Edge smoothness enhancement of digital lithography based on the DMDs collaborative modulation

The rough saw-tooth edge caused by the inherent microstructures of digital micromirror device (DMD) will reduce the quality of the lithography pattern. Comprehensively considering the manufacturing efficiency, precision and cost, we propose a DMDs collaborative modulation lithography method to improve the smoothness of the lithography pattern edge. Through combining two misaligned DMDs to collaboratively modulate exposure dose, the better edge smoothness can be achieved. Collaborative exposure with 1/2 DMD pixel misalignment and 1/4 DMD pixel misalignment are both implemented to form the step-shape lithography patterns. The experimental results show that the saw-tooth edge can approximate to a straight line when increasing the number of times of the collaborative exposure. Further error analysis indicates it is effective to improve the edge smoothness while ensuring the lithography quality by using the collaborative modulation lithography. These results indicate that the DMDs collaborative modulation lithography is a promising technique for fabrication of microstructures, which may be a solution for balancing the fabrication precision, efficiency and cost.


Introduction
Maskless digital lithography is an emerging technology, which is characterized by the outstanding advantages of low cost, high efficiency, great flexibility and simple process.Recent advances on digital micromirror device (DMD)based digital lithography have encouraged its wide applications, such as micro-optical fabrication [1][2][3][4], printed circuit * Author to whom any correspondence should be addressed.
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board manufacturing [5][6][7], microfluidic devices [8,9] and bioapplications [10,11].In digital lithography system, a DMD dynamically generates various UV patterns, controlling each micromirror to rotate to the 'ON' or the 'OFF' state.However, the lithography pattern is actually a pixel pattern due to the square microstructure of each micromirror.This pixel pattern will cause a rough saw-tooth edge, which will reduce the quality of the lithography pattern and hence cannot satisfy the increasing requirements of high-fidelity manufacturing of microstructures.
Conventionally, the higher demagnification projection lens is used to improve the smoothness of the lithography edge [12].However, the imaging field of view is significantly decreased as the demagnification of the lens increases [13], accordingly, the production throughput is decreased.
Alternatively, reducing the single pixel size of DMD can also improve the edge smoothness [14], but the smaller micromirror will aggravate the diffraction effect and affect the energy utilization efficiency and the spatial distribution of diffraction order [15,16].Besides, once the single DMD pixel reduces to 5.4 µm while guaranteeing a sufficiently large exposure area, the cost of DMD will be doubled to the current mainstream single pixel 10.8 µm.
Recently, various exposure methods have been proposed to improve the fidelity of the lithography pattern.For flexibly fabrication large-area microstructures, a digital oblique scanning lithography strategy is proposed to enhance the lithography pattern quality [17][18][19][20][21][22][23].A DMD-based lithography method using wobulation technique [24,25] is presented to improve the edge smoothness of the lithography pattern to a certain extent, which implements a static exposure by the motorized stage vibration.In order to improve the applicability of the DMD-based wobulation technique, a method combing the wobulation technique with the DMD continuous scanning is proposed [26].Later, a spatiotemporal modulation projection lithography technique is proposed to improve the edge smoothness, which is a spatiotemporal modulation technique applied to the conventional digital lithography [27,28].All the above works combine a single DMD lithography system with a high-resolution motorized stage, which uses the linkage of the motorized stage scanning, the DMD pattern and the exposure time to complete the exposure process.However, the repetitive scanning is time-consuming, which causes the decrease of the fabrication efficiency and the increase of the error introduced by the position accuracy.In addition, in order to decrease the position error introduced by the repetitive scanning, high demand for the positioning accuracy of the motorized stage becomes prominent.There is no doubt that all the abovementioned methods can improve the quality of lithography pattern to a certain extent, but the lithography resolution of the above works may only be achieved to the submicrometer region, which is close to the micrometer scale.
In this work, we report a DMDs collaborative modulation lithography method to improve the smoothness of the lithography pattern edge, which uses two misaligned DMDs to collaboratively modulate the exposure dose.This method we proposed makes full use of matching the misalignment distances and the number of times of the collaborative exposure to achieve the better resolution of lithography pattern.The lithography resolution of DMDs collaborative modulation is related to the misalignment distances between two DMDs and can be enhanced to the deep submicron scale theoretically.With the proposed method, step-shape lithography patterns are formed by combining different misalignment distances and collaborative exposure times.As a result, the saw-tooth edge can approximate to a straight line when increasing the number of times of the collaborative exposure.The error analysis of the saw teeth indicates the correctness and the effectiveness of the DMDs collaborative modulation lithography method.Finally, the grating has been fabricated with the proposed method and then the lithography resolution of the DMDs collaborative modulation has been verified to be approximately 400 nm by measuring the grating lines.The experimental results and analysis demonstrate that the DMDs collaborative modulation may be an alternative technique for balancing the lithography resolution, the fabrication efficiency and the manufacturing cost.

