*3.2. Fabricated Polymer Microstructures of Various Angles on a Flexible Substrate*

As shown in Figure 6, the polymer microstructure was fabricated on a single substrate with a single synchrotron X-ray exposure. The key to this development was that the tilt angle of the microstructures changed with the support structure. While the sample was irradiated with X-rays, the angle between the X-rays and the substrate of the microstructure determined the tilt angle of the microstructures. As shown in Figure 6a, when the exposure was performed with the PR attached to a convex support, the microstructures formed perpendicularly to the horizontal plane. When the substrate was flattened after separating the bent substrate from the convex support, the inclination angles of the microstructures were determined during exposure. For convex supports, the microstructures were inclined inwards at a greater angle as the position moved away from the center. Figure 6a shows a panoramic view of the tilted microstructures on a single substrate with tilt angles of 65◦, 55◦, and 45◦ as a representative data set. As shown in Figure 6a, the line, circle, and star microstructures had constant slopes at specific positions. For concave supports, the microstructures were inclined outwards at a greater angle as the position moved away from the center, as shown in Figure 6b. S-shaped supports were also used to fabricate microstructures on flexible substrates, as shown in Figure 6c. The S-shaped supports had two properties. The microstructures sloped inwards and outwards on the convex and concave supports, respectively.

One problem with the supports was that when a flexible X-ray mask was attached to the PR for exposure, some areas of the PR were pushed down when forces were applied to the flexible X-ray mask. In particular, it was difficult to attach the PR with a flexible X-ray mask on an S-shaped support because of its complicated structure. During the attachment, some deformation and damage occurred, and the height of the tilted microstructures varied at different positions. If slight deformation and damage occurred during attachment, the height of the tilted microstructures varied at different locations, as shown in Figure 6c.

**Figure 6.** SEM images of microstructures fabricated on the (**a**) convex support, (**b**) concave support, (**c**) S-shaped support.

We selected the line structure on the convex support to compare between the structures on the mask and the actual structures after the last processing step. The substrate of the tilted microstructures was attached to an aluminum block (Figure 7a). The block was placed on the stage of the stereo microscope (Stemi 2000-C, Carl Zeiss, Jena, Germany) with the lateral side up. The side images of the structures were recorded using a charge-coupled device (CCD) camera (Retiga 4000R; QImaging, Surrey, BC, Canada). A total of 39 angles were observed along a single row. The slanted angles were measured using the angle tool in the ImageJ software package (NIH, Bethesda, MD, USA). The measured angle was proportional to the position of the structure (Figure 7b). However, the distance from the center and the angle of the micropattern did not coincide exactly. The slopes from the experimental results were slightly higher than the calculated values due to detachment between the aluminum (AL) support and PI substrate. According to the angle measurement (Table S1), there was a gap in the center part, between the PI substrate and the support (Figure S3). When we placed the RP with the PI and mask on the Al support by hand, there was a slight air gap between the PI film and the Al support at the center.

**Figure 7.** Angle measurement of the tiled microstructures. The structures were observed by a stereo microscope with a charge-coupled device (CCD) camera. (**a**) Experimental setup, (**b**) Calculated angle vs. measured angle.

#### **4. Discussion**

#### *4.1. Interactions between the Beam Source and Materials*

The mask on top of the PR layer blocked the X-rays selectively via gold patterned on a PI substrate; the PI film acted as a structural support that was transparent to X-rays.

The micropatterns on the mask were made of SU-8 PR, which is transparent to X-rays. The background was a thick gold layer that absorbs X-rays; the SU-8 micropatterned area was selectively excluded from electroplating. The ratios of X-rays passing through gold and PI are shown in Figure 8a.

The flux of the beam on the mask was calculated by reference to the characteristics of the beam source, as shown in Figure 8b. Such analysis reveals not only the interactions between the electrons and the surrounding materials, but also the required gold thickness. We obtained a wide range of X-ray energies from the bending magnet, i.e., from a few volts to tens of kilo-electron volts (thus of both high and low energy). However, high-energy photons are detrimental, penetrating to the bottom of the PR and then scattering inappropriately into adjacent areas during X-ray exposure [22]. The schematic of Figure 8c shows a cross-section of the X-ray exposure in the lithography chamber. Such backscattered photons compromise structural accuracy and pattern/substrate adhesion. Also, backscattered photons that strike the edges of the structure damage those edges. Another problem associated with high-energy photons is secondary radiation. As photons pass through the PR, electrons emitted after photon absorption hit the walls under the gold mask (Figure 8c), thus degrading the wall. Therefore, mirrors were used to eliminate the high-energy photons with energies over 7 keV.

**Figure 8.** Experimental conditions for synchrotron X-ray lithography (XRL). (**a**) X-ray transmittance of the polyimide (PI) film and Au. (**b**) X-ray flux calculations before the beam entered the lithography chamber. (**c**) Schematic diagram of the exposure in the lithography chamber. PR, photoresist; MR, mirror; Be Win, beryllium window.

