Quantum Electron Theory of Amorphous Conductors

The electron theory of solids has attracted great attention in recent years, mainly because of the numerous practical applications of semicon­ ductors. However, all the reviews and monographs on this subject deal only with crystalline conductors. At present, mainly in the Soviet Union, experi­ mental and theoretical investigations have been extended to liquid and solid amorphous conductors, and in particular to such semiconductors. However, all the work published so far in this field is in the form of separate papers scat­ tered throughout various journals, and there has as yet been no Soviet or for­ eign review of the theoretical work on amorphous semiconductors, in spite of the increasing interest in them. The investigation of liquid and amorphous semiconductors is of great practical importance, first, because all the solid semico'nductors are usually prepared from the liquid phase and it is important to know the electrical and other properties of this phase; secondly, amorphous semiconductors are beginning to be used in industry, for example, amorphous Sb S films in vidicon tubes. In some cases, especially in optical instruments, 2 S amorphous semiconductors have advantages compared with crystals. Theore­ tical studies of amorphous semiconductors should help in these practical applications. The present monograph is the first attempt to present systematically the quantum electron theory of amorphous conductors. The most interesting-in the author's view-theoretical papers on this subject, published in journals are reviewed and critically compared.

I Review of Experimental Data on Liquid and Amorphous Conductors.- § 1. Electrical Conductivity of Liquid Metals.- § 2. Changes in the Electrical Conductivity of Semiconductors on Melting.- § 3. Correlation Between the Electrical Conductivity and Other Properties.- § 4. Characteristics of the Electrical Conductivity of Liquid Solutions of Metals and Semiconductors.- § 5. Formation of the Glassy State in Semiconducting Systems.- § 6. Electrical Properties of Amorphous Films and Glassy Semiconductors.- § 7. Photoelectric and Optical Effects in Glassy Semiconductors.- § 8. Metal — Ammonia Solutions.- II Fundamentals of the Electron Theory of Solids.- § 9. One-Electron Approximation.- §10. Heitler — London and Hund — Mulliken Methods.- §11. Method of Elementary Excitations.- §12. Justification of the One-Electron Approximation by the Theory of Collective Electron Interaction.- §13. Electron in a Periodic Field.- §14. Principal Methods of Calculating the Energy Spectrum of Electrons in a Crystal.- §15. Calculation of the Mean Free Path of Electrons.- §16. Impurity Levels and Local Electron States.- III Structure of Amorphous Substances.- §17. Phenomenological Similarity of Liquids and Solids.- §18. Molecular Structure of Liquids and Structural Diffusion.- §19. Structure of Liquid Metals.- §20. Structure of Water and of Organic Liquids.- §21. Structure of Glass.- §22. Short-Range and Long-Range Order in Alloys.- §23. Thermal Motion in Liquids.- IV Band Theory for the One-Dimensional Model of a Liquid.- §24. Mechanism of “Melting” in the One-Dimensional Model.- §25. Wave Equation on a Deformed Coordinate Scale.- §26. Calculation of the Perturbation Matrix Elements.- §27. Calculation of the Energy.- §28. Comparison with Numerical Calculations.- V Band Theory for the Three-Dimensional Model of a Liquid [1].- §29. Mechanism of Melting in the Three-Dimensional Model.- §30. Wave Equation in a Deformed System of Coordinates.- §31. Calculation of the Perturbation Matrix Elements.- §32. Calculation of the Energy.- §33. Comparison of the One- and Three-Dimensional Models.- §34. Changes in the Band Width and Effective Mass when Semiconductors Melt.- VI Scattering of Electrons in Liquids by Departures from Long-Range Order and by Defects.- §35. Statement of the Problem.- §36. Discussion of the Electron Motion in a Liquid in Terms of Cartesian Coordinates.- §37. Solution of the Transport Equation for Electrons in a Liquid.- §38. Calculation of the Matrix Element and Estimation of the Electron Mean Free Path in Liquids.- §39. Scattering of Electrons on Defects.- §40. Mechanism of Electron Motion in Liquids.- VII Scattering of Electrons on Thermal Vibrations in a Liquid.- §41. Initial Equations.- §42. Change in the Electron Distribution Function Under the Action of the Acoustical-Mode Vibrations.- §43. Blochls Integral Equation.- §44. Mean Free Path of an Electron Associated with Phonon — Liquid Scattering.- §45. Change in the Electron Distribution Function Under the Action of the Optical-Mode Vibrations.- §46. Electron Mean Free Path Associated with the Phonon — Liquid Scattering in the Case of Optical-Mode Vibrations.- VIII Electrical Conductivity, Thermal Conductivity, Thermoelectric Power, Hall Coefficient, and Nernst Coefficient of Amorphous Substances Exhibiting Electronic Conduction.- §47. General Formulas.- §48. Liquid Metals at T » ?.- §49. Amorphous Covalent Semiconductors.- §50. Amorphous Ionic Semiconductors.- IX Local and Impurity Levels in Amorphous Semiconductors.- §51. Local States in the One-Dimensional Model of a Liquid.- §52. Method of Calculating Local Levels in Many-Atom Systems.- §53. Local Fluctuation Levels in Amorphous Semiconductors [6].- §54. Impurity Levels in Amorphous Semiconductors.- §55. Possible Reasons for the Absence of Impurity Conduction in Amorphous Semiconductors.- X Electron Structure of Liquid Metals.- §56. Calculation Method.- §57. Calculation of the Density of States in Limiting Cases.- §58. Electron Spectrum of Real Liquid Metals.- §59. Wave Functions of Electrons in Liquid Metals.- XI Theory of the Electrical Conductivity of Liquid Metals.- §60. Scattering of Electrons by Metal Atoms.- §61. Plasma Scattering and the Displacement Potential.- §62. Change in the Electrical Conductivity on Melting..- §63. Dependence of the Electrical Conductivity on Temperature and Pressure.- §64. Applicability of the Theory to Multivalent Metals [2].- XII Quasi-Classical Theory of Amorphous Ferromagnets.- §65. Fraction of Antiparallel Spin Pairs.- §66. Average Magnetization and the Curie Point.- Appendix. The Electron State Density in the Band “Tail” of Amorphous Semiconductors.- Literature Cited.