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Abstract
Gratings produced by two-spherical-beam Laser Interference Lithography (LIL) will have a nonuniform period, and the associated period variation is larger with the increase of the substrate size. This work quantitatively investigates a noninvasive method for improving the period variation on 4-inch silicon wafers. By temporarily deforming the flexible silicon wafer using a customized concave vacuum chuck [J. Vac. Sci. Technol. B 19(6), 2347 (2001) [CrossRef] ], we show that the fabricated gratings will have improved period uniformity, with the period variation reduced by 86% at the 1000 nm central grating period setting. This process is a simple and efficient way to achieve linear gratings without altering the LIL configuration with two spherical beams. We present experimental results on the impact of a concave vacuum chuck on the chirp reduction at different grating period settings. Then, we compare two different LIL configurations with different wavelength sources concerning their influence on the efficiency of period variation reduction. Finally, the flatness of the 4-inch silicon wafers due to the temporary bending process is verified using optical profilometry measurements.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Grating structures are of great interest in laser applications and nanotechnology and can be used as antireflective mirrors and optical filters for wavelength and polarization stabilization [1–5]. Several techniques are used to develop periodic structures, such as nanoimprint lithography or e-beam lithography [6–9]. However, these techniques are limited in patterning area, time, cost, and throughput. The Laser Interference Lithography (LIL) technique provides a fast and cost-effective way to pattern grating structures on a large area [10–12]. Spherical-beam LIL is based on the interference of two coherent spherical beams to form a grating pattern that can be inscribed on a photoresist. The grating periods recorded on the photoresist depend on the wavelength of the laser beam and the half-angle of two incident beams [13]. To manufacture high-quality grating structures with LIL, uniformity of the gratings over the whole area in terms of period, line width, and groove depth need to be optimized. Two spherical-beam interference on a flat exposure surface gives rise to nonlinear period variation due to two effects [14]. First, the interference angle of two rays decreases with the local position away from the center of the substrate. Second, the angle of inclination of the fringes on the substrate changes along the center so that the recorded gratings will be of a larger period than the interfering fringes. A comprehensive investigation of this effect, typically described as period chirp, is given in [15]. Uniform period gratings can be obtained using the conventional LIL setup with collimating lenses and spatial filters to generate interference of coherent plane waves or collimated beams in the Lloyd mirror configuration [16–19]. However, this configuration will have phase errors well above the appreciable limit due to the imperfections found in the lenses, mainly their flatness, roughness over the entire area, and the dust on the filter mirrors will degrade the beam quality, creating speckles and scattering in the printed grating. Scanning-beam LIL-based approach is an efficient method to generate linear-phase gratings, but this method suffers from stitching errors and throughput issues [20,1]. Here, we present a quantitative investigation of reducing the period variation by temporarily bending the substrate into a spherical shape during the LIL exposure using a custom-designed concave vacuum chuck [14]. This approach shows an excellent suppression of non-linear phase error on a 4-inch substrate without damage during the bending process. This investigation provides strong proof of a simple and inexpensive way to reduce the period variation of large-area gratings significantly. This work is the first step towards optimizing the LIL technique to achieve a uniform grating period over a large area grating. With the obtained proof by experimental investigation, the next step of this work will be on the optimization to achieve a uniform duty cycle and grating depth. Therefore, in the big picture, the main objective of this work is to demonstrate the simple and corrected LIL setup in producing high-quality gratings without using complicated optical elements. This corrected LIL setup can produce gratings master in developing grating waveguide structures (GWS) which will have many applications such as pulse compressors [21–2], and intra and extra-cavity grating mirrors for high-power laser systems [22–24]. The use of this work is then only limited by the type of substrate used.
2. Two-spherical-beam laser interference lithography
2.1 Period variation on a flat substrate
In a two-spherical-beam LIL setup, as shown in Fig. 1, the interference is achieved by two beams with spherical wavefronts. These spherical beams, upon interference, produced a hyperbolic interference pattern on a flat exposed substrate due to two effects [14]. First, the interference angle of the beam changes along the substrate, decreasing with position away from the center. Secondly, the fringe inclination changes along the substrate giving rise to a larger grating period than the interference fringes at the center.
