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Abstract
A fabrication method for large-area gratings with uniform duty without using a spatial beam modulator is introduced in this study. The inhomogeneity of gratings caused by flaws of the lens and stray light was solved by controlling exposure time within an appropriate range and selecting a suitable beam expansion aperture in the optical path. A model for representing this process was established by analyzing the effects of exposure and development time length, and experimental results exhibited good agreement with the simulation results. Finally, a grating with a period of 550 nm, a uniform duty cycle, and a diameter larger than 30 mm was achieved using a Mach–Zehnder interferometer optical path without a spatial beam modulator. The uniformity of this grating was observed via atomic force microscopy, and the results were highly desirable.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Gratings are used in various fields due to their unique physical characteristics. In some fields, such as electro-optical devices [1–3], biosensing [4], physical spectroscopy [5], and laser applications [6–7], large-area gratings with good uniformity are in high demand. Existing methods for fabricating large-area uniform gratings include nanoimprinting [8–10] and laser interference exposure [11–15]. Nanoimprinting is a method for imprinting and copying a pattern on a substrate in equal proportions by pressing the template with a nanoscale pattern onto a substrate coated with a layer of polymer material though mechanical pressure [8]. However, nanoimprinting requires a mask that uses electron beam exposure, which is an extremely expensive fabrication method [9–10].
Laser interference exposure is another method for fabricating gratings, this method is mature for fabricating small-area gratings [15–16]. But it is still difficult to manufacture large-area grating because the laser source is Gaussian beam. An existing solution is to add a spatial light modulator in the optical path to shape the Gaussian beam into a flat top light [12–13,17]. However, a spatial beam modulator is extremely expensive, and building one of your own will make the beam path highly complicated. Another solution is to move the laser head [13,18] or exposure plane [19] during exposure. This method not only needs to build a complex optical path, but also needs very precise attitude angle control. Therefore, in this study we proposed a method based on laser interference exposure by simply controlling the length of exposure and development time to fabricate large-area grating with uniform duty cycle, no need to use other devices.
The influence of the lengths of exposure and development time on the duty cycle of gratings can be observed by monitoring development [20]. Varying exposure time lengths can be used to adjust the duty cycle of gratings when the development time length is fixed [11]. Light from a He–Cd laser device is a Gaussian beam. When the grating area is large, light intensity at the center and edge of a grating can be extremely different. When the exposure and development time lengths are the same, the duty cycle of a grating at center and edge will be significantly different. In addition, the flaws of the lens and stray light affect the uniformity of light intensity on a substrate and cause the duty cycle of a grating to become uneven.
We proposed this method for the first time — control exposure time length within an appropriate range, called “exposure time length window,” and select an appropriate beam expansion aperture in the optical path to reduce the inhomogeneity caused by the flaws of the lens and stray light, finally achieving the production of large-area gratings with a uniform duty cycle. We simulated the effects of different exposure and development time lengths on the duty cycle of gratings. The experimental results correspond with the simulation results. Finally, we fabricated a grating with a uniform duty ratio area larger than 30 mm in diameter without using a spatial beam modulator. The uniformity of the grating was observed via atomic force microscopy (AFM).
2. Analysis of light intensity distribution on the exposure surface
When using a Mach–Zehnder interferometer for exposure, ensuring that the two beams in the optical path are exactly the same is necessary. However, light intensity distribution on the exposure surface is not uniform due to several factors, such as the inhomogeneity of the beam, the influence of stray light, the inhomogeneity and cleanliness of the lens, the vibration of the light path, and the vibration of air in the exposure environment.
The aforementioned factors are divided into two types. The first type, which is denoted as ${I_T}(x )$, includes factors that can be quantitatively analyzed, such as inhomogeneity caused by an inhomogeneous beam. The second type, which is denoted as $\Delta {I_T}(x )$, includes inhomogeneity caused by random factors that cannot be quantitatively analyzed, such as stray light and lens cleanliness. If ${I_{sum}}(x )$ is used as the total light intensity distribution on the exposure surface, then ${I_{sum}}(x )= {I_T}(x )+ \Delta {I_T}(x )$. First, the situation of ${I_T}(x )$ is analyzed. The wave front of the beam emitted by the laser can be expressed as
If the optical path strictly maintains symmetry, then the amplitudes of split beams should be equal. In reality, however, the two beams may differ after passing through the splitter, and thus, their amplitudes should be recorded as ${\textrm{A}_1}$ and ${\textrm{A}_2}$. Coherent superposition occurs when two beams meet, and the wave front of the beam after superposition is
The intensity of the interference light is
By ensuring that the optical path is strictly symmetrical, the incident angles of the two coherent beams that are incident on the surface are equal, and the rectangular coordinates of the two are $({ - x,y,z} )$ and $({x,y,z} )$. The incident surface is defined as the plane of $\textrm{y} = 0$, and thus, the wave vector of two coherent beams can be written as
When considering the horizontal centerline of the exposure surface where $\textrm{z} = 0$, the light intensity distribution on the exposure surface is
However, light intensity will change with location during large-area exposure due to the aforementioned reasons. Therefore, ${\textrm{A}_1}$ and ${\textrm{A}_2}$ are not constants, and they will vary at different positions on the surface. Consequently, Eq. (6) should be written as Eq. (7).
