1. Introduction

Replicating optical elements with diffractive structures is appealing for industrial use. Conventional methods are photolithography with a gray-scale mask, electron-beam lithography, and laser direct writing on photoresist, where the pattern is then transferred from the photoresist to a substrate by dry or wet etching or by electroplating metal for further molding. Another method is exposing a hybrid solgel film under UV light with a gray-scale mask._1,2 In this paper we present a new method in which the diffractive structure is transferred from a designed pattern to a replica with a hybrid solgel film in only a single step. Replication error can be greatly reduced this way.

The designed pattern is formed directly on a substrate by focused ion beam milling (FIBM) and then transferred to the replica material with a hybrid solgel film by stamping. The hybrid solgel film is adopted because it offers the advantages of atomic-level mixing of high-purity starting materials, high versatility, low processing temperature, low cost, good mechanical strength, and high chemical and environmental durability.

2. Preparation of mold and hybrid solgel film

The milling experiments were carried out with our focused ion beam (FIB) machine (Micrion 9500EX) with an ion source of liquid gallium, integrated with a scanning electron microscope (SEM), energy-dispersion x-ray spectrometer facilities, and gas assisted etching functions. This machine uses a focused Ga⁺ ion beam with an energy of 5–50 keV, a probe current of 4 pA to 19.7 nA, and beam-limiting aperture size of 25–350 μm. For the lowest beam currents, the beam can be focused down to 7 nm in diameter at full width at half-maximum (FWHM). The milling process was performed with a program; the ion dose was varied for different relief depths.

The method for microfabrication of diffractive lens by FIB was described in detail elsewhere.^3,4 It takes ~1 h to fabricate a single microdiffractive optical element (micro-DOE) mold by FIB milling with a focused beam spot size of 20 nm and resolution of 8 nm.

The relief accuracy is determined by the beam spot size and pixel overlap during the raster scan. The larger the beam spot size and the smaller the pixel overlap, the worse the relief accuracy will be. With the interline step of 0.5 μm in mind, we chose a 70-nm beam spot size and 60% overlap for our processes. The fabricated mold is shown in Fig. 1 as a SEM micrograph. Figure 2 is a two-dimensional profile of the micro-DOE mold measured by atomic force microscopy (AFM). Figure 2 shows that there are some depth errors for the relief pattern, in particular in the outer zones. There are principally two possible reasons. One is that discrete data were used for FIBM with an interline step of 0.5 μm, which caused some relief summit data to be missed. The other is redeposition that is inherent in the FIBM process. Redeposition can be reduced to a certain extent by gas assisted etching (e.g., with XeF₂) during FIBM. Some sensors (the imaging sensor and the pressure sensor) in the vacuum chamber will be seriously contaminated because the milling period may be as long as 1 h. The relief depth of the master profile appears to decrease as one moves away from the center owing to the bottom alignment of the segments. Specific design strategies are characterized by the segment alignment. The choice of the segment alignment, e.g., top or bottom, is influenced by the fabrication technology. For our FIBM, the designed continuous profile needed to be expressed as discrete data points (with interline space of 0.5 μm for each milling step) before FIBM programming. The discreteness causes some data on the apex of each annulus to be missing. As the annulus width of the outer zone is decreased, the height loss is greater because of the missing height data.

 

Fig. 1 SEM micrograph of DOE mold fabricated by use of FIBM on a silicon substrate.

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Fig. 2. Two-dimensional profile of the DOE bulk silicon mold measured by AFM.

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The hybrid solgel organosilicate glass (a compound of SiO₂ and TiO₂) was prepared by hydrolysis and subsequent copolymerization of [ 3-(methacryloyloxy) propyl ] trimethoxysilane (MAPTMS) and titanium propoxide Ti(OC₃H₇)₄. The organic constituents in MAPTMS add flexibility to the resulting glass. The hydrolysis of MAPTMS was carried out with isopropanol in a molar ratio of 1:3 with HCl as the catalyst. Titanium propoxide was hydrolyzed with actelyactone in a ratio of 1:5. Titanium propoxide was selected to modify the refractive index and increase the mechanical strength of the material. Compared with conventional applications with solgel, a solgel film with greater thickness is required in our case because of the relief depth of the diffractive optical element. The solgel film was spin coated onto a fused silica substrate at 1000 rpm for 40 s with thickness of 1.5 μm and was then prebaked at 50°C for 10 min to remove the excess solvent. After that, the hybrid solgel film could be used for stamping the DOE. The temperature during prebaking is crucial for the stamping process. If the temperature is too low, releasing the replica from the mold is very difficult. On the other hand, a high temperature during baking tends to lead not only to the polymerization of the organic elements but also to the reticulation of the mineral components, which creates a rigid structure, limiting the molecular mobility during subsequent stamping. The temperature we used is 120°C for 1 h. Figures 3 and 4 are SEM micrographs of the replicated DOE and the corresponding two-dimensional profile measured by AFM.

