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igh-resolution determination of the stress

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igh-resolution determination of the stress in individual interconnect lines and the variation due to electromigration Qing Ma, S. Chiras, D. R. Clarke, and Z. Suo Materials Department, College of Engineering, University of Cal(fornia, Santa Barbara, California 93 106-5050 (Received 12 January 199.5; accepted for publication 6 April 1995) Large tensile stresses usually exist in metallic interconnect lines on silicon substrates as a result of thermal mismatch. When a current is subsequently passed any divergence of atomic flux can create superimposed stress variations along the line. Together, these stresses can significantly influence the growth of voids and therefore affect interconnect reliability. In this work, a high-resolution (-2 pm) optical spectroscopy method has been used to measure the localized stresses around passivated aluminum lines on a silicon wafer, both as-fabricated and after electromigration testing. The method is based on the piezospectroscopic properties of silicon, specifically the frequency shift of the Raman line at 520 R cm-‘. By focusing a laser beam at points adjacent to the aluminum lines, the Raman signal was excited and collected. The stresses in the aluminum lines can then be derived from the stresses in the silicon using finite element methods. Large variations of stress along an electromigration-tested line were observed and compared to a theoretical model based on differences in effective diiusivities from grain to grain in a polycrystalline interconnect line. 0 1995 American Znstitute of Physics. I. INTRODUCTION One of the difficulties in developing predictive models for the lifetime reliability of interconnect lines in integrated circuits and packaging is that the residual stresses in the lines, due to such factors as thermal mismatch and intrinsic growth stresses, are largely unknown. These stresses provide one of the driving forces for electromigration induced void formation and growth. Furthermore, the rates of these pro- cesses are coupled and are not expected to be linear in stress. In principle, the stress can be computed by finite element methods using standard continuum models for elasticity and plasticity. In practice, however, such an approach is limited by a lack of knowledge of the appropriate constitutive rela- tionships. For instance, while the yield stress and work hard- ening coefficients of bulk aluminum are known, they are not known with any certainty in the thin-film forms typically used in interconnect metallurgy, especially where there is growing evidence of thickness dependent material properties.‘*2 Similarly, the extent of diffusional relaxation of the stresses on cooling after processing, as well as during any thermal cycling, is not known. Further complications arise because the lines, although polycrystalline along their length, generally are only one, or a few, grains in cross section. This introduces elastic and plastic deformation anisotropy effects that are not normally included in standard finite element codes. Also problematic is the form of the coupling between the residual stress in the line and electromigration induced cavitation. There is thus a need to be able to measure inter- connect stresses and to do so with high spatial resolution as a means of validating finite element calculations and consti- tutive relationships. Unfortunately, obtaining information about the local stresses in interconnects is difficult and few techniques are available. For example, by extending the wa- fer curvature technique,334 originalIy designed for measuring stresses in uniform films, the average normal stress compo- nent in an interconnect line direction can be determined.5 More sophisticated x-ray-diffraction techniques can also pro- vide measurements for all three stress components in the lines6*7 but the techniques are not yet well developed and highly specialized equipment is required. Also, a drawback of both techniques is that they measure the average stresses in a large number of nominally identical lines spaced peri- odically, and hence cannot provide information about stress variations from line to line, nor the stresses along an indi- vidual line, as might occur due to stress voiding and elec- tromigration. To measure the Iocalized stresses along the interconnect lines, and provide a basis for subsequent correlation with observed voiding behavior, an alternative method is required. One such approach is described in this work, namely, the determination of the stresses in the interconnect from the stresses induced in the underlying silicon substrate. These latter stresses, which might collectively be termed the “fringing stress field,” are the result of the distortions pro- -F-__ Excited Fluorescence FIG. 1. Schematic illustration of the configurational geometry used in the piezo-spectroscopic measurement of stresses in the vicinity of a passivated interconnect. 1614 J. Appl. Phys. 78 (3), 1 August 1995 0021-8979/95/78(3)/1614/9/$6.00 Q 1995 American Institute of Physics Downloaded 20 Mar 2001 to 128.112.32.225. Redistribution subject to AIP copyright, see http://ojps.aip.org/japo/japcpyrts.htmlduced in the immediate vicinity of the interconnect by the constraint imposed by the substrate and dielectric. They are measurable with relatively high spatial resolution (-2 pm) tim the piezo-spectroscopic shiftgp9 in the Raman spectrum excited in the silicon. The stress in the interconnect is then obtained by a self-consistent matching of the measured fre- quency shift, as a function of distance from an interconnect line, with finite element computations of the stress distribu- tion for the interconnect geometry. The experimental method, described in detail in Sec. IV, consists of measuring the shift in the Raman spectrum obtained in the backscatter- ing geometry using a fine optical probe scanned across the interconnect line, shown schematically ‘in Fig. 1. In our ex- periments, the wavelength of the


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