A Model for Calculating Substrate Curvature During Coalescence of PT Islands on an Amorphous Substrate
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during the deposition of high mobility metal films by evaporation [1]. As discussed by Nix and Clemens [2], the development of tensile stresses in thin films has been associated with the coalescence of crystallites during film deposition, and the tensile stress maximum then marks the completion of film coalescence [3]. It can be shown that w\hen surfaces of the neighboring isolated crystallites come into close proximity the crystallites spontaneously snap together producing both grain boundaries and elastic strains in the film. While the model for crystallite coalescence does provide a rationale for the maximum tensile stresses that can be created in a film, it does not describe the gradual change in curvature as the crystallites coalesce to form islands and as the islands grow to cover the surface of the substrate. In this paper we present a simple quantitative model for tensile stress that develops due to crystallite coalescence, taking account of island size and areal coverage of the substrate. We use a model developed by Hutchinson and co-workers [4] for describing curvature changes associated with cracking in residually stressed films to determnine t-e curvature when the film is discontinuous. EXPERIMENT During the in-situ stress measurement, Pt layers of varying thickness were deposited onto 110 u.m thick glass coverslips. The samples were deposited in a UHV chamber, at room 39 Mat. Res. Soc. Symp. Proc. Vol. 578 © 2000 Materials Research Society
temperature and at an Ar pressure of 3 mtorr. The Pt deposition rate, measured by an oscillating quartz crystal rate monitor, was about 1 A/second. Stress behavior during growth was obtained from in-situ substrate curvature measurement, using a multiple parallel laser beam technique [5]. The frequency of data acquisition permitted observation of curvature change with sub-monolayer sensitivity. TEM samples for ex-situ investigation were prepared by depositing Pt on coated TEM grids (grid = 200 mesh). The coating is a 40 nm thick Si0 2 film providing a growth surface similar to glass slides, and completely eliminates TEM sample preparation. A Philips CM20 (200 keV FEG gun) and JEOL 4000 (400 keV) were used to obtain the TEM images shown in this paper. RESULTS Figure 1 shows curvature, K, versus nominal thickness, i for Pt deposited on the glass coverslips. The nominal thickness is a measure of the amount of material that has been deposited. As the material does not deposit uniformly, but forms discrete islands in the early stages, the average height of the islands is greater than the nominal thickness. The average island height, tf, is given by, tf =-If
where AA is the areal fraction of substrate covered by Pt. The change in curvature during growth of Pt on glass is compressive at thicknesses less than 8 A. This is followed by a change towards a tensile maximum at 35 A, after which the stress becomes compressive again. These regions have been respectively associated with island nucleation and growth, coalescence, and peening. In the present paper we focus on the ten
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