BioPHYSICAL chemistry

Since V 0 > E, the wavefunction inside the
barrier is an exponential decaying according
to the constant κ, termed the decay length.
The extent of the decay inside the barrier
depends upon the parameters aand V 0. As
the barrier width increases, the extent of
the exponential decay increases. Tunneling
decreases the value of the decay length, and
is therefore more likely for particles with
larger energies.

Research direction: probing biological membranes

In the early 1980s, the phenomenon of tun-
neling of electrons was adopted as a new
spectroscopic technique to probe the surfaces
of materials. For the development of this
spectroscopic tool, Gerd Binnig and Heinrich
Rohrer received a Nobel Prize for Physics in
1986 (Binning et al. 1982, 1986). The technique of scanning tunneling
microscopy, or STM, allows the imaging of a surface at atomic resolution
with a relatively simple conceptual approach. An essential feature of an
STM is the probe tip, which must approach a surface very closely with-
out touching (Figure 10.12). If the tip is close enough, the space, which
may be a vacuum, air, or water, between the probe and the surface
will represent a barrier that can be crossed by electrons by tunneling.
Following the discussion above, the approach must be a few decay
lengths which, from a practical viewpoint, represents a distance within
1 nm. Ideally, the tip is very sharp and the tunneling will occur from
the closest point of the tip to the surface. The tip is mounted on an
instrument called a piezoelectric device that can translate the tip across
the surface in increments of less than 1 nm. If the tip scans strictly
horizontally over the surface then a rise in the surface will decrease the
spacing and the current will increase. Alternatively, the probe can be
positioned such that the current is fixed by use of a feedback circuit that
can move the probe vertically as needed.
Since the mid-1990s, a related technique, atomic force microscopy (AFM),
has increasingly been applied to biological systems. The goal of this tech-
nique is also to characterize the surface of a material, and the equipment
is similar to that used for STM, but AFM operates by measuring the force
between the tip and sample. In a sense, AFM resembles the operation
of a stylus passing over a vinyl record to produce sounds in a record
player. In AFM the sensitivity is achieved by the use of a cantilever whose

CHAPTER 10 PARTICLE IN A BOX AND TUNNELING 211

V 0

E^



1/4

V^0

E^



3/4

V^0

0 a

x

Figure 10.11Two traveling wavefunctions

incident to a barrier. The wavefunctions have a

finite probability of passing through the barrier

despite having an energy E, which is less than

the barrier height V 0. The extent of the decay is

dependent upon the barrier width aand the

difference E−V 0.