Open Access
Add to BibSonomyAbstract
An accurate and simple optical triangulation method is proposed for determining the distance and the tilt angle between the window and the SQUID sensor in a scanning SQUID microscope (SSM) system. The surface of window near the sensor plane is roughened with Alumina powder so that the incident and reflected traces of the laser beam passing the window surface become visible and can be measured precisely with a normal optical microscope. Using the proposed approach, the distance between the sensor and the sample can be reproducibly adjusted to 30 μm or less. This method can also be applied to photolithography apparatus to detect the relative positions of the mask and the wafer.
©2009 Optical Society of America
1. Introduction
The most important components in some high-precision instruments, such as micrometer-scale mask aligners and high-T c scanning-superconducting-quantum-interference-device microscope (scanning-SQUID microscope, SSM) are high-accuracy or high-sensitivity sensors and sample alignment tools, which the required resolution is better than a micrometer. In the case of mask aligner in photolithography [1–3], mask and wafer alignment is achieved with the help of microscopes and different types of distance control of are used depending on the mask design. For example, in the Moiré approach, the alignment mask contains two pairs of 180° phase-shifted gratings, which generated two 180° out-of-phase Moiré signals. However, the use of two pairs of gratings makes this technique too complex [4]. Such an approach becomes impractical while being applied in a SSM system. Furthermore, since the SQUID sensor is very sensitive to magnetic fields or magnetic materials, only nonmagnetic materials can be used as parts of the apparatus close to the sensor and this makes the mechanical design of the alignment tool very difficult.
A typical scanning SQUID system has a spatial resolution of several mm. There are a few concerns about the design of SQUIDs for microscopy. First, the size of the SQUID is one of the main factors that determine the best spatial resolution of the system. The spatial resolution of the SSM depends on the size of the SQUID ring and the distance between the SQUID and the sample under investigation. If the SQUID is placed very close to the sample, then the size of the hole of the SQUID determines the spatial resolution. If the distance between the SQUID and the sample exceeds the diameter of the hole of the SQUID, then the spatial resolution is no better than the distance between the SQUID and the sample. Hence, to increase the spatial resolution, the SQUID should be designed with a small hole and it also should be placed very near the sample. A second key requirement is to optimize the magnetic field resolution. The spatial resolution and the sensitivity of the SSM are optimized when the SQUID is separated from the sample by no more than one hole diameter. For a SQUID-sample distance is in the 100 μm, and present high-T c systems can achieve a spatial resolution of 20-30μm, and a field resolution of approximately 30 pT/√Hz [1]. In principle, the performance can be markedly improved in both respects. Some groups have proposed a method for measuring the distance z between the SQUID and the window in z-SQUID systems in which the normal to the SQUID pickup loop is parallel to the normal to the sample surface. They made micrometer adjustments to the perpendicular distance z. The window was moved as close to the SQUID as possible using micrometer screws. A CCD camera is utilized to determine the distance z [5,6]. The distance between the sensor (or pickup coil) and the sapphire window is determined by measuring the required vertical displacement of the objective of an inverted microscope when the focus points is changed from the sensor and the inner surface of the sapphire window. Typical operational distances between the sensor and the sapphire window are around 50 μm but may be as low as 25 μm. Using similar procedure, another group has reported on the reproducible adjustment of the distance between the sensor and the sample to 100 μm [7,8].
These methods enable the distance z to be controlled, but they cannot accurately yield both the distance z and the tilt angle ϕ between window and sensor. However, the tilt angle ϕ affects the spatial resolution of SSM. This work proposes an optical method to control the distance z and the tilt angle ϕ between the sensor and the window precisely using an auxiliary laser beam and a CCD. Furthermore, the working distance of the image monitor is longer than that of a microscope so that it would be very convenient and easy to assemble and operate.
2. Experimental
Figure 1 shows the schematics of the system including the SQUID, the window and the laser beams. The CCD camera is located in front of the window and capturing of the image is managed by a computer. A laser beam of wavelength 633 nm passes through a convex lens and is incident on a smooth flat window at an angle of θ to the normal of the plane with SQUID (or holder). When the ray that travels through the window encounters a SQUID sensor, some of the incident light is reflected, and returns through the window again. Three rays that are incident on the window, incident on the SQUID sensor, and reflected from the SQUID sensor, are all captured by the CCD. The resulting distance z can be obtained directly from the geometrical relations shown in Fig. 1.