Principle of DMDs collaborative modulation lithography
Figure 1(a) shows the DMDs collaborative modulation lithography scheme, including two light sources, two DMDs, two beam splitter prisms, a projection lens and a motorized stage.Two 5 W UV light-emitting diodes with center wavelengths of 365 nm are used as the exposure light sources.Two Texas Instruments DMDs act as reflective spatial light modulators and each is composed of 1920 × 1080 array of 7.56 µm wide micromirrors.The two DMDs are both parallel to the substrate plane, however, note that DMD1 is misaligned with DMD2 by a distance less than a single DMD pixel in both the horizontal and the vertical directions, as shown in figure 1(b).The UV light beam 1 is reflected by the reflector 1, and then incident on DMD1 at a spatial angle of 24 • .The modulated light beam by DMD1 is transmitted through the beam splitter prism 1(50/50 splitting ratio).Similarly, the UV light beam 2 is reflected by the reflector 2, and then incident on DMD2 at a spatial angle of 24 • .The modulated light beams respectively by DMD1 and DMD2 are coupled by the beam splitter prism 2 (50/50 splitting ratio).The coupled light beam is projected on the substrate placed on the motorized stage by a projection lens.The principle of the DMDs collaborative modulation lithography is demonstrated in figures 1(c) and (d).For the sake of convenience, the two DMDs are both simplified to 8 × 8 pixel arrays.The misalignment distances between two DMDs in the horizontal and the vertical directions are both equivalent to half a DMD pixel.The sub-pattern 1 in figure 1(c) is simultaneously input into DMD1 and DMD2 for the first collaborative exposure.Then the sub-pattern 2 is obtained by shifting the sub-pattern 1 a distance of a DMD pixel both in the horizontal and the vertical directions, which is simultaneously input into DMD1 and DMD2 for the second collaborative exposure.And so on until the sub-pattern n is obtained by shifting the sub-pattern 1 a distance of n-1 DMD pixels both in the horizontal and the vertical directions, which is simultaneously input into DMD1 and DMD2 for the n-th collaborative exposure.The later collaborative exposure is always overlapped onto the previous collaborative exposure.After n times collaborative exposure, the simulated exposure dose distribution with smoother edge can be formed as shown in figure 1(e).It's worth noting that the motorized stage always stands stationary in the collaborative exposure implementation.The improvement of the edge smoothness of the lithography pattern does not depend on the stage movement, but relies on the combination of the misalignment distances between two DMDs and the sub-patterns.Figure 1(f) shows the theoretical lithography pattern edge formed by the exposure respectively using a single DMD and the collaborative DMDs.Obviously the size of the saw tooth in the lithography pattern is limited by the size of a DMD pixel by using a single DMD.However, by introducing the two DMDs collaborative modulation exposure, the size of the saw tooth can be reduced by half in the case of misalignment distances of half a DMD pixel.
In the lithography implementation, the exposure dose the photoresist received is generally considered to be invariable whether choosing the single DMD lithography or the DMDs collaborative modulation lithography.Therefore, the total exposure time (T) for the above-mentioned two methods is considered to be equivalent.For the DMDs collaborative modulation lithography, each sub-pattern is actually exposed twice.Hence, the exposure time for each sub-pattern (t i ) can be written as equation ( 1): where i is the number of times of the collaborative exposure.The total exposure dose the photoresist received by using the DMDs collaborative modulation lithography is E: where I i is the exposure intensity modulated by the sub-pattern i.In order to ensure that the total exposure dose received by the photoresist is the same in the collaborative exposure, the exposure dose modulated by each sub-pattern should be reduced with the increase of the number of times of the collaborative exposure.However, in order to achieve a high smoothness in lithography pattern edge, the exposure time for each sub-pattern may be slightly increased in the real lithography.

