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Abstract In this thesis, we have studied the post-weld-shift (PWS) in laser welding technique for laser module packaging. The joining method for packaging of laser module by laser welding technique can offer a number of significant advantages. It provides strong joint strength, therefore, the packaging has good long-term stability. It also provides high-speed and high-volume production, and hence the packaging is potential low cost. However, the laser welding process has caused PWS of laser module, would decay the coupling efficiency of laser module. We investigate the weld-spot by using metallographic method. The PWS in stainless steel (SS304L) plate is studied experimentally and numerically. The metallographic results are in good agreement with the Finite-Element-Method (FEM) results that the PWS in x-y plane can be neglected. Based on the experimentally and numerically results of PWS in SS304L, we investigate the yield improvement of laser module packaging. The laser hammer technique was used to improve the coupling efficiency of laser module. The results show displacement of the z-axis is from 1 to 9 (£gm) that equals to the angle changes of upper parts of laser module from 0.38¡Ñ10-2 to 3.4¡Ñ10-2 (degree). Therefore, the coupling efficiency of laser module can be improved from 4 to 20 (%).

This study aims to investigate the thermal fatigue life of the solder ball.Generally, the fatigue of the solder ball results from thermal cyclic loading in different thermal expansion coefficiency of the material in the IC package. To analyze the equivalent stress and the equivalent strain distributions of the solder ball under loading, an analysis software ANSYS was adopted in this study. To stimulate viscoplastic (creep and plastic) property of the solder ball, the Anand model was adopted. From the modified Coffin-Manson equation and the viscoplastic strain range, the fatigue life of the solder ball was obtained finally. The causes of the fatigue life of the solder ball in this study were attributed to many factors, such as the solider ball¡¦s geometry, substrate thickness, different material properties, change of pad diameter, etc. Finally, the researcher found the increasing solder joint reliability methods and supplied the improving solder joint data for the design engineer.

Elliptic partial differential equations that are used to model physical phenomena give rise to large sparse linear systems. Such systems can be symmetric positive definite and can be solved by the preconditioned conjugate gradients method. In this thesis, we develop support graph preconditioners for symmetric positive definite matrices that arise from the finite element discretization of elliptic partial differential equations. An object oriented code is developed for the construction, integration and application of these preconditioners. Experimental results show that the advantages of support graph preconditioners are retained in the proposed extension to the finite element matrices.

The solution of the secondary coupled-vector potential formulation of Maxwell??s equations governing the controlled-source electromagnetic (CSEM) response of an arbitrary, threedimensionalconductivitymodelmust be calculatednumerically.The finite elementmethod is attractive, because it allows the model to be discretized into an unstructured mesh, permitting the specification of realistic irregular conductor geometries, and permitting the mesh to be refined locally, where finer resolution is needed. The calculated results for a series ofsimple test problems, ranging from one-dimensionalscalar differentialequations to three-dimensional coupled vector equations match the known analytic solutions well, with error values several orders of magnitude smaller than the calculated values. The electromagnetic fields of a fully three-dimensional CSEM model, recovered from the potentials using the moving least squares interpolation numerical differentiation algorithm, compares well with published numerical modeling results, particularly when local refinement is applied. Multiple buried conductors in a conductive host interact via mutual induction and current flow through the host due to the dissipation of charge accumulated on the conductor boundary. The effect of this interaction varies with host conductivity, transmitter frequency, and conductor geometry, orientation, and conductivity. For three test models containingtwo highly conductive plate-like targets, oriented in various geometries (parallel, perpendicular, and horizontal), mutual coupling ranges as high as twenty times the total magnetic field. The effect of varying host conductivity is significant, especially at high frequencies. Numerical modeling also shows that the vorticity of the currents density induced in a vertically oriented plate-like conductor rotates from vertical at high frequencies, to horizontal at low frequencies, a phenomenon confirmed by comparison with time domain field data collected in Brazos County, Texas. Furthermore, the effect of the presence of a simple horst on the CSEM response of a homogeneous conductive earth is significant, even when the height of the horst is only a fraction of the skin depth of the model. When the transmitter is placedon topofthe horst, the currents inducedtherein account for nearly all of the total magnetic field of the model, indicating that topography, like mutual coupling must be accounted for when interpreting CSEM data.