Download Pseudo-non-contact AFM imaging?

Applied Surface Science 140 Ž1999. 362–365
Pseudo-non-contact AFM imaging?
I.Yu. Sokolov
a
a,b,)
, G.S. Henderson a , F.J. Wicks
a,c
Department of Geology, UniÕersity of Toronto, 22 Russell Street, Toronto, Ontario, Canada M5S 3B1
b
Department of Physics, UniÕersity of Toronto, Toronto, Ontario, Canada M5S 1A7
c
Department of Earth Sciences, Royal Ontario Museum, Toronto, Ontario, Canada M5S 2C6
Received 29 June 1998; accepted 20 August 1998
Abstract
Recent non-contact atomic force microscopy studies have demonstrated that imaging of single atom defects is possible.
However, the imaging mechanism was unclear. Long-range forces of attraction, which are normally associated with
non-contact mode, are not known to produce sufficient lateral resolution to image atoms. In this study, we suggest a
mechanism that could be responsible for the resolution achieved. We use realistic interatomic interaction parameters to do
numerical simulations. These simulations are in good agreement with experimental data. As a result, we are able to
‘separate’ the attractive and repulsive forces acting between the AFM tip and the sample surface. Calculations indicate that
the force responsible for image contrast in the experimental studies mentioned above, is in most cases the repulsive contact
force, and not the long-range attractive force. We check our conclusions against a variety of interatomic interaction
parameters and our results remain valid for any reasonable set of such parameters, including the power law of the attractive
potential N - 9. q 1999 Elsevier Science B.V. All rights reserved.
PACS: 07.79.L; 61.16.C; 34.20
Keywords: Atomic force microscopy; Molecular force interaction; Atomic force spectroscopy
1. Introduction
AFM images generally do not contain atomic level defects because of multi-tip averaging. This averaging is
a result of the high pressure between the AFM tip and sample. The monatomic tip is deformed due to the high
load force, producing a ‘multi-tip’, which usually results in the disappearance of the defects w1x. Recent studies,
however, have started to demonstrate that imaging of single atom defects, i.e., true atomic resolution, is feasible.
Excellent images of atomic defects have been obtained in non-contact mode under ultra high vacuum conditions
w2–5x. However, the imaging mechanism was unclear since the long-range forces of attraction, which are
normally associated with non-contact mode, are not known to be able to produce sufficient lateral resolution to
image atoms. In this study, we expand on our earlier suggestion w6x that the mechanism responsible for atomic
resolution under non-contact AFM operating conditions is the repulsive contact force, and not the long-range
attractive force. In contrast with the study of Sokolov et al. w6x, we consider here virtually any long-range
)
Corresponding author. Tel.: q1-416-978-0668; Fax: q1-416-978-3938; E-mail: [email protected]
0169-4332r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 9 - 4 3 3 2 Ž 9 8 . 0 0 5 5 5 - 8
I.Yu. SokoloÕ et al.r Applied Surface Science 140 (1999) 362–365
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attraction that gives reasonably stable interatomic distances. Our calculations indicate that the repulsive force is
the force responsible for image contrast in the experimental studies noted above, provided the power of the force
potential N is - 9. Furthermore, we show that the theoretical results and conclusions concerning the repulsive
force are true under a wide variety of imaging conditions.
2. Model for the simulations
Our theoretical simulations use the following assumptions. The AFM tip is considered to be a paraboloid of
rotation with a sharp apex made of a silicon ŽSi. cubic face-centered lattice oriented in the 1114 direction. The
radius of the tip curvature corresponds to the best commercial tips at 10 nm and the Si lattice constant is 0.54
nm. The tip apex is considered to consist of three layers of atoms Ž34 atoms in total. while the paraboloid is
treated as a continuous medium.
The sample surface is treated as a cubic lattice with a lattice constant ranging from 0.3 to 0.6 nm, of no
defined composition and with some atomic vacancies present. The plane surface is assumed to be three atomic
layers thick while the bulk is treated as a continuous medium. This configuration is convenient for numerical
calculations although the numerical error of considering a continuous medium rather than a discrete structure is
no more than 4%, depending on the tip–sample distance.
The interatomic interaction between the tip and sample is described by a Lennard–Jones potential:
ÕŽ r . s´
žž
(r
01 r 02
r
12
/
12
y
N
ž
(r
01 r 02
r
N
//
,
Ž 1.
where ´ is the binding energy between atoms, r 01 , r 02 are the approximate equilibrium distances between
bound atoms in the sample and tip, respectively, r is interatomic distance, and N is an integer number
representing the power of the attractive forces. Unless otherwise stated we use N s 6, which corresponds to
either van der Waals forces, or dipole–dipole interaction. The energy ´ can be considered as the energy of
interatomic interaction and is initially taken as ´ s 10 kJrMf 0.1 eVratom, with r 01 s 0.4 nm. However, a
wide range of possible r 01 , ´ , and N values are considered later.