Theoretically, the laser output beam is a Gaussian beam, and light intensity distribution on its cross section conforms to the ideal Gaussian distribution as Eq. (8) [21], causing uneven beam distribution on the exposure surface.
$\sigma (z )$ is the radius of the Gaussian beam that changes with the propagation of the beam, and $P$ is the total power of the beam. $\textrm{z}$ is determined during exposure progress, and thus, it is a constant. In the actual emitted beam, the center may deviate from the center position of the exposure surface; hence, due to we directly measure the light intensity at the geometric center of the substrate, a constant $\mathrm{\mu}$ must be added to indicate the deviation of the Gaussian beam from the substrate center. Accordingly, light intensity distribution on the exposure surface is Eq. (9).
After passing through the beam splitter and the spatial filter, the parameters of the two beams are independent of each other. In the case of 1D measurement, we use the optical power meter to measure the center and the two edges of the exposure surface, when the two beams incident separately and incident at the same time. In accordance with Eq. (9), three unknowns must be determined in each beam. The two beams have a total of six unknowns, but nine equations can be listed on the basis of nine measurements, as indicated in Eq. (10). Equation (10) is a nonlinear overdetermined equation system, and a numerical solution method is adopted to solve it.
The optical power dates were measured by optical power meter (THORLABS S130VC). In order to improve measurement accuracy, a small aperture diaphragm was added in front of the probe. The device is shown in the Fig. 1. After multiple measurements, the average value was taken as the result.
Table 1 lists a set of data obtained during the actual experiment.
Table 1. Actual measured power
The power distributions on the exposure surface after calculating in accordance with the preceding method are shown in Fig. 2(a). During the propagation, at the Gaussian beam central position the curvature radius will increase and intensity will decrease. Collimator lens intercepts and collimates the central part of the expanded Gaussian beam with a fixed aperture, so it is called beam expansion aperture. The wave-front stops diverging after passing through the collimator lens. Using different beam expansion aperture will intercepts beam with different shape, as shown in Fig. 2(b). If using collimator lens with a small focal length, the beam expansion aperture will become large, and the curvature radius of the beam will be very small, as shown by the orange line in the Fig. 2(b). This will result in a significant light intensity difference between the center and the edge on the exposure surface, thus the uniformity of the grating will reduce. Using lens with a long focal length, the distribution of optical intensity will be more uniform, but the intensity will decrease, as shown by the green line in the Fig. 2(b). Because of the decrease of intensity, the exposure time should be longer and will increase the influence of the $\Delta {I_T}(x )$ at the dark stripes on the uniformity. A suitable focal length choosing will get the most optimized result of considering the intensity and distribution uniformity of light on the exposure surface, as shown by the blue line in the Fig. 2(b). In the optical path, according to the parameters of the laser beam and the light intensity and distribution need to be achieved on the substrate, the suitable beam expansion aperture can be determined.
Fig. 2. (a) Gaussian beam power distribution. Fit_r represents the power distribution by fitting the right optical path, fit_l represents the power distribution by fitting the left optical path, and fit_sum represents the power distribution by fitting the total optical paths. ● denotes the power that is actually measured at the corresponding position in Table 1. (b) Effect of different beam expansion aperture on substrate exposure light intensity. Orange line represents when using a small focal length collimator lens, blue line represents when using an appropriate focal length collimator lens, green line represents when using a long focal length collimator lens.
