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Abstract
Blazed gratings play a key role in advanced fields such as metaverse, AR and VR, etc. A good triangular cross section morphology is critical for its performance and applications. To investigate how triangular blazed gratings are evolved from rectangular masks, blazed gratings were fabricated by ion beam etching process. A new theoretical model called six-surface intermediate (SSI) model is proposed to explain the morphological evolution from rectangular homogeneous masks to triangular blazed gratings. The actual morphologies of blazed gratings with different process parameters were characterized by scanning electron microscopy. These observations confirm the correctness of the new model. Our research is of important guiding significance for the fabrication of blazed gratings with controllable morphology.
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1. Introduction
The blazed grating, known as the small step grating, is a type of high-performance optical component with periodic sawtooth structure [1,2]. Because of its characteristic, blazed gratings have important applications in AR/VR. In fact, the most important component in AR/VR is the imaging system. The images produced by the system are commonly under the function of couple-in and couple-out. However, what causes couple-in and couple-out of the waveguide is diffractive gratings. Actually, there are so many types of diffractive gratings. In order to decrease light intensity of couple-out process, Triangular blazed gratings which possess a high efficiency are commonly suggested. They can make the zeroth order of diffraction on a single slit be staggered with the zeroth order of interference between the slits when light shines on the working surface of blazed gratings slits [3,4]. Therefore, it makes the optical coupling efficiency of diffracting towards the eye reach the highest and is the best choice for AR/VR devices. What’s more, because it can make the optical path deflect and the obtained optical signal more pure, blazed gratings have also been widely used in grating monochromator, precision measurement instruments and other fields [5–7].
Figure 1(a) shows the schematic diagram of blazed gratings. The quality of blazed gratings is determined by blazed angle, anti-blazed angle, blazed surface. There are many technologies to fabricate blazed gratings, such as mechanical ruling, wet etching, electron-beam lithography, ion beam etching and so on. Mechanical ruling is direct and convenient, but the main disadvantage is that the processing cycle is long while the lifetime of the equipment is short [8]. Wet etching is isotropic, and there is always a small platform left on top of the grating groove after etching [9]. This leads to stray light and decrease in diffraction efficiency [10]. Electron-beam lithography can control the morphology of blazed gratings directly [11]. However, this method requires a long exposure time and the equipment is complex and costly. Ion beam etching removes materials and forms blazed gratings structures by argon ion sputtering [12]. This method has good directivity and the etching rate is controllable, thus the pattern etched can have good steepness. Because it is a physical etching, it can etch almost any material. The shapes of blazed gratings can be adjusted conveniently by changing the ion beam incident angle. This method is widely used in the field of semiconductors because of its high resolution and excellent anisotropy.
Fig. 1. (a) Schematic diagram of blazed gratings; (b) the SEM image of homogeneous masks morphology; (c) Schematic diagram of ion beam incident angle.
Generally, blazed gratings are made of materials with high reflective efficiency, such as glass, aluminum, etc [13,14]. However, these materials are difficult to be etched in the actual process, which makes large-scale production difficult to realize [15]. Nano-imprint technology has been proposed to solve this problem. Silicon is often used to fabricate templates for nano-imprint because of its high hardness [16]. During the etching process, different etching rate (ER) of photoresist (most used etching masks) and silicon will result in distinct steps at their interfaces. This phenomenon can negatively impact the formation of blazing gratings [17,18]. Homogeneous masks, means the material of masks is the same as the substrate, have been proposed to alleviate this problem in recent years [19,20]. Peiliang Guo et al. analyzed the relationship between blazed angles and incident angle of the ion beam when using homogeneous masks. Quan Liu et al designed the convex dual-blazed grating to realize higher and uniform diffraction efficiency [21]. Extensive research on the fabrication of blazed gratings had been done but the evolution of blazed gratings morphology during the etching process has not been studied systematically.
In this paper, experimental data were analyzed and found that there will always be a series of intermediate states in the etching process. Therefore, a Six-surface intermediate model (SSI model) was proposed to analyze the evolution process from homogeneous masks to blazed gratings in detail. To verify the correctness of the model, experimental tests were designed in the different incident angles. Ion beam etching was adopted in the experiments involved and the etching intermediate states were characterized by Scanning Electron Microscope (SEM).
