This review covers important advances in recent years in the physics of thin-film ferroelectric oxides, the strongest emphasis being on those aspects particular to ferroelectrics in thin-film form. The authors introduce the current state of development in the application of ferroelectric thin films for electronic devices and discuss the physics relevant for the performance and failure of these devices. Following this the review covers the enormous progress that has been made in the first-principles computational approach to understanding ferroelectrics. The authors then discuss in detail the important role that strain plays in determining the properties of epitaxial thin ferroelectric films. Finally, this review ends with a look at the emerging possibilities for nanoscale ferroelectrics, with particular emphasis on ferroelectrics in nonconventional nanoscale geometries.

/pdf/physics-of-thin-film-ferroelectric-oxides-3zmqphtpv1.pdf

Physics of thin-film ferroelectric oxides

Electronic conduction in thermally grown SiO2 has been shown to be limited by Fowler‐Nordheim emission, i.e., tunneling of electrons from the vicinity of the electrode Fermi level through the forbidden energy gap into the conduction band of the oxide. Fowler‐Nordheim characteristics have been observed over more than five decades of current for emission from Si, Al, and Mg. If previously measured values of the barrier heights are used, the slopes of the Fowler‐Nordheim characteristics (log J/E2 vs 1/E) imply values of the relative effective mass in the forbidden band of about 0.4. These values take into account corrections for image‐force barrier lowering and for temperature effects. The absolute values of the currents are lower by a factor of five to ten than the theoretically expected values, probably due to trapping effects. The temperature dependence of the current was found to follow the theoretical curve from 80°–420°K. However, an inconsistent relative effective mass of about 0.95 had to be assumed....

Fowler‐Nordheim Tunneling into Thermally Grown SiO2

Field emission and thermionic-field (T-F) emission are considered as the phenomena responsible for the excess currents observed both in the forward and reverse directions of Schottky barriers formed on highly doped semiconductors. Voltage-current characteristics are derived for field and thermionic-field emission in the forward and reverse regime. The temperatures and voltages where these phenomena are predominent for a given diode are discussed. Comparison with experimental results on GaAs and Si diodes shows good agreement between theory and experiments.

Field and thermionic-field emission in Schottky barriers

We review various methods of deriving expressions for quantum-mechanical quantities in the limit when hslash is small (in comparison with the relevant classical action functions). To start with we treat one-dimensional problems and discuss the derivation of WKB connection formulae (and their reversibility), reflection coefficients, phase shifts, bound state criteria and resonance formulae, employing first the complex method in which the classical turning points are avoided, and secondly the method of comparison equations with the aid of which uniform approximations are derived, which are valid right through the turningpoint regions. The special problems associated with radial equations are also considered. Next we examine semiclassical potential scattering, both for its own sake and also as an example of the three-stage approximation method which must generally be employed when dealing with eigenfunction expansions under semiclassical conditions, when they converge very slowly. Finally, we discuss the derivation of semiclassical expressions for Green functions and energy level densities in very general cases, employing Feynman's path-integral technique and emphasizing the limitations of the results obtained. Throughout the article we stress the fact that all the expressions obtained involve quantities characterizing the families of orbits in the corresponding purely classical problems, while the analytic forms of the quantal expressions depend on the topological properties of these families. This review was completed in February 1972.

https://iopscience.iop.org/article/10.1088/0034-4885/35/1/306/pdf

Semiclassical approximations in wave mechanics

1. The real variable 2. Scalars and vectors 3. Tensors 4. Matrices 5. Multiple integrals 6. Potential theory 7. Operational methods 8. Physical applications of the operational method 9. Numerical methods 10. Calculus of variations 11. Functions of a complex variable 12. Contour integration and Bromwich's integral 13. Contour integration 14. Fourier's theorem 15. The factorial and related functions 16. Solution of linear differential equations of the second order 17. Asymptotic expansions 18. The equations of potential, waves and heat conduction 19. Waves in one dimension and waves with spherical symmetry 20. Conduction of heat in one and three dimensions 21. Bessel functions 22. Applications of Bessel functions 23. The confluent hypergeometric function 24. Legendre functions and associated functions 25. Elliptic functions Notes Appendix on notation Index.

