Chapter 18
Downloaded via UNIV OF SYDNEY on July 15, 2018 at 20:14:17 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
Resolution Limits of Force Microscopy R. Lüthi, Meyer, M . Bammerlin, A. Baratoff, J. Lü, M . Guggisberg, and H.-J. Güntherodt Institute of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
Applications of contact force microscopy in ultrahigh vacuum are presented where the resolution is limited to approximately 1 nm under optimum conditions. It will be shown that even small van der Waals forces of 0.1nN are sufficient to explain the finite contact area. One way to circumvent this problem is to measure in liquid environment where van der Waals forces can become repulsive. However, this environment is not compatible with the controlled surface preparation in ultrahigh vacuum. Recently, progress has been made in non-contact force microscopy where the cantilever is oscillated at its resonance frequency. Under appropriate conditions true atomic resolution can be achieved. Vacancies, adsorbate atoms and step sites are being imaged showing that individual atoms are resolved by force microscopy.
Resolution limits of contact force microsopy Force microscopy has been introduced in 1986 by Binnig, Quate and Gerber (1,2). Contact-mode A F M is accompanied by the jump-in of the soft cantilever. When the condition
is met, an instability occurs, where 3F/3z is the attractive force gradient and k the cantilever spring constant. The probing tip jumps toward the sample. Long-range attractive forces, F, , such as van der Waals forces, capillary forces or electrostatic r
300
©1998 American Chemical Society
Ratner and Tsukruk; Scanning Probe Microscopy of Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1998.
301
forces, have to be compensated by short-range repulsive forces on the foremost tip apex F . After the instability, the operator will try to minimize the forces on the tip apex by compensating the long-range attractive force with the bending of the cantilever F = k z sr
L
t
The equilibrium is given by: F
s , =
F
L , -
k
Zt
which determines the force on the tip apex F (cf. Figure. 1). The minimum F (min) is achieved close to the jump-out of the contact. Experimentally, it is found that F (min) is a significant fraction of F (typically 10% - 50%). Thus, the compensation by the cantilever bending is not complete. This incomplete compensation is explained by local variations of the attractive force. These forces can change quite drastically above hillocks compared to valleys. During scanning, the tip will either jump out of contact above areas with low attractive forces or will experience high forces on the areas with high attractive forces. Thus, the minimum, experimentally achievable force on the tip apex depends also on the roughness and scan area. s r
sr
sr
l r
The consequences for the resolution of contact force microscopy become evident. Depending on the environment, the long-range forces F, will vary significantly. In ambient pressure, capillary forces, originating from the formation of a liquid meniscus between probing tip and sample, will be dominant. With a tip radius R=100nm, the maximum attractive, capillary force is r
F
4
c a = * Y c o s ( 0 ) ~ 9 O nN P
2
where 7^=0.07 N/m is the surface tension of water and 0 is the contact angle. After the jump to contact this large force acts uncompensated on the tip apex and can deform the tip or sample. Even with optimum bending of the cantilever, the force will be still in the nN-regime. Capillary forces can be eliminated by measuring in liquids or in vacuum conditions. In liquids, attractive forces can become very small. In best case, van der Waals forces become repulsive by choosing a suitable liquid (3). Such a situation is met, when the refractive index of the liquid, n,, is between the refractive index of the probing tip, n, , and the refractive index of the sample, n : n < n,< n . . Ohnesorge and Binnig have shown that it is possible to achieve true molecular resolution on calcite in water, thus demonstrating that the contact diameter is of atomic dimensions (4). s
s
t
In ultra-high vacuum conditions, van der Waals forces will always be present. Goodman and Garcia (5) have shown that typical van der Waals forces are between 1-10 nN, where the exact values depend on the materials. A collection of their results is shown in table 1. A tip radius of R=100 nm at a distance of z=l nm has been assumed.
Ratner and Tsukruk; Scanning Probe Microscopy of Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1998.
302 Comparison of V a n der Waals Forces T A B L E 1. Van der Waals Forces Materials Graphite-Graphite Diamond-Diamond Metal-Graphite Si0 -Graphite
Forces 8nN 17 nN 10 nN 1.2 nN
9
In conclusion, the attractive forces in ambient conditions are the largest: 1-100 nN. In ultra-high vacuum, van der Waals forces are always present and give values between 0.1-10 nN. In liquids, van der Waals forces can become repulsive suitable liquids and forces can become below 100 pN. The Hertz model, gives us an estimate of the contact diameter: m
a =2(D-R-F) min
D
=
^L
^l
+
E,
E
2
and V; and E are the Poisson ratii and Youngs modulii of probing tip and sample. {
2
With typical parameters ( E ^ E ^ l . 7 10" N/m , v = 0.3 and R = 90 nm), the contact diameter in ambient pressure is 2-10 nm (1 nN
