Self-consistent theory of scattering at disordered interfaces in layered nanostructures

A self-consistent theory of electron scattering at the real disordered interfaces in the layered nanostructures is developed. This theory generalizes, particularly, the well known quantum mechanics results for the electron transmission through and reflection from the perfect potential steps/wells/barriers on the case of the intermixed (alloylike) interfaces. The closed analytical expressions for the probabilities of the specular and diffuse electron transmission and reflection at a single disordered interface are obtained in the self-consistent single-site coherent potential approximation (CPA) and the effective mass approximation for the electronic spectra of different layers. The exact (in the adopted approximations) quantum mechanical transmission amplitude for the electron traveling through two disordered interfaces of a trilayer is also obtained. These results allow studying the interfacial scattering at any angle of an electron incidence at an interface, any materials making up a multilayer (any potential profile and effective masses) and any concentrations of atoms mixed at an interface (particularly, at a nonzero average defect scattering strength). It is shown that the diffuse scattering (caused by the imaginary part of the coherent potential) vanishes at the grazing (with a very small perpendicular to an interface component of velocity) electron incidence at an interface leading to practically specular reflection from an interface (channeling affect). The specular scattering also dominates at close to normal to an interface electron incidence and small interfacial scattering potential fluctuations (from its average value). The diffuse scattering diminishes the specular transmission but may increase or decrease the specular reflection at a disordered interface and permits scattering to the areas (of the parallel to an interface electron momentum component) inaccessible for specular scattering at the perfect interfaces. The obtained specular transmission probability over a potential well of a metallic trilayer exhibits additional (to the conventional resonance states) oscillations caused by the real (average) part of the coherent interfacial potential. The interface roughness associated with the long-range layers' thicknesses fluctuations is accounted for through the semiclassical approximation for the obtained specular transmission probability through a metallic trilayer. For the case of an insulating spacer the obtained tunneling magnetoresistance (TMR) ratio may be expressed (for thick spacer) in the Slonczewski-type form but with the electron polarization and interface factors defined by the electron transmission probabilities (for different spin channels) through a spacer with disordered interfaces. The obtained results are believed to be important for the giant magnetoresistance (GMR) and TMR effects in the real nanostructures with disordered interfaces.