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where V rms is the modulation voltage, k B is the Boltzmann constant, and T is the
temperature. The typical resolution of IETS is expected to be 1-4 meV at low
temperature (*5 K).
2.2.4 STM-IETS
The capability detecting molecular vibrations by combining STM and IETS was
already mentioned in the 1980 s. Since tunneling electrons in STM pass through
an area that is smaller than a single molecule, in principle, STM-IETS is able to
measure molecular vibrations within a single molecule. The first result was
reported in 1998 by Stipe et al. [ 23 ] and the C-H(D) stretch mode was clearly
observed with the correct ratio of the isotope substitution. This result demonstrated
the STM ability to be used as not only a microscope but also a chemically sensitive
tool. At the same time, the result provided following questions. (i) Why only the
C-H stretch mode is detected? (ii) What determines the shape of spectra? (i) is
related to the selection rule, which is important and useful in vibrational spec-
troscopy for understanding the molecular states. (ii) is related to fundamental
processes of a vibrational excitation/de-excitation of adsorbates. To answer these
questions several experimental and theoretical attempts have been devoted in the
last decade. The basic concept describing the elementary process of STM-IETS
dates back to theoretical works reported in the late 1980s [ 24 , 25 ]. Persson and
Demuth first discussed the inelastic tunneling with the scheme of dipole scattering
theory using Bardeen's formula for electric current [ 24 ]. After that, Persson and
Baratoff showed that the resonant tunneling via adsorbate induced states is a
dominant channel for inelastic process and the inelastic fraction of electronic
current is associated with the vibrational damping rate due to the electron-hole
pair excitation [ 25 ]. Figures 2.8 a illustrates an STM junction consisted of a tip,
substrate, and molecule chemisorbed on the substrate. The molecule forms the
molecule-derived state q a around the Fermi level E F of the substrate, which is
derived form a molecular orbital |a [ [ 16 ]. Such molecular-induced resonances
frequently occur in the vicinity of E F [ 26 ]. The width of the molecular state C is
determined by the strength of the interaction between a molecule and an electronic
state of an electrode. Tunneling electrons pass through the molecule-derived state
q a . When an electron has tunnel into q a , it is temporary trapped in q a for a time
t * h/C. If a tunneling electron has enough energy to excite a molecular vibration
(hx), it becomes possible to leave a vibrational excitation in the molecule and the
electron inelastically-tunnels, which eventually opens an additional channel for the
electron transport and results in the increase of a total current. This resonant
tunneling model was experimentally examined by Kawai and her co-workers at
RIKEN, Japan. They showed that the vibrational excitation depends on the spatial
distribution of the molecular orbitals formed near the Fermi level of metal [ 27 , 28 ].
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