Calculation of Stress Gradients in Thin Al-0.5%Cu/Ti Lines from Strain Gradients Measured as a Function of Temperature U
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CALCULATION OF STRESS GRADIENTS IN THIN AL-0.5%CU/TI LINES FROM STRAIN GRADIENTS MEASURED AS A FUNCTION OF TEMPERATURE USING GRAZING INCIDENCE X-RAY SCATTERING t
Paul Bessert, Ramnath Venkatramant, Sean Brennan* and John Bravman l"
"*Stanford Materials Science Department, Stanford Synchrotron t
University, Stanford, CA 94305 Radiation Lab, Menlo Park, CA 94025
ABSTRACT Strain gradients in AI-0.5%Cu lines on a 1000A Ti barrier layer have been measured during thermal cycling from room temperature to 400°C using X-rays from a Synchrotron Source in the Grazing Incidence Geometry. The stress gradient calculated from the strain gradient is shown at four temperatures during thermal cycling. The surface of the line is relaxed relative to the bulk during heating and more stressed during cooling. It was also found that the width direction of the line supports essentially no stress throughout the thermal cycle and that the much of the stress along the length of the line is relaxed during the first few minutes at elevated temperatures. INTRODUCTION Stresses in thin, lithographically patterned aluminum lines used in the integrated circuit industry have been the subject of much research. Greenebaum et al. have used x-ray methods to 1 measure stresses in excess of 500 MPa in a series of parallel, passivated Al-Cu lines. Assuming purely elastic behavior, Sauter and Nix have used finite element methods to model the stress state 2 in lines, and the calculations agree well with measured values in the absence of voiding.) These large hydrostatic stresses cannot be relieved by plastic deformation. Voiding is commonly observed in passivated lines as a method of relaxation. Since the lines are rigidly constrained to the substrate, the stresses originate from the large difference in thermal expansion coefficients between 6 6 Al (25.5 x10" ) and the Si (2.6 x10- ). Determination of the distribution of the stress through the thickness of the lines will lead to a better understanding of the relaxation and failure mechanisms operating. In the present work, grazing incidence x-ray scattering (GIXS) has been used for the first time as a method for measuring strain distributions through the thickness of unpassivated Al alloy lines. The stress distribution is calculated from the measured strain distribution. GRAZING INCIDENCE X-RAY SCATTERING OF LINES 3
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The GIXS technique has been fully described elsewhere. ,4, Briefly, GIXS utilizes the principle of total external reflection (TER). For many materials, the index of refraction is less than unity at x-ray energies. According to Snell's Law, x-rays going from a material of higher index of refraction (air) to one having a lower index (the diffracting material) will be nearly perfectly reflected below a certain critical angle of incidence. The penetration depth of x-rays into the material and, hence, the depth in the material from which signal is detected, can thus be tailored by varying the incident angle. Since the critical angle of incidence for TER is typically less than a degree, planes p
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