A new one-step method, which has been named self-organized formation, for microfabrication of blazed-grating-like structures after bombardment with a focused ion beam (FIB) with an ion energy of 50 keV and a beam current of 0.5 nA is presented. The structure is fabricated by the FIB by raster scanning (not by patterned scanning) upon a substrate of a silicon wafer, Si(100), with total scanning time of 14 min. With this method the parameters are unchanged during the whole process, unlike for the point-by-point direct writing technique, in which the exposure intensity or the electron- or ion-beam dose is changed for each point. The surface roughness of the structure, Ra, is 2.5 nm over an area of 1 µm×1 µm. To evaluate the performance of this method we carried out a simulation, using the PCGrate program. The simulated diffraction efficiency, of diffraction order -3 working in the reflection mode, can be as much as 79.1% for the violet wavelength of 400 nm. Using a He–Ne laser as the light source produced a measured diffraction efficiency of the order of -2 of 70.4%, which is near the simulated value of 76.9% at a wavelength of 600 nm. The depth and the period of the structure can be controlled by process parameters of the FIB, such as ion energy and ion flux.
©2004 Optical Society of America
The fabrication of optical elements with diffractive structures is appealing for both institutional and industrial use. Conventional fabrication methods are photolithography with a gray-scale mask, electron-beam lithography, and laser direct writing upon a photoresist to form a pattern that is then is transferred from the photoresist to a substrate by dry or wet etching or by electroplating metal for further molding. Another method is exposure of a hybrid solgel film to ultraviolet light with a gray-scale mask.1,2 In addition, our focused-ion-beam direct milling method was reported in Refs.  and . It is similar to techniques of e-beam lithography and laser beam exposure upon photoresists because all these methods are direct writing techniques by which one writes a pattern point by point by changing the intensity of the exposure or the beam dose for each point. In this paper we present a new fabrication method in which the diffractive structure is generated upon a substrate by scanning of a focused ion beam (FIB) in a specific area only; no patterned direct writing is required here. This new method differs from that reported previously in Refs.  and  in that the processing parameters are constant during scanning instead of being changed for each point as in the direct writing method. The microstructure was generated by self-organized formation.5 The feature sizes of the structure can be altered by ion energy, beam incident angle, and scan time. Once the parameters are determined, they will be fixed in the whole scanning process. The blaze- gratinglike structure can be used in the infrared in the transmission mode or in the reflection mode for shorter wavelengths.
2. Experimental setup
The FIB scanning experiments were carried out with our FIB machine (Micrion 9500EX) with a liquid-gallium ion source integrated with a scanning-electron microscope, 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–19.7 nA, and a beam-limiting aperture size of 25–350 µm. For the lowest beam currents, the beam can be focused to 7 nm in diameter at full width at half-maximum. One can obtain ion-beam incident angles from 0° to 85° by tilting the stage in the vacuum chamber of the machine. The scanning process is point by point; in a defined area the process is line by line.
In this experiment we use an ion energy of 50 keV, a beam current of 0.5 nA, an ion beam incident angle of 30°, a beam spot overlap of 60%, an ion dose of 6.5 nC/µm2, and a beam spot dwell time of 5 µs. The substrate material is an n-type silicon wafer, Si(100), polished on one side. The temperature in the vacuum chamber of the FIB machine is 25 °C (room temperature). The substrate was placed in the vacuum chamber at room temperature and was not heated by a thermal coupler during rastering. During scanning, the beam is deflected by high-voltage lenses, and the stage is stationary. There are two types of scan for our machine. One is a raster scan, for which the beam scans a defined area of 30 µm×30 µm point-by-point and line-by-line from left to right. The other is a serpentine scan, for which the beam scans a defined area in a along serpentine path. Pattern scanning took 14 min.
