NUMERICAL SIMULATIONS OF DISLOCATIONS IN SEMICONDUCTOR MATERIALS USING XFEM

Abstract

The electronic items involve components such as diodes, transistors, LEDs, lasers, and infrared sensors/detectors which are made of semiconductor materials. The semiconductors are crystalline materials with electrical conductivity between metals and insulators, and are substantially affected by minute defects. Sometimes, crystal defects are caused by atoms that do not adhere to the ideal crystal lattice. Point defects are created when there is even the minor divergence in a single lattice point. However, when combined, a large number of point defects will cause the crystal lattice to shift, resulting in line defects (dislocations). The dislocations in a material can be identified and defined with the help of the Burgers circuit and Burgers vector, respectively. The dislocations can be perfect or partial depending on the Burgers vector. For a perfect dislocation, the Burgers vector is a lattice vector, whereas for partial dislocations, the Burgers vector is a non-lattice vector. The dislocation existence and motion can affect the performance and behavior of a material; hence, there is a need to understand the behavior of dislocations. Edge dislocations are examined under various stress fields in the semiconductor materials. A continuum mechanics-based approach is used for analyzing dislocations. Extended finite element method (XFEM) is used to approximate the solution of partial differential equations governing the physics of dislocation problems. This work aims to compute the force acting on the dislocations due to surrounding stress fields, popularly known as the Peach-Koehler force. This force is important to understand the motion of dislocations and their interactions with other defects, such as free surfaces, interfaces, and inclusions. Initially, the thermo-elastic analysis of the edge dislocations is performed using XFEM. Various two-dimensional problems are solved, such as an edge dislocation near a free surface, an edge dislocation near a bi-material interface, a finite edge dislocation dipole in an infinite domain, and a finite edge dislocation dipole near a bi-material interface. One of the conclusions of the numerical simulations for different temperatures suggest that the heat flux direction can affect the Peach-Koehler force significantly. Further, the simulations are extended to observe the impact of temperature-induced nonlinearity and the Joule heat generation on the thermo-elastic fields. The Joule heat due to the electric field in the direction of the dislocation line is taken into account. The change in electrical conductivity due to the piezo-resistive behavior of the material under the dislocation stress field is also considered for evaluating the Joule heat around the dislocation core. As temperature increases, the electrical conductivity and, hence, the Joule heat increases, directly increasing the Peach-Koehler force. Furthermore, the multiphysics analysis combining the effects of thermal, electric and elastic fields is also accomplished. High-performance devices can be fabricated through heteroepitaxy that results in misfit. The present work focuses on analyzing the dislocations near the material interface with misfit strain. Also, the temperature is a key parameter affecting both the development of thermal strain and the material properties. One significant novelty of this research is proposing a new enrichment function in XFEM to model the singularity in the electric potential at the dislocation core. Finally, the material heterogeneity due to compositional grading is incorporated in the multiphysics simulations to replace the heterostructure misfit. Linear and power law variation of the constituent material is assessed for the dislocation Peach-Koehler force computation. This force in the graded material is found to be more sensitive to the voltage than the temperature. Different edge dislocation problems with glide planes in the grading direction or at an angle are evaluated. Further, various parametric studies are also performed to compute the Peach-Koehler force when temperature, voltage, or dislocation location changes. Overall, XFEM is found to be a simple and efficient tool for analyzing edge dislocations in homogeneous and heterogeneous materials under multiphysics environment. The force on the dislocations can help to better understand the dislocations that can cause performance degradation of the components and devices.