Laurent Aebi

Acoustic field radiated into a transversely isotropic solid from a small aperture spherical surface

The acoustic field modelling reported in this paper finds application in the design of a scanning probe tip for measuring the near-surface elastic properties of solids and surface structures at high frequencies and with high spatial resolution. The underlying concept is for a longitudinally polarized pulse to be launched from a spherically-shaped portion of the upper surface of the pyramidal or conical shaped tip, and focused towards the narrow lower end. The change in the reflectivity when the narrow end is brought into contact with a solid will provide a measure of the local frequency dependent compliance of that solid. The calculations assume the material from which the tip is fabricated to be transversely isotropic, with symmetry axis coinciding with the axis of the tip. The main issue addressed in this paper is the role of the curvature of the radiating surface and anisotropy of the medium in determining the focal length and focal spread of the radiated field. Two complementary approaches are taken, firstly the discretization of the equations of motion on an irregular mesh of around 3×10(5) triangular elements and solution using the commercial FE package ABAQUS/Explicit, and secondly an analytical approach based on ray tracing and a Greens function method exploiting the angular spectrum method and stationary phase approximation in its evaluation. Consistency is achieved between these approaches regarding the characteristics of the focal region. With the combination of the two approaches it is thus possible to model the wave field from low frequencies, where the FE method is computationally economical and able to handle complex geometries, to high frequencies, where advantage increasingly lies with ray tracing and the Greens function method.

P1G-4 Characterization of Nanoimprinting Polymer Films Using Picosecond Ultrasonics

laser acoustic setup is used to determine mechanical properties of polymer thin films which are used for nanoimprinting. Until now mechanical properties like the Youngs Modulus or the Poisson Ratio are not well known for these polymers in such small dimensions (100 - 600 nm thickness). The polymer films are spincoated on a silicon wafer and covered with a thin aluminum layer for a better energy absorption of the laser pulses. The measurements are performed on a femtosecond laser pump- probe setup with a collinear beam guidance. This measurement method is contact-free and non-destructive. Mechanical waves are excited and detected thermoelastically using infrared laser pulses of approximately 80 fs duration. The entire experimental setup is simulated numerically: The heat distribution and wave excitation in the thin films caused by the laser pulse, the wave propagation, and the photoacoustic detection. Results of the simulation are shown and a short overview of the simulation procedure is given. With the simulation it is possible to interpret and assign the various measured wave pulses. The laser acoustic measurements are compared with profilometry measurements performed on the same thin film structures in order to quantify the mechanical properties of the polymer films.

P2F-4 Frequency Selective Wave Propagation in Graded Materials

Lets consider a mechanical stress pulse propagating in an elastic medium. When this pulse encounters a material or phase interface, which generally represents a change of the acoustic impedance, the pulse is split up into two parts. The first part is propagating further into the new material and the second part is reflected. The amplitude ratio of the reflected and the transmitted part is governed by the normalized difference of the acoustic impedance only, provided that the impedance change is a pure step function in space. If the acoustic impedance change is broadened spatially, the ratio of the transmitted and reflected part becomes frequency dependent and the effect can therefore be used for filtering, damping, acoustic isolation, and/or spectrum analysis purposes or for quantitative analysis of interfaces. The effect is of growing importance for micro- and nanostructures since the relative size of the interface layers is generally larger than in macroscopic structures. In this work, a pulse propagating in a linear elastic graded material is investigated with one-dimensional simulations. The numerical scheme is based on the Finite-Difference Time-Domain method (FDTD). The validation of the numerical model is carried out by comparing the simulated pulse propagation stress history with an analytical solution based on Chiu et al. [1].

Validation of an algorithm for wave propagations in graded materials with an analytical solution

When a mechanical stress pulse, which is propagating in an elastic medium, encounters a material- or phase interface, which generally represents a change of the acoustic impedance, it is split up into a part, which propagates further into the new material and another part, which is reflected. The amplitude ratio of the reflected and the transmitted part is governed by the normalized difference of the acoustic impedance only, provided that the impedance change is a pure step function in space. If the acoustic impedance change is broadened spatially, the ratio of the transmitted and reflected part becomes frequency dependent and the effect can therefore be used for filter-, damping-, acoustic isolation-, and/or spectrum analysis purpose or for quantitative analysis of interface. The effect is of growing importance for micro- and nanostructures since the relative size of the interface layers is generally larger than in macroscopic structures. In this work, a pulse propagating in a linear elastic graded material is described with analytical solutions and one dimensional simulations. The numerical scheme is based on the Finite-Difference Time-Domain method (FDTD). The validation of the numerical model occurs by comparing the simulated pulse propagation-history with an analytical solution based on.1 On-coming research is also given at the end of this study.