The formation of a blazed-grating-like structure is a spontaneous process that occurs during sputtering erosion under ion bombardment. It is a self-organized formation that is caused by competition between smoothing driven by surface energy and roughening induced by sputter removal of material. A radiation-enhanced surface transport process results in surface smoothing in which relaxation by viscous flow (for amorphous materials) or surface diffusion (for crystal materials) plays a dominant role. The mechanism by which a blazed-grating-like structure is formed is usually discussed within the linear stability framework of Bradley and Harper5 and Carter.6 The self-formed structures are due to the dependence of the sputter yield on the curvature of the surface. Because the deposition rate of ion energy increases as the ion penetrates the solid, concave regions are sputtered more than convex regions, resulting in growing instability on the surface. This instability is counteracted by a smoothing mechanism, e.g., thermal diffusion, surface diffusion, or viscous flow, which has a different dependence on wavelength from that of the roughening effect. The interplay of these two effects produces a characteristic wavelength for the ripples. Our experiments were carried out according to this paradigm. Compared with conventional broad beam bombardment, FIB ion bombardment more easily generates straight instead of bent ripples. This may be so because continuous bombardment by a broad beam causes competition of the roughening and smoothing processes. The FIB bombardment is a discrete process that depends on the scanning frequency. Smoothing balances ion-sputtering-induced roughening for each point during the self-formation process. The ripples are formed by competition between the smoothing and roughening, which is from the frequently scanning.
3. Results and analysis
Figure 1 is a micrograph of the FIB image of the blazed-grating-like structure generated by self-organized formation after FIB bombardment. We obtained the corresponding multimedia figure by taking 27 FIB images during a total scanning time of 14 min with time intervals of 31 s. The other parameters that we used are listed in Section 2. All the process parameters were constant during the scanning. The feature sizes of the structure were measured by use of an optical interferometer (WYKO NT 2000), as shown in Figs. 2 and 3. The mean depth and period are 130 nm and 2.5 µm, respectively. The left facet angle of the structure is 10.52°. The surface roughness of the structure measured by an atomic-force microscope (Digital Instruments, NanoScope IIIa), Ra, is 2.5 nm over an area of 1 µm×1 µm. It can be seen from Fig. 2 that the depth of the structure is not uniform. This may be the result of nonuniformity of the substrate material itself, e.g., density nonuniformity, local defects, and nonuniform thickness. In addition, stability of the FIB machine will also influence the scan quality, e.g., fluctuation of the beam current during scanning.
A real groove profile and its depth have strong influences on the grating efficiency for small wavelength-to-period ratios, especially for blaze gratings operating in the violet range. To date the integral method is perhaps the only rigorous method that enables one to investigate rather easily the efficiencies of gratings with real groove profiles in any spectral range. A considerable improvement in computers and the perfection of programming techniques enable such modeling to be carried out on a desktop personal computer by use of a standard operating system.7 It was shown that the analysis produced by this program is in good agreement with those of experimental measurements.8–11 We use this program to analyze characteristics of our blaze gratings as we work with the reflection mode, assuming that the incident light is in the normal direction. It can be observed from the measured profile that the mean value of the left facet angle and the period of the grating are 4.13° and 400 periodic lines/mm, respectively. We use realistic groove profiles as the user-specified data and input them into the PCGrate computer program; only the left facet angle is required as the input of groove angles. The refractive index of Si was added to the refractive-index library of the software (PCGrate 2000) by a refractive-index editor that is a function of the software. The corresponding data were cited from Ref. 12. Figure 4 shows feature sizes as simulated by the PCGrate 200 software.
It can be seen that there are four peaks, with values of 77%, 79.1%, 76.9%, and 62.2% at diffraction orders -6, -3, -2, and -1, which correspond to wavelengths of 200, 400, 600, and 1200 nm, respectively. The results are obtained for the normal incidence angle working in reflection mode. A large blazed-grating-like structure with a size of 500 µm×500 µm was made for measurement. The measured diffraction efficiency of diffraction order -2 is 70.4% for a wavelength of 632.8 nm (He–Ne laser as the light source), which is close to the simulated results of the 600 nm wavelength. In practical use, the efficiency can be further improved by addition of a metal thin-film coating with high reflectivity.
The process of self-organized formation is sensitive to the operating parameters of the FIB machine and the substrate material. For example, the structure will disappear when the ion beam’s incident angle decreases to 0° in the normal direction. Different materials generate different structures, such as curved ripples, and nanodots. However, when we tried to change the raster direction of the beam or the overlapping percentage between adjacent FIB points, the characteristics of the ripples did not change. Changing the process parameters of the FIB, such as ion beam energy and ion flux, can change the depth and period of the ripples.
