Thermal strains in passivated aluminum and copper conductor lines
- PDF / 550,055 Bytes
- 7 Pages / 584.957 x 782.986 pts Page_size
- 70 Downloads / 192 Views
Antoinette M. Maniatty Department of Mechanical, Aerospace & Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180 (Received 27 October 2010; accepted 7 January 2011)
Line width and line thickness thermal strain components in passivated Al and Cu lines were observed to relax much more than the line length strain component. Although the width-tothickness ratios were large, 3.5 and 4.4 for Al and Cu lines, respectively, the behaviors of the thermal stresses were far from the equibiaxial. Observed changes in deviatoric strains between room temperature and 190 °C for Al and 300 °C for Cu were consistent with a model in which the changes in line width and line thickness strains were simply related to changes in line length strains by the uniaxial Poisson’s ratio. Changes in line length strains were determined by the differences in metal and substrate thermal expansion coefficients and the magnitudes of temperature changes through retained elastic strain coefficients for Al of 30% for heating and for Cu of 60% for heating and 80% for cooling, with the balance accommodated by relaxation.
I. INTRODUCTION
Elastic strains in passivated conductor lines have been studied by wafer curvature measurements1 and by x-ray diffraction (XRD) measurements on arrays of parallel lines,2–4 yielding average strain values as a function of sample temperature or of thermal history. Analytical5,6and finite element methods (FEM)7,8 have also been used to predict thermal strains in passivated conductor lines. X-ray microbeam diffraction measurements have been used to determine spatially resolved elastic strains in conductor lines, sometimes on a grain-by-grain basis.9–12 In some cases, changes in conductor line strains resulting from temperature changes and relaxation have been measured and compared with FEM calculations.13,14 In this article, results of x-ray microbeam deviatoric strain measurements in passivated Al and Cu conductor lines at room temperature (RT) and at elevated temperatures are described and are compared with limiting case models of equibiaxial and uniaxial thermal stress. Good agreement is found between the experimental results for elastic strains resulting from temperature changes and a uniaxial thermal stress model that incorporates full relaxation along line width and line thickness directions and partial relaxation along the line length direction of thermal stresses resulting from temperature changes. II. SAMPLES
The Al conductor line samples were 30 lm long, 2.6 lm wide, and 0.75 lm thick, with Ti-rich top and a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2011.9 J. Mater. Res., Vol. 26, No. 5, Mar 14, 2011
http://journals.cambridge.org
Downloaded: 16 Mar 2015
bottom layers, as shown in Fig. 1 and described in Reference 12. The transmission electron micrograph Fig. 1(b) shows that the conductor line consists of micronsize columnar grains of about 0.35 lm thickness. On the top and bottom surfaces of the large grain Al line are smaller (,100 nm) grain size
Data Loading...
