In this chapter we consider examples of photoinduced defect processes in a number of other amorphous semiconductors for comparison with the results previously described. These examples are drawn from research on amorphous AlGaAs, compensated amorphous silicon, amorphous germanium, alloys of amorphous silicon and germanium, amorphous silicon nitride, and finally the amorphous chalcogenides. General references for these subject areas are Disordered Semiconductors (Kastner, Thomas, and Ovshinsky 1987), the International Conference on Amorphous Semiconductors (1993), and the review paper “Photoinduced effects and metastability in amorphous semiconductors and insulators” (Shimakawa, Kolobov, and Elliott, in press).

DX Centers in Amorphous AlGaAs Films

A comparison of DX-center effects in crystalline and amorphous Si-doped A10.34Ga0.66As has been reported by Lin, Dissanayake, and Jiang (1993). Two questions are treated: How are the relaxation properties of the DX center affected by changes from crystalline to amorphous? What is the connection between the DX type of defect in crystalline and amorphous semiconductors?

Below 250 K, DX centers in amorphous AlGaAs exhibit persistent photoconductivity behavior, such as is characteristic of their behavior in crystalline materials. The decay of PPC can be described by a stretched exponential with decay time constant τ and decay exponent β, such that τ decreases with increasing temperature. A comparison of the temperature dependence of τ for amorphous and crystalline material is shown in Figure 6.1, and a similar comparison of the temperature dependence of β is shown in Figure 6.2. The values of r are larger for the crystalline than for the amorphous material, but the temperature dependence is approximately the same for both.

Kinetics of Generation and Annealing of Photoinduced Defects

In efforts to elucidate the nature and origin of the metastable defects induced by light in a-Si:H (Staebler and Wronski 1977), there have been many studies of the kinetics of their generation and annealing. Although such studies do not establish any microscopic models, they can provide significant guides as to which models may be acceptable. In the interpretation of such studies it is useful to be mindful of the various other ways of producing dangling-bond defects with similar properties. In particular, the observation that such defects can also be produced in the dark by passage of forward current in a p–i–n device (Staebler et al. 1981) has led to the general belief that the defects are not produced by the light directly, but rather by the energy released when excess carriers recombine (Staebler et al. 1981) or are captured (Crandall 1991) at a localized center. Another significant observation is that light of photon energies down to and below 1 eV can cause this degradation even though the band gap is ≈ 1.75 eV.

The earliest observations of photoinduced degradation of lightly doped a-Si:H – the Staebler–Wronski effect – found that both the dark conductivity and photoconductivity decreased as a result of light exposure (see Fig. 1.2), and that these effects could be annealed away at about 150 °C for a few hours (Staebler and Wronski 1977). Thus there were two kinetic terms evident for the rate of change of the defect density N: a positive, defect-generating term that must contain the light intensity, and a negative, thermal annealing term.

Types of Defects

This discussion of defects in semiconductors deals with those having significant photoelectronic interactions. The word defect is used here as a shorthand for “imperfection.” It may therefore include any departure from the ideal periodic lattice of a crystal or, in the case of amorphous materials, any departure from an ideal continuous random network. These defects may take a variety of forms:

1. native point defects, such as isolated vacancies, interstitials, or antisite atoms of the host crystal;

2. point defects associated with the presence of isolated impurity atoms, in either substitutional or interstitial positions;

3. defect complexes formed by the spatial correlations between different point defects, such as donor–acceptor or impurity–vacancy pairs;

4. line defects, such as dislocations;

5. defects associated with grain boundaries in a polycrystalline material; and

6. defects associated with the existence of a surface or interface.

In keeping with the thrust of this book, some defects (e.g., phonons, dislocations, and interfaces or surfaces) are not treated independently.

General Effects of Defects on Electronic Properties

Any of the above defects can play a variety of electronically active roles that affect the electrical and optical properties of a semiconductor. Some of the traditionally accepted roles can be summarized as follows.