4H-6 Guided Elastodynamic Waves in Radially Graded Cylindrical Structures

The three-dimensional time boundary value problem for axisymmetric elastic waves in radially graded full cylinders is solved numerically. Elastic waves are initiated with a linear-sweep-displacement signal multiplied by a Hanning window in the time domain. The displacement excitation is applied to the cross section at the end of the cylinder. Time shots of the displacement fields for various structural configurations and material gradients are presented and discussed. Due to axisymmetry the displacement field remains two-dimensional, consisting of a radial- and a longitudinal component. Material properties of aluminum and gold are chosen for the numerical simulations. The multimode nature of the guided waves propagating along the axis is analyzed with a two dimensional spectrum analysis method. The spectrum analysis in the space domain i.e. the longitudinal axis, and in the time domain leads to the projections of the dispersion curves into a plane formed by the real part of the wave number of the guided waves and the frequency. Influences of the radial material gradient on the shapes of the dispersion diagrams are presented

ULTRASONIC WAVE FIELD MODELING IN A CONICAL SCANNING PROBE TIP

The ultrasonic wave field modeling reported in this paper has been undertaken with a view to optimizing the design of a conical scanning probe microscope tip to be used in measuring the near surface elastic properties of solids at high frequencies and high spatial resolution. The modeling is concerned with the evolution of a pulse which is launched from the upper spherical shaped surface of the tip, and is aimed at achieving the greatest possible concentration of acoustic energy at the lower sharp end of the tip. The calculations assume a transversely isotropic medium. Two complementary approaches have been taken, firstly the discretization of the equations of motion on a 1000×1000 mesh and solution using the commercial FE package ABAQUS, and secondly an analytical approach based on the angular spectrum method and stationary phase approximation. A high degree of consistency is achieved between the two approaches regarding the characteristics of the focal region, dispersion of the pulse attendant on the di...

Pulse laser induced wave propagation in graded media and focusing devices

Near-infrared-laser pulses having durations of 100 fs are used to excite elastic waves thermoelastically propagating in a sub-THz frequency range. The elastic waves interact with inhomogeneities and carry information to the surface. The arrivals of the elastic pulses at the surface lead to transient changes of the optical reflectance which are monitored with short laser pulses which have a defined and controlled time delay relative to the initial pulses. Two activities of the research group are presented: The reflection and transmission behavior of acoustic waves propagating in graded media shows a frequency dependent nature and can therefore be used for filtering purpose. Time-boundary value problems are solved for various gradients with a finite-dierence method. Results of the numerical simulation are presented and compared with laser-acoustic measurements. A ’classical’ photoacoustic set-up provides an in-depth resolution of about 5 nm whereas the lateral resolution is in the order of 5 to 10 microns. To enhance the lateral resolution of the pump-probe technique, the elastic wave propagation along structures with arbitrary tip-like geometries consisting of orthotropic material is analyzed. With such structures representing ultrasonic lenses, the elastic energy is focused to a spot size given by the sharpness of the tip thereby leading to a higher lateral resolution.

Photoacoustic metrology of nanoimprint polymers

Nanoimprint lithography (NIL) is an alternative lithography method for patterning of thin polymer films using a rigid stamp, which is being developed as desired minimum feature sizes reduce to the scale of tens of nanometres. To characterise nanoimprinted structures, there is a need for more convenient and non‐destructive wafer‐scale metrologies to complement scanning electron microscopy and atomic force microscopy. The photoacoustic method, with a resolution in the range of 10 nm, and normally used to measure metal and dielectric layer thicknesses and physical properties, has been used for the first time to study nanoimprinting polymer layers. A good signal was obtained from the top and the bottom interfaces of two polymers, mr‐I PMMA 75k300 and mr‐NIL 6000.3, with thicknesses ranging from 100 to 500 nm. From the measured time of flight of the acoustic wave, and modelling physical parameters of the polymers, thicknesses calculated agree well with those measured by profilometry. The measurements are perfo...