On the grain size and coalescence stress resulting from nucleation and growth processes during formation of polycrystall
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On the grain size and coalescence stress resulting from nucleation and growth processes during formation of polycrystalline thin films Carl V. Thompsona) Max-Planck-Institut fu¨r Metallforschung, Stuttgart, Germany (Received 24 November 1998; accepted 19 April 1999)
When polycrystalline films form by nucleation, growth, impingement, and coalescence of islands on a substrate surface, the grain size at impingement depends on the relative magnitudes of the nucleation rate, the growth rate, and the dimension of the zone from which adatoms diffuse to a growing island. A simple description of the interdependence of these parameters is developed. It is used to discuss the dependence of the grain-size-at-impingement and the intrinsic stress resulting from coalescence on the deposition rate and the substrate temperature, and to discuss how these might affect texture evolution during film growth.
I. INTRODUCTION
Polycrystalline thin films form through crystal nucleation, growth, and coalescence. In vapor phase deposition, nucleation usually occurs through the formation of stable clusters on a substrate surface. These clusters grow into the vapor phase and in directions lying in the plane of the interface. The rates of nucleation and in-plane growth are affected by the growth morphology of the growing stable nuclei or islands and by the deposition rate and the substrate temperature. The relative rates of nucleation and growth affect the average size of the crystals when they impinge to form grain boundaries. Assuming that the newly formed grain boundaries are immobile, the relative rates of nucleation and growth also affect the average grain size of the resulting film as well as the film thickness at which coalescence occurs. The grain sizes of films strongly affect their properties. Films deposited under conditions leading to low atomic mobilities tend to have very small grain sizes in the plane of the interface.1 Refractory materials tend to have low atomic mobilities at or near room temperature and atomic mobilities for all materials decrease with decreasing temperature. Small grain sizes have been associated with high intrinsic tensile stresses.2 Nix and Clemens3 have recently argued that this stress arises from the replacement of free surfaces of the islands with grain boundaries, which extend immediately upon impingement through elastic straining of the impinging islands. They specifically argue that the resulting tensile stress varies
inversely with the square root of the grain size at coalescence. They show that, for a grain size around 10 nm, the intrinsic stress resulting from this mechanism can be in the gigapascal range. II. ANALYSIS
The purpose of this note is to discuss the dependence of the grain-size-at-coalescence on nucleation and growth characteristics and, through them, the dependence on film deposition conditions. The simple analysis provided below gives an approximate treatment of the dependence of the grain size at coalescence, and therefore the film thi
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