Atomistic Modeling of {311} Defects and Dislocation Ribbons
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1070-E06-04
Atomistic Modeling of {311} Defects and Dislocation Ribbons Bart Trzynadlowski, Scott Dunham, and Chihak Ahn Electrical Engineering, University of Washington, Seattle, WA, 98195 ABSTRACT Ab-initio calculations of dislocation and {311} defect structures in silicon were performed in order to investigate the formation energies as functions of geometry, including the effects of applied strain, with a simple model. Predictions were made concerning the size at which a {311} defect becomes less favorable than a dislocation ribbon, and it was shown that this is affected by applied strain. INTRODUCTION Extended defects in silicon have adverse effects on device performance and it is therefore desirable to better understand their formation and evolution, particularly as a function of stress and strain, which arises both intentionally and unintentionally in modern nano-scale CMOS processes. Ab-initio calculations can be used to investigate the properties of extended defect, and this study aims to offer a simple model for the conditions under which dislocation loops become energetically more favorable than {311} defects. CALCULATIONS Ab-initio calculations of edge dislocation structures were performed using VASP, a density functional theory (DFT) code, with generalized gradient approximation (GGA) pseudopotentials [1,2]. Both full and partial stacking faults, present in the (111) plane, were simulated in a local coordinate system where the X axis is along the [11¯ 0] direction, Y is [112 ¯ ], and Z is [111]. In this rotated coordinate system, the minimum repeatable (primitive) cell consists of 12 atoms and has dimensions a0/√2 × a0√6/2 × a0√3, where a0 is the silicon lattice constant. A 180-lattice site volume (“Si180”) was used to create the full stacking fault (20 interstitials, Si200) and two dislocation “ribbon” systems (Si188, Si192, with 8 and 12 interstitials, respectively.) In this case, the dislocation line extends infinitely along [11¯ 0] due to periodic boundary conditions. A 252-lattice site volume (Si252) was used for the Si260 and Si264 (also 8 and 12 interstitials) systems, with the dislocation line extending along [112 ¯ ]. Figure 1 shows Si264 as well as Si134, a {311} defect system, described below.
Figure 1. Si264 dislocation ribbon structure (left) with the edge dislocations marked, and a single chain of {311} defects, with interstitials marked green. {311} defect structures were generated in a local coordinate system with X along [01 ¯ 1], Y along [23¯ ¯3 ], and Z along [311] [3]. The primitive cell in this orientation contains 44 atoms and has dimensions a0/√2 × a0√11/√2 × a0√11. The chains are elongated in the X direction and multiple chains are positioned side-by-side along Y. Single and two-chain systems were simulated in a volume three cells wide (132 lattice sites). Due to periodic boundary conditions, only two interstitials are required to form an infinite chain. Energy as a function of chain length was investigated by creating systems where the periodicity results in an infinite number
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