Electronic States and Optical Transitions in Semiconductor Heterostructures

This book provides the theoretical basis and the relevant experimental knowledge underlying our present understanding of the electrical and optical properties of semiconductor heterostructures. Although such structures have been known since the 1940s, it was only in the 1980s that they moved to the forefront of research, largely due to technological developments that made it possible to grow several ultrathin layers of different materials _ down to a few atoms in thickness _ on top of a silicon or other substrates. The resulting structures have remarkable properties not shared by bulk materials. One can, for example, confine the motions of electrons to a single layer, making it possible to investigate effectively two-dimensional systems. One can also build materials with large-scale periodicities by alternating layers of different compositions, thereby modulating the optical and electronic properties of the resulting structure. The text begins with a description of the electronic properties of various types of heterostructures, including discussions of complex band-structure effects, localized states, tunneling phenomena, and excitonic states. The focus of most of the remainder of the book is on optical properties, including intraband absorption, luminescence and recombination, Raman scattering, subband optical transitions, nonlinear effects, and ultrafast optical phenomena. The concluding chapter presents an overview of some of the applications that make use of the physics discussed. Appendices provide ackground information on band structure theoy, kinetic theory, electromagnetic modes, and Coulomb effects. Intended for graduate students, physicists, and engineers beginning research on semiconductor heterostructures or interested in their

1 Electronic Structure of Abrupt Heterojunctions.- 1.1 Band Diagrams of Heterostructures.- 1.2 k · p Model for Heterojunctions.- 1.3 Shallow Electronic States at Heterojunctions.- 1.4 Field-Induced Interface States.- 1.5 Intervalley Mixing at Heterojunctions.- 1.6 Numerical Methods for the Description of Heterostructures 27 Bibliography Notes.- 2 Electrons in Low-Dimensional Structures.- 2.1 Formation of Confined Electronic States.- 2.2 Electronic States in Quantum Wells, Wires, and Dots.- 2.3 Self-Consistent Electronic States in Quantum Wells.- 2.4 More Complex Quantum Wells.- 2.5 Mixing of Hole States in Heterostructures.- 2.6 Multiband k · p Approximation.- 2.7 Electronic States in the Presence of Strain.- Bibliography Notes.- 3 Tunneling in Heterostructures.- 3.1 Tunneling Transmission.- 3.2 Tunnel-Coupled Levels.- 3.3 Superlattices.- 3.4 Superlattices Formed by States of Different Origin.- Bibliography Notes.- 4 Impurity States and Excitons in Heterostructures.- 4.1 Electron Localization on Imperfections.- 4.2 Impurity States in Quantum Wells.- 4.3 Quantum Well Excitons.- 4.4 Excitons in Other Heterostructures.- Bibliography Notes.- 5 Interband Optical Transitions in Heterostructures.- 5.1 Absorption of Light by a 2D Layer.- 5.2 Polarization Dependence of the Interband Transitions.- 5.3 Interband Absorption Spectra in Heterostructures.- 5.4 Excitonic Absorption.- 5.5 Electrooptics of Heterostructures.- 5.6 Modulation Spectroscopy of Heterostructures.- Bibliography Notes.- 6 Radiative Processes in Heterostructures.- 6.1 Theory of Luminescence in 2D Systems.- 6.2 Spectral and Polarization Dependencies of Luminescence.- 6.3 Luminescence from Complex Heterostructures.- 6.4 Radiative Recombination.- Bibliography Notes.- 7 Scattering of Light on Low-Dimensional Electrons.- 7.1 Scattering Cross-Section.- 7.2 Raman Spectroscopy of Intersubband Excitations.- 7.3 Scattering on Collective Electronic Excitations.- Bibliography Notes.- 8 Intersubband Optical Transitions.- 8.1 Resonant Transitions and Excitation into the Continuum.- 8.2 Intersubband Transitions for In-Plane Electric Field.- 8.3 Depolarization Shift and Coulomb Renormalization.- 8.4 Submillimeter Intersubband Transitions.- 8.5 Radiative Intraband Transitions in Heterostructures.- Bibliography Notes.- 9 Nonlinear Optics of Heterostructures.- 9.1 Nonlinear Response.- 9.2 Nonlinear Susceptibilities.- 9.3 Photoelectric Phenomena.- 9.4 Nonlinearities Induced by Electron-Hole Pairs.- Bibliography Notes.- 10 Ultrafast Processes in Heterostructures.- 10.1 Ultrafast Optical Excitation.- 10.2 Carrier Relaxation Processes.- 10.3 Coherent Optics of Heterostructures.- 10.4 Ultrafast Charge Dynamics in Heterostructures.- Bibliography Notes.- 11 Heterostructure-Based Optoelectronic Devices.- 11.1 Heterostructure Lasers.- 11.2 Electrooptic Modulators.- 11.3 Photodetectors.- 11.4 Intersubband Optoelectronic Devices.- 11.5 Optical Characterization of Heterostructures.- Bibliography Notes.- A k · p Method for Bulk Semiconductors.- A.I Nondegenerate Band.- A.2 Two-Band Model.- A.3 Luttinger Model.- A.4 Kane Model.- A.5 Effects of External Fields.- A.6 Effects of Deformation.- Bibliography Notes.- B Electromagnetic Waves in Layered Media.- B.I Modes in a Layered Medium.- B.2 Second Quantization of the Field.- Bibliography Notes.- C Kinetic Equations for Electrons and Photons.- C.I Kinetic Equations Approach.- C.2 Wigner Function for Photons.- C.3 Electron Response.- C.4 Conductivity and Generation Rate.- Bibliography Notes.- D Coulomb Effects in Heterostructures.- D.I Mean Field Treatment of Coulomb Effects.- D.2 Matrix Elements for 3D, 2D, and ID States.- D.3 Intraband Density Matrix Equations.- D.4 Semiconductor Bloch Equations.- D.5 Beyond the Mean-Field Approximation.- Bibliography Notes.- References.