Introduction

In Chapter 6, we saw that a semiconductor driven away from thermodynamic equilibrium can emit light (in addition to blackbody radiation) when excited carriers recombine from one band to another. We also derived the Bernard–Durrafourg condition, which the energy distributions of the carrier populations must satisfy before optical amplification can occur. We will now show how this light emission can be put to use in electroluminescent diodes (alternatively known as light emitting diodes or LEDs) and laser diodes. In doing so, we will draw upon the contents of no less than five of the previous chapters:

• Chapter 4, which describes the physics of laser oscillations;

• Chapter 7, which describes the various optical emission mechanisms in semiconductors;

• Chapter 8, which describes the physics of semiconductor heterostructures and quantum well structures;

• Chapter 9, which describes waveguiding in optical heterostructures;

• Chapter 10, which describes carrier injection mechanisms in p–n diodes.

This chapter is fairly complex (and exciting!) in that it brings into play many of the different physical concepts elaborated over the course of this book. While making frequent use of material developed in other chapters, we will take the time to recap many of the key concepts to allow the reader to progress through this chapter without breaking stride on too many occasions.

Electrical injection and non-equilibrium carrier densities

Light emission in a semiconductor usually proceeds from electron–hole recombination in regions where they are in excess in comparison with levels allowed by thermodynamic equilibrium.

Introduction

As early as 1850, Antoine Cesar Becquerel discovered that certain materials generate an electrical current when exposed to a flux of light. It took, however, until about 1935 before a quantum theory of condensed matter could be developed to give a satisfactory account of this phenomenon. In spite of a lack of any firm theoretical understanding for these empirical observations, photodetectors were fashioned from these materials and put to work in photography and in military infrared detection applications.

The basic general principles behind the operation of semiconductor detectors are illustrated in Fig. 11.1. In the absence of photoexcitation, the carriers in these materials do not conduct electricity either because: (a) they are in a band where they cannot participate in conduction (e.g. a full valence band), (b) they are blocked by a potential barrier (as in a Schottky detector), or (c) they are trapped in quantum bound states (e.g. extrinsic photoconductors or quantum well detectors).

Optically driven transitions between two ensembles of quantum levels (one conducting and the other insulating), are at the origin of photodetection. For this reason, semiconductor detectors are sometimes referred to as quantum detectors.

Sections 11.3 and 11.4 describe (with reference to Fig. 11.1) type (a) photodetectors (photoconducting and photovoltaic), Section 11.5 describes type (b) internal emission Schottky photodetectors, and Section 11.6 describes type (c) quantum well photodetectors. We will see that all these detectors share a common feature.

The field of optoelectronics is currently in full expansion, drawing to its classrooms and laboratories numerous science and engineering students eager to master the discipline. From the lecturer's perspective, optoelectronics is a considerable challenge to teach as it emerges from a complex interplay of separate and often seemingly disjointed subjects such as quantum optics, semiconductor band structure, or the physics of carrier transport in electronic devices. As a result, the student (or lecturer) is left to navigate through a vast literature, often found to be confusing and incoherent.

The aim of this text is to teach optoelectronics as a science in itself. To do so, a tailored presentation of its various sub-disciplines is required, emphasizing within each of these, those concepts which are key to the study of optoelectronics. Also, we were determined to offer a partial description of quantum mechanics oriented towards its application in optoelectronics. We have therefore limited ourselves to a utilitarian treatment without elaborating on many fundamental concepts such as electron spin or spherical harmonic solutions to the hydrogen atom. On the other hand, we have placed emphasis on developing formalisms such as those involved in the quantization of the electromagnetic field (well suited to a discussion of spontaneous emission), or the density matrix formalism (of value in treating problems in non-linear optics).

Similarly, our treatment of semiconductor physics ignores any discussion of the effect of the crystallographic structure in these materials.

Introduction

In Chapter 5 we saw that the principal characteristic of a semiconducting material is the existence of forbidden energy bands, or gaps, acting to separate the electronrich valence band from the electron-poor conduction band. Both the bandgap and the energy bands are determined by the bulk potential of the crystalline material.

At the basis of bandstructure engineering is the heterojunction, which is obtained by growing one semiconductor layer onto another. For certain carefully selected semiconductors possessing compatible crystal structures and lattice spacings, it is possible to achieve epitaxial growth of one material onto another. In this case, the atomic positions of the second material form a virtually perfect continuation of the underlying substrate lattice. Under carefully controlled conditions, the compositional transition between the two materials can be made almost perfectly abrupt (i.e. with heterointerfaces in many instances being defined on a monolayer scale).

Away from the heterojunction, and deep within the bulk of the two materials, the electrons are subject to volumetric potentials (bandgaps and band structures) characteristic of each of the constituent bulk semiconductors. In the vicinity of the heterojunction, the crystal potential changes abruptly from one material to the other. A quantitative description of this change in potential requires that calculations be performed at the atomic level. These calculations (performed numerically on computers) are extremely involved and lie outside the scope of this book. Such calculations indicate, however, that over the scale of a few atomic layers near the interface, there is a transfer of electrical charge.

Introduction

One of the most impressive accomplishments of wave optics is its success in providing a coherent and succinct description of the interactions between electromagnetic waves and matter (gases, solids, etc.). Maxwell's equations, which describe the propagation of light, and the Laplace–Lorentz equations, which describe the source terms of light, allow one to take into account the phenomena of refraction, diffusion, and diffraction of light by dense media. It is amazing – to say the least – that such a theory can account for the complex interactions of an electromagnetic wave with an immense ensemble of atoms (each approximated in terms of individual harmonic oscillators), by means of a simple optical index nop. Such an achievement is reminiscent and, indeed, on par with the level of concision achieved by the concept of effective mass in representing the interaction of a conduction electron with a crystalline lattice.

In the description of all these effects, an electromagnetic wave with (angular) frequency ω forces free carriers into oscillatory motion at the same frequency, leading to radiative re-emission at this same frequency. This behaviour is a natural by-product of the linear equations we have employed up until now. In this chapter, we will see that non-linear media (i.e. materials whose response to external excitations contains non-linear terms), may by used to perform frequency conversion as evidenced, for example, by second harmonic light generation or optical parametric oscillations.