Current-Induced Stabilization of Surface Morphology in Stressed Solids

A training effect on electrical properties in nanoscale BiFeO3

“…Several authors have already reported influence of electromigration on electrical properties in both metallic and oxide nanosized systems and have resorted to measurements such as relaxation of the conductivity, noise spectra [5], to even direct imaging of defect migration by transmission electron, scanning tunneling or atomic force microscopy [6,7,8]. While electromigration of defects in nanoscale interconnects or thin film surfaces leads to destabilization and even failure, it can also train the sample by healing the stress developed otherwise [9]. In this paper, we too observe an example of healing in an interesting training effect on the electrical properties of nanochains of BiFeO 3 .…”

Rippling instability on surfaces of stressed crystalline conductors

“…orientation. [6][7][8][9] For ⌶ = 0, i.e., for finite stress ϱ in the absence of electric field, ͑k͒ is positive for all k Ͻ k c , i.e., the planar surface is unstable for all perturbations with wavelength ˜Ͼ ˜c ϵ 2 / k c ; ˜ϵ / l. For a given parameter set, A, m, and , R͑⌶͒ decreases as ⌶ increases from 0 to ⌶ c , i.e., as E ϱ is increased from zero to some critical value. For ⌶ Ͼ⌶ c , R vanishes, i.e., ͑k͒ Ͻ 0 for all k; therefore, a stronger-than-critical E ϱ stabilizes fully the morphological response of a stressed solid at given ϱ .…”

“…Such a well-known phenomenon is the Asaro-Tiller-Grinfeld ͑ATG͒ instability, [1][2][3] which leads to the formation of a regular pattern of cracklike grooves emanating from the surface of a stressed elastic solid and deepening by surface diffusion. 4,5 Recently, we carried out an analysis of morphological stability of stressed solid surfaces under the simultaneous action of an electric field and reported that surface electromigration through the action of a sufficiently strong electric field can be utilized to inhibit the stress-induced ATG instability and prevent surface cracking; 6,7 a linear stability theory 6 predicted fairly accurately the current-induced stabilization of surface morphology in stressed elastic solids. However, complex aspects of surface morphological evolution and pattern formation, not accounted for by linear theory, still remain elusive.…”

“…8 We consider a semi-infinite, single crystalline, conducting solid bounded by a planar surface ͑y =0͒ under a uniform uniaxial stress and an electric field of magnitudes ϱ and E ϱ , respectively, both along the x-direction in a Cartesian frame of reference. 6,7 We parameterize the surface morphology according to the height function y = h͑x , t͒. An important element of our model is the anisotropy of surface diffusivity through the inhomogeneity …”

“…where ͑k͒ is the dimensionless frequency characteristic of the growth or decay of the initial perturbation from the planar morphology, with k ϵ kl, l ϵ ␥M / ϱ 2 , being the corresponding dimensionless wave number of a low-amplitude sinusoidal perturbation, and ⌶ ϵ E ϱ q s ‫ء‬ l 2 / ͑␥⍀͒ is a dimensionless parameter that expresses the relative strength of the two externally applied forces; 6 in the above equations, q s ‫ء‬ is the surface effective charge, ␥ is the surface free energy per unit area, ⍀ is the atomic volume, and M is the elastic modulus. ͑k͒ exhibits two maxima: at k = 0 and at…”