Model for stress generated upon contact of neighboring islands on the surface of a substrate

Abstract

In the early stage of growth of a metal film on a substrate by the Volmer–Weber mechanism, a tensile stress in the film is observed to arise at about the point in the process when islands of deposited material begin to coalesce. The mechanism commonly proposed as the origin of this tensile stress is that the coalescing islands deform in order to form a relatively low energy grain boundary, at the expense of some surface energy by surface area reduction, and that this proceeds until a stress is generated that has magnitude sufficient to prevent further area reduction. Several models have been proposed for this process, but the inferred tensile stress estimates have been much larger than observed stress magnitudes in many cases. The purpose here is to introduce a model for the process based on the theory of contact of elastic solids with cohesion. A description of the process is developed on this premise for one-dimensional, two-dimensional, and three-dimensional states of deformation of coalescing islands. It is found that the latter case leads to an estimate of film stress generally consistent with observations. The features of the model for different dimensionalities are compared and contrasted with each other, as well as with other models which have been proposed for this process.

Direct Evidence for Effects of Grain Structure on Reversible Compressive Deposition Stresses in Polycrystalline Gold Films

“…During continued growth the tensile stress reduces and the stress state usually becomes compressive. There is general agreement in the literature that the initial tensile stress develops due to elastic strain associated with grain boundary formation during island coalescence [4][5][6][7]. However, a clear consensus has not emerged with respect to the mechanism that leads to the development of the compressive stress [8][9][10][11][12].…”

Dynamic Stress Analysis Applied to the Electrodeposition of Copper

“…2 indicates that under the deposition conditions examined here and at low to moderate overpotentials, stress relaxation will be a small component of the DSA stress response. Equation 11 then simplifies to [12] where σ(h f ) is replaced by σ ss since DSA is applied in the linear region of the stress-thickness curve. The change in thickness can be equated to charge (q), through Faraday's law dh = −dq M F f ar nρ [13] where F far is the Faraday constant, and M, ρ, and n are the molar mass, density, and number of equivalents, respectively for Cu.…”

“…Several quantitative models have been suggested for the tensile stress generation during coalescence, but the basic premise of these models is the same. [9][10][11][12][13][14][15][16][17] The surface energy of the islands is larger than the free energy of a grain boundary; therefore, the system energy can be reduced if the individual nuclei coalesce into a continuous film. The reduction of surface energy is balanced by an increase of elastic strain energy which gives rise to tensile stress in the film.…”

Molecular dynamics simulation of stress and grain evolution

“…Recently, there has been observed an increasing interest in the investigation of stresses in thin films prepared by different techniques [2][3][4][5][6][7][8][9][10]. Much of publications were devoted to the modeling of metallic thin film grown by Volmer-Weber mode.…”