Born-von Karman boundary conditions; density of states in bulk materials, quantum wells, and quantum wires. Carrier statistics in semiconductors: Fermi-Dirac distribution function, electron and hole density in the conduction and valence bands. Nondegenerate semiconductors; effective density of states; intrinsic semiconductors. Mass-action law. Doped semiconductors: donors and acceptors; hydrogen-like model. Degenerate semiconductors. Quasi-Fermi levels in nonequilibrium systems. Charge transport in semiconductors. Diffusion current.

Vertical cavity surface-emitting lasers (VCSELs): general structure; threshold conditions. Distributed Bragg reflectors for VCSELs. Threshold conditions and current confinement. Applications.

Light emitting diodes (LEDs): photon flux, injection efficiency, internal quantum efficiency. Double-heterostructure LEDs. Burstein-Moss shift. Carrier overflow. Carrier leakage over the barrier. External efficiency of a LED: transmission efficiency and external quantum efficiency. Output power, responsivity, and wall-plug efficiency. Emission pattern of LEDs. Luminous efficiency. Blue LEDs.

Quantum dot lasers. Fabrication techniques of quantum dots: self-assembling formation of quantum dots (Stranski-Krastanov growth mode). General scheme of quantum dot lasers. Electronic states in quantum dots: particle in a cubic box; spherical quantum dots. Coulomb interaction. Carrier statistics in quantum dots. Optical transitions. Absorption and gain spectrum. Threshold current density and its temperature dependence. Linewidth enhancement factor.

The field of quantum research is currently undergoing a revolution. A variety of tools and platforms for controlling individual quantum particles have emerged, which can be utilized to develop entirely new technologies for computation, communication, and sensing. In particular, these technologies will enable applications of quantum information science that can fundamentally change the way we store, process, and transmit information. Exciting theoretical predictions exist for quantum computers, with some proof-of-principle experiments, to perform calculations that would overwhelm the world’s best conventional supercomputers. Quantum research is rapidly developing, and the race is intensifying for quantum technology development, involving some of the high-tech giants. In this chapter we will introduce some key concepts in the materials and devices behind these technological developments. Becoming familiar with these concepts in this first chapter should provide the reader with concrete goals and motivations for studying the quantum methods and tools described in subsequent chapters.

Quantum mechanics is currently the most fundamental theory in use in many disciplines of science and engineering. It is particularly important when one is dealing with nanoscale and atomic-scale systems. However, many phenomena and properties that occur at atomic scales are strange and nonintuitive. There are a number of concepts that simply do not exist in the macroscopic world where we live. Wave–particle duality is one of them. In this chapter, we examine how and when classical particles start behaving as quantum mechanical waves, derive the most important wave equation that quantum particles obey, Schrödinger’s equation, and solve it for the elementary problems of electron waves in given potential energy landscapes. We will also learn how to calculate the expectation values of observables when the wavefunction is known. Schrödinger’s equation will be extensively used throughout the rest of this textbook. More complicated potential energy problems, particularly those relevant to materials and devices, will be dealt with in Chapters 5 and 7, building upon the formulations developed in this chapter.

The band theory of solids provides a general framework with which to understand properties of materials. It not only explains the fundamental differences in electronic structure between insulators, semiconductors, and metals but also provides guidelines for finding optimum materials for specific device applications. For example, a semiconductor with a light effective mass is suited for high-electron-mobility transistors (HEMTs) because the mobility ${\mu }_{\mathrm{e}}$ is inversely proportional to the effective mass, ${\mu }_{\mathrm{e}}=e\tau /m^{*}$, where τ is the scattering time. For developing LEDs and laser diodes, a direct band gap material – i.e., a material in which the conduction-band bottom and the valence-band top occur at the same k – is necessary for momentum conservation since the momentum of photons is negligibly small compared with crystal momenta. In this chapter, after reviewing the basic concepts of atomic and molecular orbitals, bonds and bands, crystal lattices and reciprocal lattices, we provide an overview of the band structure of technologically important materials, including both traditional and emerging materials.

The theory of the interaction of radiation with matter is fundamentally important for describing how modern semiconductor devices generate, detect, and modulate light. These devices, known as optoelectronic devices, are behind today’s technology in diverse areas, including communications, imaging, spectroscopy, sensing, and energy harvesting. They may also become essential components in future quantum technology based on photons. In this chapter we will learn the basic theoretical formalism for describing light–matter interaction phenomena, starting from microscopic processes such as absorption, spontaneous emission, and stimulated emission and ending with the conditions for achieving gain, which is a fundamental requirement for a laser.