In Fig. 1, A and B are the points of incidence and reflection at which the laser beam contacts with the window respectively. The distance between point A and point B is defined as 2x. The relation between θ, x, and z is given by,
therefore, the distance z is obtained via the relationship z = tan θ / x, where the angle θ is known. Additionally, the tilt angle ϕ between the window and the sensor holder can also be obtained. One important thing we want to mention is that normally it is very difficult to observe the laser beam image in a smooth and flat window. In order to get a clear image of laser beam traces, the surface of the window close to the sensor is polished by Alumina powder. Figure 2 presents the relative positions of the SQUID and the window at various distances. Figures 2(a) and 2(c) show the side views of the SSM system (Fig. 1), and Figs. 2(b) and 2(d) present the bottom views at distances z and z’, respectively. The angle θ is the same in Fig. 2(a) and 2(b). Obviously distance x decreases as z decreases. From Eq. (1), θ should be measured before we can calculate z. However, measuring θ is not that straight forward.
Fig. 2 (a) and (c) present lateral views that correspond to Fig. 1 at z and z’. (b) and (d) are the front views that correspond to (a) and (c).
Figure 3(a) shows an image captured by a CCD camera at arbitrary distance z and arbitrary angle θ. The laser beam is scattered by the window and the sensor, and appears as a bright line in the image. The left line in Fig. 3(a) is the image of the incident ray that is scattered by the window. The right line in Fig. 3(a) is the image of the ray after it is reflected from the sensor and scattered by the window again. The central line is the image of the incident ray on the SQUID sensor. The background image is the pattern of the SQUID sensor. Figure 3(b) shows the image obtained when the window is moved away from sensor by a distance Δz, 1.0 mm. Based on Eq. (1),
Figure 3(b) yields a Δ2x of 1.43 mm. The incident angle θ is obtained from Eq. (2) and is 35.6 degree. Then, the resulting distance z is obtained from Eq. (1). The distance z is easily obtained from Fig. 3.
The sensor and window at a tilt angle ϕ, as presented in Fig. 4 , were considered. For the geometrical correlation that is given by Fig. 4(a) and 4(b), the relationship among θ, ϕ and ϕ is given by,
where θ is the incident angle; ϕ is the angle indicated in Fig. 4(b), and ϕ is the tilt angle between the window and the sensor. Δx and Δy are also indicated in Fig. 4(b). Δx and Δy can be measured from an image captured using a CCD camera. The tilt angle ϕ is derived from Eq. (3). From Figs. 3 and 4(b), Δx and Δy are 0.234 and 2.06 mm, respectively. The tilt angle is 9.14 degree. The tilt angle is adjusted slowly using an adjustment micrometer.Fig. 4 (a) The schematic of the window and sensor at a tilt angle ϕx. (b) Δx and Δy can be measured from an image captured using a CCD camera. The tilt angle ϕ can obtain from Eq. (3).
3. Results and discussion
Figure 5 clearly presents images taken by a CCD camera at various distances z. Figure 5(a) was taken as the distance z between SQUID and window is unknown. The window was move interval Δz toward the sensor then. Figures 5(a)-5(f) and Figs. 5(g)-5(l) were taken after the window moving at intervals of Δz, 400 μm and 100 μm, respectively. The distance x clearly decreased as z declined. The smallest distance z obtained in this experiment is 30 μm, as shown in Fig. 5(l). Figures 6(a) -6(e) present images of the incident and reflected rays for various tilt angles ϕ. The angle ϕ clearly declined as the micrometer was adjusted. The incident rays and the reflected rays gradually became parallel as the tilt angle decreased. These tilt angles ϕ were 9.14, 6.67, 4.72, 2.28 and 0 degrees, as shown in Figs. 6(a)-6(e), respectively. The proposed method also allows for tilt in relation to the x and y axes.
