
Nanostructures Fabricated by Physical Techniques
305
the tipatom-sample interaction in the absence of electric field. Therefore,
the theory is also applicable to
AFM.
When an electric field is applied between the tip and the sample, two
theoretical models, known as the charge-exchange model'
l3
and the
image-hump mode1,l
l4
have been developed and well accepted, which can
be directly applied in the
STM
configuration. Similar discussion to the
preceding paragraph can be applied here, except that an applied electric
field,
E,
is present and the interaction between the electric field and
charged species needs to be considered.'
l2
When the tipsample distance
is shortened, both the atomic potential curve and the ionic potential curve
are changed. In the absence of an electric field, the atomic and ionic
curves are simply the sum of
U,,
and
U,,
and that of
U,
and
Uit,
respec-
tively. When a positive electric field is applied to the tip, an externally
applied electric potential, -neEz, is added to the ionic potential and these
potential curves are modified to
U,
=
UI(0)
-
neEz.
Here
n
is the charge
state of ions and z is the distance from the tip.
As
a result, the potential
barrier a tip atom has to activate over to reach the sample is greatly
reduced, in the case of field evaporation of positive ions. On the other
hand, the potential barrier an atom at the sample surface has to activate
over to reach the tip surface is greatly increased. Thus, atom transfer
between the tip and the sample surface can occur only from the positive
electrode to the negative electrode, not the other way around, in the case
of field evaporation of positive ions. It should be noted that field evapo-
ration of negative ions is a more complicated issue, since field electron
emission starts at an electric field of
-0.3
V/A.
When the electric field
increases to
0.6V/A,
the field emission current density will be large
enough to melt tips of most metals by a resistive heating.
l2
Field-gradient induced surface diffusion.
Figure
7.19
explains the basic
mechanism of field-gradient-induced surface difision.81~82~'
l29l
157'
l6
In the
absence of a voltage pulse, the field at the sample surface produced by the
probing tip is too small to have an effect. Thus, the adatom sees a horizontal
but periodic surface potential, assuming the sample has a periodic structure
such as single crystal. There will be no net difision. However, when a volt-
age pulse is applied to either the tip or the sample, a field with a large gradi-
ent will be created at the sample surface around the tip due to the asymmetry
of the tipsample configuration.
As
a result, the polarization energy is posi-
tion dependent and given by E,(r)
=
-k
E
-
1/2aE2.
When this energy is
added to the periodic surface potential, the potential-energy curve becomes
inclined toward the center where the field is the strongest. Therefore, the
sur-
face diffusion becomes directional and the adatoms always move from the