olympus, U-TLU, focal length of 180 mm) and objective lens (Nikon, 100 ×, N.A. 1.45, focal length of 2 mm), which shrinks the image by 90 times. A 3D stage (XMS160, GTS30V, NEWPORT) is used for the accurate movement. The 2D designed patterns on DMD chip are generated by preprogrammed 8-bit grayscale map in computer.
3. DMD chip structure and simulation of light field distribution
3.1 Detailed structure of DMD
The detailed structure of DMD chip is illustrated in Fig. 2(a). Each micromirror can be deflected by +12° or -12° along the diagonal direction of No. 1. DMD chip is used for generating the desired 2D pattern. In the 4f system of the MOPL, the spectrum and image plane are located at the focal plane of tube lens and objective lens, respectively. Tube lens plays the role of decomposing the information to obtain the spatial spectrum of the 2D pattern generated by DMD, while the objective lens is utilized to synthesize the information to restore the 2D pattern.
Fig. 2. DMD chip structure and calculation principle of light field distribution on the focal plane. (a) Diagram of DMD chip and micromirror array. (b) Rated phase difference relationship between adjacent micromirrors. (c) The spectrum of the DMD pattern after the tube mirror and the principle of the low-pass filtering of the objective lens
3.2 Rated phase difference between the micromirrors
Since a coherent femtosecond laser is used as the light source, we should consider the effect of multi-beam interference reflected by the DMD micromirrors. Taking two adjacent micromirrors as an example, it is assumed that the wavefront of the parallel beam incident on the DMD has an isophase plane in the propagation direction as shown in Fig. 2(b). A and C are two points on the isophase plane. There is no optical path difference between the light beams in single micromirror, but there is a rated optical path difference of the length of the BC line between two adjacent mirrors. Taking the micromirror array in Fig. 2(a) as an example, each micromirror coordinated as Mjk is represented by its row j and column k, and the first micromirror M11 in the upper left corner is the zero-phase point. The rated phase difference between the micromirror Mjk and M11 can be expressed as:
3.3 Light distribution simulation by multi-slit diffraction model and Abbe imaging principle
The light intensity at any point on the spectrum of the tube lens is equal to the product of the Fraunhofer diffraction light intensity of a single DMD micromirror and the interference light intensity of all micromirrors at that point. The amplitude of that point is expressed as:
The function after objective lens aperture filtering is expressed as follows:
The edge and the sharply changed area in the 2D designed pattern on the DMD will become high-frequency components after passing through the tube lens, as shown in the red and yellow lines in Fig. 2(c). If the aperture diameter of the objective lens is small, the high-frequency components will be missing. Therefore, the edge shape of the 2D pattern after the MOPL is not only related to the design of the pattern itself, but also directly related to the aperture diameter of the objective lens.
4. Simulation of the effect of the aperture diameter of objective lens and exposure energy on light field distribution
4.1 Effect of different gap structures and the aperture diameter on light field distribution
We have designed a 2D pattern with the gap (g) of 1, 6, and 12 pixels and the side lengths L and W of 10 pixels on the DMD objective plane, as shown in Fig. 3(a). The cross-sectional light intensity distribution on the focal plane calculated by the above formula is shown in Fig. 3(b). Figure 3(c) is a magnified view in the red box of Fig. 3(b). When the gap is 1 pixel, the edge of the two structures cannot be separated due to the superposition of the diffraction light field. When the gap is 6 pixels or 12 pixels, the gap structures can be obviously separated although there is still an obvious high-order diffraction light field between the structural gaps.
Fig. 3. The simulation diagram of the effect of designed structural gap width and the numerical aperture of objective lens on the light field distribution of the focal plane. (a) 2D designed pattern. (b) The light field distribution diagram of the cross-section on the focal plane of the double-block patterns with a 10-pixel side-length and a gap of 1,6,12-pixel. (c) The magnified light field distribution diagram of the structural gap in (b). (d-f) The simulation diagrams of the light field distribution on the focal plane when the 2D pattern with a 10-pixel side-length and a gap of 6 pixels, assuming the objective lenses with the aperture diameter of 4 mm, 8 mm and 20 mm, respectively
Furthermore, we have designed the same structures with a gap of 6 pixels, and assumed different aperture diameters of 4 mm, 8 mm, and 20 mm of the objective lenses with the same magnification. The light field distributions on the focal plane are shown in Figs. 3(d), 3(e) and 3(f). The smaller the aperture diameter of the objective lens, the smoother the gradient of the light field distribution at the edge of the structure. When the aperture diameter of the objective lens is large enough, the edge of the structure has a high steepness, even each gap morphology between the micromirrors can be distinguished. That is, the larger the diameter of the objective lens, the higher the graphic fidelity theoretically.