2. Experimental
2.1 Sample tools
In this work, the sample was 8-inch silicon substrates with homogeneous masks on them, provided by Jiangsu Leuven Instruments Co. Ltd. The morphology of samples used is shown in Fig. 1(b). The period of the masks was ∼410 nm with the linewidth of 119 nm and masks height of 315 nm. The duty cycle was ∼29%.
Morphological characterization is performed by Hitachi 8200 scanning electron microscopy. The acceleration voltage, magnification and working distance were set at ∼5 KV, 80 K and 8∼9 mm, respectively. Ion Beam Etching (IBE) equipment used is Jiangsu Leuven Instruments Lorem with the sample stage can be adjusted from - 90° ∼+80°. As shown in the Fig. 1(c), the incident angle refers to the angle between the ion beam and the normal of the sample holder thus the equipment can achieve different ion beam incident angle.
2.2 Details of the theoretical model
As shown in Fig. 2(a), the incident angles of the ion beam are divided into three types according to the period, critical dimension (CD) and height of the masks. If the point A (bottom of masks that connect with the substrate) in the graph can be etched by ion beam from the beginning of the process, the incident angle of this situation is defined as medium angle. The expression for the medium angle is as follows:
Fig. 2. Different ion beam incident angles: (a) Small angle; (b) Medium angle; (c) Large angle; (d) Diagram of masks; (e) Diagram of SSI model; (f) Evolution of surface IV of SSI model
The incident angles smaller than medium angle are defined as small angles, otherwise they are large angles (The definition of large and small angles is based on the premise that there should be enough ER at this angle). It should be noted that this situation of medium angle is a momentary state thus it cannot be discussed by relevant experiments.
Based on our daily experiments, we found there are always six surfaces in the process of etching the blazed gratings, and the evolutionary trend of each surface depends on the incident angle. Therefore, SSI model was proposed. Figure 2(d) and (e) show the process that rectangular homogeneous masks evolve into SSI model. When the ion beam is incident from the upper right direction, surface I is the gap surface that is not shielded by the homogeneous masks; therefore, it is etched from beginning and form a slope. Surface II is the gap surface shielded by homogeneous masks, and therefore it is not etched yet. Surface III is the side of the homogeneous masks opposite to the direction of the incident ion beam; therefore, it maintains the vertical profile. Surface V is the side of the homogeneous masks bombarded by the ion beam, which transforms into one or two slopes during the process. Surface VI only appears at small incident angle because the gap between masks is shielded. Surface VI merges into surface V at medium or large incident angle. Surface IV is the top of the masks and its evolution relates to the ER of metals. The details will be discussed in the following sections. This paper seeks to explain how SSI model can be used to explain the morphological evolution from rectangular homogeneous masks to triangular blazed gratings.
As shown in Fig. 2(f), surface IV can be further modeled by three sub-surfaces: IV-1, IV-2, IV-3. This is because the two top corners of the homogeneous masks are most exposed and susceptible to etching and will be sputtered away first. Once these three surfaces are formed, the surface with the highest sputtering yield (ER) will dominate the evolution direction of surface IV. Therefore, there are three possibilities for the evolution of surface IV. When ERIV-1 is larger than ERIV-2 and ERIV-3, surface IV-1 dominates the etching trend and this surface will expand while surface IV-2 and IV-3 shrink. This continues until the morphology of the entire surface IV is consistent with IV-1. Finally, this surface will evolve into a part of the blazed surface. When ERIV-2 is larger than ERIV-1 and ERIV-3, surface IV-2 dominates the etching trend and expands until the whole surface IV is in a flat platform. Therefore, the rectangular masks will evolve into a trapezoid rather than a triangular grating in this case. When ERIV-3 is the largest, the principle of the evolution is the same with mentioned above, and surface IV will evolve into a part of anti-blazed surface in the end.
When the ion beam is incident at a small angle, the detailed process of evolution is shown in Fig. 3 (a), (b) and (c) show three cases when the ERIV-1, ERIV-2, ERIV-3 is the largest. In this incident angle, the gap of the rectangular masks can be divided into two parts because of different shielding effect. The part of gap where it is exposed to ion beam evolves into surface I and the other part evolves into surface II. Due to the right side of the rectangular masks can be etched by the ion beam all the time, surface V formed and will be etched towards the left and keeps vertical.
