Accurate direct fabrication of diffractive gratings is an important task in optical engineering. Several methods have been reported to realize optical diffractive gratings on a silicon substrate using focused ion beams. A method, however, is necessary to improve the overall shape and dimensional accuracy. In this paper a simulation-based technique is presented taking into account redeposition fluxes. First, the influence of the process parameters on the blazed grating structure is studied experimentally. Then the process parameters for a structure with a planar sidewall, a maximum depth of 200 nm, and an opening width of 350 nm are determined. The approach is finally verified by comparing the designed with the fabricated structure. The method may be readily extended to various micro/nano structures in optics.
© 2007 Optical Society of America
Focused ion beam (FIB) direct fabrication is a promising technology that is currently used for a variety of structures . Although some FIB induced fabrication methods have been established over the past decade, additional research is necessary to develop new methods for fabricating arbitrary curved structures.
A diffractive grating is an optical surface shaped and spaced so as to disperse incident polychromatic light into a sharply defined spectrum. The most common type is the classical plane grating, a flat rectangular surface with equally spaced grooves running parallel to each other. The blazed grating is used to direct the light only into the diffracted order of interest with high efficiency .
Conventional fabrication methods for optical diffractive structures are photolithography with a gray-scale mask and high resolution lithography, such as e-beam. These methods are fundamentally indirect methods and need a pattern transfer process such as dry or wet etching. As a convenient and efficient method, Fu et al. reported the focused ion beam direct milling method  and a “self-organized” method [4, 5] for diffractive gratings. The direct milling method is similar to the e-beam and laser beam exposure in that the desired pattern is formed point by point by changing the beam dose. In the “self-organized” method the beam is scanned across the substrate with constant process parameters such as ion energy, current density, and pixel dwell time instead of being changed for each point, and the desired structure is formed by the redeposition effect in addition to sputtering. More general approaches to the fabrication of predefined surfaces were reported in Refs.  and . It is also mentioned that periodic topographical features can form in a self-organized way due to the curvature dependence of the sputtering yield . It was speculated  that this phenomenon, known as ripple formation, could also be used for the fabrication of diffraction gratings. However, ripples form only after a considerable amount of material has been removed and are difficult to control.
With the methods mentioned above it is difficult to obtain the desired geometry because of the redeposition flux generated by sputtered atoms. We have recently developed simulation codes based on the string method [9, 10] and the level set method  which take redeposition fluxes into account. These codes also take into account the incidence angle dependence of the sputtering yield, which can be obtained from either binary collision simulations or from experiment. In this paper, we present an accurate method of blazed diffractive gratings fabrication on a silicon substrate using the 3D version of the simulator .
2. Characteristics of FIB fabrication
For the purpose of the investigation of the basic characteristics of blazed grating structures, experiments were performed with single pass box milling. The experiments were carried out using a Micrion 2500 twin-lens FIB system equipped with a Gallium liquid-metal ion source (LMIS). The system was operated at an acceleration voltage of 50 kV with a selectable 50 µm beam-limiting aperture corresponding to a beam current of 45 pA with a silicon substrate. The beam diameter (FWHM) was 68 nm and the current density at the center of the beam 0.8 A/cm2. The pixel overlaps were 40, 50, and 60 % corresponding to 40.8, 34.0 and 27.2 nm pixel spacing. The pixel dwell times were 7, 9, and 11 ms.
As shown in Fig. 1(a), a serpentine scan strategy was used with fixed 30 pixels in one direction. In the other direction the number of scan lines was fixed to 12 and the specimen was cross sectioned for the SEM investigation in the middle. During each experiment all process parameters were kept constant.
The fabricated blazed grating structures are shown in Fig. 2. Pixel overlap and dwell time greatly affect the maximum depth and sidewall planarity. As can be seen, gratings with planar sidewalls can be fabricated with certain process parameters. At low ion fluencies the left sidewall has a concave shape, while at high fluencies it assumes a convex shape. The latter is mainly due to the redeposition flux of atoms sputtered from the right sidewall and directed towards the left sidewall. As reported by Santamore et al. , the sputtering yields change as a function of scan speed. This sputtering yield change is due to the angle between the ion beam and the surface normal. The slower the scan speed the larger the angle and the larger the sputtering yield. This effect makes it difficult to estimate the maximum depth without simulation.