 

Fig. 3. SEM micrograph of DOE replicated in hybrid solgel film.

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Fig. 4. Two-dimensional profile of DOE replicated in hybrid solgel film, measured by AFM.

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3. Results and discussion

We transferred the AFM two-dimensional section analysis data for the replica and replotted the profile with the designed DOE data in Fig. 5. Except for fabrication error during FIBM of the mold, the geometry difference between the designed relief and the replica’s profile is attributed mainly to air in the small chamber formed between the surface of the mold and the hybrid solgel film during the stamping process; the air produces higher pressure during stamping and prevents the solgel from fully filling the mold cavity. Thus the relief height (sensitive to diffraction efficiency) of the replica is lower than the design’s. It is possible to avoid this problem by carrying out the stamping process in a vacuum chamber or by changing the softness of the hybrid solgel film to improve its filling ability.

To determine how much of the profile difference is due only to the replication, we transfered the FIB master profile from the AFM data and replotted it with the replica profile in Fig. 5. It can be seen that the maximum difference that is due to replication is ~90 nm, which is permissible for practical microlens use.

The surface roughnesses of the replica and of the master, Ra, measured by AFM, are 4 and 2.8 nm, respectively, in the same 5 μm × 5 μm area. To measure the diffraction efficiency of the replica, we used a He–Ne laser with a wavelength of 632.8 nm (designed wavelength) and a beam size of ~0.7 mm, with an objective lens with magnification of 10×, to illuminate it. The designed focal length of the DOE is 350 μm. The measured diffraction efficiency of the replica for the designed diffraction order of 1 is 86%. Table 1 presents comparisons to the results for conventional DOE fabrication and replication methods.

Table 1. Optical performance data for several DOE fabrication methods as reported in the literature and in our hybrid solgels

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Compared with the other binary technique and with analog methods, a major advantage of FIB mastering and hybrid solgel replication is the potentially high efficiency of transfer with one simple step, which eliminates the pattern transfer error that occurs in conventional methods.^5–13 The efficiency can be improved further by increasing the number of annuli in the DOE.

For a conventional solgel process with a material of pure silica (pure SiO₂), the gel shrinks by a factor of ~2.5 during aging, drying, and densification.^7,15. It can be seen from Fig.5 that the shrinkage is quite small compared with that of the conventional solgel process. Shrinkage can be decreased further by optimizing the hybrid film compound. To avoid film cracking caused by gel shrinkage during drying, the total film thickness of 1.5 μm was built up of four ~350-nm coats (so-called multiple layers) deposited at 5-min intervals by spin coating. The internal stress of the film can be dispersed this way.

 

Fig. 5. Comparison of designed DOE relief, FIB master profile, and replica profile.

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We had also tried other replication method, such as hot embossing, using metal and glass molds with plastic materials,^14,16 It was proved that a mold composed of bulk silicon and glass with both sides polished has less surface roughness after FIBM than a mold composed of metal, such as copper, tungsten, or stainless steel. However, the wear resistance of the silicon mold is low, and the form’s accuracy will be lowered by surface wear after several cycles of molding. The mold’s hardness and wear resistance can be improved with a coating of TiN₄ film or diamondlike film.⁷ When a diffractive structure is molded with a relief depth of ~1 μm and a diameter as small as 70 μm, it is difficult to fill the small cavity with plastic by means of a hot embossing process; so plastic may not be a better choice than solgel glass. Although glass has a higher wear resistance than silicon, and the surface roughness of a glass mold is as better than that of silicon, charging will occur during FIBM of the mold that will deflect the ion beam and affect the machining accuracy, because glass is a pure insulator. Silicon is a semiconductor; thus no charging occurs during FIBM. Considering these factors, on balance, we prefer bulk silicon as the mold material.

4. Summary

In summary, a micro-DOE mold fabricated in bulk silicon by FIBM is suitable for replication by stamping on a hybrid solgel glass (a compound of SiO₂ and TiO₂). The mold’s lifetime can be improved by coating with a TiN₄ film or diamondlike film.