Stress relaxation of passivated aluminum line metallizations on silicon substrates

Abstract

In the present study, the Eshelby theory of inclusions is applied to model the stresses arising after heat treatment at 400 °C in aluminum line metallizations, embedded in silicon/passivation matrix. The stresses obtained are about 200 MPa higher than the ones previously reported. Moreover, the stresses in the axial and width directions of the lines are shown to be on the same order, while the normal stress is smaller, especially in the lines of low thickness-to-width ratio. A modification of the familiar sin2 ψ method of x-ray stress measurement is presented to deal more accurately with the [111]-fiber texture present in the aluminum lines studied. The lateral and normal stresses in the aluminum metallizations after a heat treatment at 400 °C are measured in room temperature by x-ray diffraction from 4 h after the heat treatment at 400 °C up to 3 months. The experimental results are well in accord with predictions obtained from the Eshelby model. Particularly, the lateral stresses are found to be about equal, while the initial normal stress is smaller, but eventually becomes the largest stress component. Dislocation mechanisms to rationalize the present observations are discussed: at longer times, diffusion-controlled dislocation climb and void growth connected to it appear to be the most important mechanisms to relieve the stress, while during cooling dislocation glide is also significant.

Elastic fields in two jointed half-planes with an inclusion of arbitrary shape

“…This fact is of great value since both P (z) and Q(z) admit simple elementary representations, whereas D(z) involves the inverse of ω(ξ) making it relatively troublesome to work with. The present method is particularly useful for many practical problems in which the internal stresses are of major interest, for example, those related to thermal stresses in passivated interconnect lines and strained semiconductor devices (see Niwa et al 1990, Korhonen et al 1991, Hu 1991, Gosling & Willis 1995and Faux et al 1996.…”

“…Finally, in view of their practical significance (see Hu 1989, Niwa et al 1990, Korhonen et al 1991), we consider thermal inclusions. In this case, the stressfree eigenstrains are caused by a uniform change in temperature throughout the whole plane and thermal mismatch between the inclusion and the surrounding materials.…”

“…Among the various physical phenomena which lead to Eshelby's problem, of particular significance are the intrinsic stresses caused by thermal or lattice mismatch between dissimilar materials. Examples of current interest include passivated interconnect lines in large scale integrated circuits (see Hu 1989, 1990, Niwa et al 1990, Korhonen et al 1991 andBurges et al 1996), and strained semiconductor laser devices (see Nishi et al 1994, Gosling & Willis 1995, Faux et al 1996, where residual stresses induced by thermal or lattice mismatch between buried active components and surrounding materials significantly affect the electronic performance of devices and, in some cases, lead to degradation and failure. In each of these cases, since the difference in material constants of buried active components and surrounding materials is usually small, a common simplification made by many researchers is to assume that the elastic constants describing all constituent materials are identical (Niwa et al1990, Hu 1991, Gosling & Willis 1995, Faux et al 1996.…”

Some Practical Issues of Curvature and Thermal Stress in Realistic Multilevel Metal Interconnect Structures

“…In contrast, analytical predictions provide very good insight into the parameter controlling the deformation process, and also provide reasonably accurate results in a time-efficient manner. [15][16][17] Using EshelbyÕs inclusion theory, Niwa et al 15 modeled the line as a cylinder of elliptical cross-section embedded in an infinite isotropic matrix having the same elastic properties as the line. This model was generalized by Korhonen et al 16 by using different elastic properties between the line and the matrix while still neglecting the substrate.…”

Elastic fields in two imperfectly bonded half-planes with a thermal inclusion of arbitrary shape

“…Among the numerous physical situations that lead to Eshelby's problem, thermal stresses or lattice mismatch between different materials are of particular importance. Interesting practical examples include: passivated interconnect lines, isolation trenches in large scale integrated circuits (see, for example, [2][3][4][5][6][7] for details) and strained semi-conductor laser devices (see, for example, [8][9][10][11] for details) where residual stresses induced by thermal or lattice mismatch between buried active components and surrounding materials crucially affect electronic performance of devices, and, in some cases, are identified as the major cause of degradation and failure. For the majority of problems arising from electronic packaging and since the difference in material constants of buried active components and surrounding materials is usually small, a common simplification adopted by many researchers is that the elastic constants of all constituents are identical ( [4][5], [8][9][10]).…”