Vibrational spectroscopy of an amorphous∕crystalline sandwich structure for silicon:  Numerical results

We study the lattice dynamics of an amorphous∕crystalline∕silicon sandwich model using the environment-dependent interatomic potential (EDIP). We establish a base line by computing the vibrational properties of the component bulk crystal and bulk amorphous structures, which show reasonable agreement with experiment and with Stillinger-Weber (SW) potential results. We study the confinement of the modes in the different structural regions (crystal, amorphous, and interface). Low-frequency modes have disproportionate weight in the amorphous structure because of its lower shear elastic constants, and there are some narrow frequency bands with confinement of modes to the crystal. We examine the localization properties of modes at different frequencies by computing the inverse participation ratio. We find Anderson-localized modes in the amorphous structure with a mobility edge at a frequency below the maximum crystal vibration frequency. This frequency relation leads to modes that are extended in the crystal but localized or evanescent in the amorphous. We also find evidence for disorder-inducded quasilocalized modes in the crystal near the amorphous∕crystal interface. Resonance modes, which appear in the bulk amorphous structure, are not present in the EDIP results for the sandwich structure, although they do exist in the SW results. We discuss the lowest- (nonzero-) frequency modes, which arise from transverse-acoustic vibrations propagating perpendicular to the amorphous∕crystal interface.