We calculated the thickness of the gold layer by calculating the X-ray flux and then estimating the dose incident on the PR numerically. The thickness of the gold was selected to minimize the transmission energy and was proportional to the product of the transmittance and the flux. The flux ejected from the linear accelerator fell by 66% after passing through the two Be windows (Figure 8b). The following equation [24] was used to calculate the number of transmitted X-rays (*STP*):

$$S\_{TP} = \ S\_M \times \exp(-\mu\_P \mathbf{x}\_P) \tag{1}$$

where *xP* is the depth, *SM* is the X-ray energy spectrum of the PR, and *μ<sup>P</sup>* is the absorption coefficient. The bottom doses should be about 90 J to promote cross-linking conditions. The thickness of the gold layer was calculated to be 10 μm. Thus, the SU-8 thickness must be >10 μm. The thickness was thus set to 12 μm, which was about 120% of the target thickness, with some margin.

#### *4.2. The Utility of the Fabricated Structures in Real Applications*

Again, we electroplated the microstructures with gold to make a mold for replicating the structure (Figure S4). We conducted a simple feasibility test to determine whether this mold can be used to fabricate microarrays for optical components, and tilted microchannels for many industrial applications. Further, the proposed development could also be applied to the manufacture of flexible electronics.

#### *4.3. Limitations of the Fabrication Process*

In the process described in Figure 4, both the substrate and the mask were bent. Due to the synchrotron beam being parallel across the entire FoV, there were deviations in the geometry over the whole FoV. There was a masking effect that resulted in a decreased structural width and increased structural height at the edge of the FoV. For 45◦ inclined structures, structures with a width of less than 12 μm were no longer illuminated by X-rays that did not partly pass through the gold absorber, thus reducing the dose absorbed by the resist. Theoretically, it is not possible to fabricate microstructures with critical dimensions less than the height of the mask pattern. The structures in this research were from tens of microns to a few hundred microns in height, so this effect was not obvious. This was not visible in the optical micrograph pictures of structures with a width of several 100 μm (Figure S2). However, it was of major relevance for the fabrication of structures smaller than the height of the mask pattern (12 μm).

The process can be modified to overcome this hindrance. For instance, the mask can be flat, and there can be a gap between the mask and the PR. In this case, the distance between the structures needs to be calculated exactly to achieve the desired pitch on the bending structure. In this research, we focused on providing a proof of concept and demonstrating the feasibility of using a simple dimensional transformation to produce polymer microstructures of various angles and shapes on a single substrate.

#### **5. Conclusion**

In this paper, we proposed a method of fabricating polymer microstructures with various angles on a single substrate by a simple dimensional transformation using synchrotron X-ray lithography. In the past, various techniques have been attempted to obtain various features on a 2D substrate, focusing on the exposure technology, material properties, and light source. Few research groups have attempted to create microstructures on 3D substrates. In this research, by the simple dimensional transformation of the substrate, we created tilted microstructures at various angles. Due to the high collimation of the synchrotron X-rays, microstructures with high aspect ratios could be realized simultaneously. The inclination angle of the microstructure changed depending on the support structure, which was at a constant inclination at each specific position. Three different-shaped supports: convex, concave, and S-shaped, were used to fabricate the microstructures. The microstructures had high aspect ratios of 1 to 11 for the line-shaped structures, and high inclination angles of 80◦ for the star-shaped structures. Further, the inclination angle of the microstructure can also be controlled by adjusting the degree of bending of the flexible substrate.

The developed method is simple, but can be extended to various microstructure applications. As a typical application, this technology can be applied to microarrays for optical components, and tilted micro/nanochannels for biological applications.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/1996-1944/11/8/1460/ s1, Figure S1: Experimental chamber, Figure S2: Photograph of the microstructure, Figure S3: Schematics of attachment of PI film on the Al support, Figure S4: Fabrication process of the electroplated mold. Table S1. Sampled measured angle, measured position of the microstructures, and the calculated position.

**Author Contributions:** For "Conceptualization, J.H.K.; Methodology, K.P., S.C.L. and K.K.; Validation, K.P. and K.K.; Formal Analysis, K.P. and K.K.; Investigation, J.H.K.; Resources, J.H.K.; Data Curation, K.P.; Writing-Original Draft Preparation, K.P.; Writing-Review & Editing, K.P. and J.H.K.; Visualization, K.P. and K.K.; Supervision, J.H.K. and G.L.; Project Administration, J.H.K.; Funding Acquisition, J.H.K."

**Acknowledgments:** K.P. thanks Daeil Kim for the help with imaging the samples using a scanning electron microscope (SEM). This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (No. 2015R1A2A1A14027903, No. 2017M3C1B2085309, and No. 2017R1D1A1B03032928), Innovation Program funded by the Ministry of Trade, Industry & Energy (MI, Korea) (No. 10048358). It was further supported by a Gumi Electronics & Information Technology Research Institute (GERI) (No. 40015088).

**Conflicts of Interest:** The authors declare no conflict of interest.