Power at the main dark stripes of an ideal interference exposure should be 0. However, the existence of ${({{A_1}(x )- {A_2}(x )} )^2}$ in Eq. (7) and $\Delta {I_T}(x )$ will cause power distribution at the dark stripes, and thus, the optical power at the bright stripes is ${I_{min}}(x )= {({{A_1}(x )- {A_2}(x )} )^2} + \Delta {I_T}(x )$ and that at the dark stripes is ${I_{min}}(x )= {({{A_1}(x )+ {A_2}(x )} )^2} + \Delta {I_T}(x )$. In accordance with the quality of the devices and the actual experimental results, the power of these factors is estimated at approximately 10% of the total power. For simplicity, 10% of the total power in Fig. 2(a) is the actual power at the dark stripes at that position. The light intensity distribution envelope curve in the actual interference is shown in Fig. 3.
Fig. 3. Envelope curve of the extremum power distribution. The green solid line represents the envelope of ${I_{min}}(x )$ on the exposure surface, and the orange solid line represents ${I_{max}}(x )$ on the exposure surface. However, the envelope of power will exhibit fluctuation due to the existence of $\Delta {I_T}(x )$, and thus, the actual ${I_{min}}(x )$ and ${I_{max}}(x )$ envelopes should in green and orange areas. The four points are the extreme positions of the envelope.
The properties of the photoresist will change during exposure. For the positive photoresist S1805 used in the current study, the long-chain molecules of the polymer at the illuminated area melt into short-chain molecules during exposure and are developed. By contrast, the photoresist in the areas that are not illuminated will remain after development. The ratio of broken long-chain molecules per unit volume is called conversion concentration, and it is denoted as De. During actual exposure, the value of De is related to the amount of received exposure dose [22], and the relationship is presented as Eq. (11).
$E({x,t} )$ is the distribution of received exposure dose on the surface. $\mathrm{\alpha }$ is the exposure constant of the photoresist, and its value is determined by the wavelength of light, the optical path, and the properties of the photoresist. From the experimental results, the value of $\mathrm{\alpha }$ is approximately ${10^{ - 4}}/({mW \cdot s} )$. In accordance with Lambert’s law, light intensity in the photoresist will be attenuated [23], satisfying Eq. (12). $\mathrm{\delta }$ is the attenuation coefficient of light in the photoresist, and it will change during exposure [24]. In accordance with the technical documentation provided by the photoresist manufacturer, $\mathrm{\delta }$ is generally within the range of 103–104 m−1. The thickness of the photoresist film used in the experiment is approximately 500 nm, and light attenuation is below 0.5%; thus, the effect of this factor is small. $E({x,t} )$ is primarily related to light intensity and exposure time [22]. Their relationship is presented in Eq. (13). $\mathrm{\gamma }$ is the exposure correction constant. From Eq. (13), $E({x,t} )$ and ${I_{sum}}(x )$ exhibit a linear relationship within a short time. However, after a long exposure period, the influence of $\mathrm{\gamma }$ dominates the experimental results. In our experiment, exposure time is approximately 100 s, and thus, $\mathrm{\gamma }$ exerts considerable influence on the results. From the experimental results, the value of $\mathrm{\gamma }$ is approximately $5 \times {10^{ - 5}}({mW/{s^2}} )$.Data from Table 1 are used as an example. When light intensity data are calculated using Eq. (11) to (13), the relationship between De and exposure time is illustrated in Fig. 4.
Fig. 4. Relationship between De and exposure time length. Orange and green represent the De value at different extreme positions on the exposure surface at varying exposure time. The De value varies at different positions in the same exposure time length. Each point in Fig. 3 on line ${I_{max}}$ corresponds to an orange curve, and these curves constitute the orange area. Each point in Fig. 3 on line ${I_{min}}$ corresponds to a green curve, and these curves constitute the green area. The four extreme points in Fig. 3 constitute four boundaries.
3. Analysis of exposure process
As shown in Fig. 4, the ${I_{max}}$ area rapidly reached a high De value, whereas the ${I_{min}}$ area was slowly exposed. However, the speed of De changing between the two areas was considerably different. A method similar to finite element analysis was used to divide a grating period into many equal-sized square cells. If the number of divided cells is sufficiently large and the volume of each cell is sufficiently small, then a small cell is considered to receive the same exposure dose, and thus, De in a small cell is the same. Simulating the data in Table 1 by exposing for 80 s, Fig. 5 shows the distribution of De at the center and edge grating periods. The center period receives a large dose of exposure, and De is significantly larger than that in the edge period. The theoretical dissolution speed of the center period should be faster, and such condition is consistent with the experimental phenomenon that the line widths of the center and edge periods are different.
