Elastic Constants of a Stressed Layer from Surface Acoustic Wave Measurements

Abstract

Parks Road Oxford OXl 3PH England INTRODUCTIONIt is well known that the propagation of both bulk and surface acoustic waves (SAWs) is affected by the presence of static stresses, a phenomenon known as the acoustoelastic effect. Ultrasonic measurements of velocity therefore depend on the stresses within the material, as well the elastic constants and the density. Although the effect of stress on the velocity is small, many ultrasonic methods are sufficiently accurate to detect the changes involved. When inverting such measurements to obtain elastic constants, it is desirable to take the effect of stress into account. Similarly, when using ultrasonic methods to measure stress, it is necessary to have accurate values for the elastic constants. In practice, the material parameters of the 'natural', unstressed state are often either completely unknown or not known with sufficient accuracy (as is usually the case for residual stresses), or else cannot be assumed to be equal to bulk values (as in the case of layered materials). This is a major distinction between situations involving residual as opposed to applied stress, since a reference state of some description is always available in the latter case.In this paper we show how to improve the estimation of the elastic constants of the natural state of a residually stressed layer from SAW measurements. To do this, we incorporate the stress into the forward calculation of the SAW velocity, so that fitting of the measured SAW dispersion then yields the elastic constants of the unstressed state. We then apply the procedure to GaAs wafers implanted with Si+ ions. BACKGROUND

Influence of the short-range structural properties on the elastic constants of Si/Ge superlattices

“…Sklar et al [32] have shown that the most important elastic constant change of a stressed layer is due to the strain. They have calculated a decrease of 4%, 0% and 12% from the bulk values of C 11 , C 12 and C 44 elastic constants, respectively, for a GaAs layer subjected to a perpendicular strain of 0.4%.…”