Elastic strain gradients and x-ray line broadening effects as a function of temperature in aluminum thin films on silico
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Paul R. Bessera) and John C. Bravman Department of Materials Science and Engineering, Stanford University, Stanford, California 94305-2205
Sean Brennan Stanford Synchrotron Radiation Laboratory, Stanford, California 94305 (Received 10 November 1992; accepted 28 September 1993)
Grazing incidence x-ray scattering (GIXS) with a synchrotron source was used to measure elastic strain gradients as a function of temperature in aluminum and aluminum alloy thin films of different thicknesses on silicon. The stresses in the films are induced as a result of the difference in thermal expansion coefficient between film and substrate. Disregarding minor deviations at the surface, it is shown that there are no gross strain gradients in these films in the range of temperatures (between room temperature and 400 °C) considered. Significant x-ray line broadening effects were observed, suggesting an accumulation of dislocations on cooling the films and their annealing out as the films were being reheated. The variation of the dislocation density during thermal cycling compares well in nature with that of the concurrent variation in film stress, indicating that large strain hardening effects contribute toward the film flow stress.
I. INTRODUCTION The variation of stresses with thermal cycling in thin films of aluminum is often determined by measuring the curvature of the substrate onto which the film is deposited.1^3 The stress values thus obtained reflect only the average value of stress in the film. This is also true of stress measurements which are made using x-ray diffraction in conventional scattering geometries, where the scattering volume includes the entire thickness of the film. However, large strain gradients, when present, may be additionally deduced from the x-ray line profiles obtained using such setups. Murakami4 in his work on the mechanical behavior of lead thin films on Si obtained diffraction peaks from planes parallel to the film surface. From the asymmetry in the line profiles he deduced that the surface of the film when cooled from room temperature to 77 K is relaxed with respect to the bulk. There is ample reason to believe that, due to the variety of deformation processes that are possible in Al thin films at elevated temperatures, there may be large strain gradients present in the films at those temperatures. For example, consider an Al thin film on a Si substrate that has been heated to an elevated temperature and has significant equibiaxial stresses induced in it. The grain structure of such a film is columnar; this is commonly found in many metallic thin films.5 The tractions
on the grain boundaries can be relaxed by grain boundary diffusion, a process that involves transport of atoms between the grain boundaries and the surface of the film. Formation of annealing hillocks, for example, has been suggested to occur by this process. However, as pointed out by Jackson and Li,6 this would not relieve stresses throughout the film since the film is rigidly bonded to the substrate. A local relaxation at the grain
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