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This chapter presents the basic designs and working principles of STM and AFM, as well as an elementary theory of tunneling and the imaging mechanism of atomic resolution. Three elementary theories of tunneling are presented: the one-dimensional Schrödinger's equation in vacuum, the semi-classical approximation, and the Landauer formalism. The relation between the decay constant and the work function, and a general expression of tunneling conductance versus tip-sample distance are derived. A brief summary of experimental facts on the mechanism of atomic resolution STM and AFM is presented, which leads to a picture of interplay between the atomic states of the tip and the sample, as well as the role of partial covalent bonds formed between those electronic states. As an introduction to the concept of equivalence of tunneling and atomic forces, atom and molecule manipulation is briefly presented.

This chapter discusses atomic force microscopy (AFM), focusing on the methods for atomic force detection. Although the force detection always requires a cantilever, there are two types of modes: the static mode and the dynamic mode. The general design and the typical method of manufacturing of the cantilevers are discussed. Two popular methods of static force detection are presented. The popular dynamic-force detection method, the tapping mode is described, especially the methods in liquids. The non-contact AFM, which has achieved atomic resolution in the weak attractive force regime, is discussed in detail. An elementary and transparent analysis of the principles, including the frequency shift, the second harmonics, and the average tunneling current, is presented. It requires only Newton's equation and Fourier analysis, and the final results are analyzed over the entire range of vibrational amplitude. The implementation is briefly discussed.

This chapter focuses on the two experimental techniques — the surface force apparatus (SFA) and the atomic force microscope (AFM) — that are commonly used for measuring molecular level forces that act between two surfaces at small separation distances. The first part of this chapter covers the fundamental principles of SFA and AFM design. The second half of this chapter illustrates the application of AFM to measuring surface forces with examples the measurement of van der Waals forces, meniscus forces from liquid films and from capillary condensation, and electrostatic double-layer forces.

Valiant attempts were made to increase the resolution of acoustic microscopy by employing ever higher frequencies and ever less attenuating coupling fluids. But this did not prove the ultimate way to resolution, which was achieved instead by abandoning the concept of focusing to a diffraction‐limited spot, and instead adopting a scanning probe to give near‐field resolution. In the ultrasonic force microscope (UFM), excitation is fed through the sample to the contact with the tip of an atomic force microscope (AFM). Modulation of the ultrasonic excitation is detected through the non‐linear stiffness of the tip–sample contact, which acts as a mechanical diode. The technique can be used for a wide range of materials characterization, for both soft materials such as polymers and stiff materials such as semiconductor nanostructures. In each case UFM gives contrast from the mechanical properties and structure, with resolution of a few nanometres or better. Variations of the technique, such as the heterodyne force microscope (HFM), enable phase resolution on a nanosecond timescale to be combined with stiffness measurement with nanometre spatial resolution.

This chapter starts chronologically with the first measurement, by means of a torsion pendulum, in the recent phase of Casimir force experiments. Then the main breakthroughs in the measurement of the Casimir force between metallic surfaces are presented. One of them was the first demonstration of corrections to the Casimir force due to the nonzero skin depth and surface roughness by means of an atomic force microscope. Another breakthrough was a series of precise indirect measurements of the Casimir pressure by means of a micromechanical torsional oscillator. These measurements allowed a definitive choice between different theoretical approaches to the thermal Casimir force for real metal surfaces. Many other experiments performed in the last few years are also presented, specifically one measurement using the configuration of two parallel plates. The chapter ends with a brief discussion of proposed experiments using metallic surfaces.

This chapter focuses on the two experimental techniques—the surface force apparatus (SFA) and the atomic force microscope (AFM)—that are commonly used for measuring molecular level forces that act between two surfaces at small separation distances. The first part of this chapter covers the fundamental principles of SFA and AFM design. The second half of this chapter illustrates the application of AFM to measuring surface forces with examples the measurement of van der Waals forces, atomic level repulsive forces, frictional forces, electrostatic double-layer forces, and meniscus forces from liquid films and from capillary condensation.

This chapter presents the basic designs and working principles of STM and AFM, as well as an elementary theory of tunneling and the imaging mechanism of atomic resolution. Three elementary theories of tunneling are presented: the one-dimensional Schrödinger’s equation in vacuum, the semi-classical approximation, and the Landauer formalism. The relation between the decay constant and the work function, and a general expression of tunneling conductance versus tip-sample distance are derived. A brief summary of experimental facts on the mechanism of atomic resolution STM and AFM is presented, which leads to a picture of interplay between the atomic states of the tip and the sample, as well as the role of partial covalent bonds formed between those electronic states. Four illustrative applications are presented, including imaging self-assembed molecules on solid-liquid interfaces, electrochemical STM, catalysis research, and atom manipulation.

This chapter discusses atomic force microscopy (AFM), focusing on the methods for atomic force detection. Although the force detection always requires a cantilever, there are two types of modes: the static mode and the dynamic mode. The general design and the typical method of manufacturing of the cantilevers are discussed. Two popular methods of static force detection are presented. The popular dynamic-force detection method, the tapping mode is described, especially the methods in liquids. The non-contact AFM, which has achieved atomic resolution in the weak attractive force regime, is discussed in detail. An elementary and transparent analysis of the principles, including the frequency shift, the second harmonics, and the average tunneling current, is presented. It requires only Newton’s equation and Fourier analysis, and the final results are analyzed over the entire range of vibrational amplitude. The implementation is briefly discussed.

The concept of wavefunction was introduced in the first 1926 paper by Erwin Schrödinger as the central object of the atomic world and the cornerstone of quantum mechanics. It is a mathematical representation of de Broglie’s postulate that the electron is a material wave. It was defined as everywhere real, single-valued, finite, and continuously differentiable up to the second order. Nevertheless, for many decades, wavefunction has not been characterized as an observable. First, it is too small. The typical size is a small fraction of a nanometer. Second, it is too fragile. The typical bonding energy of a wavefunction is a few electron volts. The advancement of STM and AFM has made wavefunctions observable. The accuracy of position measurement is in picometers. Both STM and AFM measurements are non-destructive, which leaves the wavefunctions under observation undisturbed. Finally, the meaning of direct experimental7 observation and mapping of wavefunctions is discussed.