The approach of bending the substrate during the exposure to correct for this period chirp was proposed by Walsh and Smith [14] in 2003. By applying a spherical curvature, they already showed a reduction of the period chirp, although no full elimination could be achieved. The reason for this was investigated by Bienert et al., who showed that a spherical bending could not create an ideal compensation for the chirp. The ideal surface to obtain the “zero-chirp” geometry is given by the rotation of the solution of a first-order differential equation [25]. However, Bienert et al. also showed that a spherical deformation already leads to a reduction of the chirp while having the advantage of comparatively easy mechanical implementation. For this reason, we also chose spherical deformation.
To calculate the expected period distribution, we used the approach shown by Bienert et. al. for the exposure case considering an arbitrarily shaped substrate exposed by convex wavefronts emitted by arbitrarily positioned point sources [15]. Using this formalism, the period on a point P on the substrate is calculated by
The vectors ${\vec{a}_S}$ and ${\vec{g}_{vex}}$ are given by
and
Fig. 2. Sketch of the spherically curved substrate with an exemplary point P and its normal vector ${\vec{n}_S}$ indicating the parameters used in Eqn. (1) to (5).
The laser source used to pattern the grating is a continuous wave HeCd laser source at a wavelength of 442 nm of output power 200 mW, and the distance (d) between the two single-mode fiber arms is 65 cm from Fig. 1. The aim period is 1000 nm. Using the presented equations, the expected period distributions for a 4-inch grating for both flat and curved exposure are calculated. Figure 3(a) shows the case of flat exposure where the maximum period increase is around 1.5 nm. In the case of curved exposure, shown in Fig. 3(b), the period chirp is much smaller, having a maximum period variation of only 0.4 nm.
Fig. 3. Calculated period distributions with the equations from Bienert et al. [15]. The color scale indicates the period. (a): Flat substrate. (b): Curved substrate with a radius of curvature of 1000 mm.
2.2 Deformation of a flat substrate
To obtain the desired curvature of the substrate, a concave vacuum chuck is custom-made using aluminum alloy-3D printing. As shown in Fig. 4, the substrate on the concave chuck will take the curvature shape upon applying the vacuum beneath the substrate. To achieve the substrate bending successfully, the wafer must be flexible with a thickness of 525 µm compared to its size of 4 inches. The lowest ratio of substrate thickness to its size will yield elastic deformation without the breakage of the substrate [26]. The radius of curvature of the concave vacuum chuck is designed for 100 cm. For good quality large-area gratings, the wafer must be of a planar surface. The effect of deformation on the silicon wafer can be determined using optical profilometry.
Fig. 4. (a) Sketch of the bending process of a silicon wafer by concave vacuum chuck. (b) Image of concave vacuum chuck mounted on substrate holder stand with silicon wafer curved using vacuum supply.
3. Results and discussion
3.1 Period variation of flat exposure vs. curved exposure
In this section, the experimental results are presented by carrying out a series of grating period measurements on both flat exposed and curved exposed 4-inch gratings samples at 1000 nm. For the fabrication part, 4-inch silicon wafers of 525 µm are coated with S1805 negative photoresist of the thickness of about 600 nm by spin coating. The photoresist-coated wafer is exposed to the interference fringes for 3 minutes and developed using MF319 developer at room temperature 21°C for 5 seconds, as seen in Fig. 5. The exposure was performed using a flat vacuum chuck and a concave vacuum chuck of 1000 mm curvature radius.
The period measurement of the patterned 4-inch wafer samples is measured along the x-axis and y-axis using the Littrow configuration optical setup. The data obtained are plotted for the period variation along the x-axis and y-axis concerning the position of the wafer sample.
Fig. 5. Photograph of fabricated photoresist grating on a 4-inch silicon wafer of thickness 525 µm using concave vacuum chuck holder by two-spherical-beam 442 nm LIL setup with an exposure time of 3 minutes and developing time of 5 seconds at 21°C.
Figure 6 shows that the periodic variation of flat exposure is improved by using the concave chuck to make the curved exposure. The period variation of the flat exposed sample is 1.41 nm. With curved exposure, the period variation is reduced by 86%, with a maximum period variation of 0.2 nm. The error bars indicate the uncertainty observed during the experiment, with the Littrow angle varying due to the diffraction order beam spot resolution limit.
