Inelastic Electron Tunneling Spectroscopy of Langmuir-Blodgett Monolayers on Silicon Substrate

Abstract

Based on the recently introduced orthonormal Hermite-Gaussian-type modes, a general class of sets of non-orthonormal Gaussian-type modes is introduced, along with their associated bi-orthonormal partner sets. The conditions between these two bi-orthonormal sets of modes have been derived, expressed in terms of their generating functions, and the relations with Wünsche's Hermite twodimensional functions and the two-variable Hermite polynomials have been established. A closed-form expression for Gaussian-type modes is derived from their derivative and recurrence relations, which result from the generating function. It is shown that the evolution of non-orthonormal Gaussian-type modes under linear canonical transformations can be described by the same mechanism as used for the evolution of orthonormal Hermite-Gaussian-type modes, when, simultaneously, the associated bio-orthonormal modes are taken into account.

Theoretical Bounds on Electron Energy Filtering in Disordered Nanomaterials

“…Tunneling electrons are scattered when their energies are resonant with molecular vibrational frequencies, and in this way vibrational spectra are encoded in the voltage dependence of the tunneling current. [11][12][13][14][15][16][17] Unfortunately, achieving the spectral resolution required to reliably distinguish molecular vibrational signatures (∼ 0.5meV) [18][19][20] presents a technical challenge that has limited current experiments to cryogenic conditions. Nonetheless, by constructing custom tunneling junctions that contain specific analytes, IETS has been used to measure the vibrational spectra of organic and inorganic molecules,, [21][22][23][24][25][26][27] to chemically analyze materials adsorbed on surfaces in scanning tunneling microscopy experiments, 28,29 and even to sequence DNA.…”

Theoretical Bounds on Electron Energy Filtering in Disordered Nanomaterials

“…Tunneling electrons are scattered when their energies are resonant with molecular vibrational frequencies, and in this way vibrational spectra are encoded in the voltage dependence of the tunneling current. [11][12][13][14][15][16][17] Unfortunately, achieving the spectral resolution required to reliably distinguish molecular vibrational signatures (∼ 0.5meV) [18][19][20] presents a technical challenge that has limited current experiments to cryogenic conditions. Nonetheless, by constructing custom tunneling junctions that contain specific analytes, IETS has been used to measure the vibrational spectra of organic and inorganic molecules,, [21][22][23][24][25][26][27] to chemically analyze materials adsorbed on surfaces in scanning tunneling microscopy experiments, 28,29 and even to sequence DNA.…”

“…Here, we focus our motivation on a specific probe of chemical structure known as inelastic electron tunneling spectroscopy (IETS). − In this technique, vibrational spectra are measured by transmitting a flow of electrons through a sample that is contained within a tunneling junction. Tunneling electrons are scattered when their energies are resonant with molecular vibrational frequencies, and in this way vibrational spectra are encoded in the voltage dependence of the tunneling current. − Unfortunately, achieving the spectral resolution required to reliably distinguish molecular vibrational signatures (∼0.5 meV) − presents a technical challenge that has limited current experiments to cryogenic conditions. Nonetheless, by constructing custom tunneling junctions that contain specific analytes, IETS has been used to measure the vibrational spectra of organic and inorganic molecules, − to chemically analyze materials adsorbed on surfaces in scanning tunneling microscopy experiments, , and even to sequence DNA. , …”