We should emphasize that the self-organized formation method strongly depends on the substrate material. Different materials will generate different topography (ripples) and feature sizes. Only a few materials can generate straight and regular ripples after the FIB scanning. For the majority materials, the ripples generated by the FIB bombed self-formation are bent and discontinuous. Sometimes, even no topography will appear after the bombardment for some materials, no matter how long time they are scanned by the FIB.
In summary, a micro blazed-grating-like structure was directly generated by self-organized formation after fiber-based ion-beam raster scanning in a defined area. A major characteristic of the structure is its strong dependence on the substrate material. The structure may be quite different for the same material under different preparation conditions. The operation parameters of the FIB machine also play a dominant role in the final formation of the structures, however. Further study will focus on two points: One is producing the self-formation of a diffractive structure for working extreme-ultraviolet or even x-ray wavelengths by searching for suitable substrate materials. The other is improving the uniformity of groove depth by optimizing processing parameters of the FIB machine.
This research was supported in part by the Funding for Strategic Research Program on Ultraprecision Engineering of the the Agency of Science, Technology and Research, Singapore, and by the Innovation in Manufacturing Systems and Technology Singapore— Massachusetts Institute of Technology Alliance.
1. H. Jiang, X. Yuan, Z. Yun, Y.-C. Chan, and Y.-L. Lam, “Fabrication of microlens in photosensitive hybrid sol-gel films using a gray scale mask,” Mater. Sci. Eng. C 16, 99–102 (2001). [CrossRef]
2. P. Coudray, P. Etienne, Y. Moreau, J. Porque, and S. I.. Najafi, “Sol-gel channel waveguide on silicon: fast direct imprinting,” Opt. Commun. 143, 199–202 (1997). [CrossRef]
3. Y. Fu and N. K. A. Bryan, “Investigation of diffractive optical element fabricated on diamond film by use of focused ion beam direct milling,” Opt. Eng. 42, 2214–2217 (2003). [CrossRef]
4. Y.-Q. Fu, N.-K. A. Bryan, and N. S. Ong, “Diffractive optical elements with continuous relief fabricated by focused ion beam for monomode fiber coupling,” Opt. Express 7, 141–147 (July 2000), http://www.opticsexpress.org. [CrossRef]
5. R. M. Bradley and J. M. E. Harper, “Theory of ripple topography induced by ion bombardment,” J. Vac. Sci. Technol. A 6, 2390–2395 (1988). [CrossRef]
6. G. Carter, “The effects of surface ripples on sputtering erosion rates and secondary ion emission yields,” J. Appl. Phys. 85, 455–459 (1999). [CrossRef]
7. A commonly used software based on the modified integral method for simulation and analysis of gratings; see Internet site http://www.pcgrate.com.
8. L. I. Goray and J. F. Seely, “Efficiencies of master, replica, and multilayer gratings for the soft-x-ray-extreme-ultraviolet range: modeling based on the modified integral method and comparisons with measurements,” Appl. Opt. 41, 1434–1445 (2002). [CrossRef] [PubMed]
9. M. P. Kowalski, J. F. Seely, L. I. Goray, W. R. Hunter, and J. C. Rife, “Comparison of the calculated and the measured efficiencies of a normal-incidence grating in the 125–225-wavelength range,” Appl. Opt. 36, 8939–8943 (1997). [CrossRef]
10. L. I. Goray, Modified integral method for weak convergence problems of light scattering on relief grating, in Diffractive and Holographic Technologies for Integrated Photonic Systems ,R. I. Sutherland, D. W. Prather, and I. Cindrich, eds., Proc. SPIE 4291, 1–12 (2001).
11. L. I. Goray and S. Yu. Sadov, “Numerical modeling of coated gratings. I. Sensitive cases,” in Diffractive Optics & Micro-OpticsR. Magnusson, ed., Vol. 75 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 365–379.
12. E. Palik and G. Ghosh, The Electronic Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1999).