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We propose a new laser lithographic technique with enhanced resolution. A calcite wave plate is introduced in our system to separate an input lithographic beam into two orthogonally polarized beams. After going through an imaging lens, these two beams meet again on the focal point, and generate a small interferogram that sharpens the shape of the focused beam spot. Using this phenomenon, we can overcome the diffraction limit of the imaging lens and achieve a 486-nm-linewidth.
©2010 Optical Society of America
1. Introduction
A computer generated hologram (CGH) is widely used for null testing of large aspheric surfaces [1]. The well-known electron beam (E-beam) lithography is not proper to fabricate the CGH because of the size restriction (CGH requires a 50 to 1,000-mm-diameter) and the high cost. On the contrary a direct lithography using a laser [2–7] (‘direct’ means the system fabricate a pattern directly without photo-masks) is superior to the E-beam method because of relatively low-cost system constitution and fine pattern fabrication in the range from several hundred nanometers to several micrometers in which one has fast and novel performance for a large area substrate.
Most CGHs have rotationally symmetric patterns whose linewidths gradually decrease along the radial direction as shown in Fig. 1 . Unfortunately the previous direct laser lithographic techniques have been confined in a diffraction limit (the central width of the Airy pattern [8]) as described in Eq. (1).
where λ is the wavelength of the lithographic source light, and NA is the numerical aperture of the imaging lens. In the previous system, the minimum linewidth is commonly about 661.5 nm (λ: 488 nm, NA: 0.9). To overcome this limitation, we propose a new method that uses the interference. Several studies have investigated ways to improve lateral resolution in stimulated emission depletion microscopy [9] and confocal microscopy [10,11]. The laser lithographic application, however, is not investigated yet. In our system, the calcite wave plate separates the input lithographic beam into two orthogonally polarized beams. After going through the imaging lens, these two parallel beams meet again on the focal point in the target surface, and generate a small interferogram that sharpens the focused beam spot. Using this phenomenon, we can overcome the diffraction limit of the imaging lens. The details of the proposed method are present in Section II. In Section III, we show some experimental results.2. Direct laser lithographic system with a calcite wave plate
A schematic of our system is illustrated in Fig. 2 . The system includes (1) an intensity stabilization part, (2) a writing head, (3) a linear and rotary stage set, and (4) alignment stuffs (jigs and tilt tables). For CGH fabrication, a cylindrical-type system is more suitable than a rectangular one because most diffractive optics elements and CGHs have rotationally symmetric or asymmetric patterns. Our system shown also uses cylindrical coordinates. The writing head is moved in radial direction with the linear stage while the target surface is rotated on the rotary stage. The blue line in Fig. 2 represents the lithographic beam. The direct laser lithographic system requires a high stability of the intensity of the lithographic source. In the fluctuating spectrum of a gaseous laser, however, some variations are found in the low frequency range, from dc to several hundred Hz, and considerably smaller variations in the frequency band to several hundred kHz. The first is attributed to such main factors as thermal effects, mechanical vibrations, dust particles and air currents, instability, and the hum of the power supply. The second is mainly due to the oscillations in the plasma of the discharge column, especially in the region of the space charge at the cathode. The Ar+ laser that is used as a source in our system also shows the above-mentioned beam fluctuations. For the source stabilization, we used an acousto-optic modulator (AOM), a photodetector, and a servo controller [12]. The stabilized beam from the AOM is directly fed into the polarizer in the writing head as shown in Fig. 2 and Fig. 3 .
In Fig. 3, the polarizer makes s- and p-polarized beams have equal intensity, and the analyzer causes two separated beams to interfere each other. The tilting mirror in Fig. 2 permits a direction change of the lithographic beam with a 0.02° resolution in order to compensate for the run-out error of the rotary stage.
