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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 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.

Quantum tunneling, wherein a quanject has a non-zero probability of tunneling into and then exiting a barrier of finite width and height, is the subject of Chapter 13. The description for the one-dimensional case is extended to the barrier being inverted, which forms an attractive potential well. The first application of this analysis is to the emission of alpha particles from the decay of radioactive nuclei, where the alpha-nucleus attraction is modeled by a potential well and the barrier is the repulsive Coulomb potential. Excellent results are obtained. Ditto for the similar analysis of proton burning in stars and yet a different analysis that explains tunneling through a Josephson junction, the connector between two superconductors. The final application is to the scanning tunneling microscope, a device that allows the microscopic surfaces of solids to be mapped via electrons from the surface molecules tunneling into the tip of the STM probe.

This chapter, which discusses the roles of IBM and Bell Labs in the initial development of the scanning tunnelling microscope (STM), finds that scientists at both these organizations followed a different set of rules and processes to develop the STM. Surface scientists within IBM and Bell Labs also played a key role in the design and adaptation of the STM. Their association with the surface science network also meant that STM community members were more acquainted with each other than with any other part of the probe-microscopy community, a relationship and interaction which played a key role in the effective replication and adaptation of the STM at the two organizations.

The concept of the atom dates back to the speculations of Democritus and other Ancient Greek philosophers, but it was only in modern times that atoms were shown to exist and physicists began to investigate their structure. Rutherford’s team in Manchester discovered the atomic nucleus and Rutherford proposed that atoms consist of a tiny positively charged nucleus surrounded by negatively charged orbiting electrons. Rutherford and his colleagues went on to discover the nucleus is composed of protons and neutrons. It is now possible to produce pictures of atoms using the scanning tunnelling microscope (STM) invented by Binnig and Rohrer.

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.