Donor or Acceptor Fundamentally, a donor is a defect that is neutral when electron-occupied, or positive when unoccupied; an acceptor is a defect that is negative when electron-occupied, or neutral when unoccupied.

In Chapter 5, it was shown that time reversal or magnetic symmetry becomes important only when we deal with ‘special magnetic properties’, defined by the following two criteria:

1. The matter tensor K is a c-tensor, due to the fact that eitherXorY is a c-tensor, and

2. the property in question is not a transport property (involving an increase in entropy).

Such properties are given an asterisk in Table 1–1. In dealing with these properties we must take cognizance of the magnetic symmetry of the crystals in which they are observed, that is, of the 90 magnetic classes, as distinct from the 32 conventional crystal classes which sufficed for the study of all other properties.

Since the principal special magnetic properties of interest do not involve tensors of rank higher than 3 (see Table 1–1), and such ranks have already been covered for the conventional properties in Chapters 6 and 7, a diversion to special magnetic properties at this point seems appropriate. We then resume the main thrust of the book with Chapter 9, that is, continuing to consider higher tensor ranks.

As shown in Chapter 5, if K represents a special magnetic property, it must be identically zero for non-magnetic (i.e. diamagnetic or paramagnetic) crystals, as well as for antiferromagnetic crystals belonging to type-II groups. Therefore, the special magnetic properties which we consider in this chapter only exist for crystals that possess magnetic symmetry, namely, those of types I and III (see Section 5–1).

The study of the anisotropic properties of crystals, often called ‘Crystal Physics’, is the oldest branch of solid-state physics, dating back to the turn of the twentieth century and the treatises of W. Voigt. It deals with the ‘matter tensors’ that describe such anisotropic properties, and the way that these tensors are simplified as a result of the existence of crystal symmetry. In recent years, there have been many textbooks on this subject. Most widely known is that by J. F. Nye (Physical Properties of Crystals, Oxford University Press, 1957), who introduced matrices and tensors to create a more compact notation than that used earlier, but did not use group theory.

Group theory provides the ideal mathematical tools for dealing with these problems elegantly and compactly. These methods have been used by various authors, notably Fumi, Bhagavantum and Juretshke. However, the usefulness of group theory was not always recognized. In fact Nye (page 122 of his book), commenting on work using group theory, states: ‘group theory … does not reveal which moduli are independent but only the total number of independent ones’. The present book is dedicated to showing, not only that this statement is untrue, but that the use of group theory lends elegance and beauty to what would otherwise be dull calculations. In this book we utilize the method of symmetry coordinates, very much as is used in the study of molecular vibrations (e.g. as described in the book by Wilson, Decius and Cross).

The only matter tensor having a rank as high as 6 that appears in Chapters 1 and 2 is the so-called ‘third-order elastic constant’ tensor of type Ts(6). (See Section 1–6 and Table 1–1.) This tensor couples a quantity Y, which is a thermodynamic tension, ti, of type Ts(2) to a quantity X, which is the symmetric product of Lagrangian strains, ηiηi, of type Ts(4). (Here, both ti and ηj are second-rank symmetric tensors whose six components are written in single-index hypervector notation.) The resulting matter tensor K is then a Ts(6) tensor, symmetric in the interchange of all the indices. The first objective of this chapter will be to obtain the independent components of such a Ts(6) tensor. This will require us to go beyond the material contained in the S-C-T tables (Appendix E).

Relation betweenTs(2) andTs(4)

We wish to consider the usual relation: Y = KX, in which Y is a Ts(2) tensor that transforms as a six-vector, and X is a Ts(4) tensor which transforms as the 21 symmetric products of six-vectors, αiαj. (Here we use the notation α for a Ts(2) tensor as in the S-C-T tables and Eq. (4–4).) In terms of the single-index quantities Y and X, K then become a two-index (6 × 21) matrix.