This chapter presents basic experimental methods and the basic theory of tunneling. The classical metal-insulator-metal tunneling junction experiment of Giaever, designed to verify the Bardeen-Cooper-Schrieffer theory of superconductivity, is the motivation for Bardeen to invent his perturbation theory of tunneling. That Bardeen theory then became the starting point of the most useful models of STM. Section 2.2 presents the Bardeen tunneling theory from time-dependent perturbation theory of quantum mechanics, starting from a one-dimensional case, then proceeds to three-dimensional version with wave-function corrections. The Bardeen theory in second-quantization format, the transfer-Hamiltonian formalism, is also presented. As extensions of the original Bardeen theory, the theories and experiments of inelastic tunneling and spin-polarized tunneling are discussed in depth.
Keywords: tunneling junction, metal-insulator-metal tunneling, Bardeen theory, time-dependent perturbation, tunneling matrix elements, Fermi golden rule, transfer-Hamiltonian formalism, inelastic tunneling, spin-polarized tunneling
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