Tsai, Chi-Tay

The objective of this work is to perform the current induce thermal stress analysis of heterojunction bipolar transistor and to determine the implications of the variation of the thermal shunt thickness. A thesis presented on multi-physics using finite element analysis, covering fluid, thermal and stress with fatigue life analysis of a microelectronic heterojunction bipolar transistor.

A computational approach for characterization of curl of paper under humidity changes is presented. Asymmetric papers with nonuniform through-thickness fiber orientation distribution are considered. Testing of the constituent layers of the papers considered was conducted at various constant relative humidities to obtain the mechanical properties, moisture content, moisture expansion coefficients and stress relaxation curves. Experiments were performed on asymmetric two-ply laboratory made papers to determine the curl response under moisture loading. The influence of viscoelastic stress relaxation on the curl response was first investigated. Geometrically nonlinear finite element analysis was conducted. It was found that the curvatures relax at an increasing rate with increasing humidities because of moisture enhanced viscoelastic dominance. Computed time-dependent curvatures were compared to experimental measurements which verified the mode shape and time-dependent relaxation response. Geometrically nonlinear finite element analysis revealed that initial deflections may strongly influence the subsequent curl behavior. A sheet with initial curvatures may undergo a bifurcation transition (buckling curl response) if the curvatures strongly interact. After the bifurcation transition, the sheet may or may not assume an unexpected shape. Experiments showed sensitivity of the response to the directions of the initial curvatures, and there are indications of a bifurcation as a result of curvature interaction. A two-ply laminate model was used to analyze curvatures of various asymmetric papers. Differences in fiber orientation distribution and principal fiber orientation angle between the two plies were considered. The analysis showed that the sheet typically bifurcated into a cylindrical and/or twisted shape. A sheet with known through-thickness fiber orientation demonstrated a complex curl response that could be simulated using the approach presented, given that the initial curl shape is known.

The development of a parallel data structure and an associated elemental decomposition algorithm for explicit finite element analysis for massively parallel SIMD computer, the DECmpp 12000 (MasPar MP-1) machine, is presented, and then extended to implementation on the MIMD computer, Cray-T3D. The new parallel data structure and elemental decomposition algorithm are discussed in detail and is used to parallelize a sequential Fortran code that deals with the application of isoparametric elements for the nonlinear dynamic analysis of shells of revolution. The parallel algorithm required the development of a new procedure, called an 'exchange', which consists of an exchange of nodal forces at each time step to replace the standard gather-assembly operations in sequential code. In addition, the data was reconfigured so that all nodal variables associated with an element are stored in a processor along with other element data. The architectural and Fortran programming language features of the MasPar MP-1 and Cray-T3D computers which are pertinent to finite element computations are also summarized, and sample code segments are provided to illustrate programming in a data parallel environment. The governing equations, the finite element discretization and a comparison between their implementation on Von Neumann and SIMD-MIMD parallel computers are discussed to demonstrate their applicability and the important differences in the new algorithm. Various large scale transient problems are solved using the parallel data structure and elemental decomposition algorithm and measured performances are presented and analyzed in detail. Results show that Cray-T3D is a very promising parallel computer for finite element computation. The 32 processors of this machine shows an overall speedup of 27-28, i.e. an efficiency of 85% or more and 128 processors shows a speedup of 70-77, i.e. an efficiency of 55% or more. The Cray-T3D results demonstrated that this machine is capable of outperforming the Cray-YMP by a factor of about 10 for finite element problems with 4K elements, therefore, the method of developing the parallel data structure and its associated elemental decomposition algorithm is recommended for implementation on other finite element code in this machine. However, the results from MasPar MP-1 show that this new algorithm for explicit finite element computations do not produce very efficient parallel code on this computer and therefore, the new data structure is not recommended for further use on this MasPar machine.

Two-dimensional and three-dimensional methodologies are developed to determine the dislocation multiplication in microelectronic and optoelectronic devices/circuits. A two-dimensional finite element code is developed to simulate the dislocation multiplication in microelectronic and optoelectronic devices/circuits. Example two-dimensional analyses are performed and analysis results are presented. The three-dimensional methodology is successfully implemented using ANSYS APDL Language within the ANSYS program. A three dimensional heterojunction bipolar transistor model is generated. CFD-thermal and structural analyses are performed to determine temperature fields and dislocation densities, which are calculated as functions of time, thickness of the thermal shunt, and heat generation rates.

The generation and multiplication of dislocations in Gallium Arsenide (GaAs) and Indium Phosphide (InP) single crystals grown by the Vertical Gradient Freeze (VGF) process is predicted using a transient crystallographic finite element model. This transient model is developed by coupling microscopic dislocation motion and multiplication to macroscopic plastic deformation in the slip system of the grown crystals during their growth process. During the growth of InP and GaAs crystals, dislocations are generated in plastically deformed crystal as a result of crystallographic glide caused by excessive thermal stresses. The temperature fields are determined by solving the partial differential equation of heat conduction in a VGF crystal growth system. The effects of growth orientations and growth parameters (i.e., imposed temperature gradients, crystal radius and growth rate) on dislocation generation and multiplication in GaAs and InP crystals are investigated using the developed transient crystallographic finite element model. Dislocation density patterns on the cross section of GaAs and InP crystals are numerically calculated and compared with experimental observations. For crystals grown along [001] and [111] orientations, the results show that more dislocations are generated as the temperature gradient, the crystal growth rate and the crystal radius increase. For the same growth process, it shows that the crystal grown along [111] orientation is a favorable growth direction to grow lower dislocation density crystals. All the results show a famous "W" shape and four fold symmetry dislocation density pattern in GaAs and InP crystals grown from both orientations regardless of crystal growth parameters, which agree well with the patterns observed in actual grown crystals. Therefore, this developed crystallographic model can be employed by crystal grower to design an optimal growth parameters and orientations for growing low dislocation density in advanced semiconductor and optical crystals.

Dislocations in Gallium Arsenide (GaAs) and Indium Phosphide (InP) single crystals are generated by excessive stresses that are induced during the crystal growth process, and the fabrication and packaging of microelectronic devices/circuits. The presence of dislocations has adverse effects on the performance, lifetime and reliability of the GaAs and InP-based devices/circuits. It is well known that dislocation density can be significantly reduced by doping impurity atoms into the GaAs and InP crystal and/or decreasing the thermal stresses in these crystals during their growth process. In order to reduce the dislocation density generated in the GaAs and InP crystals, the influence of crystal growth parameters and doping impurity atoms on the dislocations reduction in GaAs and InP crystals has to be understood. Therefore, a transient finite element model was developed to simulate the dislocation generation in GaAs and InP crystals grown from the melt. A viscoplastic constitutive equation that couples a microscopic dislocation density with a macroscopic plastic deformation is employed to formulate this transient finite element model, where the dislocation density is considered as an internal state variable and the doping impurity is represented by a drag-stress in this constitutive model. GaAs and InP single crystals grown by the vertical gradient freeze (VGF) process were adopted as examples to study the influences of doping impurity and growth parameters on dislocations generated in these grown crystal. The calculated results show that doping impurity can significantly reduce dislocation generation and produces low-dislocation-density or dislocation free GaAs and InP single crystals. It also shows that the dislocations generated in GaAs and InP crystals increase as the crystal diameter and imposed temperature gradient increase, but do not change or increase slightly as the crystal growth rate increases. Therefore, this finite element model can be effectively used by crystal growers to select acceptable levels of doping impurity, crystal diameter, temperature gradient, and growth rate to produce the lowest dislocation density in GaAs and InP crystals through a thorough numerical investigation using this developed finite element model.