Fig. 6. A measured period variation on the x-axis of the silicon wafer exposed by two spherical waves. The orange plot (▴) is the period variation on the flat exposed substrate. The blue plot (●) is the period variation on the curved exposed substrate. The error bars reflect the uncertainty in the diffraction angle measurements.
The measurement for period variation is carried out along the y-axis for both flats exposed and curved exposed wafer samples. As shown in Fig. 7, the period variation for both flat and curved exposed samples is nearly the same on the y-axis, with the period variation correction being 24% with curved substrate exposure. Theoretically, the rotational axis around AB (Fig. 2) will result in the surface curvature being rotationally symmetric, and the period variation is eliminated. However, during the LIL exposure, the offset of the position of the concave vacuum chuck from the center alignment (vertical translation along the y-axis) will disturb the period correction along the y-axis. By aligning the concave vacuum chuck exactly in the center of the exposure, the bending of the substrate is perfectly rotationally symmetric, and the complete elimination of period variation can be achieved along the y-axis.
Fig. 7. A measured period variation on the y-axis of the silicon wafer exposed by two spherical waves. The orange plot (▴) is the period variation on the flat exposed substrate. The blue plot (●) is the period variation on the curved exposed substrate. The error bars reflect the uncertainty in the diffraction angle measurements.
3.2 Period variation at different grating period settings
The influence of different grating period settings in the two spherical-beam LIL optical setups on the period variation is studied by patterning the 4-inch wafer samples for grating periods 500 nm, 600 nm, 700 nm, 800 nm, 900 nm, and 1000 nm. The samples were patterned using both flat chuck and concave vacuum chuck. From Fig. 8, it is shown that period variation is more significant for the lower grating period setting. This is due to the interference angle of the two beams decreasing at the lower grating period than in the larger period setting. The curved exposed wafer samples show an excellent reduction in the period variation irrespective of the grating period settings. It can be observed from Fig. 8 that the measured period variation values for curved exposed substrates indicated by the blue dotted line ($\blacksquare$) follow the curve of the simulated value indicated by the solid blue line (●) with the parabolic fit even though the circular concave vacuum chuck is of spherical curvature. This difference is due to the silicon substrate following the parabolic shape during the deformation process rather than the spherical curvature shape, as estimated by the presented Eqn. (1) to (5). The parabolic shape is facilitated due to the vacuum hole present only at the center.
Fig. 8. Calculated and measured maximum period variation along the x-axis of the flat- and curved-exposed substrates for the grating period varying from 500 nm to 1000 nm. The solid orange plot (▴) is the calculated maximum period variation, and the dotted orange plot ($\blacksquare$) is the measured maximum period variation on the flat exposed substrates. The solid blue plot (●) is the estimated maximum period variation with the parabolic fit, and the dotted blue plot ($\blacksquare$) is the measured maximum period variation on the curved exposed substrates.
3.3 Period variation reduction using two LIL optical configuration
A concave vacuum chuck was implemented, and the measured period variation reduction was compared in two different LIL setups. For this experiment, the central grating period is set to 500 nm in both the LIL configuration. The difference in the two LIL configurations is given by their laser source employment and the optical element used for beam exiting, as specified in the Table. 1
Table 1. Key differences between the two LIL configurations
The period variation reduction with a 266 nm LIL setup is seen to be much better compared to the 442 nm LIL setup due to the shorter wavelength resulting in less divergence of beams, and the large distance between the sources will approximate the spherical waves to planar waves by increasing the source and substrate holder distance.
In Fig. 9, the orange plot (▴) shows the flat exposure of the wafer sample on a 442 nm LIL setup. The blue plot (●) indicates the flat exposure of the wafer sample at the 500 nm grating period setting on the 266 nm LIL setup. It is evident from the figure that the period variation of the flat exposed grating sample obtained by the 266 nm LIL setup shows a substantial reduction in the period variation with a maximum period variation of 0.40 nm.
Fig. 9. A measured period variation on the x-axis of the flat exposed substrate with two LIL optical set-ups for the grating period of 500 nm. The orange plot (▴) is the period variation on the flat exposed substrate using a 442 nm LIL setup. The blue plot (●) is the period variation on the flat exposed substrate using a 266 nm LIL setup.