Figure 4 (a) shows a lithographic imaging relationship. The input intensity I1, previous (without the interference generator) in Fig. 4 (a) can be expressed as
Then the output intensity I2, previous is derived aswhere x1, y1, x2, and y2 are defined in Fig. 4 (a) and J1 is a Bessel function of the first kind. In Eq. (3), a ⓧ symbol between any two functions indicates that those functions are to be convolved. Figure 4 (b) shows the profile of I2, previous when y2 is 0. Much the same, I1, proposed (with the interference generator) is expressed as
Fig. 4 (a) Imaging relationship. Intensity profile (b) without and (c) with the interference generator on x2, y2 plane (imaging plane). Λ represents the fringe space of the interferogram. In this case, the reduction ratio of the linewidth is about 35%.
Then the output intensity I2, proposed is
The profile of I2, proposed is shown in Fig. 4 (c). Note that the interference generator causes the side lobes that may have a bad influence on lithographic quality. We, however, are able to eliminate the effect of this side lobe by changing Λ (see Fig. 4 (c) and Eq. (4) and adjusting the lithographic intensity. Figure 5 shows a contour plot of I2, previous and I2, proposed.
Another important function of the writing head is autofocusing [13,14]. The autofocusing helps the lithographic beam continuously focus on the target surface during the fabrication. We introduced an astigmatic scheme to build a high speed precision autofocusing system [14]. In our previous work, the tolerance of the control was 500 nm, which was estimated by
Now the tolerance is only 301.2 nm because we change the imaging lens from NA 0.7 to 0.9. (Wavelength is still 488 nm.) To maintain the tough tolerance, we introduced an auxiliary laser diode, a couple of cylindrical lenses, a quadrant detector (EG&G UV140BQ-4), a PZT actuator (PI P-721.0LQ), and a newly designed controller. The maximum speed of our autofocusing mechanism is 150 Hz. Four imaging lenses (20X (NA: 0.42), 50X (NA: 0.55), 100X (NA: 0.70), and another 100X (NA 0.9)) are available in our system to alter the lithographic spot size. Each imaging lens requires a different set of cylindrical lenses for the best autofocusing performance.
3. Experimental results
Figure 6 shows the direction effect of the interferogram. As shown in Fig. 6(b), a smaller linewidth can be obtained when the focused writing beam is properly sharpened. Figure 7 and Table 1 show a fabrication result obtained by a stylus. Before the measurement, the stylus was calibrated by a standard height specimen for vertical- and a commercial heterodyne interferometer for horizontal-direction, respectively. A standard high-pass Gaussian filter with a long-wavelength cutoff of 0.25 mm was also used to minimize long spatial wavelengths and a low pass Gaussian filter with a short-wavelength cutoff of 2.5 μm was used for smoothing [15]. In Fig. 7, the reduction ratio of the linewidth is about 27.5% and it is match for the simulation result in Fig. 4.
Fig. 6 Linewidth change according to the direction of the interferogram. (a) Wrong and (b) right interferogram direction.
Fig. 7 Fabricated results on a chromium coated surface whose thickness is slightly over 75 nm (a) without and (b) with the interference generator.
Table 1. Measure Linewidth values. First we fabricated a circle pattern, and then measured the linewidth of the pattern from 12 difference positions (every 30°) by using the stylus.
As shown in the Table 1, the proposed method remarkably reduces the linewidth, but the standard deviation is worse than the previous method. We suppose that this is due to the source stabilization. If we insert the interference generator in our system, we should increase the source power to maintain the lithographic intensity on the focal plane. Furthermore, Fig. 8 shows a 300-mm-diameter CGH we fabricated. The minimum linewidth of the CGH is about 490 nm.
4. Conclusion
To improve the linewidth of direct laser lithography, we have proposed a new method that uses the interference. By using the proposed method, we could overcome the diffraction limit of the imaging lens and achieve a 486-nm-linewidth. We also successfully fabricated a 300-mm-diameter CGH with this linewidth.
Acknowledgement
We would like to thank Dr. Jae-Bong Song and Mr. Hyun-Su Yi (Korea Research Institute of Standards and Science) for useful discussions.
References and links
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