Abstract
We developed a simple and efficient way to simulate stress from arbitrary shape dislocations within the finite element method (FEM) framework. The new method is implemented as a single-step FEM simulation using analytic solutions in an infinite medium as input terms of FEM solver with special internal boundary treatment. It is fundamentally equivalent to the multistep “image method” proposed by Van der Giessen and Needleman [Modell. Simul. Mater. Sci. Eng. 3, 689 (1995)], but the force equilibration is achieved by a single step FEM method. The singularity at the dislocation core line is removed without mesh modification, which removes many technical difficulties to couple the dislocation stress model to other process/device simulation models.
Highlights
Mechanical stress plays an important role in both detrimental1 and beneficial2,3 ways in modern semiconductor device fabrication and, improving stress simulation capability, especially dislocation stress model, has been of great interest in the technology computer-aided design (TCAD) community for decades
Research on the inclusion problem focused on the analytic solution in special geometries and boundary conditions
In 1993, Lubarda et al reduced Eshelby’s inclusion problem in a finite size domain with traction-free boundary conditions to a boundary value problem,6 which was extended to the general boundary conditions by Van der Giessen and Needleman7 and led to several different types of finite element method (FEM) solutions
Summary
Mechanical stress plays an important role in both detrimental and beneficial ways in modern semiconductor device fabrication and, improving stress simulation capability, especially dislocation stress model, has been of great interest in the technology computer-aided design (TCAD) community for decades. There has been no practical dislocation stress simulation methodology applicable to routine semiconductor modeling activity. In principle, solving stress distribution generated by dislocations is Eshelby’s inclusion problem, which has a history longer than a half century. Zhou et al. provided a review on the research history of the inclusion problem. Research on the inclusion problem focused on the analytic solution in special geometries and boundary conditions. In 1993, Lubarda et al reduced Eshelby’s inclusion problem in a finite size domain with traction-free boundary conditions to a boundary value problem, which was extended to the general boundary conditions by Van der Giessen and Needleman and led to several different types of finite element method (FEM) solutions.
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