Fig. 5 The window was move interval Δz toward the sensor then. (a)-(f) and (g)-(l) were taken after the window moving at intervals of Δz, 400 μm and 100 μm, respectively.
Fig. 6 The angle ϕ was adjusted. The incident rays and the reflected rays gradually became parallel as the tilt angle decreased. These tilt angles ϕ in (a)-(e) were 9.14, 6.67, 4.72, 2.28 and 0 degrees.
Figure 7(a) indicates that the tilt angles in relation to the x and y axes are both zero degree. Figures 7(b) and 7(c) plot the tilt angle from the x axis, ϕx, and from the y axis, ϕy. The distances Δx and Δy are determined from an image captured using a CCD camera. The tilt angles ϕx and ϕy are also given by Eq. (3). In Fig. 7(b), ϕx and ϕy are 1.42 and zero degree, respectively. Figure 7(c) presents a plane tilted from the y axis by ϕy = 3.53 degree. In Fig. 7(d), ϕx and ϕy are 1.53 and 2.10 degree, respectively. From Fig. 7, images of the incident and reflected ray on the tilted window from any axis can be easily captured using CCD. The tilted window can also be adjusted until it is parallel to a sensor, by observing the bright lines in the images.
Fig. 7 The tilt angles in relation to the x and y axes. The tilted window can be adjusted until it is parallel to a sensor, by observing the bright lines in the images.
4. Conclusions
This work presents an accurate and simple method for determining the distance and the tilt angle between the window and the SQUID sensor in an SSM system. The proposed method is simple in that it utilizes a light source, a CCD camera and a computer. In the experiments that were performed in this work, the distance and the tilt angles of the sensor and the window were adjusted using a micrometer head, and were accurately observed and measured. The angle of incidence of the laser beam was easily obtained and the distance z between the sensor and the window was determined from an image captured by the CCD camera. The shortest distance z was 30 μm in this system; it will be reduced using a laser beam of shorter wavelength. A small tilt angle can also be measured from such an image. The proposed approach is useful for improving alignment systems or other microscopic systems.
Acknowledgements
The authors would like to thank the National Science Council of the Republic of China, Taiwan, for financially supporting this research under Contract No. NSC95-2112-M-005-014-MY3 and NSC95-2112-M005-016-MY3.
References and links
1. J. Clarke and A. I. Braginski, “The SQUID handbook,” Vol. 2, 391–440 (2004).
2. D. Koelle, R. Kleiner, F. Ludwig, E. Dantsker, and J. Clarke, “High-transition-temperature superconducting quantum interference devices,” Rev. Mod. Phys. 71(3), 631–686 (1999). [CrossRef]
3. Z. Chenggang, W. Yingnan, C. Yuhang, and H. Wenhao, “Alignment measurement of two-dimensional zero-reference marks,” Precis. Eng. 30(2), 238–241 (2006). [CrossRef]
4. Y. Uchida, S. Hattori, and T. Nomura, “An automatic mask alignment technique using moire interference,” J. Vac. Sci. Technol. B 5(1), 244–247 (1987). [CrossRef]
5. K. Sata and T. Ishida, “Development of high-Tc SQUID microscope,” Physica B 329–333, 1502–1503 (2003). [CrossRef]
6. K. Sata, M. Tsuji, S. Nakata, and T. Ishida, “Observation of square array of nickel dots by using high-Tc SQUID microscope,” Physica C 392–396, 1406–1410 (2003). [CrossRef]
7. F. Baudenbacher, N. T. Peters, and J. P. Wikswo Jr., “High resolution low-temperature superconductivity superconducting quantum interference device microscope for imaging magnetic fields of samples at room temperatures,” Rev. Sci. Instrum. 73(3), 1247–1254 (2002). [CrossRef]
8. L. E. Fong, J. R. Holzer, K. K. McBride, E. A. Lima, F. Baudenbachera, and M. Radparvar, “High-resolution room-temperature sample scanning superconducting quantum interference device microscope configurable for geological and biomagnetic applications,” Rev. Sci. Instrum. 76, 053703–1-9 (2005).
