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
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 . 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).8], as described in Eq. (2).6] and stimulated emission depletion microscopy . Height resolution of direct laser lithography, however, has not yet been reported.
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 . 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 , 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.
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.
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 isEq. (3) and the Helmholtz equation, A(x, y, z) must satisfy
One basic solution of Eq. (4) is
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
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.
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) , 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.
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.
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).
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