Electron Spectrum of Gapless Semiconductors

1. Introduction.- 2. Band-Structure Calculation Methods.- 2.1 Adiabatic Approximation.- 2.2 The One-Electron Hartree-Fock Approximation.- 2.2.1 The Hartree Approximation.- 2.2.2 The Hartree-Fock Method.- 2.2.3 Discrete Distribution.- 2.3 Correlation Phenomena.- 2.3.1 The Drude-Sommerfeld Gas of Free Electrons.- 2.3.2 Binding Energy.- 2.3.3 Correlation Energy.- 2.4 Methods Used to Solve the Schrödinger Equation.- 2.4.1 General Concept.- 2.4.2 Cellular Method.- 2.4.3 Variational Methods.- 2.4.4 Classification of Computational Methods.- 2.4.5 Tight-Binding Method.- 2.4.6 The APW and KKR Methods.- 2.4.7 OPW and Pseudopotential Methods.- 2.4.8 Linear Methods.- 2.4.9 The k p-Method.- 3. Insulators, Semiconductors, Metals.- 3.1 The Detection of the Gapless State.- 3.1.1 The Very-Small Gap in HgTe.- 3.1.2 The Intrinsic Gapless Semiconductor.- 3.2 Gray Tin.- 3.2.1 Crystal Structure.- 3.2.2 Original Band Schemes.- 3.2.3 Inverse Band Model for ?-Sn.- 3.2.4 Experimental Confirmations of the Inverse-Band Model.- 3.3 Mercury Chalcogenides HgTe and HgSe.- 3.3.1 Crystal Structure and Herman´s Perturbation Method.- 3.3.2 Inverse-Band Model for II-VI Crystals.- 3.3.3 Experimental Confirmations of the Inverse-Band Model.- 3.3.4 The Role of Relativistic Effects.- 3.3.5 Shape of the Energy Bands Near the Edge k = 0.- 3.3.6 Effect of the Electron-Electron Interaction.- 3.3.7 Rearrangement of the Band Structure Subject to a Magnetic Field.- 3.3.8 Rearrangement of the Band Structure Under the Influence of a Hydrostatic Pressure.- 4. Impurities.- 4.1 The Problem of Residual Electron Concentration.- 4.2 Impurities and Intrinsic Defects in Mercury Chalcogenides..- 4.3 Energies of Impurity States.- 4.3.1 Features Peculiar to the Localization of Impurity Levels.- 4.3.2 Energy and Wave Functions of an Electron (Hole) at an Impurity Center.- 4.3.3 Experimental Data for the Binding Energy ?A in HgCdTe Gapless Semiconductors.- 4.3.4 Short-Range Potential.- 4.3.5 Experimental Data for the Binding Energy ?A in HgCdTe Narrow-Gap Semiconductors.- 4.4 Metal-Insulator Transitions.- 4.4.1 Doped Semiconductors.- 4.4.2 The Mott Transition.- 4.4.3 The Anderson Transition.- 4.5 The Mott Transition in n-Type Crystals.- 4.6 The Influence of Compensation on the Mott Transition.- 4.7 An "Anomaly" in the Temperature Dependence of the Electron Concentration.- 4.8 Freeze-Out of Electrons onto Acceptors in a Magnetic Field.- 4.9 Freeze-Out of Electrons onto Acceptors Subject to Hydrostatic Pressure.- 4.10 On the Mobility of Holes in Gapless HgCdTe Crystals.- 5. Semimagnetic Semiconductors.- 5.1 HgMnTe Crystals.- 5.1.1 Peculiarities of Crystalline and Band Structures.- 5.1.2 Magnetic Properties.- 5.1.3 Exchange Interaction.- 5.1.4 Shubnikov-de Haas Oscillations.- 5.1.5 Magnetoresistance.- 5.2 HgSe:Fe Crystals.- 5.2.1 Resonance Donor States of Iron.- a) Spatial Correlation of Charged Fe3+Donors.- b) Experimental Evidence Confirming the Existence of Two Charge States of Fe in HgSe.- c) Anomalies of the HgSe:Fe Properties.- d) The Hall Effect.- e) Stabilization of the Fermi Level.- f) Stabilization of the Electron Concentration with Time.- g) Temperature Variation of the Electron Concentration.- h) Fermi-Level Variations in HgFeSe Doped with Cadmium and Tellurium.- i) Quantum Oscillations.- 5.2.2 Electron Scattering in HgSe:Fe.- a) Anomalies of the Electron Mobility and the Dingle Temperature.- b) Resonance Electron Scattering.- c) Mycielski´s Ordering Model.- d) Analysis of Mycielski´s Ordering Model.- e) Consideration of Disorder in the System of Fe3+Ions.- f) Effect of Vibrations and Non-Ideality of the Wigner Charge Lattice on the Temperature Dependence of the Electron Mobility.- g) A Quantitative Analysis of the Variation in the Electron Mobility when HgSe is Doped with Iron.- 5.3 HgSe:Cr Crystals.- 5.4 DX Centers.- 5.5 The Improved Short-Range Correlation Model.- 6. Conclusion.- 6.1 Practical Applications of Gapless Semiconductors.- 6.2 Some Results and Problems.- References.