Effect of electromigration on onset of morphological instability of a nanowire

Nanowire breakup via a morphological instability enhanced by surface electromigration

“…where a is the 'amplitude', ℓ = 20λ max = 40π/k max is the size of the computational domain (with k max , λ max the most dangerous wavenumber and the most dangerous wavelength from linear stability analysis [12]),…”

“…The model in [12] and in this paper allows for inclusion of a stress field, in a manner similar to [18]. Stress is expected to contribute to the instability of a wire surface and thus decrease the breakup time and likely increase the number of a breakup points.…”

“…In this section, the model is briefly presented; full details and extensive discussions are in [12].…”

“…Effects of surface electromigration 3 on morphological and compositional instabilities and evolutions of crystal surfaces were considered experimentally and theoretically since 1960s (see [12] for references to major modeling and computational works in this area). In addition, morphological evolution of wires by surface diffusion, absent electromigration, received a lot of attention in the modeling and applied mathematics communities in 1980s and 1990s [13][14][15][16][17][18][19][20].…”

“…Advancements in that area may enable future breakthrough applications, such as measurement of the electrical conductivity and surface electron states of a single organic molecule. It is therefore very strongly surprising that a morphological evolution of metallic wires subjected to electromigration was not explored via basic theory and modeling, until very recently [12]. In that paper, we considered the base linear stability problem for 'electromigrated' nanowire that is either freestanding or is pre-grown on a substrate, such that it makes two contact lines with the latter.…”