Alloys and Exotic Materials

The chapter describes how the band parameters of ternary and quaternary alloys can be interpolated over the entire range of compositions, and tabulate the non-vanishing bowing parameters for most of the common alloys with both zinc-blende and wurtzite lattice structure. It also describes ordering in some of the ternary alloys, and how ordering affects the energy gap. The band parameters of dilute nitrides, dilute bismides, and hexagonal boron nitride are also examined. Finally, the chapter presents schemes for interpolating the optical parameters of III–V alloys, i.e., the real and imaginary parts of the permittivity or dielectric function.

Absorption and Emission of Light in Quantum Structures

This chapter shows how to calculate the absorption coefficient, optical gain, and radiative recombination rates in quantum wells and superlattices. A detailed treatment of both interband and intersubband transitions is presented, and their differences and similarities are considered in detail. The optical properties of wurtzite quantum wells and zinc-blende quantum wires and dots are also discussed. Finally, the interaction of excitonic transitions with incident light in quantum wells is considered as a model for other two-dimensional materials.

Basics of Envelope-Function Theory

The chapter shows how the bulk theory described in Part I can be generalized within the envelope-function framework to model the band structure of layered materials with quantum confinement of carriers such as quantum wells or superlattices. In practice, the approach amounts to substituting derivatives for wavevector components in suitably chosen Hamiltonians as well as augmenting them with interface terms. It also discusses the spin splitting of the states of the quantum structures that arises from structural and intrinsic asymmetries.

Basics of Crystal Structure and Band Structure

III–V semiconductors form crystalline structures with three-dimensional periodic arrangements of the atoms. In this chapter, we will explore the nature of the crystal lattice starting from lower dimensions and progressing to real semiconductor crystals. We also learn why we expect distinct energy bands to form in the solids that crystallize in such lattices. The carrier statistics and occupation of the bands will also be examined.

Superlattice and Quantum-Well Band Structure

This chapter presents typical band structures for superlattices and quantum wells computed using the methods described in Chapter 9. It identifies important features of the conduction and valence subbands and minibands, their dispersions, optical matrix elements, and characteristic dependences on the materials, thicknesses, and compositions. The changes that occur when the energy gap becomes very small are also discussed. To complete the picture, it considers how the band structure of wurtzite materials differs from their zinc-blende counterparts, as well as the band structure of quantum wires and dots that feature multidimensional confinement.

Interband Semiconductor Lasers and LEDs

This chapter discusses the operation of conventional diode lasers based on quantum wells and quantum dots as a function of emission wavelength. The recombination processes that control the threshold current density of the devices are described in detail, including recombination at defects, radiative, and Auger recombination. The high-speed modulation and spectral characteristics of semiconductor lasers are also discussed. It continues by illustrating why interband cascade lasers can outperform diode lasers at mid-infrared wavelengths and describing their design and operating characteristics in detail. On the short-wavelength side of the spectrum, the nitride lasers and the factors that limit their performance are discussed. In addition to lasers, the principles underlying light-emitting diodes (LEDs) are outlined, and the proposed mechanisms for improving the extraction of the light from high-index semiconductor materials are described. The chapter concludes with a discussion of the performance of semiconductor optical amplifiers designed to amplify a weak input signal.

Quantum Cascade Lasers

This chapter describes the most commonly used approaches for computing the band structure of active materials with intersubband optical transitions. The physics of quantum cascade lasers (QCLs) is discussed in detail, including the mechanisms that limit the threshold current density, threshold voltage, wall-plug efficiency, and temperature sensitivity of state-of-the-art devices. The important roles of phonon and interface roughness scattering in determining threshold are emphasized. The chapter also compares the performance of QCLs to other mid-IR lasers in considerable detail and makes some conclusions as to which sources are preferred depending on the emission wavelength and application. Finally, the physical principles of laser-based frequency combs, including self-starting frequency-modulated QCL combs, are discussed.

Absorption and Emission of Light in III–V Semiconductors

Previous chapters discussed the crystal structure and bandstructure of III–V semiconductors. This chapter shifts to the book’s second major topic: electronic interactions with light. It introduces the main ideas about how light waves propagate in semiconductor crystals and induce absorption, spontaneous emission, and stimulated emission in bulk semiconductors. It also considers the differences between the electronic interactions with light in zinc-blende and wurtzite crystals and what happens as the energy gap of the semiconductor is reduced to zero or when the crystal is two-dimensional.

Detailed k·p Theory for Bulk III–V Semiconductors

The chapter discusses a full implementation of k·p theory for the eight bands near the energy gap in a III–V semiconductor. This model can precisely calculate the band structure for both conduction and valence bands near the energy gap. Even though only eight bands are explicitly included, the terms due to interactions with “remote” bands are present in the complete version of the theory. The chapter consider the physical meaning of the results and the effect that strain has on the semiconductor band structure. The Hamiltonians for both zinc-blende and wurtzite crystals are introduced.

Binary Compound Semiconductors

To apply the band structure models discussed in Part I (extended to structures with quantum confinement in Part III and applied to photonic devices in Part IV), a reliable set of input parameters is necessary. The chapter overviews the literature related to these parameters that has appeared since our published reviews. It also recommends specific values for all of them, including the dependence on temperature and alloy composition. If reliable experimental reports are available, they are used preferentially in the recommendations. Otherwise, it falls back to extrapolations from the existing data and theoretical estimates to fill in the gaps. It starts by reviewing and tabulating band parameters for the III–V compound semiconductors GaAs, AlAs, InAs, GaSb, AlSb, InSb, GaP, AlP, InP, GaN, AlN, and InN. The parameters include energy gaps, electron and hole mass parameters, deformation potentials, elastic constants, band offsets, and their temperature dependences.