Fig. 5. Distribution of De between center and edge grating periods. The abscissa denotes the distribution within a grating period of 550 nm, and the ordinate denotes the photoresist thickness of 500 nm. The vertical line in the figure indicates the contour lines of the De value after exposure (the same in Fig. 7 –9, 11).
4. Analysis of development process
The positive photoresist is gradually dissolved during the development process, and the neutralization reaction only proceeds on the surface of the photoresist. The dissolution speed during the development process is presented in Eq. (14) [22].
${V_0}$ is the dissolution speed under no exposure. ${\epsilon }$ is the magnification coefficient between the dissolution speed at the center of bright and dark stripes, and its value is related to the grating structure. By measuring the photoresist dissolution speed at different De values and using the least squares method to fit the parameters, a dissolution speed that is consistent with the experimental results and theory is obtained and fitted into Fig. 6. It is evaluated as V0=3 nm/s and ${\epsilon = 9}\textrm{.58}$ in our experiment.Fig. 6. Relationship between development dissolution speed and De. ▴ denotes the actual measured dissolution speed at different De values.
The development and exposure processes are inseparable, and thus, the two are combined for analysis. The influence of different exposure time lengths on the duty cycle of a grating is discussed. Exposure time within an appropriate range for fabricating large-area gratings, called “exposure time window,” is proposed.
4.1 Exposure time is seriously insufficient: nearly no stripes appear
As indicated in Fig. 7, exposure time is seriously insufficient. During this exposure time, the ratios of long-chain molecules to short-chain molecules in the bright and dark stripes are both low. The gap of the development speed between the bright and dark stripes is small, and thus, the time during which the bright and dark stripes dissolve to the bottom is the same. Nearly no stripes remain at any development time. Using the data in Table 1 as example, the exposure time is 30 s and the development time is 60 s. In the simulation process, the dissolution speed of a certain point is assumed to depend only on the De at that point, and the direction of dissolution speed is always along the normal direction of the profile of the grating [25]. The simulation program for the development process adopted the same elastic string sliding model in [22] to simulate the change in grating groove shape with development time. Figures 7(b) and 7(c) present the simulation result for a grating profile. Both grates dissolve minimally, and nearly no stripes appear.
Fig. 7. Simulation of severely insufficient exposure time. (a) Comparison of exposure speed at the bright and dark stripes after reversing Fig. 6 to make the vertical axis consistent with Fig. 4. The dashed line is the dissolution speed after exposure for 30 s. (b) and (c) One grating period at the center and the edge after development for 60 s, respectively. The abscissa is a grating period of 550 nm, and the ordinate is the remaining mask thickness. The right half represents De after exposure, and the left half represents the development results. Symmetry around the central axis shows the complete profile of a grating period after exposure and development (the same in Fig. 8, 9, 11).
4.2 Exposure time is insufficient: stripes can be developed, but the line width is highly uneven
For the preceding example, exposure time is increased to 80 s. The edge and center De values are different at this exposure time due to the uneven light intensity distribution caused by the Gaussian beam, the flaws of the lens and the stray light, and the change in light intensity that makes the value of ${I_{max}}(x )$ different. Meanwhile, dissolution speed is considerably affected by De at such position, causing inhomogeneity of the line width at the center and the edge. In such case wherein the center and the edge are toward bottoming up, as shown in Fig. 8, the line width of the edge is wider than that of the center.
Fig. 8. Results of insufficient exposure time. (a) The dashed line is the dissolution speed after exposure for 80 s at different positions. (b) and (c) One grating period at the center and the edge after development for 20 s, respectively. (d) Result of the experiment observed under a 500-fold microscope after development. (e) Result of the experiment observed under a 5000-fold microscope after development.
The different colors in Figs. 8(d) and 8(e), captured by a super deep scene 3D microscope, represent different thickness values of the remaining photoresist. When the color is deeper, the thickness of the remaining photoresist is greater. The lighter part shows where the photoresist has bottomed out. The relatively mottled state in Figs. 8(d) and 8(e) is primarily caused by the fluctuation of the actual light intensity distribution, i.e., the orange dotted line $\Delta {I_T}(x )$ in Fig. 3. In such exposure time length, the inhomogeneity of the beam simultaneously affects the bottoming time and line width of a grating. By continuing to extend exposure time, the disparity in dissolution speed at the bright stripes caused by the Gaussian beam and the flaws of the lens and the stray light is reduced and uniformity is improved. This finding is confirmed by the results of the experiments and simulations.