The period variation is further improved in the 266 nm LIL setup by implementing the concave vacuum chuck. From Fig. 10, the period variation of the curved exposed sample on a 266 nm LIL setup with a maximum period variation of 0.06 nm at the edge is much lower than the curved exposed sample on a 442 nm LIL setup with a maximum period variation of 0.54 nm. To obtain near-perfect linear gratings on a large thin substrate, it is ideal to use the LIL configuration with the shorter wavelength laser source.
Fig. 10. A measured period variation on the x-axis of the curved exposed substrate with two LIL optical set-ups for the grating period of 500 nm. The orange plot (▴) is the period variation on the curved exposed substrate using a 442 nm LIL setup. The blue plot (●) is the period variation on the curved exposed substrate using a 266 nm LIL setup.
3.4 Substrate flatness analysis
The after-effect of the temporary deformation process of silicon wafers using a concave vacuum chuck on the flatness of the substrate itself was studied using optical profilometry. The surface topology is measured using the profilometer CHRocodile S by Precitec with the chromatic sensor of the measurement range of 1 mm. The sensor has a numerical aperture of 0.7 and a resolution of 35 nm along a vertical direction. The thin thickness of the 4-inch silicon wafer compared to its surface diameter provide good flexibility during the bending treatment. In Fig. 11(a)-(b), the plot shows the deflection height in the center of the substrate during the deformation. The maximum deflection height is measured to be 1.10 mm without the wafer breakage.
Fig. 11. Optical profilometry (a) Measurement data of deformed 4-inch silicon wafer during the vacuum treatment. (b) Surface topography of the wafer during the vacuum treatment. The maximum deflection at the center of the wafer is 1.10 mm.
The profilometry measurement was made after the bending treatment of the wafer sample for 30 minutes. As shown in Fig. 12, the horizontal axis indicated by the orange plot (▴) on the substrate maintains good flatness with a deviation of 1.17 µm compared to the measurement before the vacuum treatment indicated by the blue plot (●) with a maximum deviation of 0.8 µm.
Fig. 12. Optical profilometry measurement data of deformed 4-inch silicon wafer after the vacuum treatment for 30 minutes. The orange plot (▴) is the flatness of the wafer measured along the horizontal axis with a maximum deviation of 1.17 µm. The blue plot (●) is the flatness of the wafer along the horizontal axis with a maximum deviation of 0.8 µm.
4. Conclusion
The potential of implementing a customized concave vacuum chuck to reduce the period variation of large-area gratings developed using two spherical-beam LIL processes is quantitatively investigated. The concave vacuum chuck with a 100 cm radius of curvature is used to create grating patterns on 4-inch silicon wafer samples. The period variation of wafer samples patterned using flat and concave chuck are studied and compared. The period variation in the flat exposed grating substrate has a maximum period variation of 1.41 nm at the 1000 nm central grating period setting. The period variation is reduced by 86% on a curved exposed grating substrate. The period variation reduction is further improved by implementing the concave vacuum chuck in the LIL setup with a shorter laser wavelength of 266 nm and a larger distance between the sources and from the source to the substrate holder. The maximum period variation with the combination of concave chuck and the more extensive LIL setup is measured to be 0.06 nm at a 500 nm central grating period setting. The substrate flatness is verified using the optical profilometry measurement. The maximum deviation on the surface is 1.17 µm along the horizontal axis and a deviation of 4.31 µm along the vertical axis. By this quantitative analysis, implementing a concave vacuum chuck combined with the LIL setup of the laser source with a shorter wavelength is ideal for achieving near-perfect uniform period gratings in large substrates.
Funding
This project has received funding from the European Union’s Horizon 2020 research and innovation 256 program under the Marie Skłodowska-Curie grant agreement number (813159); Supported partially by the French 257 RENATECH+ network led by the CNRS, on the Nano Saint-Etienne platform..
Acknowledgment
The authors would like to thank the GREAT consortium partners for their support with the work on grating waveguide structures fabrication and the University Institutes of Technology of Saint-Etienne, France (Mechanical and Production Engineering department) for the manufacturing of the concave vacuum chuck.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available but may be obtained from the authors upon reasonable request.
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