Semiconductors, point defects

The unique electronic properties of semiconductor devices arise at the regions where p-typc and ra-typc materials ate in close proximity, as in p-n junctions. Typical impurity levels ate about 0.0001 at %, and their inclusion and distribution need to be very strictly controlled during preparation. Without these deliberately introduced point defects, semiconductor devices of the type now commonly available would not be possible. 

In addition to atomic point defects, semiconductor materials can also have electronic point defects. These defects provide mobile charge carriers that move about the crystal lattice. They provide the basis for many useful applications. In fact, the entire microelectronics industry is based on being able to control electronic defects in these materials. 

Point defects and complexes exliibit metastability when more than one configuration can be realized in a given charge state. For example, neutral interstitial hydrogen is metastable in many semiconductors one configuration has H at a relaxed bond-centred site, bound to the crystal, and the other has H atomic-like at the tetrahedral interstitial site. 

However, most impurities and defects are Jalm-Teller unstable at high-symmetry sites or/and react covalently with the host crystal much more strongly than interstitial copper. The latter is obviously the case for substitutional impurities, but also for interstitials such as O (which sits at a relaxed, puckered bond-centred site in Si), H (which bridges a host atom-host atom bond in many semiconductors) or the self-interstitial (which often fonns more exotic stmctures such as the split-(l lO) configuration). Such point defects migrate by breaking and re-fonning bonds with their host, and phonons play an important role in such processes. 

Electrical Properties. Generally, deposited thin films have an electrical resistivity that is higher than that of the bulk material. This is often the result of the lower density and high surface-to-volume ratio in the film. In semiconductor films, the electron mobiHty and lifetime can be affected by the point defect concentration, which also affects electromigration. These effects are eliminated by depositing the film at low rates, high temperatures, and under very controUed conditions, such as are found in molecular beam epitaxy and vapor-phase epitaxy. 

The beginnings of the enormous field of solid-state physics were concisely set out in a fascinating series of recollections by some of the pioneers at a Royal Society Symposium (Mott 1980), with the participation of a number of professional historians of science, and in much greater detail in a large, impressive book by a number of historians (Hoddeson et al. 1992), dealing in depth with such histories as the roots of solid-state physics in the years before quantum mechanics, the quantum theory of metals and band theory, point defects and colour centres, magnetism, mechanical behaviour of solids, semiconductor physics and critical statistical theory. 

The topic of defects in semiconductors encompasses point, line, planar and volume defects. Point defects include those defects occupying, or sharing, a single lattice site these would include substitutional impurities... 

Bourgoin, J.C. and Lannoo, M, (1981, 1983). Point Defects in Semiconductors, Springer Verlag, Berlin, Vols. I and II. 

Emtsev, V.V. and Mashovets, T.V. (1981). Impurities and Point Defects in Semiconductors, Radio i Svyaz , Moscow (in Russian). 

There is now an extensive and rapidly growing theoretical literature on the nature of hydrogen or muonium defects in silicon and to some extent in other semiconductors (Van de Walle, 1991 DeLeo, 1991). Much of this has dealt with isolated hydrogen or muonium where the most frequent comparisons have been with the muon hyperfine parameters, at least qualitatively, and other features of the muonium centers that can be inferred from /rSR experiments. Isolated interstitial hydrogen or muonium is certainly one of the simplest point defects conceivable. Hence explaining the existence and properties of the two drastically different forms of muonium observed in silicon and several other semiconductors has been a particular challenge to current theoretical methods. 

At all temperatures above 0°K Schottky, Frenkel, and antisite point defects are present in thermodynamic equilibrium, and it will not be possible to remove them by annealing or other thermal treatments. Unfortunately, it is not possible to predict, from knowledge of crystal structure alone, which defect type will be present in any crystal. However, it is possible to say that rather close-packed compounds, such as those with the NaCl structure, tend to contain Schottky defects. The important exceptions are the silver halides. More open structures, on the other hand, will be more receptive to the presence of Frenkel defects. Semiconductor crystals are more amenable to antisite defects. 

Zinc oxide is normally an w-type semiconductor with a narrow stoichiometry range. For many years it was believed that this electronic behavior was due to the presence of Zn (Zn+) interstitials, but it is now apparent that the defect structure of this simple oxide is more complicated. The main point defects that can be considered to exist are vacancies, V0 and VZn, interstitials, Oj and Zn, and antisite defects, 0Zn and Zno-Each of these can show various charge states and can occupy several different... 

