Near-equilibrium transport. Fundamentals and applications
With the term ``near-equilibrium transport'', the author of the present textbook describes transport of charged particles in materials where the electrical current varies linearly with the voltage. This near-equilibrium transport is the foundation to understand transport properties in general, it gives reference points for the comparison with more complicated situations, and it strongly influences the performance of most electronic devices. Besides, recently, scientists are interested in near-equillibrium transport in extremely short conductors, e.g.\ of the dimension of a molecule.NEWLINENEWLINEThus, the present new book is designed to introduce the reader into the fundamentals of carrier transport in nano-devices using a novel ``bottom-up approach'' that agrees with traditional methods when the devices are large, but which also works for nano-devices. The goal is to make the reader acquainted with the carrier transport at the nanoscale and to show how the bottom-up approach provides a new perspective to traditional concepts like mobility and drift-diffusion equations.NEWLINENEWLINENear-equilibrium transport may be -- in dependence on the mean free path of the charged particles and the dimensions of the systems -- diffusive or ballistic. In case of strong electric fields, the transport may be non-local, and electron overshoot can occur. Under the condition that the potential changes rapidly on the scale of the electron wavelength, quantum physical effects like reflection and tunnelig become important. Also, the various kinds of possible material disorders determine the transport of charged particles. All these phenomena are briefly discussed in the textbook. Further, although the focus of the book is on electron transport in semiconductors and metals, also phonon transport is considered. Moreover, thermoelectric phenomena are also explained.NEWLINENEWLINEIn detail, after a short introduction, the book consists of nine chapters, the aim of which (see pages 7--9) is formulated by the author as follows:NEWLINENEWLINE\textit{Lecture 2: General model for transport:} ``Datta's model of a nanodevice (a version of the Landauer approach) is introduced as a general way to describe transport in nanodevices -- as well as in bulk metals and semiconductors.'' NEWLINENEWLINE\textit{Lecture 3: Resistance: Ballistic to diffuse:} ``The resistance of a ballistic conductor and concepts such as the quantum contact resistance are introduced and discussed. The results are then generalized to treat transport all the way from the ballistic to diffusive regimes.'' It is shown ``how to treat bulk conductors (electrons free to move in 3D)... 2D conductors (electrons free to move in 2D) and 1D conductors (electrons free to move along a wire).'' Thus, the reader learns how to use the Landauer expression for the electrical conductivity to systems with uniform temperature. NEWLINENEWLINE\textit{Lecture 4: Thermoelectric effects: Physical approach:} ``The effect of temperature gradients on current flow and how electrical currents produce heat currents'' is considered. ``Coupled equations for the electric and heat currents'' are presented, ``and applications to electronic cooling and the generation of electrical power from thermal gradients'' are briefly explained. In this chapter, a physical approach is used and mathematics is only introduced when necessary. NEWLINENEWLINE\textit{Lecture 5: Thermoelectric effects: Mathematics:} Starting with the general formulation of charged particle transport, the expressions for four thermoelectric transport coefficients are mathematically derived, for the electrical conductivity, the Seebeck coefficient (or thermopower), the Peltier coefficient, and the heat conductivity of the electrons. The results are valid for arbitrary band structures and scattering mechanisms, and from the ballistic to diffusive limits. Also well-known relationships between these coefficients as the Kelvin relation and the Wiedemann-Franz law are discussed. NEWLINENEWLINE\textit{Lecture 6: An introduction to scattering:} In the lectures 1-5, ``scattering is described by a mean-free path... for backscattering.'' Now, it is shown how the mean free path ``is related to the time between scattering events''. It is briefly discussed ``how the scattering time is related to underlying physical processes''. Further, it is shown, how the mean free path may be estimated by measurements of conductivity and carrier density. NEWLINENEWLINE\textit{Lecture 7: Boltzmann transport equation:} ``Semi-classical carrier transport is traditionally described by the Boltzmann transport equation (BTE)... .'' In this lecture, the BTE is presented, it is shown how to solve this equation, and the BTE is related to the Landauer approach used in the book. As application, it is shown how to use the BTE to describe the conductivity in the presence of an external magnetic field. NEWLINENEWLINE\textit{Lecture 8: Near-equilibrium transport: Measurements:} ``Measurements of near-equilibrium transport are routinely used to characterize electronic materials. This lecture is a brief introduction to commonly-used techniques such as van der Pauw and Hall effect measurements.'' Also temperature-dependent measurements are treated, which help experimentalists to determine the most dominant scattering mechanisms in the material. NEWLINENEWLINE\textit{Lecture 9: Phonon transport:} ``Most of the heat flow in semiconductors is carried by phonons (i.e.\ quantized lattice vibrations). In the presence of a small temperature gradient, phonon transport is also a problem in near-equilibrium transport, and the techniques developed for electron transport can be readily extended to phonons. This lecture is an introduction to phonon transport. Key similarities and differences between electron and phonon transport are discussed.'' NEWLINENEWLINE\textit{Lecture 10: Graphene: A case study:} In the chapters 1-8, applications of near-equilibrium electron transport to traditional materials are considered, e.g.\ to semiconductors with parabolic energy bands. But the presented theory is much more general. Thus, here, for the interesting example of graphene, near-equilibrium transport is treated. Graphene recently attracted a lot of attention and was the subject of the 2010 Nobel Prize in Physics. Graphene possesses linear energy bands.NEWLINENEWLINETo assist the reader of the textbook in performing computations, the key results of the book are once more summarized in an appendix, which includes pointers to the specific results of the different lectures. Expressions of the four transport coefficients electrical conductivity, Seebeck coefficient, Peltier coefficient, and electron heat conductivity are also listed in the appendix for materials with simple band structures.NEWLINENEWLINEThe present textbook is designed for electrical engineers, but also for students in physics, material science, chemistry and other fields, who need a working knowledge of near-equilibrium (i.e.\ linear or low-field) transport theory. Only a very basic understanding of solid-state physics, semiconductors, and electronic devices is assumed.
scientific article; zbMATH DE number 6047069