Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Dimensional Effects on Densities of States and Interactions in Nanostructures | Nanoscale Res Lett 2010 5 1546-1554 DOI s11671-010-9675-1 NANO EXPRESS Dimensional Effects on Densities of States and Interactions in Nanostructures Rainer Dick Received 15 April 2010 Accepted 7 June 2010 Published online 2 July 2010 The Author s 2010. This article is published with open access at Abstract We consider electrons in the presence of interfaces with different effective electron mass and electromagnetic fields in the presence of a high-permittivity interface in bulk material. The equations of motion for these dimensionally hybrid systems yield analytic expressions for Green s functions and electromagnetic potentials that interpolate between the two-dimensional logarithmic potential at short distance and the threedimensional r-1 potential at large distance. This also yields results for electron densities of states which interpolate between the well-known two-dimensional and threedimensional formulas. The transition length scales for interfaces of thickness L are found to be of order Lm 2m for an interface in which electrons move with effective mass m and Le 2e for a dielectric thin film with permittivity e in a bulk of permittivity e. We can easily test the merits of the formalism by comparing the calculated electromagnetic potential with the infinite series solutions from image charges. This confirms that the dimensionally hybrid models are excellent approximations for distances r Z L 2. Keywords Density of states Coulomb and exchange interactions in nanostructures Dielectric thin films R. Dick Physics Engineering Physics University of Saskatchewan 116 Science Place Saskatoon SK S7N 5E2 Canada e-mail Introduction When we suppress motion of particles in certain directions through confining potentials . in quantum wells or quantum wires we often model the residual low energy excitations in the system through low-dimensional quantum mechanical systems. Prominent examples of this concern layered .