4.2 Effect of the exposure energy on gap structure
The aperture diameter of the objective lens is 8 mm in our MOPL system. The aperture diameter isn’t large enough so that the light field distribution at the edge of the structure will have gradient change. The exposure energy will become the main parameter to modulate the structure morphology. Taking a double-block pattern with a 10-pixel side-length and a gap of 12 pixels as an example, the light field distribution on the focal plane of the normalized exposure energy ratio of 1, 0.87, 0.74, 0.61, 0.48, 0.35, 0.22 is shown in Fig. 4(a). Figure 4(b) is an enlarged view in the red box of Fig. 4(a). For a photoresist with the same exposure threshold, the edge of the structure will inevitably expand outward, and the gap width between the double-block structures will be reduced at large exposure energy. Note that this method would bring in more flexibility while adjusting the gap width of the structure in a certain range only by controlling the exposure energy.
Fig. 4. The simulation diagram of the light field distribution of the double-block pattern with a 10-pixel side-length and a gap of 12 pixels with different exposure energies. (a) The light field distribution of the cross section on the focal plane under normalized exposure energy. (b) Magnified part in the red box of Fig. 4 (a)
5. Experimental verification of exposure energy to the gap width
The commercial negative UV photoresist AR-N 4340 with 2-Acetoxy-1-methoxypropane as main component and the single-photon absorption at 400 nm is used in the experiment. The photoresist is spin-coated at 4000 rpm and baked at 85 °C for 2 minutes before exposure. After exposure, it is baked at 95 °C for 5 minutes and developed by AR 300-475 developer for 1 minute. The 2D designed patterns with a 132-pixel side-length and a gap of 6, 12, and 24 pixels are used as graphics presented on the DMD. The effect of exposure energy on the final structure morphology is analyzed experimentally. The average power (P) of the 400 nm femtosecond laser is fixed at 51 µW, which is measured on the focal plane of the objective lens with all micromirrors of DMD fully opened. The exposure time (T) is changed from 500 ms to 2300 ms with an interval of 100 ms. The exposure energy E of a single micromirror is equal to:
where Nm = 1024 × 768 is the size of the DMD micromirror array.The dependence of the gap width on the exposure energy is shown in Fig. 5. Figures 5(a)-(c) are the SEM images of the three different gap structures with the same exposure time of 1800 ms. Figures 5(d)-(f) are the SEM images of the gap structures magnified by 10,000 times for the three patterns with different exposure time from 2300 ms to 500 ms, respectively. The variation of the gap width with the exposure energy of a single micromirror is shown in Fig. 5(g). The gap widths approach to the theoretical values for perfect imaging when the exposure energy is between 117.65 pJ and 124.18 pJ in the red box of Fig. 5(g). The high exposure energy accumulated by the high-order diffraction light field in the structure gap would also cause the polymerization of the photoresist, which will have an obvious impact on the narrow structure gap. As shown in Fig. 5(d), the structure gap becomes blurred when the exposure time is longer than 1900 ms, and the minimum gap width obtained at 2300 ms is 638 nm, which is 274 nm smaller than the theoretical value of 912 nm in Fig. 5(h). This exposure energy of the diffraction light field at the large structure gap is insufficient so that the oligomer will be removed in Figs. 5(e) and 5(f). The minimum gap width of 1619 nm and 3562 nm are 205 nm and 86 nm less than the theoretical value of 1824 nm and 3648 nm, which indicates that the larger the structural gap, the smaller the influence of the high-order diffraction light field under the sufficient exposure energy. When the exposure energy increases, the gap width of the structures tends to be a constant as shown in Fig. 5 (g). On the contrary, the gap width increases rapidly with the decrease of exposure energy. The maximum gap widths are 2782 nm, 3777 nm, 5265 nm, which are 1870 nm, 1953 nm, 1617 nm larger than the theoretical value shown in Fig. 5(h). This phenomenon can be explained that self-shrinking behavior would occur when the polymer network density of the material is loose at small exposure energy. The difference of the continuously adjustable structural gap width between the minimum gap widths and the maximum gap widths are 2144 nm, 2158 nm and 1703 nm for the 6, 12, 24 pixels gap structures. Therefore, exposure energy plays an important role in controlling the width of gap structure and an appropriate network crosslink density by enough exposure energy is needed to achieve a pattern with high consistency.
