Residual Stress Analysis of Al Alloy Thin Films by X-Ray Diffraction as a Function of Film Thickness
- PDF / 244,248 Bytes
- 6 Pages / 420.48 x 639 pts Page_size
- 1 Downloads / 236 Views
RESIDUAL STRESS ANALYSIS OF Al ALLOY THIN FILMS BY X-RAY DIFFRACTION AS A FUNCTION OF FILM THICKNESS and D. A. Jeannotte** CARLA J. SHUTE*, J.B. COHEN* *Northwestern University, Department of Materials Engineering, Evanston, IL 60208. **IBM, IBM-U.S. Technology Products,
Hopewell
Science
Junction, NY
and
12533.
ABSTRACT Residual stress has been measured as a function of layer thickness in thin films of an Al alloy on oxidized Si by the x-ray "d" versus sin 20 technique. Samples with and without a passivation layer were examined. The results show an increase in residual stress with decreasing film thickness for the passivated samples and indicates that the interface between the metal film and SiO2 may be a region of high stress.
INTRODUCTION As the integrated circuit industry pushes for smaller and smaller metal interconnects, the mechanical properties of the thin films used for these connections becomes more and more important to the lifetime of VLSI devices. However, the difficulty of examining these materials increases as their size decreases. One of the major concerns for these materials is the residual stress level present in these films as a result of the fabrication process. These stresses arise due to the thermal expansion mismatch between substrate and film, growth mismatch and lattice mismatch (1,2]. Residual stresses in thin films are typically measured by cantilever beam or curvature techniques 11J. To determine the stress with these techniques, a homogeneous, isotropic, biaxial state of stress must be assumed. These techniques also require special specimen configurations and are destructive in nature. X-ray diffraction techniques, on the other hand, have been developed and in use for many years and offer a non-destructive means of measuring residual stresses in these materials.
THEORY The polycrystalline x-ray technique for stress analysis involves measuring the d-spacing of a single reflection for several orientations of a sample to determine the strain along different directions of the sample. Referring to Fig.l, the strain is determined along a direction perpendicular to the diffracting planes from the following Eqn.,
Mat Res. Soc. Symp. Proc. Vol. 130. ý1989 Materials Research Society
30
Fig. I. Coordinate systems and geometry used polycrystalline x-ray residual stress determination.
(e'33 )•
-~ W3)k=-
for
dop - do
(i (1)
do
where do is the unstressed lattice parameter and (f' 3 )0 is the strain along the L3 direction. Six independent strain measurements must be performed in order to completely determine the symmetric strain tensor. The strains determined for the L or measurement (laboratory) coordinate system can then be transformed to strains in the sample coordinate system, S, and converted to stresses through the use of Hooke's law. The following "stress" equation results for an isotropic material (3]: =I+ 14' d
do
-
-
E
2
21022
+ r12 sin2o + a 2 2 sin 4
(UI 1 cos
I+P
+ -
P
o33 ---
E I4 + -
E
2
_ U33 )sin t
(OIl + O22 + 0'33)
(2)
E
(r 1 3cOS-0 + G723 sin4)s
Data Loading...