Edge improvement simulation of step-shape pattern based on DMDs collaborative modulation lithography
To testify the DMDs collaborative modulation lithography, a step-shape lithography pattern is used to demonstrate the process of the edge improvement.In the simulation, for the sake of convenience, we only consider the saw-tooth edge in spite of the straight edges.Figure 2 shows the edge improvement process by using one time collaborative exposure.The misalignment distances between two DMDs in the horizontal and the vertical directions are mechanically adjusted to be equivalent to half a DMD pixel as shown in figure 2   As can be seen that the saw-tooth size is obviously reduced compared with the simulation result (figures 2(h) and (i)) using a single DMD. Figure 3 shows the edge improvement process by using two times collaborative exposure.The misalignment distances between two DMDs in the horizontal and the vertical directions are mechanically adjusted to be equivalent to 1/4 DMD pixel as shown in figure 3(e).Sub-pattern 1 is simultaneously input into two DMDs (figures 3(a) and (b)) for the first simultaneous exposure.Sub-pattern 2 is obtained by shifting the sub-pattern 1 a distance of 1/2 DMD pixel both in the horizontal and the vertical directions.Then sub-pattern 2 is simultaneously input into two DMDs (figures 3(c) and (d)) for the second simultaneous exposure.The exposure dose of the two times collaborative modulation are formed as schematically shown in figure 3(e).A partial region in figure 3(f) is magnified to demonstrate the exposure dose distribution under different modulation, as shown in figure 3(g).The black, the blue, the green, the pink and the white blocks respectively represent the regions corresponding to the exposure dose from 0 to 4. The two times collaborative exposure result of the stepshape lithography pattern is shown in figure 3(h).Figure 3(i) shows the region magnified in the yellow box of figure 3(h).It can be seen that the saw-tooth size is further reduced with the increase of the number of times of the collaborative exposure.During the developing, by reasonably controlling the process parameters, only the photoresist (eg, a positive photoresist) in the regions corresponding to the maximum exposure dose is totally stripped, and the photoresist in other regions is totally remained.
It can be clearly seen that the edge smoothness of the lithography pattern is related to the misalignment distance and the number of times of the collaborative exposure by the above simulation results.As shown in figure 4(a), the number of steps of the lithography pattern formed by the single DMD lithography is N 0 and the saw-tooth size is W 0 .For convenience, the saw-tooth size of the original mask pattern on DMD is always designed to be an integer multiple of the DMD pixel.Thus, W 0 can be written as follow: where M represents the number of the DMD pixels included in a saw tooth, σ is the demagnification factor of the projection lens and P is the size of a DMD pixel (7.56 µm in our lithography system).
The misalignment distances between two DMDs in the horizontal and the vertical directions are both configured to be equivalent to P/2i and then the shifting distances of subpatterns are P/i both in the horizontal and the vertical directions, where positive integer i denotes the number of times of the collaborative exposure.By being implementing M × i times collaborative exposure, the number of steps increases and it can be written as follow: The size of the saw tooth reduces and it can be expressed as follow:

Misalignment adjustment of two DMDs
Before the exposure experiment of collaboration modulation, the two DMDs should be mechanically adjusted to be misaligned.DMD1 is installed on a six-axis stage with nanometer precision.The adjusting method includes two steps.First, the two DMDs are mechanically aligned.We predesign an original mask pattern as shown in figure 5

