Surface stress model for intrinsic stresses in thin films
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D.J. Srolovitz Princeton Materials Institute and Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544 (Received 26 November 1999; accepted 10 August 2000)
A simple model was presented for intrinsic stress generation in thin films resulting from surface stress effects. This mechanism can explain the origin of compressive stresses often observed during island growth prior to coalescence, as well as intrinsic compressive stresses reported for certain continuous, fully grown films. In some cases, surface stress effects may contribute to a sudden change in the intrinsic stress during island coalescence.
I. INTRODUCTION
Almost all thin films grown on a substrate are in a state of internal stress. The types of stresses observed in thin films include thermal stresses, coherency stresses, and intrinsic stresses. Thermal stresses are generated by a temperature change when the film and substrate have different coefficients of thermal expansion. Coherency stresses result when a film, whose bulk, in-plane lattice spacing is different from the lattice spacing of the substrate, grows epitaxially (lattice-matched) on the substrate. Intrinsic stresses are generally associated with processes occurring during growth that would change the dimensions of the film were it not attached to the substrate. Various theories have been proposed to explain the development of intrinsic stresses in thin films that involve mechanisms that would densify a free standing film.1–9 Examples of such mechanisms that are believed to occur during deposition include relaxation of the grain boundary structrue,10,11 grain growth,7,12 and processes that result in the structural ordering of films that were highly disordered (e.g., with an excess concentration of vacancies) during the initial stage of growth.2,7,13 If the films are constrained to maintain their in-plane dimensions because they are firmly attached to the substrate, these mechanisms lead to the development of tensile stresses. The intrinsic stress behavior during growth of metal films not lattice-matched to the substrate has recently been reviewed by Nix and Clemens,11 who based much of their discussion on the work of Abermann and coworkers.14 –18 Compressive stresses commonly develop during the early stage of metallic film growth, prior to the 2468
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J. Mater. Res., Vol. 15, No. 11, Nov 2000 Downloaded: 28 Sep 2014
film becoming continuous. This compressive stress can become very large in magnitude. For example, a stress of about −1 GPa was measured in a sputtered Mo film with a nominal thickness of 3.3 nm that was deposited onto a surface native oxide of silicon.19 During island coalescence, the intrinsic stress generally displays a very rapid increase that results in the intrinic stress becoming tensile. If the metal being deposited has a low adatom mobility, the intrinsic stress generally remains tensile during growth after coalescence [see Fig. 1(a)]. If the metal being deposited has a high adatom mobility, the
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