4.3 Most suitable exposure time: “exposure time window,” the line width reached the most even
By continuing to increase exposure time, the disparity in dissolution speed at the bright stripes caused by the Gaussian beam and the flaws of the lens and the stray light is minimized. Thus, the influence of uneven beam power is reduced to an extremely low level, and the uniformity of the line width is the most even, as shown in Fig. 9. During this exposure time, the dissolution speed of dark stripe is slightly faster but still different from that of the light stripe; hence, the thickness of the mask remains high. This exposure time is the most optimized result of considering the homogeneity of the line width and the thickness of the mask. It is called “exposure time window.”
Fig. 9. Results of the “exposure time window.” (a) Dashed line denotes the dissolution speed after exposure for 110 s at different positions. (b) and (c) One grating period at the center and the edge after development for 10 s, respectively. (d) Result of the experiment observed under a 500-fold microscope after development. (e) Result of the experiment observed under a 5000-fold microscope after development.
Compared with the result of exposure for 100 s, the mottled color is reduced and the inhomogeneity caused by $\Delta {I_T}(x )$ at the bright fringe is nearly overcome. When observed under a microscope, the line width at this time length is the most optimized, and thus, exposure time is highly appropriate for our experimental conditions. Simultaneously, if exposure time is closer to the “exposure time window,” then the range of development time during which good results can be achieved will also be larger, as determined through simulation and experiments. During the simulation, development time within the range of 8–13 s can obtain good line width and masking thickness. This finding is consistent with the experimental results.
Meanwhile, for an exposure time near the “exposure time window,” such as exposure for 105 s and development for 11 s, the experimental and simulation results show that the final mask results are nearly the same as the results of exposure for 105 s and development for 10 s. That is, when exposure time is slightly excessive (or insufficient), a good result can be obtained by shortening (or extending) development time. Therefore, the “exposure time window” is highly significant for fabricating large-area grating masks.
Through Eq. (11), Eq. (13) and Eq. (14) these equations, the change of the grating profile can be calculated and simulated. According to the simulation results and fabrication requirements, the “exposure time length window” can be got roughly. Taking the data in Table 1 as an example, the required duty cycle of grating is 40%, the difference of duty cycle on substrate is no more than 5%, and the mask thickness is above 300 nm. Considering the exposure time and development time at two extreme positions - the periods at center and the edge, the time required at other substrate positions should be between these two periods theoretically. The exposure time and the corresponding development time range was calculated and shown in the Fig. 10. The violet area represents for the period at center, the relationship between the exposure time and the development time range. The cyan area represents for the period at edge, the relationship between the exposure time and the development time range. The overlapping part of two areas means a grating fabricated in this exposure time and development time range will meet the requirements, and outside this part the result will be poor. Of course, to keep the development time range with an appropriate width, the “exposure time length window” will be a little shorter, as shown by $\Delta t$ in the Fig. 10. The asterisks in the picture represents the grating fabricated with the corresponding exposure and development time in actual experiment. Orange asterisks represents that the fabricated grating meets the requirements, and gray asterisks represents that the fabricated grating does not meet the requirements. The experimental results are basically corresponding with the simulation results, so the exposure time window can be determined according to actual requirements in this way. If the period of the grating is unchanged, and the thickness of the photoresist is increased but below 1000 nm. According to the simulation results, after exposure and development process the grating can maintain good uniformity. Of course, due to the change of the thickness, the “exposure time length window” and development time need to be re-determined.
Moreover, according calculation result it can be found that the exposure time window can appear only when the appropriate beam expander is selected. Therefore, it is necessary to calculate an appropriate light intensity and select a proper beam expansion aperture according to the above model, before establish the experimental light path.
4.4 Exposure time is too long: dark stripes also dissolve quickly
If exposure time is increased again above the “exposure time window,” then the photoresist will be overexposed. During this phase, the dissolution speed of the photoresist at ${I_{min}}$ also reaches a higher value, and the dissolution speed gap between ${I_{min}}$ and ${I_{max}}$ decreases. In such case, if the development time is short, then the center area stripes can be maintained but the edge area dark stripes will remain thick, as shown in Figs. 11(b) and (c). However, extending development time frequently causes the grating to have no stripes in the center area but still have some in the edge.
Fig. 11. Results of overexposure. (a) The dashed line denotes the dissolution speed after exposure for 150 s at different positions. (b) and (c) One grating period at the center and the edge after development for 4 s, respectively. (d) and (e) One grating period at the center and the edge after development for 8 s, respectively. (f) Result of the experiment observed under a 500-fold microscope after development.
