Determination of elastic constants using a scanning acoustic microscope

Würz, K. U.; Wesner, Joachim; Hillmann, K.; Grill, Wolfgang

doi:10.1007/bf01322428

Cited by 33 publications

(5 citation statements)

References 15 publications

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“…2(b) resembles that of Si, but the gating has eliminated the diagonal caustics. Figure 2(c) shows a calculated amplitude image for h = 4.8 mm and f = 362 MHz, which is in good agreement with the corresponding measured image [3] in Fig. 2 (d).…”

Section: Time Gated Results For Gaassupporting

confidence: 83%

“…Owing to the small size of the dominant phonon wavelength in relation to the sample, source and detector dimensions, and partly to the incoherent nature of thermal phonons, phonon focusing patterns conform accurately to the predictions of ray acoustics. Analogous transmission acoustic microscopy experiments, performed with focusing transducers at ultrasonic frequencies, yield so-called internal diffraction patterns [1][2][3]. To account for these requires wave field calculations that go beyond the ray approximation and incorporate interference effects.…”

Section: Introductionmentioning

confidence: 99%

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Progression from ballistic phonon focusing to internal diffraction of ultrasound in crystals

Every

Pluta

Grill

et al. 2004

phys. stat. sol. (c)

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PACS 43.35.+d, 62.65.+k The aim of this paper is to bridge the divide between phonon focusing and internal diffraction patterns of crystals. We show how phonon caustics,at finite frequency, unfold into characteristic diffraction patterns. Then, as the frequency is lowered further, the fringes progressively broaden and merge, until ultimately only the broadest vestiges of the original focusing pattern can be discerned. Time gating and limiting the wave vector domain over which the requisite Fourier integrals are done, is used to isolate the diffraction patterns of elementary caustic structures such as cusps and folds. Calculations are reported for GaAs and Si, which are in good agreement with experiment.

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Section: Time Gated Results For Gaassupporting

confidence: 83%

Section: Introductionmentioning

confidence: 99%

Progression from ballistic phonon focusing to internal diffraction of ultrasound in crystals

Every

Pluta

Grill

et al. 2004

phys. stat. sol. (c)

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“…Furthermore, the imaging scheme allows for determination of slight misalignments of the crystal axis with respect to the sample surface. The holographic detection scheme described above is currently employed in a refined scheme for the determination of the elastic constants based on similar methods as already demonstrated for gallium arsenide crystals 14 .…”

Section: Resultsmentioning

confidence: 99%

Acoustic holography of piezoelectric materials by Coulomb excitation

et al. 2006

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Electric surface excitation of ultrasound in the Coulomb field of scanned electrically conductive spherical local probes and similar detection has been employed for imaging of the transport properties of acoustic waves in piezoelectric materials including singlecrystalline wafers. The employed Coulomb scheme leads to a fully predictable and almost ideal point excitation and detection. In combination with two-channel quadrature transient detection it allows high precision spatially and temporally resolved holographic imaging. Via modeling of the excitation and propagation properties, the effective elastic tensor and the piezoelectric properties of the observed materials can be determined with high resolution from a single measurement. The generation and detection scheme as well as the theoretical background are demonstrated and applications are exemplified.

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“…The measured image of GaAs shown later in the paper in figure 5 has been obtained in this way. Images such as this reveal a wealth of diffraction phenomena (Weaver et al 1993;Grill et al 1994;Wolfe & Hauser 1995;Würz et al 1995). For directions not too far removed from the x 3 direction normal to the sample's surface, the transmitted signal corresponds fairly closely to the elastodynamic Green's function G 33 ðx; uÞ for the infinite continuum, which we discuss next.…”

Section: Transmission Acoustic Microscopy (Tam)mentioning

confidence: 85%

“…The precision of agreement between the measured and calculated TAM diffraction patterns of GaAs reported here attests to the validity of the model and also to the accurate match between the material constants used in the calculations and those of the sample. Fitting of interference patterns of this type thus represents a sensitive tool in the determination of material constants (Würz et al 1995). The model shows that while the fringes are observed at the surface, they must be present in a similar form in the acoustic field throughout the volume, and might be observable by elasto-optic scattering or other methods.…”

Section: Discussionmentioning

confidence: 99%

Interference of non-aligned Airy diffraction patterns in transmission acoustic microscopy images of crystals

2005

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This paper describes interference effects present in narrow band transmission acoustic microscopy images of crystals that arise from the superposition of pairs of non-aligned but symmetry equivalent Airy diffraction patterns. In the cases we examine, these Airy patterns are associated with folded portions of the slow transverse (ST) sheet of the acoustic wave surface of cubic crystals intersecting in the {110} symmetry planes. Each set of Airy fringes is inclined in the (001) observation plane to its overlapping counterpart, giving rise to curved Moiré-like fringes. Also, because of tilting of the two portions of the wave surface in opposite directions out of the (001) plane, each composite Airy fringe breaks up along its length into a large number of narrow, regularly spaced fringes, in a manner akin to wedge diffraction. We present calculations of these effects in GaAs and Ge, based on the elastodynamic Green's function, , for the infinitely extended anisotropic elastic continuum. A measured time-gated diffraction image is presented for GaAs, which is in good agreement with calculation.

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Determination of elastic constants using a scanning acoustic microscope

Cited by 33 publications

References 15 publications

Progression from ballistic phonon focusing to internal diffraction of ultrasound in crystals

Progression from ballistic phonon focusing to internal diffraction of ultrasound in crystals

Acoustic holography of piezoelectric materials by Coulomb excitation

Interference of non-aligned Airy diffraction patterns in transmission acoustic microscopy images of crystals

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