Chemistry Reference
In-Depth Information
Chapter 2
Principles and Techniques
Abstract I describe a brief summary of quantum mechanics and principles of
scanning tunneling microscopy (STM) in this chapter. Quantum tunneling is an
important concept to describe the transportation of small particles, like electron
and hydrogen. In Sect. 2.1 I focus on H-atom tunneling in a double minimum
potential that is the simplest but a ubiquitous system in physics and chemistry.
Quantum tunneling of electron directly relates to the principle of the STM. In Sect.
2.2 the principles and applications of STM are described. I focus on the inelastic
electron tunneling process in an STM junction, which can be applied to the
vibration spectroscopy and reaction control of single molecules.
Keywords Quantum tunneling
Double minimum potential
Scanning tunneling
microscope/spectroscopy
Inelastic electron tunneling
2.1 Quantum Mechanics
2.1.1 Basics of Quantum Tunneling
Quantum tunneling is derived from the concept of quantum mechanics, where a
particle can pass through a barrier that is classically insurmountable. This is a
result of the wave-particle duality of matter. Quantum tunneling becomes pro-
nounced in light particles such as electron and H atom.
Figure
2.1
shows the simplest model in which a particle tunnels through a one-
dimensional rectangular barrier. The time-independent Schrödinger equation of
the particle is written by
h
2
2m
d
2
dx
2
w
ð
x
Þþ
V
ð
x
Þ
w
ð
x
Þ¼
Ew
ð
x
Þ
ð
2
:
1
Þ
