Open Access
Add to BibSonomyAbstract
To address the requirements of multi-level semiconductors, we propose a new technique for overcoming the height limitation of direct laser lithography. In the proposed system, an original source beam is fed into an interference generator that divides the input beam by 50: 50 into two output beams. After going through an imaging lens, these two beams make two focusing spots, which are slightly separated in the axial direction. In the overlapped region, these two spots generate a small interferogram that shortens the depth of focus. By using this phenomenon, we are able to overcome the height limitation of direct laser lithography. The governing equations are also derived in this manuscript by using the Gaussian beam model.
©2011 Optical Society of America
1. Introduction
In recent years, the semiconductor industry has shown a keen interest in multi-level semiconductor devices that can store a plurality of data bits in one cell. Much the same, multi-level circuits have also become attractive in many industries and these circuits can be applied in many applications. In the prototype development stage, electron beam lithography is not proper to fabricate multi-level circuits because of its high cost. On the contrary direct laser lithography [1–6] is superior to electron beam lithography because of its relatively low-cost and easy operation. Here ‘direct’ means that the system fabricates a pattern directly without photo-masks. In order to fabricate a multi-level circuit, it is important to accurately know the height limitation of the lithographic system for quality control [7]. In the emerging field of circuit packaging, which circuits are realized by stacking multiple interconnected layers, the focused lithographic beam should be precisely controlled and confined within a layer because a stray beam can lead to serious problems such as undesired connection between multiple layers, as shown in Fig. 1 . Moreover, in order to increase the component count of the multi-level circuits, the depth of focus (DOF) of the focused lithographic beam should be improved because the height limitation is highly proportional to the DOF, as described in Eq. (1).
where λ denotes the wavelength of the lithographic source beam and W0 is the beam waist radius at the focal point. The waist diameter 2W0 is called the spot size. In most of cases W0 is proportional to the central width of the Airy pattern [8], as described in Eq. (2).where NA represents the numerical aperture of the imaging lens. Unfortunately, previous techniques have been confined the DOF. To overcome this limitation, we propose a novel method that uses the interference in the axial direction. Several studies have investigated ways to improve the lateral resolution of direct laser lithography [6] and stimulated emission depletion microscopy [9]. Height resolution of direct laser lithography, however, has not yet been reported.
Fig. 1 (a) Fabrication of a pattern in multiple layers, and (b) after etching process. Undesired defects commonly occurred when the depth of focus (DOF) of the lithographic system was larger than the thickness of the layer.
In the proposed system, an original source beam is fed into an interference generator that divides the input beam by 50: 50 into two output beams. After going through an imaging lens, these two beams make two focusing spots, which are slightly separated in the axial direction. In the overlapped region, these two spots generate a small interferogram that shortens the DOF. By using this phenomenon, we are able to overcome the height limitation of direct laser lithography. The details of the proposed method are presented in Section II. The governing equations are derived in Section III by using the Gaussian beam model [10]. In Section IV, we show some experimental results.
2. Direct laser lithographic system with the interference generator
Figure 2 shows a schematic of the proposed system, which includes a source stabilization part, a lithographic head, a two-axes-stepper stage controlled by a heterodyne laser interferometer, and some alignment related devices. The target specimen is installed on the stepper stage as shown in Fig. 2. An Ar+ laser is employed as a source beam. A gaseous laser such as the Ar+ laser generally has some fluctuations in the low frequency area, from dc to several hundred Hz, and considerably smaller fluctuations in the frequency band to several hundred kHz. The first type of fluctuations are attributed to such large factors as thermal effects, dust particles and air currents, mechanical vibrations, instability, and the hum of the power supply. The second type of fluctuations are mainly due to the oscillations in the plasma of the discharge column, especially in the region of the space charge at the cathode. Thus a source stabilization part is required to remove the power fluctuation. We used an acousto-optic modulator (AOM), a photodetector (PD), and a servo controller to stabilize the lithographic beam [11], which is directly fed into the interference generator in the lithographic head, as shown in Fig. 2 (blue solid line). The PD on the lithographic head monitored the intensity level of the lithographic beam.
Fig. 2 Schematic configuration of the proposed lithographic system: AOM, acousto-optic modulator; BS, beam splitter; PD, photodetector; IG, interference generator; QD, quadrant detector; LD, laser diode.
In order to fabricate a fine pattern, we adopted an autofocusing control that makes the lithographic beam continuously focus on the target surface during the fabrication. A well-known astigmatic scheme [12, 13] was introduced in our system to build a high speed precision autofocusing mechanism. An LD, a couple of cylindrical lenses, a quadrant detector, and a computer controlled motor were used. The maximum speed of our autofocusing mechanism is up to 150 Hz. The red line in Fig. 2 represents the auxiliary laser beam, of which the wavelength is 650 nm. The interference generator divides the input beam by 50: 50 into two output beams. One of them is reflected on the flat mirror and maintains the plane wave, while the other slowly converges on the focal area, as shown in Fig. 3 . These two beams make two focusing spots, which are slightly separated in the axial direction, as shown in Fig. 4 . In the overlapped region, these two spots generate a small interferogram that shortens the DOF.