To find the force, or force gradient, of interaction between the tip and the sample, we integratersum the
potential ŽEq. Ž1.. over the volume number of atoms in the sample and the tip. This treats the interatomic
potential as additive which is a good approximation for repulsive force, however, attractive forces, e.g., van der
Waals interaction, are not additive. However, our conclusions considering the force responsible for image
formation under non-contact conditions are independent of the manner in which the van der Waals force is
treated. Consequently, we also treat, for simplicity, the van der Waals force as additive. The composition of the
sample is not considered.
The force interactions between atoms are summed numerically, whereas those between the paraboloid of
rotation and the sample are calculated by integrating analytically. According to Sokolov et al. w6x, the
contribution to the tip Žparaboloid. –sample potential due to this interaction is given by
´ r 06 n1 n 2 p 2 R
,
Ž 2.
6d
where n1,2 are the atomic densities of the tip and sample materials, d is the tip Žparaboloid. –sample distance,
and R is its curvature radius.
y
3. Results and discussion
Excellent images of atomic defects, against which we can compare the results of our numerical simulations,
have been observed, for example, by Giessibl w2x and Sugawara et al. w3x. Both sets of experiments employ
364
I.Yu. SokoloÕ et al.r Applied Surface Science 140 (1999) 362–365
positive feedback in order to maintain constant cantilever vibration amplitude. In addition, the force gradient
and frequency shift, respectively, were the parameters detected and used in generating the images. Giessibl w2x,
used constant frequency shift gradient mode, and Sugawara et al. w3x used variable force gradient mode, keeping
the mean frequency shift constant Žlow feedback gain.. In both experiments the force gradient Ž F X . used was
between y2 to y5 = 10y3 Nrm give comparable results under the same imaging conditions.
The results of a scan over a cubic lattice are shown in Fig. 1. We used a force gradient value
F X s y4 = 10y3 Nrm Žin the middle of the range employed in the experimental studies above., and N s 7.
The atomic structure is clearly distinguished under these conditions.
The minimum tip–sample distance of ; 0.4 nm determined from the simulation corresponds to a maximum
total force of F ; y0.1 nN in excellent agreement with the estimation of Giessibl w2x Ž F s y0.14 nN. and
indicates that we are simulating non-contact mode. More importantly, if we consider a range of values for r 0
and ´ Žsee below., keeping F X s y4 = 10y3 Nrm, the force changes by up to an order of magnitude but
remains negative, i.e., attractive.
Additional evidence indicating that we are reproducing the experimental imaging conditions of Geissibl w2x
and Suragawa et al. w3x, comes from the agreement between the experimental height contrast Ž0.02–0.05 nm, w2x.
with that determined from our simulations Ž0.04 nm..
We can now use our model to determine the nature of the contrast mechanism responsible for image
formation. We can estimate whether this repulsive force gradient component is responsible for the imaging
mechanism in non-contact mode for different types of materials and interactions. This is done by comparing the
force gradient changes for a broad range of N Žfrom 5 to 9., r 01 Ž0.3–0.6 nm. and ´ Ž0.1–10 eVratom. values.
Fig. 2 represents the ratio of the force gradient contrasts:
repulsion gradient over an atom y repulsion gradient between two atom
attraction gradient between two atoms y attraction gradient over an atom
100%.
We put the maximum change of gradient for both numerator and denominator. The contrast due to repulsion
considerably exceeds the attraction for any reasonable values of N, r 01 and ´ , provided N - 9. If N G 9, the
X
Fig. 1. Simulation of an AFM scan with constant F s 4=10y3 Nrm over a cubic lattice with an atomic vacancy defect.
I.Yu. SokoloÕ et al.r Applied Surface Science 140 (1999) 362–365
365
Fig. 2. Ratio of the repulsive to attractive force gradient contrasts for different attractive force powers N. Error bars indicate the ratio
variations for different r 0 Ž0.3–0.6 nm. and ´ values Ž0.1–10 eVratom..
attractive force becomes dominant in the imaging contrast. However, the regular interactions, such as van der
Waals, covalent bonding, electrostatic, dipolar, magnetic interactions correspond to N - 7.
4. Conclusions
Our numerical simulations of AFM images under non-contact conditions indicate that the repulsive
component of the contact force gradient is the main contributor to the image contrast mechanism, provided we
consider attractive potential with a power N - 9. If N G 9, the attractive force is no longer long-range, and
consequently, the contrast could originate from such an attractive force. However, the later situation is unlikely
because the common interactions, such as van der Waals, covalent bonding, electrostatic, dipolar, magnetic
interactions, correspond to N - 7. Therefore, the most probable mechanism of contrast formation originates
with the repulsive force. We suggest the term ‘pseudo-non-contact’ rather than non-contact as a more realistic
description of the imaging mechanism.
References
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