Finite-Difference Time-Domain Analysis of Scanning Tunneling Microscope Light Emission Spectra

Abstract

A theory describing multiphonon resonant Raman scattering (MPRRS) processes in wide-gap diluted magnetic semiconductors is presented, with Cd 1−x Mn x Te as an example. The incident radiation frequency ω l is taken above the fundamental absorption region. The photoexcited electron and hole make real transitions through the LO phonon, when one considers Fröhlich (F) and deformation potential (DP) interactions. The strong exchange interaction, typical of these materials, leads to a large spin splitting of the exciton states in the magnetic field. Neglecting Landau quantization, this Zeeman splitting gives rise to the formation of eight bands (two conduction and six valence ones) and ten different exciton states according to the polarization of the incident light. Explicit expressions for the MPRRS intensity of second and third order, the indirect creation and annihilation probabilities, the exciton lifetime, and the probabilities of transition between different exciton states and different types of exciton as a function of ω l and the external magnetic field are presented. The selection rules for all hot exciton transitions via exciton-photon interaction and F and DP exciton-phonon interactions are investigated. The exciton energies, as a function of B, the Mn concentration x, and the temperature T , are compared to a theoretical expression. Graphics for creation and annihilation probabilities, lifetime, and Raman intensity of second and third order are discussed.

Creation and Luminescence of a Single Silver Nanoparticle on Si(111) Investigated by Scanning Tunneling Microscopy

“…Although this method allows us to reproduce various types of experimental STM-LE results, it is only applicable to the system consisting of simple layered structures. In contrast, the FDTD method has been recently applied to the spectral analysis of the STM-LE. , One of the advantages of the FDTD is that the electromagnetic calculations can be performed for the sample with the arbitrary shapes. Recently, it was confirmed that the FDTD calculation provides predictions which are consistent with those of the calculation based on the dielectric theory .…”

“…In contrast, the FDTD method has been recently applied to the spectral analysis of the STM-LE. , One of the advantages of the FDTD is that the electromagnetic calculations can be performed for the sample with the arbitrary shapes. Recently, it was confirmed that the FDTD calculation provides predictions which are consistent with those of the calculation based on the dielectric theory . Since the present study deals with the optical responses of nanoparticles, we employed the FDTD method to calculate the STM-LE spectra.…”

“…Since the present study deals with the optical responses of nanoparticles, we employed the FDTD method to calculate the STM-LE spectra. For details on the calculation, refer to the previous papers . Here, the brief explanation is provided as follow.…”

“…For details on the calculation, refer to the previous papers. 52 Here, the brief explanation is provided as follow. The spectrum P(ω) of the STM-LE excited by electron tunneling in the tip− sample gap of an STM can be given by…”

“…Recently, it was confirmed that the FDTD calculation provides predictions which are consistent with those of the calculation based on the dielectric theory. 52 Since the present study deals with the optical responses of nanoparticles, we employed the FDTD method to calculate the STM-LE spectra. For details on the calculation, refer to the previous papers.…”