Electron scattering by a C₆₀molecule in a projection configuration

Abstract

The objective of this paper to discuss the observation of a C60 molecule by projection microscopy, in order to highlight the availability of structural information in the sample. In this context, a model for the potential energy relevant to an imaging electron encountering a carbon molecule is developed. The carbon atoms are characterized by static and dynamic polarizabilities to account for the effects of the static extraction bias and the moving imaging electrons. In agreement with previous papers, Fraunhofer and Fresnel diffraction are encountered. The C60 molecule turns out to have a strong focusing effect near polarizability resonances. The simulations reveal that, below a given bias, little structural information is available in the potential-energy distribution, due to the large dynamic polarizability of the carbon atoms. Although this information is present for larger bias and appears in the local current density, the resolution of the technique (in its present form) is too limited for the atomic structure of the sample to appear in projected images.

Simulations of transport and field-emission properties of carbon nanotubes

“…The carbon atoms in region II are represented by the Bachelet et al 17 pseudopotentials 18,24 for the ion-core potential and by Gaussian distributions for the valence electronic densities. 17 These two contributions are displaced from both sides of the atomic position according to the polarization p j of each atom 25 when an external field is present ͑i.e., in the simulations of field emission͒.…”

“…15 It is also known that the coupling between neighboring layers in a multiwall structure is relatively small, so this coupling hardly affects the band-structure properties of the tubes. 16 By applying the transfer-matrix methodology [17][18][19] already used to simulate field emission from carbon nanotubes, 7,8,[20][21][22] we aim at simulating how an electronic signal, when injected into a single layer of a multiwall nanotube, keeps propagating in this layer before spreading significantly to neighboring ones.…”

Three-dimensional calculation of field emission from carbon nanotubes using a transfermatrix methodology

“…[ 11], with a pseudopotential for the ion-core potential. For this ion-core contribution, we used the expression given in Ref.…”

“…To study field emission from carbon nanotubes, we used the transfer matrix technique developed in previous publications [11][12][13]. From a given three-dimensional potential-energy distribution (describing two biased electrodes), this methodology predicts the corresponding emitted current.…”

Inverse electronic scattering by Green’s functions and singular values decomposition

“…Our approach of the problem was based on both the transfer-matrix and Green's functions formalisms. [9][10][11][12][13][14] This approach enables direct-scattering simulations [15][16][17] with reduced storage requirements. However, due to the fact that the potential energy remains explicitly present in the Green's functions formulation, this latter will be used in this inverse scattering approach.…”