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·Methods and Instrumentation
Principle and Applications of Practical Shear Wave Lens at Low frequencies for Scanning Acoustic MicroscopyChiaki MIYASAKA, and Bernhard R. TITTMANN
Department of Engineering Science & Mechanics
The Pennsylvania State University
212 Earth and Engineering Science Building, University Park, PA 16802, USA
This paper presents the principles and applications of a new acoustic lens designed for scanning acoustic microscopy at low frequencies (less than 100MHz). Whereas designs of most current lenses emphasize the use of longitudinal waves, designs of the practical shear wave lens focus on the use of shear, and surface waves as well. The lens provides
Key Words: Acoustic lens, Scanning Acoustic Microscope, Aperture angle, Shear wave, Transverse wave, Interior resolution
The SAM has also frequently been used in the field of inspecting microelectronic integrated circuits (IC) because the cross-sectional images provide details of defects located within an IC package. However, the interior structures have been compactly and complicatedly designed, so that it is more difficult to obtain a clear cross-sectional image. Conventional images obtained with longitudinal wave transducers tend to suffer from layer-to-layer overlap. Therefore, one issue is how to obtain clearly resolved interior cross-sectional images.
When increasing the resolution of an acoustic image, three approaches can be considered. The first approach is to raise the acoustic frequency. However, in the first approach, the ultrasonic wave is attenuated in proportion to the square of its frequency; therefore, when the high frequency ultrasonic wave is used as a probe, the wave may not penetrate the inside of the specimen, and the interior information may not be obtained.
The second approach is to use low velocity coupling media such as super-fluid liquid helium. However, in the second approach, the acoustic impedance between the coupling medium and the specimen are very different. Therefore, most of the ultrasonic waves are reflected at the interface between the coupling medium and the specimen, so that it is unlikely that the acoustic image from any significant depth may be obtained.
The third approach is to design a new acoustic lens. By means of this approach, B. T. Khuri-Yakub et al proposed an acoustic lens with a transducer generating horizontally polarized shear waves to image the anisotropy of materials . D. A. Davids et al proposed an acoustic lens with a restricted aperture for only generating Rayleigh waves . A. Atalar et al proposed an acoustic lens with a non-spherical aperture for generating Lamb waves , and slit aperture for pseudo line focusing to image the anisotropy of materials . However, although those lenses give us an improvement for obtaining sub-surface information, the resolution at deep penetration depths is not improved.
It is well known that resolution may be enhanced by using shear waves rather than longitudinal waves, since the wavelength of a shear wave is much shorter than that of the corresponding longitudinal wave at the same frequency. This paper presents the principle and applications of the acoustic lens working the center frequency at 30 MHz, and forming images with longitudinal, shear and surface waves. The use of these lenses also gives as additional benefits reduction in spherical aberration and decrease in image noise from surface roughness. In this paper, we provide applications emphasizing on these factors.
The description above can be applied to the case of an ultrasonic source in the shape of a lens sending longitudinal waves through a liquid into a solid. The considerations above lead to the existence of two separate focal points, one for longitudinal waves and the other for the shear waves. Moreover, the relative ultrasonic power level at each focal point depends on the critical angles of the material. In particular, in order to excite a shear wave strong enough to form an acoustic image of the sample interior, the aperture angle of the lens portion of the acoustic lens must be designed to be large. Therefore, acoustic waves can be incident at angles exceeding the critical angle of the longitudinal wave. The shear wave can be excited in most of the materials when the full aperture angle is designed to be 100º or more.
An acoustic image may be represented mathematically by an acoustic field. Acoustic fields of the different planes (Plane 0' is the transducer plane, 'Plane 1' is the back focal plane, 'Plane 2' is the front focal plane, and 'Plane 3' is the surface of the specimen) are expressed by a spatial distribution ui±(x,y) where (i=1,2,3) or a frequency distribution
Ui±(kx,ky), where(i=1,2,3). Superscripts + or - indicate that the direction of field travel, i.e. in the + Z or - Z direction, respectively. The spatial and frequency distributions are related by the following equations.
When the distance between the transducer and the back focal plane is sufficiently long, the acoustic field is expressed by the Fourier transform as follows:
where l is the distance between the transducer and the back focal plane.
where f ' is the distance between the back focal plane and the front focal plane, and P is the pupil function.
where R is the reflection.
Insertion of Eqs. (4) - (8) into Eq. (3), leads to the final result for the acoustic field of the transducer as follows:
When normalizing the PSF, in Eq. (10) is omitted.
The output of the transducer V( Z ) is expressed as follows:
Considering Eqs. (9), (10), and (11) in the final output at the transducer, the reflected acoustic field is integrated over a larger surface area leading to a "washing out" of surface roughness details. This is a key issue for the reduction of superimposed surface roughness.
Acoustic Images for Reducing Superimposed Surface Information
Figs. 1 (a) and 1(b) show images formed by a conventional and a practical shear wave lens at a frequency of 30 MHz. Fig. 2(a) is an interior image showing an IC chip included in the package, wherein the surface image (i.e., marks) was superimposed onto the interior image. Fig. 2(b) is an interior image showing the same IC chip, but the surface image was not superimposed.
|Fig 1: Acoustic images using (a) conventional and (b) practical shear wave lenses (frequency: 30MHz), wherein the images are from the IC chip internally located in the IC package. Clearly visible are the improvement in resolution and reduction in surface features for the high N. A. lens.|
|Fig 2: Schematic diagram for simulation of wave propagation by ray tracing technique.Frequency: 100 MHz; specimen: epoxy, (a) Conventional lens, (b) Practical shear wave lens.|
A ray tracing software program was used to provide a two-dimensional view of the rays associated with the combination of lens, coupling media, and specimens. For example, Figs. 2(a) and 2(b) show loci of longitudinal wave rays at 30 MHz for the conventional and practical shear wave lens, wherein their full aperture angles are 30° and 100° respectively. The lenses are focused on an internal plane, located 1.0mm below the surface of the specimen (i.e., epoxy resin) via water. The beam spot size of the practical shear wave lens is smaller than that of the conventional lens.
Acoustic Images for Reducing Spherical Aberration
Figs. 3(a) and 3(b) show acoustic images of a delamination located at the first interface of the CFRP laminates, having structures as [0° 6/90° 6]s , wherein the images were formed with the frequency at 30 MHz by the conventional and practical shear wave lenses, respectively. The delamination was introduced by impacting a steel spherical ball, having a diameter of 10mm, with a velocity of 39.5 m/s. The shape of the CFRP laminates was substantially rectangular (180 mm x 180 mm).
|Fig 3: Acoustic images of delamination introduced at an interface of the CFRP Frequency: 30 MHz, (a) Conventional lens (b) Practical shear wave lens|
In Fig. 3(b), the vertical black lines located at regular intervals were observed within the delamination image. The black lines can be considered as a configuration of transverse cracks and fringes, wherein the transverse crack may be located underneath of the delamination and the fringes may be caused by interference between waves incident onto the interface and waves reflected from the edge of the crack.
In order to confirm the above assumption, the specimen was horizontally sectioned crossing the black lines (See Fig. 4). The cross-section of the specimen was observed with the optical microscope (See Fig. 5). In Fig. 5, the transverse crack is seen to reach to the interface having the delamination. Hence, the interpretation of the image made above was confirmed.
|Fig 4: Magnification of upper portion of Fig. 4(b) showing the position to be cut.||Fig 5: Optical image of the vertical cross-section of the CFRP|
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