The result presented in Fig. 11(f) shows that light power changes at this time as indicated by the light green area in Fig. 3, making the dissolution speed of the dark stripes at different parts evident. The overall grating becomes extremely mottled again, the color difference in various areas is highly evident, and the photoresist disappears completely in some areas. These conditions represent the typical result of the overexposure effect. In the experiments and simulations, dissolution speed becomes extremely fast after overexposure, and the stripes on the silicon substrate may change from underdeveloped when the stripes do not bottom to overdeveloped when the stripes are completely dissolved within the development time change of 2–3 s.
5. Experimental device and experimental results
In the experiment, we build a Mach–Zehnder interference optical path, as shown in Fig. 12. The emitted beam is first collimated and then split into two equal beams. The split beam passes through the mirror, the spatial filter, the small aperture diaphragm and the collimator lens on the exposure surface, forming light and dark stripes.
The laser used here is a single longitudinal mode He–Cd laser (KIMMON-KOHA). The wavelength of the emitted beam is 442 nm, which is the photoresist sensitive wavelength, and the rated output power is 180 mW. However, the actual output power is 126 mW during the experiment. The collimator lens is a plano-convex lens, its focal length is 300 mm, and its diameter is 75 mm. The substrate of the grating is a 50 mm double-sided polished silicon wafer, and the photoresist is S1805. Firstly, the silicon wafer was pre-baked at 115 ℃ for 15 min, then the photoresist was coated under the parameters of low-speed rotation of 500 rpm, 5s and high-speed rotation of 3000 rpm, 40s. After the photoresist coating is completed, the film is dried at 115 ℃ for 90s. The light intensity at the center of the substrate is 1.47 mW. Finally, when exposure time is 110 s and development time is 10 s, we fabricate a grating in which the diameter of the uniform area is more than 30 mm and the average duty cycle is 0.43.
The actual large-area photoresist grating is observed through AFM, and the period and duty cycle are calculated at different positions. The results are presented in Fig. 13. The grating exerts a good diffraction effect on the entire plane as shown in Fig. 13(a). Meanwhile, Fig. 13(b) displays the 13 positions we measured. The distance between each position is 5 mm. The entire measured area is a circle with a diameter of 30 mm. A highly uniform period and line width can be observed, as shown in Fig. 13(c). The diameter of the grating meets the design requirement of larger than 30 mm. This result is obtained with the laser which output power is only 126 mW, if using a laser with higher output power, the larger grating can be fabricated by this method.
Fig. 13. (a) Fabricated large-area grating with a uniform period and duty cycle. (b) Partial diagram of AFM marking point locations. (c) AFM observation result diagram. The sub-icon number corresponds to the position in (b).
The average period and duty cycle at each position are measured on the basis of the AFM scan data. As indicated in Table 2, the positions also correspond to those in Fig. 13(b). The data in Table 2 show that the period of the entire grating is highly uniform and consistent with the designed period of 550 nm, and the deviation is less than 1%. The duty cycle at the 13 positions is also the same, the average is approximately 0.44, and the difference between the edge and the center is less than 4%. These data indicate that the Gaussian beam, stray light, and flaws of the lens mentioned earlier are overcome by controlling exposure and development time. The entire area exhibits high uniformity.
Table 2. Period and duty cycle of the grating measured via AFM
6. Conclusion
By controlling exposure time within an appropriate “exposure time window” and selecting an appropriate beam expansion aperture in the optical path, we reduced the inhomogeneity caused by the flaws of the lens and stray light and established a large-area grating with a uniform duty cycle. We simulated the influence of exposure and development time lengths on the homogeneity of the grating, and the final experimental results observed via AFM were consistent with the simulations. Finally, a grating with a uniform duty ratio larger than 30 mm in diameter was fabricated. The deviation of the period was less than 1%, and the deviation of the duty cycle between the edge and the center was less than 4%.
Funding
Shenzhen Fundamental Research Funding (JCYJ20200109143006048, JCYJ20200109143008165); Shenzhen Supporting Fund for National Project (GJHS20160331183418317); National Natural Science Foundation of China (51835007).
Acknowledgments
Part of this research was conducted at the Testing Technology Center of Materials and Devices of Tsinghua Shenzhen International Graduate School of Tsinghua University.
Disclosures
The authors declare no conflicts of interests.
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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