1. Introduction

A sinusoidal grating with well-developed diffractive periodic structures is useful for optical measurements and testing [1]. Conventional fabrication methods include inscribing a polymer film that contains azobenzene moieties [2,3], and direct writing on photoresist according to a designed pattern and specific calibration data for a certain photoresist by an electron beam and a laser beam. The depth and period of the gratings is limited by the resolution of the photoresist and the polymer, but these parameters do not limit the one-step fabrication technique, which involves the design of a three-dimensional pattern directly onto the substrate without the need for pattern transfer. A simple one-step self-organized formation method with focused ion-beam (FIB) raster scanning on Si (100) was reported [4]. By virtue of the focused Ga⁺ beam with raster scanning, a surface relief structure with regular geometry of blazed gratinglike structures can be automatically formed in a defined scanning area. During the scanning process, the beam is deflected by high voltages and the stage is stationary. To raster scan, we scanned the beam in the defined area line by line from left to right. This process with spontaneous formation strongly depends on the substrate material. From our recent experiments, we determined that a sinusoidal structure can be generated by FIB bombardment on the substrate material of Ti–Ni thin film. Diffractive structures fabricated on Ti–Ni thin film are more suitable for use as gratings that work in the reflection mode than that of Si(100) because Ti–Ni thin film functions over the ultraviolet to near-infrared wavelength range By scanning the defined area point by point and line by line with fixed process parameters, one can form a sinusoidal structure spontaneously. This method differs from the conventional direct-writing technique because the beam intensity and the exposure time for each point in terms of the calibration data are changed according to the design pattern and provide a simple way to fabricate a diffractive structure. Different feature sizes (depth and period) can be derived by changing the process parameters.

2. Experimental setup

The milling experiments were carried out by our FIB machine (Micrion 9500EX) with an ion source of liquid gallium, integrated with a scanning electron microscope, energy dispersion x-ray spectrometer facilities, and gas-assisted etching. This machine uses a focused Ga⁺ ion beam with 5–50-keV energy, a 4-pA–19.7-nA probe current, and a 25–350-µm beam-limiting aperture. For the smallest beam currents, the beam can be focused down to a 7-nm diameter full width at half-maximum. The ion beam is focused on the sample surface with a normal incident angle. The ion beam raster scan, not patterned scanning, in the area of 12 µm×12 µm has milling process parameters of 0.3-nC/µm² ion dose, 2-Hz raster mode scanning frequency, 15-nm pixel space, 60% overlap, 100-pA beam current, and 25-nm beam spot size. The substrate was placed in the vacuum chamber at room temperature and not heated by any thermal coupler during sputtering. After milling for 19 min., the sinusoidal shape structure was self-formed at the bottom of the pattern. The formation of the sinusoidal structure is a spontaneous process during sputtering erosion under ion bombardment, which is a self-organized formation caused by a competition between smoothing driven by surface energy and roughening induced by sputter removal of material. The radiation-enhanced surface transport process resulting in surface smoothing in which relaxation by viscous flow (for amorphous materials) and surface diffusion (for crystal materials) plays a dominant role. Because the ion energy deposition rate increases as the ion penetrates the solid, concave regions are sputtered more than convex regions, resulting in a growing instability on the surface. This instability is opposed by a smoothing mechanism, e.g., thermal diffusion, surface diffusion, or viscous flow, which has a different dependence on wavelength than the roughening effect. The interplay of these two effects selects a characteristic wavelength for the ripples. Our experiments were carried out according to this mechanism.

3. Results and discussions

As an example, we fabricated a sinusoidal structure by FIB bombardment, as shown in Fig. 1. The structure is so regular that it can be used as a sinusoidal grating working in reflectivity. Its profile sizes (depth and period) are suitable for gratings that work from the ultraviolet to the near infrared. We tried the same experiment using some other materials, such as Si (111), fused silica, tungsten carbide, and stainless steel, and only the Ti–Ni crystal with a low phase transformation temperature (near room temperature) could generate such a structure.

 

Fig. 1. FIB micrograph of self-organized straight ripples by FIB random scanning with ion energy of 30 keV on the thin film of a Ti–Ni 2-µm-thick crystal.

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The self-organized structure was characterized by an atomic force microscope (AFM) with a Nanoscope IIIa from Digital Instruments, which is a type of AFM. The scanner was calibrated with a 160-nm height standard. The AFM image typically had a scan range of 1–20 µm. The silicon probe had a pyramid shape, the base of which measured 3–6 µm, with a 10–20-µm height of the pyramid probe, and a height-to-base ratio of ~3. The tip of the pyramid had a radius of curvature of less than 20 nm. The AFM scans were performed with the tipping mode, at which the change in oscillation amplitude of the probe is sensed by the instrument. Figure 2 is part of the three-dimensional topography of the grating measured with the AFM over an area of 2.5 µm×2.5 µm. Figure 3 shows the profile of the grating measured with the AFM over an area of 6 µm×6 µm.

 

Fig. 2. Part of the three-dimensional topography of the grating measured with the AFM in an area of 2. 5×2. 5 µm².

