Introduction

We were able to show in Chapter 3 that a medium in which we can obtain a population inversion (i.e. a situation in which the population density in the excited state is greater than that in the fundamental level) allows for optical gain of an electromagnetic wave having a frequency near to the resonant frequency of the system. By introducing feedback of the amplified signal into the medium, the system can be made to oscillate naturally, resulting in laser oscillations. To obtain this population inversion, we must introduce at least a third (and perhaps even a fourth) energy level into the system. (We saw how a two-level system under the influence of an intense pump beam will saturate with no resulting population inversion.) The aim then of this chapter is to introduce the concepts necessary to extend our two-level system into a working model capable of illustrating the phenomenon of laser oscillation. We will not spend too much time discussing atomic transition lasers as they do not figure readily in our treatment of quantum electronic properties of semiconductors. An exception will be made, however; we brush upon the particular topics of a diode pumped laser in Complement 4.E and a quantum cascade laser in Complement 13.H.

Population inversion and optical amplification

Population inversion

We will show how population inversion can be achieved by carrier transfer from higher lying levels to the upper level of a two-level subsystem of interest.

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.