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Low-dimensional semiconductors have become a vital part of today's semiconductor physics, and excitons in these systems are ideal objects that bring textbook quantum mechanics to life. Furthermore, their theoretical understanding is important for experiments and optoelectronic devices. The author develops the effective-mass theory of excitons in low-dimensional semiconductors and describes numerical methods for calculating the optical absorption including Coulomb interaction, geometry, and external fields. The theory is applied to Fano resonances in low-dimensional semiconductors and the Zener breakdown in superlattices. Comparing theoretical results with experiments, the book is essentially self-contained; it is a hands-on approach with detailed derivations, worked examples, illustrative figures, and computer programs. The book is clearly structured and will be valuable as an advanced-level self-study or course book for graduate students, lecturers, and researchers.
List of contents
1 Optical Transitions in Semiconductors.- 2 Numerical Calculation.- 3 Fano Resonances.- 4 Zener Breakdown in Superlattices.- A Mathematical Supplement.- A.1 Basic Definitions and Relations.- A.2 Special Functions of Mathematical Physics.- A.3 Miscellaneous Relations.- B Physical Supplement.- B.1 Physical Constants and Material Parameters.- B.2 Dimensionless Quantities.- B.3 Crystal Symmetry.- C Essentials of Quantum Mechanics.- C.1 The Quantum-Mechanical Eigenvalue Problem.- C.1.1 The Spectrum of Schrödinger Operators.- C.1.2 Selected Eigenvalue Problems.- C.2 Angular Momentum in Quantum Mechanics.- C.2.1 The Eigenvalue Problem.- C.2.2 Orthogonal Transformations.- C.2.3 Addition of Angular Momenta.- C.2.4 Time Reversal.- C.3 Perturbation Theory.- C.3.1 Degenerate Time-Independent Perturbation Theory.- C.3.2 Time-Dependent Perturbation Theory.- D Computer Programs.- D.1 Cartesian Coordinates.- D.2 Polar Coordinates.- D.3 Time-Reversal Symmetry.- D.4 Absorbing Boundary Conditions.- D.5 Cylindrical Coordinates.- References.
Summary
Low-dimensional semiconductors have become a vital part of today's semiconductor physics, and excitons in these systems are ideal objects that bring textbook quantum mechanics to life. Furthermore, their theoretical understanding is important for experiments and optoelectronic devices. The author develops the effective-mass theory of excitons in low-dimensional semiconductors and describes numerical methods for calculating the optical absorption including Coulomb interaction, geometry, and external fields. The theory is applied to Fano resonances in low-dimensional semiconductors and the Zener breakdown in superlattices. Comparing theoretical results with experiments, the book is essentially self-contained; it is a hands-on approach with detailed derivations, worked examples, illustrative figures, and computer programs. The book is clearly structured and will be valuable as an advanced-level self-study or course book for graduate students, lecturers, and researchers.