Experimental results and discussion
In In order to further analyze the lithography quality by using the collaborative modulation lithography, we conduct the error calculation by choosing five continuous saw teeth in the lithography pattern.Figures 8(a)-(c) show the saw-tooth edges drawn according to the theoretical sizes and the measured sizes of the five continuous saw teeth respectively by using a single DMD lithography and collaborative exposure with 1/2 pixel misalignment and 1/4 pixel misalignment.In figures 8(a)-(c), the black solid lines connecting pentagrams represent the theoretical saw-tooth edge and the green dashed lines connecting triangles represent the actual edge.In addition, we calculate the absolute error and the average absolute error of the five saw teeth along the x and y directions respectively.Figure 8(d) shows the saw-tooth errors corresponding to figure 8(a), in which the average absolute error is 1.402% in the x direction  7(c)) observed at a 100 × magnification, (e) Lithography result observed at a 10 × magnification by using collaborative exposure in the case of misalignment distance of 1/4 DMD pixel, (f) a partial edge (red box in (e)) observed at a 100 × magnification.and 1.244% in the y direction.Figures 8(e) and (f) show the saw-tooth errors by using collaborative exposure with 1/2 pixel misalignment and 1/4 pixel misalignment.In figure 8(e), the average absolute error is 1.744% in the x direction and 1.426% in the y direction.Figure 8(f) describes the average absolute error as 5.410% in the x direction and 5.350% in the y direction.As we can see in figure 8, the absolute error and the average absolute error both increase with the decrease of the sawtooth size.Overall, the average absolute errors of the saw teeth denoted by the straight blue and red dotted lines in figures 8(e)  and (f) can be controlled below 6%, which illustrates that it is effective to improve the edge smoothness while ensuring the lithography quality by using the collaborative modulation lithography we proposed.
According to equation ( 5), for the fixed M, σ, and P, the saw-tooth size should be reduced by one time when the number of times of the collaborative exposure is increased by one time (namely the misalignment distance between two DMDs is reduce by half).Theoretically, in the case of M = 32, σ = 32 and P = 7.56, collaborative exposure with 1/2 DMD pixel misalignment leads to a saw-tooth size as 3.78 µm, and collaborative exposure with 1/4 DMD pixel misalignment leads to a saw-tooth size as 1.89 µm.However, the experimental results provide a 3.73 µm saw tooth for collaborative exposure with 1/2 DMD pixel misalignment and a 1.79 µm saw tooth with 1/4 DMD pixel misalignment, which seems representing a high-quality edge much smoother than the above theoretical calculation.Actually, the comprehensive effect introduced by the projection lens distortion, the developing process and the measuring error may greatly contribute to the better smoothness.
To further evaluate the edge quality by using the collaborative modulation lithography, we observe the step-shape lithography pattern fabricated with 1/2 DMD pixel misalignment  From figures 9(c), we can see that the edge of the steps does not descend sharply but gently.The descending slope is measured to be approximately 10.10 • .The gentle step edge may be caused by the insufficient exposure dose.So we may conclude that the collaboration modulation lithography may lead to the exposure dose decrease at the lithography patterns' edge due to multiple collaborative exposure.Actually, in the exposure process, we specially increased the exposure time for each subpattern slightly.However, the measurement result still shows the insufficient exposure at the step edge.
Note that the extent of improvement of the saw-tooth edge ultimately depends on the lithography resolution of two DMDs collaborative modulation system.Theoretically, different misalignment distances between two DMDs correspond to different lithography resolution.The resolution vertification experiment based on two DMDs collaborative modulation is carried out.We set the misalignment destances between two DMDs as half a DMD pixel.The grating fabricated by using the DMDs collaborative modulation lithography is shown in figure 10.The measurement results in figure 10 are respectively 0.40 µm by the optical microscope (100×) and 402.7 nm by the optical profiler (50×).After repeated experiments, it is found that the grating line becomes indistinguishable when we try to further decrease the grating line.Hence, the limited linewidth of the grating formed by two DMDs collaborative modulation method is approximately 400 nm, which may be affected by multiple factors such as the uniformity of the UV light source and the alignment of two DMDs.
For the single DMD lithography in our laboratory, the fundamental resolution of the optical system, which is limited by diffraction, can be approximately estimated to be 456 nm through Abbe's equation R = λ/2NA (λ = 365 nm, NA = 0.4).The DMDs collaborative modulation can be denoted by figure 11.Due to the spatial misalignment between two DMDs, three types of exposed regions are formed on the substrate.The white block represents the unexposed region.The rosy and light-green blocks both represent the exposed region modulated by a single DMD.The dark-green block represents the exposed region formed by two DMDs collaborative modulation, namely, the exposure dose of dark-green block regions is related to both the DMD1 pattern and the DMD2 pattern.Thus, the free control to the exposure dose of the dark-green block regions can be realized by collaboratively modulating the two DMD patterns.Obviously, the resolution of two DMDs collaboration (δ) is better than the resolution of single DMD (∆).δ is related to the misalignment distances between two DMDs.For example, if the misalignment distances between two DMDs are both half a DMD pixel in the horizontal and vertical directions, the theoretical resolution will be doubled to be 228 nm.The above grating fabrication results shown  that the lithography resolution of our two DMDs collaborative modulation system is superior to the theoretical resolution (456 nm) of single DMD system and inferior to the theoretical resolution (228 nm) of two DMDs system.

