Modeling of multilevel structures: a general method for analyzing stress evolution during processing

Abstract

This paper presents a general modeling technique for following the evolution of the stress field during the manufacturing of multilevel structures. This technique combines the finite element method with a modeling strategy that uses artificial nodes to simulate material interfaces. It can be applied to both linear and nonlinear structures. The main advantage of this approach is that it allows one to account For all topological and geometric changes during the manufacturing process, as well as the residual stresses introduced at each stage. Its implementation is very straightforward since it is compatible with current finite element technology and most commercial codes. The usefulness of this technique is illustrated with an example concerning an encapsulated copper line.

<title>Characterization of micro-opto-electro-mechanical devices</title>

“…L-+R--+!Q=V (5) dt2 dt C A series PlC circuit is used to represent the above equation. The complete equivalent circuit representation is shown in Figure 9.…”

“…The implementation of the addition and removal of materials has been demonstrated in electronic packaging applications by a few researchers. Artificial nodes with multi-point constraints to activate and deactivate different layers have been used [5]. They have used the models to study the manufacturing ofa copper line.…”

An investigation of the impact of a Ti barrier metal on the thermal stress field in passivated aluminium lines and vias in VLSI systems using finite element modelling approach

“…Recently FEM techniques (Cifuentes andSharref 1992, Igic andMawby 1998 a,b) have been proposed which overcome all previously noted weaknesses of the so called`frozen view' FEM approach (Jones and Basehore 1987, Greenebaum et al 1991, Sauter and Nix 1992, Besser et al 1993. The`frozen view' technique assumes that at some high temperature (determined by the processing) the structure is in a stress-free state, and that the stresses are generated as the temperature is reduced to room temperature.…”

“…Although attention has mainly been focused on failure in straight lines with a small cross-sectional area, it has recently been realized that the vias (or studs) which connect lines in di erent metallization layers tend to su er a much higher failure rate than the Al lines themselves. Thus, the use of the ® nite element modelling (FEM) technique (Jones and Basehore 1987, Greenebaum et al 1991, Cifuentes and Shareef 1992, Sauter and Nix 1992, Besser et al 1993, Shi and Tu 1994, Shen 1997 in assessing residual thermal stress patterns in multilevel metal structures has become more and more important. Using the FEM approach it is possible to identify`weak' parts of the structure (the highest stress regions) and to optimize the structure with respect to the residual stress, as well as the processing parameters (temperatures, layer thickness).…”

Residual thermomechanical stresses in thinned-chip assemblies

“…Furthermore, residual stresses may develop plastic deformations at intermediate process steps, a feature that can not be captured by "frozen models." Previous approaches to solve this problem were based on the addition of artificial nodes or multipoint constraints [2], [3]. However, we base our strategy in the birth/death of elements capability [4], [5].…”