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Fig. 3. Two-dimensional profile of a grating measured with an AFM over an area of 6 µm×6 µm.

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The measured depth and period of the grating are 98 and 931 nm, respectively, and its structure is regular and symmetric. The depth and period were determined mainly by ion energy and scan time. Depth h increases quickly initially when the ion dose rate increases, which is proportional to the scan time, and finally saturates at a high ion dose. Depth h grows nearly exponentially with ion penetration depth as h∝h₀ exp(ad), d=f(E, t), where a is the growth parameter, d is the ion penetration depth, E is the ion energy, and t is the scan time. The period increases approximately linearly when the ion energy increases. This reported structure was obtained with an ion energy of 50 keV, a scan time of 19 min, and a beam current of 1 nA. The surface of the grating is smooth, and the cross-sectional profile is near that of a sinusoidal grating.

A real groove profile and its depth have a strong influence on the grating efficiency for small wavelength-to-period ratios, especially for the sinusoidal gratings that operate in the ultraviolet range. The integral method is one of the rigorous methods that makes it possible to investigate the efficiencies of gratings with real groove profiles in any spectral range. A considerable improvement in computers and the perfection of programming techniques enable one to carry out such modeling on a desktop personal computer by using a standard operating system [5]. It has been shown that the analysis results of this program are in good agreement with the experimental measurements [6–9]. We used this program to analyze characteristics of our sinusoidal gratings. The incident angle is 15° in a normal direction. The refractive indices of Ti–Ni and Si were added additionally to the refractive-index library of the software (PC Grate 2000) by the refractive-index editor, which is one of the functions of the software. The corresponding data were taken from Ref. 10.

We analyzed optical properties of the self-organized structure using realistic profile data: a depth of 98 nm and a period of 1074 lines/mm. The program runs at a specified wavelength range from 50 to 1500 nm. The diffraction efficiencies for different orders are shown in Fig. 4. It can be seen that, for the 231.25-nm wavelength, the diffraction efficiencies are 20.3%, 20.7%, 24.4%, and 16.7% for orders of -2, -1, +1, and +2, respectively. For the 632.8-nm wavelength, the diffraction efficiencies for orders of 0, -1, and +1 are 41.5%, 11.1%, and 4.02%, respectively, and they can be further improved by increasing the incident angle or by changing the feature sizes by adjustment of the process parameters as mentioned above. The diffractive structure mentioned above with a depth of 98 nm and a period of 1074 lines/mm is cited here only as an example to illustrate the self-organized formation technique. It seems that the grating can be used at the ultraviolet wavelength. Further improvements are needed to obtain grating profiles with greater depth and a smaller period by optimizing process parameters, such as the ion energy, the scan time, and the ion incident angle during future scanning.

To compare the simulated values, we measured the diffraction efficiency with a He–Ne light source. We measured a large 1 mm×1 mm area in which is spelled together by a 4×4 array diffractive structure with a single unit area of 200 µm×200 µm self-organized by FIB scanning by use of the same process parameters mentioned above, because resolution of the FIB scanning will be greatly degraded within the area as large as 1 mm×1 mm. The measured diffraction efficiencies of the grating for the 632.8-nm wavelength are listed in Table 1.

The 2-µm-thick Ti–Ni thin film was prepared by arc plasma ion plating with a low transformation temperature. The physical properties of Ti–Ni films are sensitive to metallurgical factors (alloy composition, contamination, thermomechanical treatment, annealing and aging processes, and phase changing temperatures); sputtering conditions (co-sputtering with multitargets, target power, gas pressure, target-to-substrate distance, deposition temperature, and substrate bias); and application conditions (loading conditions, ambient temperature and environment, heat dissipation, heating or cooling rate, and strain rate). In addition, uniformity of composition is another key factor for the self-organized formation of ripples. The microstructure features could differ for the samples prepared in different conditions, which would strongly depend on the preparation conditions of thin film.

Table 1. Measured and Calculated Diffraction Efficiencies for the 632.8-nm Wavelength

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Fig. 4. Efficiency (TE) of the sinusoidal grating versus wavelength range from 50 to 1500 nm with an incident angle of 15° with normal direction. Simulation was done with the PC Grate2000 computer program. The inset shows diffraction efficiency versus different diffraction orders for the 231.25-nm wavelength and a grating depth of 98 nm.

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4. Summary

In summary, we determined a self-organized formation of a sinusoidal grating on Ti–Ni film by use of FIB milling. We have shown by measurement and simulation results that the sinusoidal structure can be used as a grating in the wavelength range from the ultraviolet to the near infrared. For gratings with an area of several square centimeters or larger, a broad ion beam can be used to replace a FIB for structuring, such as inductive coupled plasma or electron cyclotron resonance. The self-organized structure can be replicated by polymer injection or hot embossing techniques for mass production. Further study will focus on other materials that can generate a sinusoidal grating with smaller features to function at the extreme-ultraviolet wavelength and possibly even the x-ray wavelength by use of self-organized formation.