Fig. 3 Interference generator: PBS, polarized beam splitter; QWP: quarter wave plate. A Haidinger fringe is observed when we put a screen at plane A.
Fig. 4 (a) Axially separated two focused beam. (b) Intensity profile without and (c) with the interference. The parameter zo is known as the Rayleigh range [10].
3. Governing equations
Light propagates in the form of waves, and obeys the wave equation. In the case of monochromatic light, the wave function is a harmonic function of time, so we simply use the Helmholtz equation instead of the original wave equation. One of the simplest solutions of the Helmholtz equation is
where A(x, y, z) and k denote the amplitude and the wave number, respectively. In most cases, A(x, y, z) is assumed to be constant, but this assumption does not hold near the focal point because the beam power is concentrated within a small cylinder surrounding the beam axis of the focal area. From Eq. (3) and the Helmholtz equation, A(x, y, z) must satisfyOne basic solution of Eq. (4) is
In Eq. (5), A1 is a constant. R(z) and W(z) are measures of the wavefront radius of curvature and beam width, respectively. Substituting Eq. (5) into Eq. (3), we can obtain
Then the optical intensity I can be expressed as,
At any position on the z-axis, the intensity in Eq. (7) is a Gaussian function of the radial distance (x2 + y2)1/2, as shown in Fig. 5(b) . Moreover, on the optical axis (x = 0, y = 0), the intensity has a maximum value at z = 0 (exact focal point) and gradually drops with increasing |z|, reaching half its maximum value at z = ±z0, as shown in Fig. 4(b). Note that 2z0 is known as the DOF. Then the wave functions U1 and U2 in Fig. 4(a) can be expressed as
Fig. 5 (a) Τhe phase retardation ζ(z) along with the optical axis, and (b) contour plot of the intensity distribution at focal plane (z = 0).
From Eq. (8), the interfered intensity Inew is derived as
In Eq. (9), ζ(z+α) − ζ(z-α) has a Gaussian behavior and its peak value is π at z = 0 and α = ∞. Figure 6 illustrates the intensity profiles at the focal position (x = 0, y= 0) with various α. Note that the DOF is drastically reduced with the proposed method. The side lobe, as shown in Fig. 6, is ignorable because its intensity is too weak to fabricate a pattern.
Fig. 6 (a) Intensity profiles with various α, and (b) comparison between the previous and the proposed method (α=0.82z0). EDOF means the effective depth of focus with the interference generator.
4. Experimental results
Figure 7 and Fig. 8 show the fabrication results obtained by a commercial white-light scanning interferometer (WLI) [14, 15] and an atomic force microscope (AFM) [16], respectively. A photoresist film was coated on a silicon wafer by using a spin-coater. A 100X imaging lens (NA = 0.9, DOF = 2z0 = 240 nm, focal length = 2 mm) was installed in our system to fabricate a fine pattern. The radius of curvature of the spherical mirror shown in Fig. 3 was measured as 20.00015 m with a coordinate measuring machine. Therefore, α was approximately 100 nm. The WLI was calibrated by a standard height specimen before measuring. The average heights shown in Fig. 7(a) and (b) were 269.6 nm and 182.1 nm, respectively. The reduction ratio was about 32.5%. The AFM was also calibrated by the same standard height specimen, and the average heights were 262.3 nm and 179.9 nm, respectively. Table 1 shows the height values from 10 different patterns. As shown in Table 1, the proposed method certainly improved the height, but the standard deviation was worse than the previous method (without the interference generator). We suppose that this is due to the relative vibration between two optical paths in the interference generator.
Fig. 7 Fabricated result on the photoresist film (a) without and (b) with the interference generator.
Fig. 8 AFM readings. The pattern was fabricated (a) without and (b) with the interference generator.
Table 1. Averaged height values calculated from 10 different samples. To calculate the step heights, we used a modification of a two sided algorithm [17].
Next, a test on a multiple layers was done, as described in Fig. 9(a) . The thicknesses of the photoresist, the chromium, and the protection (SiO2) layer were approximately 180 nm, 75 nm, and 200 nm, respectively. The 200-nm-SiO2 layer is sufficient to protect the Si from the chromium etching solution. Furthermore, this protection layer prevents the oxidation of the Si. After the lithographic processes, the previous method made the stray beam and gave us the undesired pattern on the chromium layer, as shown in Fig. 9(c). The proposed method, however, did not show the undesired pattern.