The compound will be stoichiometric, with an exact composition of MX10ooo when the number of metal vacancies is equal to the number of nonmetal vacancies. At the same time, the number of electrons and holes will be equal. In an inorganic compound, which is an insulator or poor semiconductor with a fairly large band-gap, the number of point defects is greater than the number of intrinsic electrons or holes. To illustrate the procedure, suppose that the values for the equilibrium constants describing Schottky disorder, Ks, and intrinsic electron and hole numbers, Kc, are... 

S2.3 Point Defects and Energy Bands in Semiconductors and Insulators... 

A point defect in an insulator or semiconductor is represented on band diagrams as an energy level. These energy levels can lie within the conduction or valence bands, but those of most consequence for electronic and optical properties are those that lie in the band gap. The effects of these impurities on the electronic properties of the solid will... 

Within these three categories, the earliest attention was paid to point defects this arose from intellectual curiosity about the origin of the deep blue color seen in large colorless single crystals of NaCl occurring in salt deposits. From this starting point, the idea of color centers was developed. Since the color centers are point defects, they modify the electronic states around the defects and affect the heat and electronic conductivity consequently, they have become directly connected to the development of the semiconductor industry. 

Concentration equilibrium among A , A , A , and h is discussed on the assumption that these equations can be treated as chemical equilibrium ones. (Similarly, D", D, (donor levels), and e are regarded as chemical species, see Fig. 1.24(c).) We have a reasonable reason for regarding these species as chemical species. As is well known, the electrical properties of metals and alloys are independent of the concentration of point defects or imperfections existing in their crystals, because the number of electrons or holes in metals or alloys is roughly equal to that of the constituent atoms. For the case of semiconductors or insulators, however, the number of electrons or holes is much lower than that of the constituent atoms and is closely correlated to the concentration of defects. In the latter case, electrons and holes can be considered as kinds of chemical species, for a reason similar to that discussed above for the case of point defects. Let us consider the chemical potential, which is most characteristic of chemical species. Electrochemical potential of electrons is written as... 

Thus, lattice defects such as point defects and carriers (electrons and holes) in semiconductors and insulators can be treated as chemical species, and the mass action law can be applied to the concentration equilibrium among these species. Without detailed calculations based on statistical thermodynamics, the mass action law gives us an important result about the equilibrium concentration of lattice defects, electrons, and holes (see Section 1.4.5). 

The common feature of the internal reactions discussed so far is the participation of electronic defects. In other words, we have been dealing with either oxidation or reduction. We now show that reactions of the type A+B = AB can take place in a solvent crystal matrix as, for example, the formation of double oxides (CaO +Ti02 = CaTi03) in which atomic (ionic) but no electronic point defects are involved. Although many different solvent crystal matrices can be thought of (e.g., metals, semiconductors, glasses, and even viscous melts and surfaces), we will deal here mainly with ionic crystal matrices in order to illustrate the basic features of this type of solid state reaction. 

If the coupling of the electrons to certain centers is strong, their spectra may be distinguished from that of the crystal as a whole (point defect color centers in ionic crystals, polarons in semiconductors). The spectra of defects can therefore be used for analytical or even kinetic investigations. In principle, it should be possible to construct devices which have, under favorable conditions, a sufficient spatial resolution to experimentally determine the basic kinetic quantity c,( , t). 

Diffusion in ionically bonded solids is more complicated than in metals because site defects are generally electrically charged. Electric neutrality requires that point defects form as neutral complexes of charged site defects. Therefore, diffusion always involves more than one charged species.9 The point-defect population depends sensitively on stoichiometry for example, the high-temperature oxide semiconductors have diffusivities and conductivities that are strongly regulated by the stoichiometry. The introduction of extrinsic aliovalent solute atoms can be used to fix the low-temperature population of point defects. 

Crystal Self-Diffusion in Nonstoichiometric Materials. Nonstoichiometry of semiconductor oxides can be induced by the material s environment. For example, materials such as FeO (illustrated in Fig. 8.14), NiO, and CoO can be made metal-deficient (or O-rich) in oxidizing environments and Ti02 and Zr02 can be made O-deficient under reducing conditions. These induced stoichiometric variations cause large changes in point-defect concentrations and therefore affect diffusivities and electrical conductivities. 

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