Existence of surface acoustic waves(SAW) on a piezoelectric layer with the half-infinite elastic layer is investigated. This structure belongs to an open waveguide with the unbounded boundary in the transverse direction. Except for trapped modes, leaky modes have often been considered in SAW applications, which requires waves of low attenuation in order to maximize the propagation distance. Therefore, we develop an another formulation of piezoelectric layer structures for the computation of trapped and leaky modes in open waveguides. This method combines the so-called semi-analytical isogeometric analysis and a perfectly matched layer technique (SIGA-PML). The comparison between semi-analytical finite element (SAFE-PML) and SIGA-PML is given, in order to show the effective and accuracy of SIGA-PML. Finally, we analyze propagation properties of Rayleigh waves and discuss the impact of the thickness of Cu films on the dispersive relationships.