Abstract

Astigmatism exists in a focused-ion-beam (FIB) system and causes the shape of a beam spot to change from a normal circle to an ellipse. This variation influences the fabrication of diffractive structures by use of programmable controlled milling of a FIB. It is analyzed combined with the fabrication of blazed gratings and Fresnel diffractive lenses. Fabrication errors caused by a beam spot with astigmatism is discussed in detail for four cases of the long axis of an ellipse (a) in accordance with the X axis, (b) in accordance with the Y axis, (c) at 45° with the X axis, and (d) at -45° with the X axis. Finally, a method is given for correction of the astigmatism and how to determine the circularity of the beam spot qualitatively.

© 2004 Optical Society of America

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References

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Appl. Opt.

IEEE Photon. Technol. Lett.

Y. Fu, �??Investigation of microdiffractive lens with continuous relief with vertical-cavity surface-emitting lasers using focused ion beam direct milling,�?? IEEE Photon. Technol. Lett. 13, 424�??426 (2001).
[CrossRef]

J. Micromech. Microeng.

A. A Tseng, �??Recent developments in micromilling using focused ion beam technology,�?? J. Micromech. Microeng. 14, R15�??R34 (2004).
[CrossRef]

Opt. Eng.

Y. Fu and N. K. A. Bryan. �??Investigation of diffractive�??refractive microlens array fabricated by focused ion beam technology,�?? Opt. Eng. 40, 511�??516 (2001).
[CrossRef]

Opt. Express

Other

J. Orloff, ed., Handbook of Charged Particle Optics (CRC Press, Boca Raton, Fla., 1997), pp. 438�??455.

P. D. Prewett and G. L. R. Mair, eds., Focused Ion Beam from Liquid Metal Ion Sources (Research Studies Press, Baldock, Hertfordshire, UK, 1991).

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Figures (13)

Fig. 1.
Fig. 1.

Schematic of program-controlled FIB milling for diffractive structures with continuous relief. (a) Cross section of FIB milling circle by circle. Different circles correspond to different milling depths. (b) Top view of the Fresnel structure, which is the same principle for milling blazed gratings except for the substitution of straight lines for circles.

Fig. 2.
Fig. 2.

(a) An astigmatic beam and (b) the stigmatic forces exerted by the octopole. (c) For ion-beam intensity with stigmatism, the intensity distribution is a Gaussian profile with different sizes at the FWHM site (2a and 2b) in the X and Y directions.

Fig.3.
Fig.3.

Schematic of the beam spot with astigmatism for four cases: (a) long axis in accordance with X, (b) long axis in accordance with Y, (c) long axis at 45° with X, (d) long axis at -45° with X.

Fig.4.
Fig.4.

Normalized ion-beam intensity distribution along a scan line with normalized pixel spacing equal to (a) 1.5 and (b) 3.0.

Fig.5.
Fig.5.

Normalized ion-beam intensity distribution in multiple scan line milling with (a) normalized yps=3.0 and normalized xps=8.0, (b) normalized yps=1.5 and normalized xps=8.0, (c) normalized yps=1.5 and normalized xps=1.5.

Fig. 6.
Fig. 6.

Two-dimensional profile of mold of the blazed grating with the designed depth of 633 nm milled on a silicon wafer and measured by use of an AFM (NanoScope IIIa). Cross-sectional profiles for beam spot shapes (a) 2a and (b) 2b as shown in Fig. 2(c). The milling is carried out with a normal pixel overlap of 60%.

Fig. 7.
Fig. 7.

Two-dimensional profile of a circular symmetrical diffractive lens milled on bulk silicon material for the long axis of an elliptical spot in the X axis and measured with an AFM in both the horizontal and the vertical directions. The relief depth in the vertical direction is deeper than that in the horizontal direction because of the beam spot shape of case (a) in Fig. 2. The milling is carried out with a normal pixel overlap

Fig. 8.
Fig. 8.

Two-dimensional profile of mold of a circular symmetrical diffractive lens milled on bulk silicon material and measured wih an AFM. (a) Cross-sectional profiles along the (a) horizontal and (b) vertical directions. The relief depth in the vertical direction is deeper than that in the horizontal direction because of the beam spot shape of case (a) in Fig. 2. The milling is carried out with a normal pixel overlap of 60%.

Fig. 9.
Fig. 9.

Aspect ratio versus normalized redeposition for pure sputtering of a FIB [10].

Fig. 10.
Fig. 10.

Schematic of increasing the pixel spaces in both the X and theY directions with a single raster scan to check the astigmatism of the beam spot. Each spot bombed the substrate independently with zero overlap. Bombed marks remain on the surface after a single scan.

Fig. 11.
Fig. 11.

Flow chart of correction procedures of the astigmatism

Fig. 12.
Fig. 12.

Checking the quality of a beam spot with a FIB single scan and zero overlaps in both the X and the Y directions. The single-scanned pixels were measured with an AFM. (a) Astigmatism existed in the case of (d) in Fig.3, (b) astigmatism existed in the case of (a) in Fig. 3, (c) astigmatism existed in the case of (c) in Fig.3; (d) no astigmatism existed, and the shape of the spot is circular. The insets correspond to FIB images.

Fig. 13.
Fig. 13.

Fabrication example of a diffractive lens on silicon by use of FIB milling after correction of the astigmatism. It was characterized by the AFM with a tipping mode. (a) 2D profile in the horizontal direction, (b) 2D profile in the vertical direction, (c) SEM micrograph of the fabricated device after correction of the astigmatism.

Equations (3)

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δ x c = ZB 4 ( 2 q M ) 1 2 δ V V 3 2
η = [ sin ( π ε ) π ε ] 2
F ( h ) = F 0 h 2 0 d xdx r 3

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