We study the properties of localized interface optical-phonon modes in Si/3C-SiC heterojunctions within the framework of the dielectric continuum theory. Our model calculation takes into account the existence of an interfacial nonabrupt transition region, whose thickness is considered varying from 0.5 to 2.5 nm. Numerical results reveal some interesting properties of the interface effects, which can substantially shift ͑up to 20 cm Ϫ1 ) the high-frequency antisymmetric interface modes found in the abrupt case. Moreover, optical-phonon modes emerge in the low-frequency range of the spectrum, which are sensitive to the value of the nonabrupt interface thickness.The investigation of phonons in nanostructures has been very important in the last two decades due to the fundamental physical concepts employed to describe their intrinsic properties as well as for their potential device applications ͑for a review see Refs. 1,2͒. Tailoring of optical phonon modes in nanoscale semiconductors was proposed, suggesting that confined phonon effects can be used to tune quantum-well intersubband lasers. 3 The control of phonon scattering mediated intersubband transitions affect laser properties critically. Phonon modes engineering was proposed to be achieved by inserting a single alloy semiconductor step, producing three-interface heterostructures 4 as well as step quantum well structures. 5 However, the existence of micro-roughness superimposed to macroroughness gives rise to the existence of graded interfaces in semiconductor heterostructures. Even in systems such as GaAs/Al x Ga 1Ϫx As, the thickness of the graded interface regions is at least of the order of three monolayers, which is enough to have an effect on the laser optical gain, for example. 6 Consequently, it is important to investigate the role of naturally occurring graded interface on the phonon modes of semiconductor heterostructures.Progress in microfabrication techniques enables us to create various kinds of hetero-epitaxial interfaces between two dissimilar and yet closely lattice-matched semiconductors and facilitate the dramatic reduction in extrinsic interface defects detrimental to the electron mobility and other device parameters. In such heterojunctions, since experimental reality is approaching theoretical models and assumptions, detailed analysis and precise predictions are unprecedentedly made possible. 7 This is particularly true in the case of 3C-SiC/Si(100) heterojunctions, which are very promising for the fabrication of resonant tunneling diodes for highspeed and high-power applications. Successful growth of 3C-SiC(100) thin films on Si͑100͒ has been achieved by many groups mainly by chemical vapor deposition 8-11 and molecular ion beam deposition. 12 In particular, the existence of transition regions with thickness at least equal to 1 nm was found by high-resolution transmission electron microscopic observation in 3C-SiC/Si(100) heterojunctions, which were recently grown using a chemical vapor deposition technique with pulsed supersonic free jets. ...