Fig. 9 Fabricated result on the multi-level layer. (a) Test flan, (b) after the photoresist film etching, and (c) then after the chromium etching. The 3D profiles shown in (b) and (c) were obtained by the white-light scanning interferometer.
5. Conclusions
To overcome the height limitation of direct laser lithography, we proposed an axially interfered technique. By using this technique, we were able to shorten the DOF of our lithographic system (100X imaging lens, NA = 0.9, DOF = 240 nm, focal length = 2 mm) and achieved about 180-nm-height. In the previous method, the minimum height of the pattern was about 260 nm with the same imaging lens. The governing equations of the proposed technique were also derived. The proposed system is considerably sensitive to the value of α, so the anti-vibration of the system is important (α must keep constant during the fabrication).
References and links
1. M. Haruna, M. Takahashi, K. Wakahayashi, and H. Nishihara, “Laser beam lithographed micro-Fresnel lenses,” Appl. Opt. 29(34), 5120–5126 (1990). [CrossRef] [PubMed]
2. M. T. Gale, M. Rossi, J. Pedersen, and H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33(11), 3556–3566 (1994). [CrossRef]
3. A. G. Poleshchuk, E. G. Churin, V. P. Koronkevich, V. P. Korolkov, A. A. Kharissov, V. V. Cherkashin, V. P. Kiryanov, A. V. Kiryanov, S. A. Kokarev, and A. G. Verhoglyad, “Polar coordinate laser pattern generator for fabrication of diffractive optical elements with arbitrary structure,” Appl. Opt. 38(8), 1295–1301 (1999). [CrossRef] [PubMed]
4. J.-M. Asfour and A. G. Poleshchuk, “Asphere testing with a Fizeau interferometer based on a combined computer-generated hologram,” J. Opt. Soc. Am. A 23(1), 172–178 (2006). [CrossRef] [PubMed]
5. J. H. Burge, “Fabrication of large circular diffractive optics,” in Diffractive Optics and Micro-Optics, OSA Tech. Dig. 10 (1998).
6. H.-G. Rhee and Y.-W. Lee, “Improvement of linewidth in laser beam lithographed computer generated hologram,” Opt. Express 18(2), 1734–1740 (2010). [CrossRef] [PubMed]
7. J. Jin, J. W. Kim, C.-S. Kang, J.-A. Kim, and T. B. Eom, “Thickness and refractive index measurement of a silicon wafer based on an optical comb,” Opt. Express 18(17), 18339–18346 (2010). [CrossRef] [PubMed]
8. J. W. Goodman, “Analog optical information processing,” in Introduction to Fourier Optics, 2nd ed., (McGraw-Hill, Singapore, 1996), Chap. 4.
9. V. Westphal, C. M. Blanca, M. Dyba, L. Kastrup, and S. W. Hell, “Laser-diode-stimulated emission depletion microscopy,” Appl. Phys. Lett. 82(18), 3125–3127 (2003). [CrossRef]
10. B. E. A. Saleh and M. C. Teich, “Beam optics,” in Fundamentals of Photonics (John Wiley & Sons, Inc., New York, 1991), Chap. 3.
11. D.-I. Kim, H.-G. Rhee, J.-B. Song, and Y.-W. Lee, “Laser output power stabilization for direct laser writing system by using an acousto-optic modulator,” Rev. Sci. Instrum. 78(10), 103110 (2007). [CrossRef] [PubMed]
12. D. K. Cohen, W. H. Gee, M. Ludeke, and J. Lewkowicz, “Automatic focus control: the astigmatic lens approach,” Appl. Opt. 23(4), 565–570 (1984). [CrossRef] [PubMed]
13. H.-G. Rhee, D.-I. Kim, and Y.-W. Lee, “Realization and performance evaluation of high speed autofocusing for direct laser lithography,” Rev. Sci. Instrum. 80(7), 073103 (2009). [CrossRef] [PubMed]
14. L. Deck and P. de Groot, “High-speed noncontact profiler based on scanning white-light interferometry,” Appl. Opt. 33(31), 7334–7338 (1994). [CrossRef] [PubMed]
15. A. Harasaki, J. Schmit, and J. C. Wyant, “Improved vertical-scanning interferometry,” Appl. Opt. 39(13), 2107–2115 (2000). [CrossRef] [PubMed]
16. G. Binnig, C. F. Quate, and C. Gerber, “Atomic force microscope,” Phys. Rev. Lett. 56(9), 930–933 (1986). [CrossRef] [PubMed]
17. T. Doi, T. V. Vorburger, and P. J. Sullivan, “Effects of defocus and algorithm on optical step height calibration,” Precis. Eng. 23(3), 135–143 (1999). [CrossRef]