Methods of Mathematical Physics. By Harold Jeffreys and Bertha Swirles Jeffreys. Pp. viii, 679. 63s. 1946. (Cambridge University Press)

Although the theories of thermionic and field emission of electrons from metals are very well understood, the two types of emission have usually been studied separately by first specifying the range of temperature and field and then constructing the appropriate expression for the current. In this paper the emission is treated from a unified point of view in order to establish the ranges of temperature and field for the two types of emission and to investigate the current in the region intermediate between thermionic and field emission. A general expression for the emitted current as a function of field, temperature, and work function is set up in the form of a definite integral. Each type of emission is then associated with a technique for approximating the integral and with a characteristic dependence on the three parameters. An approximation for low fields and high temperatures leads to an extension of the Richardson-Schottky formula for thermionic emission. The values of temperature and field for which it applies are established by considering the validity of the approximation. An analogous treatment of the integral, for high fields and low temperatures, gives an extension of the Fowler-Nordheim formula for field emission, and establishes the region of temperature and field in which it applies. Also another approximate method for evaluating the integral is given which leads to a new type of dependence of the emitted current on temperature and field and which applies in a narrow region of temperature and field intermediate between the field and thermionic emission regions.

Thermionic Emission, Field Emission, and the Transition Region

A Lorentz covariant description of a particle and antiparticle with spin $s=0, \frac{1}{2}, 1, \ensuremath{\cdots}$ and finite rest mass is given in this paper. The wave function has $2(2s+1)$ components so that no auxiliary conditions are needed. The basic idea is to postulate the rest-system Hamiltonian and make the Lorentz transformation to the laboratory system. An algorithm which is a generalization of the Foldy-Wouthuysen transformation is found for constructing the laboratory-system Hamiltonian and polarization operators.

Description of a Particle with Arbitrary Mass and Spin

Dysprosium is ferromagnetic below 85\ifmmode^\circ\else\textdegree\fi{}K, antiferromagnetic between 85 and 179\ifmmode^\circ\else\textdegree\fi{}K, and paramagnetic above 179\ifmmode^\circ\else\textdegree\fi{}K. The spontaneous magnetic moment lies always in the basal plane, and there is anisotropy in this plane below 110\ifmmode^\circ\else\textdegree\fi{}K. In the present paper it is shown that the magnetic properties can be interpreted in terms of a two-sublattice model and a phenomenological theory similar to a theory proposed by N\'eel. Detailed agreement for the magnetization curves in the ferromagnetic and antiferromagnetic regions is obtained.

Interpretation of magnetic properties of dysprosium

In this paper the electrodynamics of a spin-one particleantiparticle is developed using a (1, 0) 0 (0, 1) six-component wave function. Anomalous magnetic dipole and electric quadrupole effects are included. The wave equation is manifestly covariant and has no auxiliary conditions. The invariant integral for the system is derived and the nonrelativistic limit is discussed.

/pdf/spin-one-particle-in-an-external-electromagnetic-field-4cw98yq3l5.pdf

Spin-one particle in an external electromagnetic field*

A wave equation for a noninteracting particle with zero mass and arbitrary spin $s$ is given in this paper. The Hamiltonian is proportional to the inner product of the momentum and spin operators so that the wave function has $2s+1$ components. As an auxiliary condition, solutions with spins not parallel or anti-parallel to the momentum are discarded. With this condition the theory is Lorentz-covariant. The energy, momentum, and angular momentum are defined in terms of expected values of the usual type of displacement operator. The specialization $s=\frac{1}{2}$ is the two-component neutrino theory and $s=1$ gives Maxwell's equations for the photon.

R. H. Good

Papers

Thermionic Emission, Field Emission, and the Transition Region

Description of a Particle with Arbitrary Mass and Spin

Interpretation of magnetic properties of dysprosium

Spin-one particle in an external electromagnetic field*

Wave Equation for a Massless Particle with Arbitrary Spin