Temperature Dependence of Residual Stresses and Stress Relaxation in Blanket Films of Various Thicknesses
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mperature. This permits heating rates as high as 15°C/min. The purpose of the present study was to measure the residual stresses in pure Al unpassivated blanket films of various thicknesses as a function of heating and cooling rate and to incorporate stress relaxation at elevated temperatures. Such direct measurement should help elucidate the genesis of mismatch dislocations which are designated as the vehicle by which the thermal mismatch strains are relieved3 45 ' . X-RAY STRESS DETERMINATION Since details of x-ray techniques have been covered extensively elsewhere6 , only a brief, qualitative description is given here. In the x-ray technique, Bragg's law is used to directly measure the strain in the crystal lattice (which behaves as an intrinsic strain gauge) by measuring the lattice spacing (a) as a function of orientation in the sample. The strain is given by: ES=(a 6 -a0 )/a0 where ao is the unstressed lattice parameter, and the subscripts refer to the components of the strain tensor and, in particular, 633=e, is the strain normal to the film and e22=e,, e,,=ex are the strains in the plane of the film. The lattice parameter in the P, (normal) direction can be measured directly with the scattering vector normal to the film. The lattice parameters in the plane of the film, however, are not directly measurable in reflection. Instead, the lattice parameter can be measured at a series of I-angles (the angle between the film normal and the scattering vector) along either the x or y directions. Plotting the data as a function of
609 Mat. Res. Soc. Symp. Proc. Vol. 356 01995 Materials Research Society
Sin 2W yields a linear behaviour that allows the extrapolation to Sin 2T=l to determine F, and C,. Once the principle strain components are known the stresses can be determined using Hooke s law. In the case of a biaxial film, cz=O and cx=O. so measurements need only be made in one arbitrary direction in the plane of the film and the unstressed lattice parameter is not needed to determine the stress tensor but can be calculated from the strain measurements 6 . Since the films have a strong (111) fibre texture, measurements with a particular reflection can only be made at discrete P-values. Also, the stiffness coefficients must be transformed to the (11) orientation of the crystals in the film. The elastic constants used in this work were: C,1 =108GPa, C 2=62GPa, and C44=28.3GPa" 8 and the elastic constants were corrected for temperature effects with the following equation2 where the temperature (T) is measured in degrees Celsius and E' is the expected effective Young's modulus at 0°C: ) x 10VT196( n E1 =E11 1-2.3 EXPERIMENTAL
In this study, the residual stresses in biaxially strained, pure Al metallizations deposited on single crystal Si substrates were measured as a function of temperature using the x-ray Sin 2T technique 6. However, since high heating rates were desired, The Al (111) and (200) reflections at Sin2T=O and 0.67 were used to increase data acquisition rates. Since these reflections are at a lower 20 (58.
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