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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 a unified theory of tunneling phenomenon and covalent bond force, as a result of the similarity between the Bardeen theory of tunneling and the Herring-Landau theory of the covalent bond. Three general theoretical treatments are presented, which show that tunneling conductance is proportional to the square of the covalent bond interaction energy, or equivalently, the square of covalent bond force. The constant of proportionality is related to the electronic properties of the materials. For the case of a metal tip and a metal sample, an explicit equation contains only measurable physical quantities is derived. Several experimental verifications are presented. The equivalence of covalent bond energy and tunneling conductance provides a theoretical explanation of the threshold resistance observed in atom-manipulation experiments, and points to a method of predicting the threshold resistance for atom manipulation.

This chapter presents a unified theory of tunneling phenomenon and covalent bond force, as a result of the similarity between the Bardeen theory of tunneling and the Herring-Landau theory of the covalent bond. Three general theoretical treatments are presented, which show that tunneling conductance is proportional to the square of the covalent bond interaction energy, or equivalently, the square of covalent bond force. The constant of proportionality is related to the electronic properties of the materials. For the case of a metal tip and a metal sample, an explicit equation contains only measurable physical quantities is derived. Several experimental verifications are presented. The equivalence of covalent bond energy and tunneling conductance provides a theoretical explanation of the threshold resistance observed in atom-manipulation experiments, and points to a method of predicting the threshold resistance for atom manipulation. Theory of imaging wavefunctions with AFM is discussed.

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.