3. Simulation based approach
It has been shown in the previous section that gratings with a planar sidewall can be fabricated by FIB. However, in a purely experimental approach it is cumbersome to find the required process parameters for a desired opening width and depth. In this section we study the influence of the process parameters on the overall shape and dimension of the grating by simulation. We show that by introducing inter- or extrapolations to the obtained data, the optimum process parameters can be determined.
The design parameters are chosen as shown in Fig. 1(b). The width and depth of the structure are fundamental for the grating performance. In addition, the sidewall nonplanarity is defined as the maximum swelled height of the sidewall. In this study a grating with a planar sidewall is chosen to fabricate, i.e. the nonplanarity should be equal to zero.
As an example, we choose the process parameters as specified in Table 1 and the opening width w is fixed to a value of 352 nm. According to Eq. (1), the pixel spacing ps is determined when the number of scan lines n is chosen at given beam diameter df and opening width w.
αd is a term to consider width broadening and is in principle a function of many variables such as acceleration voltage, beam overlap, beam diameter, etc. It was determined from the experiments discussed in Section 2 that the value of αd is in the range of 30–50 nm. So in this study we assume αd=40 nm. A slight variation of the actual opening width of the designed structure on the order of ±10 nm has to be expected therefore.
Simulations were performed with the code AMADEUS-3D . As a result, two three-dimensional graphs for the sidewall nonplanarity and the maximum depth as a function of the number of scan lines and the dwell time were obtained (Fig. 3). Because in this study the grating shape is restricted to planar sidewalls, the desired parameters are limited to the isoline curve of the nonplanarity with value zero. Therefore a graph of the number of scan lines vs. dwell time is extracted from Fig. 3(a) and is shown in Fig. 4. The scale on the right axis depicts the pixel spacing corresponding to the number of scan lines. It is calculated by Eq. (1), because the width of the grating is fixed.
In Fig. 4 four points (a)–(d) are marked corresponding to 10 scan lines and different dwell times. They were realized experimentally, and the SEM results are shown in Fig. 5. As can be seen, the fabricated shape at point (b) indeed has a planar sidewall, while negative and positive nonplanarities are observed at point (a) and (c)–(d), respectively.
In Fig. 6 the grating depth is shown as a function of dwell time for gratings with planar sidewalls. It is obtained from Fig. 3(b) along the isoline of sidewall nonplanarity. From Fig. 6 it can be seen that grating depths between 130 nm and 205 nm can be achieved in the parameter range investigated. The process parameters for the fixed opening width and a desired depth within this range can be determined from Fig. 6 (dwell time) and subsequently from Fig. 4 (number of scan lines). Notice that for certain values of the depth two solutions exist. E.g., for a depth of 200 nm dwell times of either 11 or 8.4 ms and corresponding numbers of scan lines of 8 and 9.2 can be determined (cases (1) and (2), respectively). Of course, instead of 9.2 scan lines, the nearest integral number 9 has to be chosen. The experimental result for the case (1) is shown in Fig. 7. In contrast, for a desired depth of 190 nm, only one solution is obtained [7ms dwell time and 10 scan lines, case (b)].
A fundamental investigation of blazed grating structures using box milling with focused ion beams was performed. It was found that the dwell time greatly affects the maximum depth and that the redeposition flux affects the nonplanarity of the sidewall. With the combination of certain process parameters a blazed grating with a planar sidewall can be fabricated. At low ion fluencies the sidewall shape is concave, while it changes to convex shape, passing through planarity, as the ion fluencies are increased.
A simulation-based approach has been presented for the focused ion beam direct fabrication of blazed grating structures. This approach accounts for the sputtered atoms generated during the sputter process, which otherwise makes the design of micro/nano functional structures difficult. A grating with a maximum depth of 200 nm and a width of 350 nm was designed and fabricated. In addition to accurately determining the required process parameters, the simulation can also be used to determine the range of structures that can be fabricated with the chosen scan strategy. The good results obtained are based on the accuracy of the used simulation program. This is one application of simulation based optimization in focused ion beam processing on the micro/nano scale. The approach can also be used to fabricate other optical applications such as micro lenses.
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