Dislocation Dynamics in Semiconductor Thin Film-Substrate Systems
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Dislocation Dynamics in Semiconductor Thin Film-Substrate Systems E.H. Tan and L.Z. Sun Department of Civil and Environmental Engineering and Center for Computer-Aided Design The University of Iowa, Iowa City, IA 52242-1527, U.S.A. ABSTRACT A discrete dislocation dynamics model is developed to establish the equations of motion for three-dimensional interacting dislocation loops in the semiconductor thin film – substrate system. The film is assumed to be an elastic layer and is perfectly bonded with another elastic substrate. Dislocation loops are discretized into segments, each of which is represented by a parametric space curve of specific shape functions and associated degree of freedom. The dislocation stress field is calculated as an essential ingredient in the dislocation dynamics method. Dislocation dynamics and interaction with film surface/interface are simulated. INTRODUCTION The plastic behavior of crystalline materials is primarily controlled by the microstructural dislocation activities. Dislocation dynamics is of great interest to researchers and engineers. It can be traced back to as early as 1960s [1]. Due to the geometrical complexity of dislocation loops, 3-D analytical solutions to this problem are impossible; instead, various discretization techniques are widely employed, which are known as discrete dislocation dynamics (DDD). Important work on DDD has been made since 1990s [e.g., 2-9] for homogenous and infinitely extended materials. Hartmaier et al. [10] developed a dislocation dynamics model for the halfspace solids. Microelectronic semiconductor devices are generally integrated on the basis of thin filmsubstrate heterostructures. In this paper, an effective DDD model is proposed for the thin filmsubstrate system. Most semiconductor materials behave elastically yet with anisotropic responses [16]. For simplicity, we assume that the semiconductors considered here are elastically isotropic for the ease of formulation framework. Furthermore, all dislocations glide in their own slip planes. The dislocation stress field is calculated as an essential ingredient in the dislocation dynamics method. Dislocation dynamics and interaction with film surface/interface are simulated. MODEL DEVELOPMENT We first develop a method to calculate the stress field induced by dislocation loops. Local forces acting on the dislocation loop are then obtained. Discretized dislocation governing equations are finally established. Stresses induced by dislocation loops in thin film substrate system To obtain the stresses induced by dislocation loops in the thin film-substrate system, we decompose the problem into the supposition of two problems (Figure 1):
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1). The occurrence of dislocation loops in an infinite extended bi-material medium, which will create a traction field Ti ( x ) = σ ij ( x) n j on the virtual free surface. 2). The loading of a traction field −Ti ( x) = −σ ij ( x) n j on the free surface of the thin filmsubstrate system. Since the Green’s function for the isotropic infinite bi-material med
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