Conclusions
In this study, the DMDs collaborative modulation lithography is proposed to effectively enhance the edge smoothness of the lithography pattern.In particular, the lithography method we proposed creatively combines the two misaligned DMDs with their collaborative modulation to achieve the better smoothness, instead of commonly increasing the demagnification factor of the projection lens or reducing the DMD pixel size.Simulation results of a step-shape lithography pattern formed by using the DMDs collaborative exposure testify the better smoothness comparing to the single DMD lithography.Collaborative exposure with 1/2 DMD pixel misalignment and 1/4 DMD pixel misalignment are both implemented to form the step-shape lithography patterns.The experimental results show that the saw-tooth edge can approximate to a straight line when increasing the number of times of the collaborative exposure.Moreover, we conduct the error analysis of the partial saw teeth, and further demonstrate that it is effective to improve the edge smoothness while ensuring the lithography quality by using the collaborative modulation lithography.
However, there are still some problems in the application of the DMDs collaborative modulation lithography.First, the lithography resolution of DMDs collaborative modulation is inferior to the theoretical resolution due to multiple factors such as the uniformity of the UV light source, the alignment of two DMDs and the process parameters.Second, the cost of the two DMDs system indeed increases due to the addition of a DMD exposure light path at the achieved lithography resolution.If the lithography resolution of the proposed method can be further to enhanced to the theoretical resolution, it can be an alternative technique for balancing the lithography resolution, the fabrication efficiency and the manufacturing cost.

Figure 1 .
Figure 1.Schematic diagram of DMDs collaborative modulation lithography.(a) DMDs collaborative modulation lithography scheme, (b) schematic of the misalignment between two DMDs, (c) sub-patterns, (d) collaborative exposure, (e) simulated exposure dose distribution for the collaborative exposure, (f) schematic of the theoretical edges formed by using a single DMD and the collaborative DMDs.
(a).A subpattern is simultaneously input into two DMDs (figures 2(b) and (c)) for the simultaneous exposure on the same position of the substrate.The size of saw tooth in the sub-pattern is just equal to a DMD pixel.Then the exposure dose of the collaborative modulation is formed as schematically shown in figure2(d).A partial region in figure2(d) is magnified to demonstrate the exposure dose distribution under different modulation, as shown in figure2(e).The black, blue and white

Figure 2 .
Figure 2. Edge improvement process by using one time collaborative exposure.(a) Misalignment of 1/2 DMD pixel between two DMDs, (b) sub-pattern displayed by DMD1, (c) sub-pattern displayed by DMD2, (d) schematic of the exposure dose formed by the collaborative modulation, (e) schematic of the exposure dose distribution in the yellow box of (d) and (f) simulated collaborative exposure result of the step-shape lithography pattern, (g) region magnified in the yellow box of (f) and (h) simulated exposure result of the step-shape lithography pattern by using a single DMD, (i) region magnified in the yellow box of (h).
Figure 2(g) shows the region magnified in the yellow box of figure 2(f).

Figure 3 .
Figure 3. Edge improvement process by using two times collaborative exposure.(a) Sub-pattern 1 displayed by DMD1, (b) sub-pattern 1 displayed by DMD2, (c) sub-pattern 2 displayed by DMD1, (d) sub-pattern 2 displayed by DMD2, (e) misalignment of 1/4 DMD pixel between two DMDs, (f) schematic of the exposure dose formed by two times collaborative modulation, (g) schematic of the exposure dose distribution in the yellow box of (f) and (h) Simulated collaborative exposure result of the step-shape lithography pattern, (i) region magnified in the yellow box of (h) and (j) simulated exposure result of the step-shape lithography pattern by using a single DMD, (k) region magnified in the yellow box of (j).

Figure 4 .
Figure 4. Schematic of the number of the steps and the saw-tooth size.(a) Using the single DMD lithography, (b) using the collaborative modulation lithography.
(a).Then it is divided into two mask pattern numbered as 1 and 2 (figures 5(b) and (c)).The mask patterns 1 and 2 are input into DMD1 and DMD2 respectively.If the two DMDs are aligned, the superimposition results on the substrate by simultaneously projecting pattern 1 and pattern 2 should be the same as the imaging result by projecting the original mask pattern by a single DMD.CCD camera is used to monitor the image on the substrate.The quantitative measurement by CCD is introduced to evaluate the alignment.The widths in five positions in figure5(d) should be measured to be equal.If the widths in position 1 and position 2 are not equal, we consider there is an angular position deviation between two DMDs.If the widths in position 2 and position 3 are not equal, we consider there is a horizontal deviation between two DMDs.If the widths in position 4 and position 5 are not equal, we consider there is a vertical deviation between two DMDs.According to the measurement results of the five positions, we adjust the corresponding axis of the six-axis stage on the back of DMD1 until the widths in the five positions are all equal.Second, we adjust the X-axis and Y-axis of the six-axis stage to realize the misalignment distance of 1/2 DMD pixel or 1/4 DMD pixel.

