Self-interstitial diffusion model

Figure 12. A model of self-interstitial diffusion from the bulk to the partial dislocation bounding a stacking fault. Under nonoxidizing conditions, the concentration of self-interstitials at the fault line, CiL, is greater than the equilibrium bulk interstitial concentration, Ci°. Under oxidizing conditions, Ci is greater than CiL until the retrogrowth temperature is reached. (Reproduced with permission from reference 45. Copyright 1981 The Electrochemical...

Multiple-Charge-State Vacancy Model. On the basis of the previous discussion, diffusion depends upon the concentration of point defects, such as vacancies or self-interstitials, in the crystal. Therefore, diffusion coefficients can be manipulated by raising or lowering the concentration of point defects. 

Point Defect Models of Diffusion in Silicon. Under conditions of thermal equilibrium, a Si crystal contains a certain equilibrium concentration of vacancies, C v°, and a certain equilibrium concentration of Si self-interstitials, Cz°. For diffusion models based on the vacancy, Cv° Cf and the coefficients of dopant diffusion and self-diffusion can be described by equation 27 (15)... 

For diffusion models based on self-interstitials, C° Cv°. Dopant diffusion and self-diffusion are assumed to occur via an interstitialcy mechanism (32). Mobile complexes consisting of self-interstitials in various charge states and impurities are assumed to exist. 

Equation 36 is divided into the contributions to the diffusion of substitutional impurity under nonoxidizing conditions, DSI, and the enhanced contribution due to oxidation, AD0. Figure 16 shows the data of Taniguchi et al. (44) for oxidation-enhanced diffusion of P and B versus the total number of dopant impurities per square centimeter, QT. The calculated values of DSI and AD0 are shown in comparison with the experimental data. Reasonable agreement is obtained. Thus, Taniguchi s model of self-interstitial recombination with vacancies is consistent with the models of high-concentration diffusion of B and P used by Fair in his calculations. 

Point Defect Generation During Phosphorus Diffusion. At Concentrations above the Solid Solubility Limit. The mechanism for the diffusion of phosphorus in silicon is still a subject of interest. Hu et al. (46) reviewed the models of phosphorus diffusion in silicon and proposed a dual va-cancy-interstitialcy mechanism. This mechanism was previously applied by Hu (38) to explain oxidation-enhanced diffusion. Harris and Antoniadis (47) studied silicon self-interstitial supersaturation during phosphorus diffusion and observed an enhanced diffusion of the arsenic buried layer under the phosphorus diffusion layer and a retarded diffusion of the antimony buried layer. From these results they concluded that during the diffusion of predeposited phosphorus, the concentration of silicon self-interstitials was enhanced and the vacancy concentration was reduced. They ruled out the possibility that the increase in the concentration of silicon self-interstitials was due to the oxidation of silicon, which was concurrent with the phosphorus predeposition process. 

The diffusion of Au in disiocation-free or piasticaiiy deformed Si (10 I to 10 3disiocations/m2) was measured using the spreading-resistance technique. The Au profiies produced in disiocation-free Si slices by indiffusion from both surfaces had non-erfc-type U-shapes. The kick-out model was used to calculate the contribution of self-interstitials to the (uncorrelated) Si self-diffusion coefficient,... 

A model for the tracer self-diffusivity of the interstitials is now developed for a system in which the total concentration of inert interstitials and chemically similar radioactive-tracer interstitials is constant throughout the specimen but there is a gradient in both concentrations. Since the inert and tracer interstitials are randomly intermixed in each local region,... 

The recombination of pairs of interstitials and vacancies has usually formed the basis of models for thermal annealing. It has sometimes been assumed that the vacancy is mobile (as in the vacancy model for self-diffusion) and sometimes that the vacancy is a fixed trap or sink, having a capacity of one interstitial atom, and the interstitial is mobile. The form of the kinetic equations is usually not dependent on the choice, and this is true even if both are mobile provided there is no initial correlation of interstitials and vacancies. 

The activated interstitial model which hinges on the relative ease of some f electron promotion in its initial form or on the possibility of d-f hydridization in its modified form seems to account for the main anomalous features observed in connection with self-diffusion in bcc e-Pu, S-Ce and possibly y-La and y-Yb. Beside these metals, however, anomalous diffusion has also been observed in /3-Ti, /3-Zr, /3-Hf, y-U and the rare earth metals -Pr, /3-Nd and P-Gd. The normal behavior of Eu (table 12.2), which among this latter group of metals is the only one having the bcc structure as its only allotropic form, stands out in marked contrast to the other bcc rare earth metals. It strongly supports Seeger s (1972) suggestion that anomalous diffusion in bcc metals is in some way connected to the phase transformation which precedes the bcc phase. 

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