Fig. 3. Small incident angle of SSI model, (a), (b), (c) indicates the evolutionary process when the ERIV-1, ERIV-2, ERIV-3 are the fastest respectively.
When the ion beam is incident at a large angle, the process of evolution is shown in the Fig. 4. In this case, since the gap part of the masks is shielded and cannot be etched, the homogeneous masks exposed to the ion beam is modified for a period of time at first. The upper part of the right-side of the masks will be etched and evolve into surface V-1 while the remaining part of right side evolve into surface V-2. When the height of the masks reduces to the point where the ion beam just enough can etch the gap area, its evolution principle will be the same as that under the small angle mentioned above from this moment. Detailed evolutionary processes can be seen from Fig. 4.
Fig. 4. Large incident angle of SSI model, (a), (b), (c) indicates the evolutionary process when the ERIV-1, ERIV-2, ERIV-3 are the fastest respectively.
To sum up, the evolution of surface I∼ VI depend on the incident angle. These surfaces will evolve into blazed surface and anti-blazed surface respectively in the end.
3. Results and discussions
According to the SSI model, we can explain how the homogeneous rectangular masks evolve into blazed gratings at different incident angles. Therefore, the following experiments were designed to verify the applicability of SSI model. Relevant parameters of Experiment 1∼4 are shown in the Table 1 below.
Table 1. Experimental parameters
Firstly, the ER data collected at different incident angles are plotted in Fig. 5. The ion energy, ion beam current, acceleration voltage and the working pressure were the same with the parameters above. The gas used was argon and the incident angles were set to 10° ∼ 60°. It can be seen that the maximum ER is ∼43 nm/min when the incident angle of the ion beam is ∼50°.
Fig. 5. Etch rates of silicon at different incident angles of argon ion beam. (Inset image. Angles between ion beam and normal of surface IV-1, IV-2, IV-3 at the same incident angle)
The same incident angle corresponding to surface IV-1, IV-2 and IV-3 are different as shown in the inset image of Fig. 5. The solid red arrow indicates the incident ion beam and the dotted line represents the normal line of the target surface. The incident angles correspond to three surfaces are α, β, γ and these three angles are different. Therefore, under the same incident angle, ERIV-1, ERIV-2 and ERIV-3 will be different.
As shown in the Table 1, the Experiment 1 was designed to verify the model under the large incident angle. Argon was used and the incident angle was set to 60°. The etching time was set to 200, 300, 350, 400, 500 and 600 s.
At this incident angle, the gaps between the homogeneous masks and the whole left side of the masks were shielded in the beginning. Only the top part and upper right areas of the masks were exposed to ion beam and etched. Therefore, the height of masks became shorter and the right side of the masks became inclined, as shown in Fig. 6(a). In Fig. 6 (b), surface IV-3 started to dominate the evolutionary trend and make the surface change. When the homogeneous masks were etched to an appropriate height, the ion beam started to etch the gap area. Due to the stronger shielding effect of the masks at this large incident angle, surface III will be etched short when surface I began to be formed as shown in Fig. 6 (d). Therefore, the height of the pattern was short.
Fig. 6. SEM images of the intermediate state when the incident angle was 60° and etching time was (a)200 s (b)300 s (c)350 s (d)400 s (e)500 s (f)600 s.
In Fig. 7, the morphologies of Experiment 2 with the ion beam incident angle at 50° were shown. The etching time was set to 300, 400, 500 s. The evolution of surface I ∼ III and V is the same with the above experiment. The evolution of surface IV is special at this incident angle. The top of the homogeneous masks will also transform into three surfaces soon. However, surface IV-2 dominated the evolutionary trend in this case. If continue etching, the platform pattern of surface IV will exist all the time as shown in Fig. 7(c). Therefore, rectangular homogeneous masks will transform into a trapezoidal pattern as shown above.
Fig. 7. SEM images of the intermediate state when the incident angle was 50° and etching time was (a) 300 s (b) 400 s (c) 500 s.