Figure 5 .
Figure 5. Schematic of the alignment method of two DMDs.
figure 6(f), with the increase of the number of times of the collaborative exposure, the saw-tooth size is further reduced and the edge approximates to a straight line.The edge smoothness is increased by 76.42% comparing to the single DMD lithography.Howerver, it is found that both ends of the two sides forming the right angle in figure6(e) are curved to a certain extent.It may be caused by the variable exposure dose (0,1,2,3,4 in figure3(f)) appearing at the both ends of the two sides.After development, the relief of the end regions with variable exposure dose may change with a certain slope from the unexposed region to the exposed region with the maximum exposure dose.The above pattern deformation problem can be theoretically improved by the optimization of the sub-patterns.The principle of the optimization of sub-patterns is to eliminate the changes of exposure dose at the edges of lithography pattern.Figure7shows the process of the optimization of the sub-patterns.The desired region is denoted by the diagonal grids in figure7(a), which is the overlapping region by four original sub-patterns.Thus, four boundary lines can be obtained according to the upper, lower, left and right boundaries of the desired region.Then, the new sub-patterns can be extracted from the original sub-patterns in the square region surrounded by the four boundary lines, which is shown as the regions filled with sloping lines in figures7(b)-(e).In order to further analyze the lithography quality by using the collaborative modulation lithography, we conduct the error calculation by choosing five continuous saw teeth in the lithography pattern.Figures8(a)-(c) show the saw-tooth edges drawn according to the theoretical sizes and the measured sizes of the five continuous saw teeth respectively by using a single DMD lithography and collaborative exposure with 1/2 pixel misalignment and 1/4 pixel misalignment.In figures 8(a)-(c), the black solid lines connecting pentagrams represent the theoretical saw-tooth edge and the green dashed lines connecting triangles represent the actual edge.In addition, we calculate the absolute error and the average absolute error of the five saw teeth along the x and y directions respectively.Figure8(d)shows the saw-tooth errors corresponding to figure8(a), in which the average absolute error is 1.402% in the x direction

Figure 6 .
Figure 6.Step-shape lithography patterns observed by an optical microscope.(a) Lithography result observed at a 10 × magnification by using a single DMD (b) a partial edge (red box in (a)) observed at a 100 × magnification, (c) lithography result observed at a 10 × magnification by using collaborative exposure in the case of misalignment distance of 1/2 DMD pixel, (d) a partial edge (red box in figure 7(c)) observed at a 100 × magnification, (e) Lithography result observed at a 10 × magnification by using collaborative exposure in the case of misalignment distance of 1/4 DMD pixel, (f) a partial edge (red box in (e)) observed at a 100 × magnification.

Figure 7 .
Figure 7.The schematic of the optimization of the sub-patterns.

Figure 8 .
Figure 8. Deviation of the five continuous saw teeth.(a) Deviation between the theoretical and the measured saw teeth by using a single DMD lithography, (b) deviation between the theoretical and the measured saw teeth by using collaborative exposure with 1/2 DMD pixel misalignment, (c) deviation between the theoretical and the measured saw teeth by using collaborative exposure with 1/4 DMD pixel misalignment, (d) saw-tooth errors corresponding to (a) and (e) Saw-tooth errors corresponding to (b), (f) saw-tooth errors corresponding to (c).

figures 9 .
figures 9. Step-shape lithography pattern fabricated with 1/2 DMD pixel misalignment by optical profiler.(a) Two-dimensional measurement result, (b) three-dimensional profile, (c) two-dimensional profile distribution along the black line in (a).
using an optical profiler (MicroXAM, KLA-Tencor), as shown in figures 9. Figures 9(b) shows a three-dimensional profile of the step shape.Figures 9(c) shows a two-dimensional profile distribution along the black line in figures 9(a).

Figure 10 .
Figure 10.Experimental results of the grating fabrication by using the DMDs collaborative modulation lithography.(a) Formed grating observed by 100 × optical microscope, (b) 3D grating profile observed by 50 × optical profiler, and (c) measurement result by 50 × optical profiler.