Interface acoustic modes of twisted Si(001) wafers

Abstract

Interface acoustic waves at the (001) boundary of twisted single-crystal silicon wafers are studied using analytical and numerical techniques. A secular equation of the problem in an explicit form is derived for the propagation directions along the twist-angle bisectrix and a complete numerical solution is calculated for arbitrary propagation. A new mode of leaky-wave type is predicted. This leaky mode has a low propagation loss and distinct near-interface localization at small twist angles. The leaky wave is purely longitudinal at the interface in the bisectric case. A mode without leakage is found only in the vicinity of the bisectrix directions. Its feature is a rotating movement of interface particles in the plane normal to the propagation direction in the bisectrix case. The sector of azimuthal angles permitted for the propagation of the nonleaky mode has an unusual jumplike behavior as a function of the twist angle.

On interface waves in misoriented pre-stressed incompressible elastic solids

“…Moreover this wave, of the IAW1 type, satisfies these requirements only within a limited range of misorientation angle, approximatively 16.7 o < θ < 73.6 o . This situation is in sharp contrast with the case of silicon/silicon wafers in linear anisotropic elasticity (Mozhaev et al, 1998) where the IAW1 was found to exist for all θ. Figure 2 depicts the variations of the relevant root to the secular equation, scaled as √ X = ρv 2 , with θ (thick curve).…”

“…In effect, and as displayed by Mozhaev et al (1998) in the linear anisotropic elasticity case, either one displacement component and two tractions are zero at the interface, or vice-versa. More specifically, and these details were not noted by Mozhaev et al (1998), ξ(0) must be of one of the two following forms. Either…”

“…The Appendix presents the derivation of these expressions. Following Mozhaev et al (1998), the interface acoustic wave satisfying (8) (resp. (9)) is called IAW1 (resp.…”

“…Namely, these conditions are that at the boundary, either one displacement and two tractions are zero, or two displacements and one traction are zero. Mozhaev et al (1998) noted this important result for bonded silicon/silicon wafers in linear anisotropic crystallography. It is further proved here that once the displacement-traction vector is normalized with respect to one of its non-zero components, then the normalized components are either real or pure imaginary (see Appendix for details).…”

“…Mozhaev et al (1998) considered the theoretical implications of misorientation when two identical silicon wafers are rigidly bonded. Specifically they considered, within the framework of anisotropic linear elasticity, the propagation of interface (Stoneley) waves along the bisectrix of a twist angle of misorientation .…”