Modeling of thermal stresses in metal interconnects: Effects of line aspect ratio

Abstract

Analysis of average thermal stresses in passivated metal interconnectsNumerical results are presented on the evolution of thermal stresses in metal interconnects. Finite element analyses are carried out for a series of parallel aluminum lines embedded within silicon dioxide. The effects of line aspect ratio on the longitudinal and hydrostatic stresses in lines are investigated, for various spaces between lines. Comparisons with the results based on an isolated line under passivation are also made. It is shown that, contrary to what was frequently found by employing the single-line approach, maximum stresses in periodically arranged aluminum lines do not occur when the line width and the line height are approximately equal. The variation of stresses with line aspect ratio is affected by the spacing between lines. Implications of the present findings to the modeling of stresses and to the damage evolution through void formation are discussed.

Thermomechanical response and stress analysis of copper interconnects

“…The combination of stress variation results in an increasing average hydrostatic stress with increasing aspect ratio, which is qualitatively similar to the case of densely arrayed Al interconnects. 17,19,27 The overall increase in stress magnitude throughout the range of aspect ratio considered, however, is smaller in the case of Cu (Model A). In Fig.…”

“…It has been well established for densely arrayed Al interconnects that thermal stresses increase monotonically with the aspect ratio. 17,19,27 Such kind of relationship for the copper-low-k dielectric systems remains to be explored. Here, we present modeling results based on calculations using various Cu widths (w) while keeping the line height constant at 0.40 µm.…”

“…Thermal stress modeling of Al interconnects and its implications in their structural integrity are relatively well established. [14][15][16][17][18][19][20][21][22][23][24][25][26][27] Such is not the case for Cu-based systems. Available studies 28,29 have used simplified material or mechanical models, as will be discussed in this article.…”

Externally constrained plastic flow in miniaturized metallic structures: A continuum-based approach to thin films, lines, and joints

“…16 are volume averaged values of the longitudinal component, r xx , and hydrostatic component, r H , after a thermal history of cooling from 400 to 20°C, where 400°C is taken to be the initial stress-free state (presumably the passivation deposition temperature or film annealing temperature). The passivation geometry and properties are known to affect the line stress [279,282]; here a planarized passivation is assumed and the total height of SiO 2 is taken to be twice that of Al [283]. In addition, the solid curves in Fig.…”

Analysis of thermal stresses in copper interconnect/low-k dielectric structures

“…Thermal stress modeling and its implications in the reliability features of aluminum (Al) interconnects are relatively well established. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] This is not the case for copper (Cu) or low-k dielectric-based systems. Despite the progress made in recent years on experimental techniques such as microscale diffraction, [15][16][17][18][19] successes in interconnect stress measurement are largely confined to special test structures.…”