In order to verify the correctness of this model at small incident angles, Experiment 4 with the ion beam incident angle of 20° was designed. The etching time was set to 100, 200, 250, 300, 350 and 400 s. The morphologies of the intermediate state were shown in Fig. 8 above. Because the CD of the homogeneous masks is small, surface IV-1, IV-2 and IV-3 were formed in 100 s and evolved into the pattern as shown in the Fig. 8 (a). The length of surface II is short because the gap of the masks was transformed into two parts and the part with the shielding effect is small. In this case, surface IV-1 dominated the evolution trend, it would make the tilt direction of surface IV be the same with surface IV-1.
Fig. 8. SEM images of the intermediate state when the incident angle was 20° and etching time was (a) 100 s (b) 200 s (c) 250 s (d) 300 s (e) 350 s (f) 400 s.
Because the whole right side of masks can be etched from the beginning at this incident angle, the surface V will be etched vertically. With the etching time increase, surface V kept etching and the length of surface VI became long. The included angle between surface V and surface VI gradually enlarges along with the time increasing. At the same time, the height of the graph gradually decreases. In the end, the two surfaces become one surface.
This evolutionary process can be seen from Fig. 8 (c) ∼ (f). Therefore, surface I ∼ IV will evolve into the blazed surface while surface V and VI evolve into anti-blazed surface by a small incident angle. Besides, surface V and VI need to take the appropriate time to evolve into anti-blazed surface, which will decide the pattern height of blazed gratings.
Experiment 3 with the incident angle at 40° was designed as shown in the Table 1. The morphologies of the process are shown in Fig. 9. When the incident angle is 40°, the varying tendency of surface V and surface VI is similar to that when the incident angle is 20°. The difference is that when the incident angle is 40°, the included angle between surface V and surface VI is larger, and the image height is relatively higher. Besides, surface IV-1 dominated the evolution trend of surface IV because of different ER of etch surface and it evolved into blazed surface together with surface I ∼ III while surface V and VI evolved into anti-blazed surface in the end. It was consistent with the above evolutionary process, which further confirmed the practicability of the SSI model.
Fig. 9. SEM images of the intermediate state when the incident angle was 40° and etching time was (a) 100 s (b) 200 s (c) 250 s (d) 300 s (e) 350 s (f) 400 s.
The height of the pattern with the incident angle of 20° and 40° are compared. During the etching process, the height of the pattern keeps decreasing because of continuous etching. However, the height of the resulting pattern at 20° is lower than that at 40°. This is because that the smaller the initial included angle of surface V and surface VI is, the longer time it takes for these two surfaces to evolve into one surface. Meanwhile, the etching amount will be relatively large, resulting in a lower blazed grating when the incident angle is 20°. To sum up, if a blazed grating with high pattern height needs to be fabricated, the incident angle of the ion beam needs to be increased as much as possible in a small angle range to achieve the goal according to its evolution principle.
4. Conclusion
In this work, an approach of explaining the evolution of etching blazed gratings is introduced and the SSI model is proposed. The model can qualitatively analyze the evolution of rectangular homogeneous masks into triangular blazed gratings at different incident angles. In this model, the ion beam incident angles are classified into three types: small, medium and large angles. The selection of the appropriate ion beam incident angle needs to be chosen according to the etching rates of different materials to avoid the generation of plateau morphology. When the incident angle is in the large angle range, it is important to evaluate whether these surfaces IV∼VI can evolve into a single one. If the pattern height of the blazed gratings obtained by etching is desired to be large, a large angle value can be selected as much as possible in the small angle range. The theoretical model has been verified by actual process to ensure its accuracy. Therefore, almost any shape that appears during the evolution of the blazed gratings can be explained by the SSI model. Our new theoretical model is an important reference for ion beam etching of the blazed gratings.
Funding
Postgraduate Research & Practice Innovation Program of Jiangsu Province (2021XKT1248); National Foreign Experts Bureau High-end Foreign Experts Project (G20190114003); Industry-University-Research Cooperation Project of Jiangsu Province (BY2020462); Key Projects of the Ministry of Science and Technology of the People’s Republic of China (SQ2020YFF0407077).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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