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As a rule, invesTIgaTIons of physical effects in solids are moTIvated by the need of understanding at a fundamental level, which facilitates their effecTIve application in the fabrication of devices. The problem of electrical polarization of piezoelectric,ferroelectric, and pyroelectric solids is no exception. In the last 15 years we have witnessed very intensive investigations of the theory of spontaneous polarization, as well as of the dielectric response of crystals to external perturbations. Our current understanding stems from the development of electronic structure calculations based on first principles, and subsequently from evolution of appropriate theoretical approaches allowing for both a proper definition of polarization and accurate calculations.From the experimental side, much of the impetus came from experimentalwork devoted to, e.g., GaN-like group-III nitrides, in which internal electric fields of both pyro- and piezoelectric origin are large, determining the properties of quantum structures and devices [1]. Spectacular progress in this area has led to innovative devices described in several chapters of this book.There are two important issues clarified by first principles calculations in the last two decades. The first achievement was to provide a link between microscopic distribution of electrons determined by first-principles calculations and the description based on classical macroscopic electrostatics. In particular, calculations have shown how actual charge densities and dipole layers at surfaces and/or interfaces in semiconductor heterostructures look like at the atomic scale, what are their localization and origin, etc. These basic concepts and ingredients of classical electrodynamics developed during the last two centuries are now visualized by first principles theory.Typical results are described in Sections 6 and 7.The second success is a demonstration of the fact that spontaneous polarizationand piezoelectric effects are bulk properties of solids, and thus may be studiedby calculations performed for infinite crystals [2, 3]. This subject was first treated in the paper by Martin [4], who showed that the piezoelectric tensor of an insulator is a bulk quantity. In fact, the development of elegant theoretical approaches [2, 3] has enabled efficient calculations, and the results are in good agreement with experiment. Furthermore, a wealth of new information has been obtained. In this chapter, we briefly summarize the theoretical approaches and illustrate them with appropriate examples.As an example of the role played by the electric field, we discuss field-inducedelectromigration of hydrogen in GaN/AlN heterojunctions rather than the impactof electric field on the electronic structure, which was discussed at length in many papers [1] and other chapters of this book.