Fig. 5. SEM images of the double-block patterns with 132-pixel side-length and the gap of 6, 12, and 24 pixels, and the dependence of the gap width on the exposure energy. (a-c) SEM images of the three structures with the exposure time of 1800 ms. (d-f) Magnified SEM images of different structures with varied exposure time from 2300 ms to 500 ms. (g) The dependence of gap width on the exposure energy of single micromirror. The red box is the gap widths approach to the theoretical values for perfect imaging. (h) The difference between the structural gap widths and the theoretical values under different exposure energies
Due to the limitation of the aperture diameter of the objective lens, the narrow and steep gap structure cannot be obtained by simply designing a small gap structure as well as controlling the exposure energy. The photoresist polymer network would be generated and then remained when the exposure energy of 17.61 pJ reaches the structural integrity requirement for 1-pixel gap structure shown in Fig. 6(a). Although the gap can be separated at a smaller exposure energy of 21.13 pJ when the gap is 2 pixels in Fig. 6(b), the polymer network density of the block is lower and the structure shrinks obviously. The minimum gap width of 714 nm is obtained in Fig. 6(c), which is more than twice the theoretical value of 304 nm. In order to obtain a narrower and cleaner gap structure, the pattern can be divided into double- block structures and the edge structures marked in white and yellow, respectively. As shown in the Fig. 6(d), a double-block structure with 2-pixel gap is designed by double blocks with 6-pixel gap and edge structures with 2-pixel gap. Different exposure energies are employed to fabricate the corresponding regions of the structure, respectively. The larger exposure energy of 52.83 pJ is used to expose the double-block structure, and the smaller exposure energy of 17.61 pJ is used to expose the edge structure. By this method, a gap structure with a narrow gap and a certain depth can be obtained in Fig. 6(e), and a minimum gap of 513 nm is obtained as shown in Fig. 6(f). Compared with the direct exposure of the 2-pixel gap structure with the consistent exposure energy, the gap width and morphology of the pattern are significantly optimized. Therefore, the proposed method for fabricating gap structures by optimizing structural decomposition design and different exposure energy control provides great potential for the achieving structures with the tunable gap width and steepness.
Fig. 6. Comparison of different methods for achieving the double-block patterns with the narrow-gap. (a) SEM image of the pattern with double blocks and 1-pixel gap at the exposure energy of 17.61 pJ. (b) SEM image of the pattern of the double-block structure with the 2-pixel gap at the consistent exposure energy of 21.13 pJ. (c) Magnified image in (b). (d) Decomposition design of the double-block structure with the 2-pixel gap, in which the white structure are double blocks with 6-pixel gap and the yellow double lines are the edge structures with 2-pixel gap. (e) SEM image of the pattern of the double blocks and the edge structure with 2-pixel gap fabricated at the exposure energy of 52.83 pJ and 17.61 pJ, respectively. (f) Magnified image in (e)
6. Conclusion
In this work, we have proposed a protocol to optimize the consistent pattern printing of gap structure in femtosecond laser DMD projection lithography. The high-frequency components representing tiny gap structure are filtered due to the limitation of the aperture diameter of the objective lens, resulting in distortion of the structural pattern. When the exposure energy is insufficient, the polymerized network density is not enough and would cause the self-shrinking effect to further influence the consistency. When the gap of the structure design is too small, it is not possible to obtain a narrow structure with a certain steepness due to the influence of the strong diffracted light field in the gap. Therefore, suitable exposure energy and structural decomposition design are important for achieving consistent pattern printing limited by the aperture of the commercial high magnification objective lens. Based on the understanding of relationship between the exposure energy and the structural morphology, we can flexibly achieve gap structures in a wide range. This study provides a method for the controlling the gap structure in the femtosecond laser MOPL, which is promising for the fabrication of micronano structures and devices for nano photonics and optics.
Funding
National Key Research and Development Program of China (2016YFA0200500); National Natural Science Foundation of China (51673208, 61975213); International Partnership Program of Chinese Academy of Sciences (GJHZ2021130).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but maybe obtained from the authors upon reasonable request.
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