Tip-sample distance

Figure Bl.19.37. Nonual force versus tip-sample distance curves for a Si3N4 tip on a Si02 surface under 1 luM NaCl solution at pH 4 and pH 9. (Taken from [189], figure 2.)...

This corresponds to the physician s stethoscope case mentioned above, and has been realized [208] by bringing one leg of a resonatmg 33 kHz quartz tiinmg fork close to the surface of a sample, which is being rastered in the x-y plane. As the fork-leg nears the sample, the fork s resonant frequency and therefore its amplitude is changed by interaction with the surface. Since the behaviour of the system appears to be dependent on the gas pressure, it may be assumed that the coupling is due to hydrodynamic mteractions within the fork-air-sample gap. Since the fork tip-sample distance is approximately 200 pm -1.120), tire teclmique is sensitive to the near-field component of the scattered acoustic signal. 1 pm lateral and 10 mn vertical resolutions have been obtained by the SNAM. 

Figure Bl.19.39. Schematic of the themiocoiiple probe in a scaiming themial profiler. The probe is supported on a piezoelectric element for modulation of tip-sample distance at frequency oi and to provide positioning. The AC thennal signal at oi is detected, rectified, and sent to the feedback loop, which supplies a voltage to the piezostack to maintain the average tip-sample spacing constant. (Taken from [209], figure 1.)...

FIG. 3 Dependence of the electrostatic force on tip-surface distance. The experimental data (square points) can he fit reasonably weU with a A/z + B function (solid curve) predicted hy the model in the previous figure for tip-sample distances smaller than the tip radius. 

FIG. 28 Changes in contact potential of mica relative to a hydrophobic tip as a function of relative humidity. The tip-sample distance during measurements was maintained at 400 A. At room temperature the potential first decreases by about 400 mV. At -30% RH it reaches a plateau and stays approximately constant until about 80% RH. At higher humidity the potential increases again, eventually becoming more positive than the initial dry mica surface. The changes in surface potential can be explained by the orientation of the water dipoles described in the previous two figures. 

Figure 5.3 Tunnel barrier pT as a function of tip-sample distance for Au(l 1 1) in 0.1 M H2S04 for three different potentials (vs. SCE). s = 0 refers to the surface plane ofAu(l 1 1). pT (s) for Au(l 1 1) in air is also shown for comparison. For details see Refs [18, 19].

Deng W, Hipps KW (2003) Tip-sample distance dependence in the STM-based orbital-mediated tunneling spectrum of nickel(II) tetraphenylporphyrin deposited on Au(lll). J Phys Chem B 107 10736-10740... 

Gopakumar TG, Meiss J, Pouladsaz D, Hietschold M (2008) HOMO-LUMO gap shrinking reveals tip-induced polarization of molecules in ultrathin layers tip-sample distance-depen-dent scanning tunneling spectroscopy on d8 (Ni, Pd, and Pt) phthalocyanines. J Phys Chem C 112 2529-2537... 

Experimentally, this quantity can be conveniently measured by varying the tip-sample distance through the z piezo, often with an ac voltage. The measured values often varies with distance. Eq. (1.13) is the definition of the... 

For simple metal surfaces with fundamental periodicity a, the corrugation amplitude of the Fermi-level LDOS as a function of tip-sample distance can be estimated with reasonable accuracy (Tersoff and Hamann, 1985) ... 

Fig. 1.27. Quantitative results from STM images of Al(lll). An exponential relation between the corrugation amplitude and the tip-sample distance is observed. The best corrugation observed is more than 20 times greater than the maximum corrugation amplitude expected from the Fermi-level LDOS contour. (Reproduced from Wintterlin et al., 1989, with permission.)...

In order to achieve atomic resolution, even with p and d tip states, the tip-sample distance should be very short. At such short distances, the tip-sample interactions arc strong. There are two kinds of interaction effects... 

