We review the physical properties of diluted magnetic semiconductors (DMS) of the type AII1−xMnxBVI (e.g., Cd1−xMnxSe, Hg1−xMnxTe). Crystallographic properties are discussed first, with emphasis on the common structural features which these materials have as a result of tetrahedral bonding. We then describe the band structure of the AII1−xMnxBVI alloys in the absence of an external magnetic field, stressing the close relationship of the sp electron bands in these materials to the band structure of the nonmagnetic AIIBVI ‘‘parent’’ semiconductors. In addition, the characteristics of the narrow (nearly localized) band arising from the half‐filled Mn 3d5 shells are described, along with their profound effect on the optical properties of DMS. We then describe our present understanding of the magnetic properties of the AII1−xMnxBVI alloys. In particular, we discuss the mechanism of the Mn++‐Mn++ exchange, which underlies the magnetism of these materials; we present an analytic formulation for the magnetic susc...

Diluted magnetic semiconductors

This book is an introduction to the modern approach to the theory of Markov chains. The main goal of this approach is to determine the rate of convergence of a Markov chain to the stationary distribution as a function of the size and geometry of the state space. The authors develop the key tools for estimating convergence times, including coupling, strong stationary times, and spectral methods. Whenever possible, probabilistic methods are emphasized. The book includes many examples and provides brief introductions to some central models of statistical mechanics. Also provided are accounts of random walks on networks, including hitting and cover times, and analyses of several methods of shuffling cards. As a prerequisite, the authors assume a modest understanding of probability theory and linear algebra at an undergraduate level. ""Markov Chains and Mixing Times"" is meant to bring the excitement of this active area of research to a wide audience.

Markov Chains and Mixing Times

Power dissipation is a fundamental problem for nanoelectronic circuits. Scaling the supply voltage reduces the energy needed for switching, but the field-effect transistors (FETs) in today's integrated circuits require at least 60 mV of gate voltage to increase the current by one order of magnitude at room temperature. Tunnel FETs avoid this limit by using quantum-mechanical band-to-band tunnelling, rather than thermal injection, to inject charge carriers into the device channel. Tunnel FETs based on ultrathin semiconducting films or nanowires could achieve a 100-fold power reduction over complementary metal-oxide-semiconductor (CMOS) transistors, so integrating tunnel FETs with CMOS technology could improve low-power integrated circuits.

Tunnel field-effect transistors as energy-efficient electronic switches

Calculations of ground-state and excited-state properties of materials have been one of the major goals of condensed matter physics. Ground-state properties of solids have been extensively investigated for several decades within the standard density functional theory. Excited-state properties, on the other hand, were relatively unexplored in ab initio calculations until a decade ago. The most suitable approach up to now for studying excited-state properties of extended systems is the Green function method. To calculate the Green function one requires the self-energy operator which is non-local and energy dependent. In this article we describe the GW approximation which has turned out to be a fruitful approximation to the self-energy. The Green function theory, numerical methods for carrying out the self-energy calculations, simplified schemes, and applications to various systems are described. Self-consistency issue and new developments beyond the GW approximation are also discussed as well as the success and shortcomings of the GW approximation.

https://iopscience.iop.org/article/10.1088/0034-4885/61/3/002/pdf

The GW method

Steep subthreshold swing transistors based on interband tunneling are examined toward extending the performance of electronics systems. In particular, this review introduces and summarizes progress in the development of the tunnel field-effect transistors (TFETs) including its origin, current experimental and theoretical performance relative to the metal-oxide-semiconductor field-effect transistor (MOSFET), basic current-transport theory, design tradeoffs, and fundamental challenges. The promise of the TFET is in its ability to provide higher drive current than the MOSFET as supply voltages approach 0.1 V.

/pdf/low-voltage-tunnel-transistors-for-beyond-cmos-logic-3w5c8knrc5.pdf

Low-Voltage Tunnel Transistors for Beyond CMOS Logic

1. Fibonacci identities 2. Lucas identities 3. Gibonacci identities 4. Linear recurrences 5. Continued fractions 6. Binomial identities 7. Alternating sign binomial identities 8. Harmonic numbers and Stirling numbers 9. Number theory 10. Advanced Fibonacci and Lucas identities.

Proofs that Really Count: The Art of Combinatorial Proof

Electronic collective modes of a system of large numbers of equally spaced, parallel two-dimensional electron layers are discussed within a self-consistent-field approach. Plasmon dispersion relations for the finite system as well as for the infinite periodic system are obtained. It is shown that the optical-plasmon frequency of the periodic system goes into the known two- or three-dimensional limit, respectively, depending on whether $\mathrm{qa}\ensuremath{\gg}1$ or $\mathrm{qa}\ensuremath{\ll}1$, where $q$ is the wave number in the two-dimensional plane and $a$ is the layer spacing. Effect of a uniform static external magnetic field oriented normal to the two-dimensional layers, on the collective-mode spectrum, is discussed with the use of the self-consistent-field and hydrodynamic approximations. It is shown that magnetoplasmons, helicon, and Alfv\'en waves can all exist in such a periodic system under suitable conditions. The theory is generalized to a system where the alternate layers are electrons and holes. The relevance of these results to semiconductor superlattice systems (both types I and II) is pointed out.

Collective excitations in semiconductor superlattices

In this paper electronic collective excitations of type-I and -II superlattices are examined in detail. Type-I superlattices consist of quasi-two-dimensional layers of electrons, while type-II superlattices consist of alternating quasi-two-dimensional layers of electrons and holes. We use a simple model of the electronic structure and linear-response theory to calculate the density response of the system to an external perturbation. From this, we obtain an expression for the dielectric tensor, the zeros of which yield the dispersion relations of the collective modes. The theory is such that one can take into account many-body effects (depolarization and excitonic shifts), magnetic fields, and electron-phonon coupling in a simple way. A rich spectrum of excitations is found: quasi-two-dimensional plasmons, intersubband plasmons, magnetoplasmons, phonon-plasmon modes, and so on. Some interesting features of the excitations are examined, and their relevance to experiment is discussed.

Theory of collective excitations in semiconductor superlattice structures

The quantum-mechanical response of a two-dimensional electron gas in the presence of a strong dc magnetic field is calculated in the random-phase approximation. The results are used to discuss the magnetoplasma oscillations of a two-dimensional electron gas. The general dispersion relation is derived, and numerical results are presented for both long and short wavelengths.

Plasma oscillations of a two-dimensional electron gas in a strong magnetic field

A cause de la quantification des niveaux d'energie electronique par le potentiel de superreseau, ce nouveau mode de polariton a la propriete remarquable de ne pas avoir d'amortissement de Landau

Jennifer J. Quinn

Papers

Proofs that Really Count: The Art of Combinatorial Proof

Collective excitations in semiconductor superlattices

Theory of collective excitations in semiconductor superlattice structures

Plasma oscillations of a two-dimensional electron gas in a strong magnetic field

Charge-density excitations at the surface of a semiconductor superlattice: a new type of surface polariton