Institute of Chemical Physics, Russian Academy of Sciences, Kosygin Str., 4, 117334 Moscow, RUSSIA, FAX: (095) 938-21-56, E-mail:firstname.lastname@example.org
We discuss investigation of wave functions and energy spectra of quantum dots with STM. Quantum dots are characterized by the presence of the electronic states localized at the surface with lateral dimensions of several nanometers and energy levels lying in the bandgap of the substrate.
In addition to the contribution of the quantum dot states to the total density of states, they give a considerable effect on the STM image and STS spectra due to the spatial deformation of tunneling barrier. The latter is determined by the effective tunneling potential(ETP) which is summed up the contributions from pure substrate and the ETP from the quantum dot itself. Since the ETP depends on the wave functions and energy levels of all the electrons of the system it results in complicated spatial configuration of tunneling current image. Moreover, since the ETP is defined by the energy and quantum numbers of tunneling electron, it is quite sensitive on the details of electronic structure of combined system, in particular, on the position of energy levels of quantum dot relative the Fermi level of the substrate.
Wave function of quantum dot is chosen as a Bloch standing wave and tunneling current is calculated in the frame of Lippmann-Schwinger & Green's function formalism. The topology of STM image is determined as a function of quantum numbers of quantum dot (attributing to the appropriate symmetry properties) as well as the atomic wave-functions from which the Bloch function is being built.
We also consider other situation which could result in appearance of the localized electronic state, so called "induced quantum dot". This electronic state is produced by the bending of the energy band of the clean surface under the influence of electrostatic filed between the sample and the scanning tip. The induced quantum dots have the lateral dimensions defined by the effective radius of curvature of the tip, and electronic levels of quantum dots are confined between the vacuum barrier and the bending energy levels. Due to the presence of the induced quantum dots we expect the interference effects of resonant character in STS spectra.
We consider the physics of the tunneling in these complex structures in order to assist in interpreting the STM images and STS spectra. Due to the interaction of various features of quantum dots with the detail of electronic structure of substrate it makes possible to formulate the numerical scheme which aims to extract the details of quantum dot electronic structure from STM/STS experimental data.