A series of first-principles calculations of the combined system, that is, the tip and the sample, has been carried out by many authors, for example, Ciraci, Baratoff, and Batra (1990, 1990a). The three-dimensional shape of the potential barrier as well as the force between the tip and the sample are calculated. Three systems have been studied graphite-carbon, graphite-aluminum, and aluminum-aluminum. All those studies reached the same conclusion The top of the potential barrier between the tip and the sample is either very close to or lower than the Fermi level within the normal tip-sample distances of STM. 

Fig. 1.31. The effect of potential barrier lowering on wavefunctions. At the normal tip-sample distance of STM operation, due to the interaction between the tip and the sample, the top of the potential barrier becomes much lower than the vacuum level. The wavefunctions of both parties in the middle of the gap are different from the "free" wavefunctions. (Reproduced from Baratoff, 1984, with permission.)...

To summarize, the existence and role of force in STM is now a well-established scientific fact. At a relatively large absolute distance, for example, 5 A, the force between these two parties is attractive. (By absolute distance we mean the distance between the nucleus of the apex atom of the tip and the top-layer nuclei of the sample surface.) At very short absolute distances, for example, 1.5 A, the force between these two parts is repulsive. Between these two extremes, there is a well-defined position where the net force between the tip and the sample is zero. It is the equilibrium distance. On the absolute distance scale, the equilibrium distance is about 2-2.5 A. Therefore, the tip-sample distance of normal STM operation is 3-7 A on the absolute distance scale. In this range, the attractive atomic force dominates, and the distortion of wavefunctions cannot be disregarded. Therefore, any serious attempt to understand the imaging mechanism of STM should consider the effect of atomic forces and the wavefunction distortions. 

Fig. 1.36. The topografiner. An instrument developed by Young, Ward, and Scire in the late 1960s, which is the closest ancestor of the STM. (a) The tip is driven by the x and y piezos, and the sample is mounted on the z piezo. By applying a high voltage between the tip and the sample, a field-emission current is induced. Using the field-emission current as the feedback signal, topography of the sample surface is obtained, (b) Close-up of the tip and the sample. The end of the tip has a small radius, typically a few hundred A. The typical tip-sample distance is a few thousand A. (After Young, 1971.)...

As seen from Fig. 1.36 and Eq. (1.31), the field-emission current is not very sensitive to the tip-sample distance xq. Using the topografiner, the best vertical resolution is found to be 30 A, and the best horizontal resolution is 4000 A (Young 1971, Young, Ward, and Scire, 1972). 

We start our discussion with a definition of the tip-sample distance. Because the STM deals with atoms, the basic definition should be microscopic. If at least part of the sample surface is atomically flat, a natural definition of the tip-sample distance is the distance from the plane of the topmost nuclei of the sample to the nucleus of the apex atom of the tip. Throughout the book, this microscopic distance is denoted by a lower-case letter, d, zo, or... 

In some cases, macroscopic models are used for simplified discussions of certain phenomena without atomic resolution. A macroscopic tip-sample distance should be defined. To avoid confusion, we use the term barrier thickness instead. Throughout the book, the barrier thickness is always denoted by a upper-case letter, such as W or L. In the Sommerfeld model of the free-electron metals, the barrier thickness is the distance between the surface of the metal pieces. In the jellium model (see Chapter 4), the barrier thickness is defined as the distance between the image-force planes. 

Because of the force and deformation, the displacement measured by the voltage applied on the z piezo may different from the true tip-sample distance. We will denote it as the apparent displacement whenever it appears. 

In this Chapter, we discuss a perturbation theory for STM, the modified Bardeen approach (MBA). The illustrate the concept of a perturbation approach, let us consider the following four regimes of interactions (zo denotes the microscopic tip-sample distance) ... 

When the tip-sample distance is large, for example, zo > 100 A, the mutual interaction is negligible. By applying a large electrical field between them, field emission may occur. Those phenomena can be described as the interaction of one electrode with the electrical field, without considering any interactions from the other electrode. 

At extremely short distances, for example, zo < 3 A, the repulsive force becomes dominant. It has a very steep distance dependence. The tip-sample distance is virtually determined by the short-ranged repulsive force. By pushing the tip farther toward the sample surface, the tip and sample deform accordingly. 

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