Abstract
Dislocation-pipe diffusion (DPD) becomes a major contribution to device failure in microelectronic components at working temperatures. Usually, the simple random walk law for diffusion (Type C kinetics t1/2) is employed to calculate of DPD coefficients. The article presents an analytically solvable model of describing the diffusion phase cone growth along dislocation pipes inside polycrystal grains involving outflow from dislocation lines (Type B kinetics). Correlative analytical method to solve differential diffusion equations for such model is suggested. Competition between phase cone growth along dislocation lines involving outflow and phase wedge growth along grain boundaries (GBs) involving outflow is analyzed. It is shown that while phase wedge growth law along GBs is the Fisher regime t1/4, phase cone growth law along dislocation lines is another diffusion regime t1/6. Real experimental data are analyzed using such diffusion regime. It is shown that it is possible to calculate DPD coefficients not only for the phase cone formation, but for migration of atoms along dislocations and self-diffusion along dislocation pipes too.
Highlights
Model of intermediate phase growth with a narrow concentration range of homogeneity, ∆C1, between low-soluble components during diffusion along grain boundaries involving outflow was suggested[1] and criteria for a transition from the Fisher regime t1/4 to a parabolic one (t1/2) was analyzed
In the Appendix we prove that the phase growth law during Type B kinetics is y(t) =
X(t,0) is the phase layer thickness formed in A-B planar specimen due to volume diffusion, x(t,y) is the phase wedge thickness formed in A-B planar specimen (B is bicrystal) due to grain boundary diffusion with simultaneous outflow in volume,[1,2] y(t) is the growing phase cone cusp along dislocation line, yGB(t) is the growing phase wedge nose along GB
Summary
Model of intermediate phase growth with a narrow concentration range of homogeneity, ∆C1, between low-soluble components during diffusion along grain boundaries involving outflow was suggested[1] and criteria for a transition from the Fisher regime t1/4 to a parabolic one (t1/2) was analyzed. It was analytically proved[2] that perpendicular grain boundaries do not influence phase growth kinetics in B-regime. Physical model of dislocation-pipe diffusion involving outflow is as follows (Fig.[1]). The dislocation steps are regarded as the point sources having a diameter of δ ≈ 1nm ≈ 2Rd
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