Michel Lannoo

Carrier Emission and Recombination

A defect whose associated energy level lies in the forbidden gap exchanges carriers with the conduction and valence bands through the emission and recombination of electrons and holes. As we discussed in [Ref.1.1, Sect. 7.3.2], the electronic transitions between level ET and the bands allow the determination of the average time a defect is occupied by a carrier, i.e., the occupancy of the level. In this chapter we consider the rates of emission of electrons or holes from the defect level to the bands and the rates of recombination. Because these rates depend on the free energy of ionization and on the cross sections for electrons and holes trapping on the defect, their study provides information from which practically all the electrical characteristics of the defect (enthalpy and entropy of ionization, trapping cross section etc.) can be deduced. Moreover, variation of the cross section versus temperature appears to be a powerful tool to get an insight into the defect-phonon interaction and consequently the correlated lattice distortion around the defect.

Atomic Configuration of Point Defects

In this first chapter, we define the objects that we shall be dealing with throughout this textbook. The defects are defined by their chemical nature and their geometrical configuration. As will be seen in [1.1], the geometrical configuration, which includes the interaction of the defect with the lattice, i.e., the lattice rearrangement around the defect, can be experimentally obtained from “spectroscopic” measurements (electron paramagnetic resonance and optical techniques). Considerations on defect geometry are necessary from the beginning for two reasons: first, atomic configurations and electronic structures are not independent, and secondly, the symmetry allows one, through the use of group theory, to simplify the treatment of electronic structures.

Deep Level Behaviour in Superlattice

In the old times there were two kinds of physicists working on semiconductors, the ones who were studying the behaviour of electrons in the bands and the other ones who were growing materials and making devices with them. One day, the second ones realized that, if their devices did not work, this was because a kind of physics had been forgotten, the physics of defects, and that it is also important to know the behaviour of electrons when they are localized inside the forbidden gap. It seems that, with the advent of heterostructures and superlattices, the same process starts again: some play with electrons in fancy band structures while others tailor new materials which are supposed to have the virtue of making working devices. However, the question of the influence of defects will arise soon. For instance, those who hope to replace a layer containing defects, such as DX centers in GaAlAs, by a GaAs-GaAlAs superlattice should fear that this superlattice could contain even more defects than a simple GaAlAs layer. There is indeed apparently no transient phenomenum associated with charge trapping on the DX centers in such superlattices, but there are other types of transients (see fig. 1) probably due to a broad continuum of electron states, originating presumably from defects at the interfaces (1).

Lattice Distortion and the Jahn-Teller Effect

Many point defects are subject to lattice distortion, i.e., the atoms in their neighborhood are displaced with respect to their perfect crystal positions. As a consequence the point-group symmetry is often lowered and this can be observed directly in different experiments such as Electron Paramagnetic Resonance (EPR) (Chap.3) and optical absorption (Chap.4).

Other Methods of Detection

In this chapter we discuss additional information that the use of a combination of optical, paramagnetic and electrical properties provide on defect characteristics and behavior. To begin with we consider photoexcited techniques, i.e., the effect of optical excitation on conductivity, paramagnetic resonance, deep level transient spectroscopy and optical absorption. In Sect.2, we consider optical detection of EPR. Finally, in Sect.3, we group the techniques which allow direct detection of phonons, i.e., which give a direct means to observe nonradiative recombination.

Electron Paramagnetic Resonance

Electron paramagnetic resonance is the resonant absorption of electromagnetic radiation by systems composed of unpaired electrons placed in a magnetic field. The ground states of partially filled electron orbitals are spin degenerate. In a magnetic field, because there are several possible orientations for the magnetic moment associated with the total spin, the degeneracy is lifted. Energy levels associated with each orientation arise and absorption occurs when transitions are induced between them.

Defect Production by Irradiation

Defects or impurities are introduced in semiconductors, intentionally or unintentionally, during the growth process or following heat treatments. Quenching, plastic deformation and irradiation are other ways by which defects can be created. The problem with heating, quenching and plastic deformation [8.1] is that the defects produced, practically all unidentified up to now in most materials, are complexes resulting from the interaction of intrinsic defects (vacancies, interstitials, divacancies) with the various impurities present initially in the material. Moreover, the concentration of these defects is difficult, if not impossible, to control (see [Ref.1.1, Sect.6.4] for the discussion of defects resulting from quenching). On the contrary, the concentration, the distribution and (to some extent) the nature of defects produced by an irradiation can be controlled. The defect concentration is proportional to the dose of irradiation; the nature and the distribution of the defects is a function of the nature of the irradiating particle, their energy, and the impurities contained in the material which have the ability to trap the intrinsic defects originally produced by the irradiation. For this basic motivation, but also for practical reasons (knowledge of the behavior of electronic devices submitted to radiations in nuclear reactors, space, etc.) radiation effects in semiconductors have been widely studied [8.2].

Simple Theory of Deep Levels in Semiconductors

This chapter is an introduction to the theory of deep electronic states in semiconductors. We shall use the tight-binding approximation which, in this context, has a great number of merits: a) it can describe the main physical properties of the bulk semiconductor; b) it leads to fairly simple calculations; and c) it gives an essentially correct description of simple defects such as the single vacancy. It is thus ideally suited to an introductory survey of the main electronic properties associated with defects.

Defect Migration and Diffusion

There are various mechanisms that allow a defect to move through a lattice. These mechanisms belong to two classes, depending on whether the defect is substitutional or interstitial. An interstitial defect migrates by jumping from its original interstitial site to a neighboring equivalent one. This is illustrated in Fig.7.1 for a two-dimensional lattice, but in a real crystal the jumps occur, of course, in a three-dimensional lattice. The interstitial can also exchange with a lattice atom which in turn is displaced into a new interstitial site; this mechanism is called the interstitialcy or dumbell mechanism.

Thermodynamics of Defects

The aim of this chapter is to examine the nature and the concentration of the intrinsic defects which exist at thermal equilibrium in a covalent material. The concentration of a given point defect, at a given temperature, is a function of its free energy of formation. Therefore, we shall first describe methods for obtaining the formation enthalpy of simple defects, the formation entropy having been previously discussed in Chap.51. Then, we shall derive an expression for the defect concentration as a function of temperature and, finally, discuss the nature of the defects that are present in silicon and germanium.