Impurity diffusivity

Mechanisms for the solid diffusions are well-defined. The impurity diffusivity in solid silicon is usually described by the Arrhenius-type equation  

The mechanism(s) for liquid diffusion are not well established yet. The Arrhenius equation is still the standard description for the self or impurity diffusivities in liquid [90,91], The preexponential factor and activation energy can be either fitted from the experimental data, or based solely on the first principle simulation [92-94] and theoretical estimation [95,96] when no experimental value is available. 

In the theoretical treatment of diffusive reactions, one usually works with diffusion coefficients, which are evaluated from experimental measurements. In a multicomponent system, a large number of diffusion coefficients must be evaluated, and are generally interrelated functions of alloy composition. A database would, thus, be very complex. A superior alternative is to store atomic mobilities in the database, rather than diffusion coefficients. The number of parameters which need to be stored in a multicomponent system will then be substantially reduced, as the parameters are independent. The diffusion coefficients, which are used in the simulations, can then be obtained as a product of a thermodynamic and a kinetic factor. The thermodynamic factor is essentially the second derivative of the molar Gibbs energy with respect to the concentrations, and is known if the system has been assessed thermodynamically. The kinetic factor contains the atomic mobilities, which are stored in the kinetic database. 

From the absolute-reaction rate theory arguments, the mobility coefficient for an element B, MB, may be divided into a frequency factor and an activation enthalpy QB, i.e., 

Both RT In Mg and Q-q will, in general, depend upon the composition, 

---

The most direct effect of defects on tire properties of a material usually derive from altered ionic conductivity and diffusion properties. So-called superionic conductors materials which have an ionic conductivity comparable to that of molten salts. This h conductivity is due to the presence of defects, which can be introduced thermally or the presence of impurities. Diffusion affects important processes such as corrosion z catalysis. The specific heat capacity is also affected near the melting temperature the h capacity of a defective material is higher than for the equivalent ideal crystal. This refle the fact that the creation of defects is enthalpically unfavourable but is more than comp sated for by the increase in entropy, so leading to an overall decrease in the free energy... 

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). 

In general, the shape and character of etch pits may reveal information about the impurity content of the crystal. "Beaked pits (pits with curved apexes, see 12) can indicate impurity haloes. Some forms of the arcuate etching we observed in quartz (16) may be examples of beaking. Very shallow pits can form at aged dislocations while very deep pits form at new dislocations. "Aging" may be related to impurity diffusion in the crystal lattice. 

This model is rather simple, because it neglects possible mixing effects caused by natural convection and convection forced by H2 flow or slider motion and the dependence of impurity diffusion coefficients on the concentrations of other impurities present in the melt. The exact mechanism by which baking influences the concentration of trace impurities is not well understood. However, the use of a prebaking step is considered necessary to achieve high-purity film growth by LPE. 

Figure 7. Donor impurity diffusion coefficient (Di) vs. electron concentration (electrons per cm3) showing regions of intrinsic and extrinsic diffusion. (Reproduced with permisssion from reference 119. Copyright 1981 Academic...

Figure 16. Measured and calculated values of boron and phosphorus diffusiv-ities as a function of total impurity doping. Data are divided into contributions to substitutional impurity diffusion under nonoxidizing conditions, DSj, and the enhanced contribution due to oxidation, AD0. Data are from Taniguchi et al. (44). (Reproduced with permission from reference 45. Copyright 1981 The Electrochemical Society, Inc.)...

In this book we are concerned only with mass transport, or diffusion, in solids. Self-diffusion refers to atoms diffusing among others of the same type (e.g., in pure metals). Interdiffusion is the diffusion of two dissimilar substances (a diffusion couple) into one another. Impurity diffusion refers to the transport of dilute solute atoms in a host solvent. In solids, diffusion is several orders of magnitude slower than in liquids or gases. Nonetheless, diffusional processes are important to study because they are basic to our understanding of how solid-liquid, solid-vapor, and solid-solid reactions proceed, as well as [solid-solid] phase transformations in single-phase materials. 

The assessed kinetic database covers the same system as in the thermochemical database and is schematically shown in Figs. 13.11 and 13.12, respectively. Diffusivities of Al, As, B, C, Fe, N, O, P, and Sb in both solid and liquid silicon have been extensively investigated. The assessment of the impurity diffusivity is basically the same as for the thermodynamic properties. Experimental data were first collected from the literature. Then, each piece of selected experimental information was given a certain weight factor by the assessor. The weight factor could be changed until a satisfactory description of the majority of the selected experimental data was reproduced. 

Silver ion vacancies move by a simple replacement mechanism in which a lattice silver ion at a nearest neighbor or 110 position (here the braces are used to represent a set of equivalent lattice positions) moves first into an interstitial position and then into the vacancy. Replacement by direct motion along a [110] direction is thought to be a higher energy process [18]. Monovalent impurities like Au+ and Cu+ diffuse like silver ions [18]. Na + and K + diffuse by a vacancy substitution mechanism in which the ion moves into a nearest neighbor vacancy position. Divalent cation impurities diffuse by exchange with an associated vacancy. Trivalent cations require a second vacancy for electrical neutrality. Their diffusion involves the concerted motion of this neutral complex [18]. Finally anions and anion impurities... 

As early as 1938, Langmuir observed the phase separation of clay suspensions into an isotropic phase and a birefringent gel at the macroscopic level in test-tubes [9]. However, in the same report, he noted that this property of phase separation was gradually lost with time, which he tentatively explained by the incorporation of impurities diffusing from the glass tubes. He also compared this system to normal liquid crystals. Later, in 1956, Emerson observed a banded texture similar to that displayed by the Tobacco Mosaic Virus [48]. The investigation of clay suspensions from the structural point of view has been recently resumed. However, the study of the nematic order of suspensions of montmorillonite clays is in fact complicated by their gel properties. In spite of sustained efforts to understand its nature, the gelation mechanism has not yet been fully elucidated [49]. 

Freer R (1980) Bibliography Self-diffusion and impurity diffusion in oxides. J Mater Sci 15 803-824 Freer R G981) Diffusion in silicate minerals and glasses A data digest and guide to the literature. Contrib Mineral Petrol 76 440-454... 

Modified by the addition, as applicable, of impurity diffusion (doping), ion implantation, epitaxy, etc. The active surface is processed into arrays of discrete devices or integrated circuits by metallization, passivation, or other means metallization of its back side (bottom surface) is optional. 

Palladium surfaces and their catalytic activity must be protected from impurities diffusing through the bulk and originating from supports. For example, although porous stainless steel is an excellent support for Pd [72], and was used successfully... 

---