Self defects

More recently, studies employing STM have been able to address surface self-diffiision across a terrace [16, 17. 18 and 19], It is possible to image the same area on a surface as a fiinction of time, and watch the movement of individual atoms. These studies are limited only by the speed of the instrument. Note that the performance of STM instruments is constantly improving, and has now surpassed the 1 ps time resolution mark [20]. Not only has self-diflfiision of surface atoms been studied, but the diflfiision of vacancy defects on surfaces has also been observed with STM [18]. 

Stampfl C, van de Walle C G, Vogel D, Kruger P and Pollmann J 2000 Native defects and impurities in InN First-principles studies using the local-density approximation and self-interaction and relaxation-corrected pseudopotentials Phys. Rev. B 61 R7846-9... 

Wachutka G, Fleszar A, Maca F and Scheffler M 1992 Self-consistent Green-function method for the calculation of electronic properties of localized defects at surfaces and in the bulk J. Phys. Condens Matter A 2831 Bormet J, Neugebauer J and Scheffler M 1994 Chemical trends and bonding mechanisms for isolated adsorbates on Al(111) Phys. Rev. B 49 17 242... 

Intrinsic defects (or native or simply defects ) are imperfections in tire crystal itself, such as a vacancy (a missing host atom), a self-interstitial (an extra host atom in an otherwise perfect crystalline environment), an anti-site defect (in an AB compound, tliis means an atom of type A at a B site or vice versa) or any combination of such defects. Extrinsic defects (or impurities) are atoms different from host atoms, trapped in tire crystal. Some impurities are intentionally introduced because tliey provide charge carriers, reduce tlieir lifetime, prevent tire propagation of dislocations or are otlierwise needed or useful, but most impurities and defects are not desired and must be eliminated or at least controlled. 

The presence of defects and impurities is unavoidable. They are created during tire growtli or penetrate into tlie material during tlie processing. For example, in a crystal grown from tire melt, impurities come from tire cmcible and tire ambient, and are present in tire source material. Depending on factors such as tire pressure, tire pull rate and temperature gradients, tire crystal may be rich in vacancies or self-interstitials (and tlieir precipitates). 

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. 

Theoretical studies of diffusion aim to predict the distribution profile of an exposed substrate given the known process parameters of concentration, temperature, crystal orientation, dopant properties, etc. On an atomic level, diffusion of a dopant in a siUcon crystal is caused by the movement of the introduced element that is allowed by the available vacancies or defects in the crystal. Both host atoms and impurity atoms can enter vacancies. Movement of a host atom from one lattice site to a vacancy is called self-diffusion. The same movement by a dopant is called impurity diffusion. If an atom does not form a covalent bond with siUcon, the atom can occupy in interstitial site and then subsequently displace a lattice-site atom. This latter movement is beheved to be the dominant mechanism for diffusion of the common dopant atoms, P, B, As, and Sb (26). 

Thrower, P.A. and Mayer, R.M., Review Article Point defects and self-diffusion in graphite, Phys. Stat. Sol. (a), 1978, 47, 11 37. 

As materials chemistry has developed, it has come to pay more and more attention to that archetypal concern of materials scientists, microstructure. That concern came in early when the defects inherent in non-stoichiometric oxides were studied by the Australian. I.S. Anderson and others (an early treatment was in a book edited by Rabenau 1970), but has become more pronounced recently in the rapidly growing emphasis on self-assembly of molecules or colloidal particles. This has not yet featured much in books on materials chemistry, but an excellent recent popular account of the broad field has a great deal to say on self-assembly (Ball 1997). The phenomenon of graphoepitaxy outlined in Section 10.5.1.1 is a minor example of what is meant by self-assembly. 

In his early survey of computer experiments in materials science , Beeler (1970), in the book chapter already cited, divides such experiments into four categories. One is the Monte Carlo approach. The second is the dynamic approach (today usually named molecular dynamics), in which a finite system of N particles (usually atoms) is treated by setting up 3A equations of motion which are coupled through an assumed two-body potential, and the set of 3A differential equations is then solved numerically on a computer to give the space trajectories and velocities of all particles as function of successive time steps. The third is what Beeler called the variational approach, used to establish equilibrium configurations of atoms in (for instance) a crystal dislocation and also to establish what happens to the atoms when the defect moves each atom is moved in turn, one at a time, in a self-consistent iterative process, until the total energy of the system is minimised. The fourth category of computer experiment is what Beeler called a pattern development... 

By way of example, Volume 26 in Group III (Crystal and Solid State Physics) is devoted to Diffusion in Solid Metals and Alloys, this volume has an editor and 14 contributors. Their task was not only to gather numerical data on such matters as self- and chemical diffusivities, pressure dependence of diffusivities, diffusion along dislocations, surface diffusion, but also to exercise their professional judgment as to the reliability of the various numerical values available. The whole volume of about 750 pages is introduced by a chapter describing diffusion mechanisms and methods of measuring diffusivities this kind of introduction is a special feature of Landolt-Bornstein . Subsequent developments in diffusion data can then be found in a specialised journal. Defect and Diffusion Forum, which is not connected with Landolt-Bdrnstein. 

A pecuhar sohd phase, which has been discovered not too long ago [172], is the quasi-crystalline phase. Quasi-crystals are characterized by a fivefold or icosahedral symmetry which is not of crystallographic type and therefore was assumed to be forbidden. In addition to dislocations which also exist in normal crystals, quasi-crystals show new types of defects called phasons. Computer simulations of the growth of quasicrystals [173] are still somewhat scarce, but an increasing number of quasi-crystalline details are studied by simulations, including dislocations and phasons, anomalous self-diffusion, and crack propagation [174,175]. 

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