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Silicon edges as one-dimensional waveguides for dispersion-free and supersonic leaky wedge waves
(2012)
Acoustic waves guided by the cleaved edge of a Si(111) crystal were studied using a laser-based angle-tunable transducer for selectively launching isolated wedge or surface modes. A supersonic leaky wedge wave and the fundamental wedge wave were observed experimentally and confirmed theoretically. Coupling of the supersonic wave to shear waves is discussed, and its leakage into the surface acoustic wave was observed directly. The velocity and penetration depth of the wedge waves were determined by contact-free optical probing. Thus, a detailed experimental and theoretical study of linear one-dimensional guided modes in silicon is presented.
In anisotropic media, the existence of leaky surface acoustic waves is a well-known phenomenon. Very recently, their analogs at the apex of an elastic silicon wedge have been found in experiments using laser-ultrasonics. In addition to a wedge-wave (WW) pulse with low speed, a pseudo-wedge wave (p-WW) pulse was found with a velocity higher than the velocity of shear bulk waves, propagating in the same direction. With a probe-beam-deflection technique, the propagation of the WW pulses was monitored on one of the faces of the wedge at variable distance from the apex. In this way, their depth structure and the leakage of the p-WW could be visualized directly. Calculations were carried out using a method based on a representation of the displacement field in Laguerre functions. This method has been validated by calculating the surface density of states in anisotropic media and comparing the results with those obtained from the surface Green's tensor. The approach has then been extended to the continuum of acoustic modes in infinite wedges with fixed wave-vector along the apex. These calculations confirmed the measured speeds of the WW and p-WW pulses.
A theoretical description is given for the propagation of surface acoustic wave pulses in anisotropic elastic media subject to the influence of nonlinearity. On the basis of nonlinear elasticity theory, an evolution equation is presented for the surface slope or the longitudinal surface velocity associated with an acoustic pulse. It contains a non-local nonlinearity, characterized by a kernel that strongly varies from one propagation geometry to another due to the anisotropy of the substrate. It governs pulse shape evolution in homogeneous halfspaces and the shapes of solitary surface pulses that exist in coated substrates. The theory describing nonlinear Rayleigh-type surface acoustic waves is extended in a straightforward way to surface waves that are localized at a one-dimensional acoustic waveguide like elastic wedges.
Surface and interface acoustic waves are two-dimensionally guided waves, as their displacement field is plane-wave like regarding its dependence on the spatial coordinates parallel to the guiding plane, while it decays exponentially along the axis normal to that plane. When propagating at the planar surface or interface of homogeneous media, they are non-dispersive. Another type of non-dispersive acoustic waves which is, however, one-dimensionally guided, has displacement fields localized near the apex of a wedge made of an elastic material. In this short review, their propagation properties are described as well as theoretical and experimental methods which have been used for their analysis. Experimental findings are discussed in comparison with corresponding theoretical work and potential applications of this fascinating type of acoustic waves are presented.
Anisotropy has been found to play an important role for the existence of edge-localized acoustic modes as well as for nonlinear effects in rectangular edges. For a certain propagation geometry in silicon, the effective second-order nonlinearity for wedge waves was determined numerically from second-order and third-order elastic moduli and compared with the nonlinearity for Rayleigh waves propagating in the direction of the apex on one of the two surfaces forming the edge. In the presence of weak dispersion resulting from modifications of the wedge tip or coating of the adjacent surfaces, solitary pulses are predicted to exist and their shape was calculated.
In a recent paper it has been shown that the effective nonlinear constant which is used in a P-Matrix approach to describe third-order intermodulation (IMD3) in surface acoustic wave (SAW) devices can be obtained from finite element (FEM) calculations of a periodic cell using nonlinear tensor data [1]. In this paper we extend this FEM calculation and show that the IMD3 of an infinite periodic array of electrodes on a piezoelectric substrate can be directly simulated in the sagittal plane. This direct approach opens the way for a FEM based simulation of nonlinearities for finite and generalized structures avoiding the simplifications of phenomenological approaches.
In einer SAW-Vorrichtung, welche einen SAW-Chip umfasst, der einen SAW-Wandler aufweist, welcher innerhalb einer ersten Signalleitung angeordnet ist, werden Parasitärsignale infolge höherer Harmonischer der Betriebsfrequenz der SAW-Vorrichtungen durch Kompensationsmittel elektrisch beseitigt, welche zumindest eine zweite Signalleitung mit Mitteln zum Erzeugen eines Aufhebungssignals, das im Vorzeichen oder in der Phase vom Parasitärsignal verschieden ist, oder eine Nebenschlussleitung zum elektrischen Verbinden des SAW-Wandlers mit einer rückseitigen Metallisierung des SAW-Chips umfassen.