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  • Multidimensional Semiconductor Device and Micro-Scale Thermal Modeling Using the PROPHET Simulator with Dial-an-Operator Framework
  • Abstract Rapid prototyping tools that combine powerful numerics with a flexible applications interface can play a significant role in micro-scale modeling and simulation. We demonstrate this idea using the PROPHET simulator. In the first part of the investigations we extend the simulator's capability to allow analysis of carrier transport in deep submicron MOSFETs using a hydrodynamic model. The model is numerically implemented within PROPHET's dial-an-operator framework by adding certain "flux'' routines. Once implemented, the model becomes available for use in any number of spatial dimensions. We present results for MOSFET type test problems in one and two dimensions. The second application…
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  • Optimal Design of Computer Experiments for Metamodel Generation Using I-OPTTM
  • Abstract We present a new and unique software capability for finding statistical optimal designs of deterministic experiments on continuous cuboidal regions. The objective function for the design optimization is the minimization of the expected integrated mean squared error of prediction of the metamodel that will be found, subsequent to the running of the computer simulations, using the best linear unbiased predictor (BLUP). The assumed response-model function includes an unknown, stochastic term, Z. We prove that this criterion, which we name IZ-optimality, is equivalent to I-optimality for non-deterministic experiments, in the limit of zero correlations among the Z's for different inputs. An…
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  • A Meshless Method for the Numerical Solution of the 2- and 3-D Semiconductor Poisson Equation
  • Abstract This paper describes the application of the meshless Finite Point (FP) method to the solution of the nonlinear semiconductor Poisson equation. The FP method is a true meshless method which uses a weighted least-squares fit and point collocation. The nonlinearity of the semiconductor Poisson equation is treated by Newton-Raphson iteration, and sparse matrices are employed to store the shape function and coefficient matrices. Using examples in two- and three-dimensions (2- and 3-D) for a prototypical n-channel MOSFET, the FP method demonstrates promise both as a means of mesh enhancement and for treating problems where arbitrary point placement is advantageous, such…
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  • Design and Fabrication of an Electrostatic Variable Gap Comb Drive in Micro-Electro-Mechanical Systems
  • Abstract Polynomial driving-force comb drives are designed using numerical simulation. The electrode shapes are obtained using the indirect boundary element method. Variable gap comb drives that produce combinations of linear, quadratic, and cubic driving-force profiles are synthesized. This inverse problem is solved by an optimization procedure. Sensitivity analysis is carried out by the direct differentiation approach (DDA) in order to compute design sensitivity coefficients (DSCs) of force profiles with respect to parameters that define the shapes of the fingers of a comb drive. The DSCs are then used to drive iterative optimization procedures. Designs of variable gap comb drives with linear,…
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  • Numerical Simulation of Fatigue Crack Growth in Microelectronics Solder Joints
  • Abstract An FEA (finite element analysis) program employing a new scheme for crack growth analysis is developed and a prediction method for crack growth life is proposed. The FEA program consists of the subroutines for the automatic element re-generation using the Delaunay Triangulation technique, the element configuration in the near-tip region being provided by a super-element, elasto-inelastic stress analyses, prediction of crack extension path and calculation of fatigue life. The FEA results show that crack extension rate and path are controlled by a maximum opening stress range, Δσθmax, at a small radial distance of r = d, where d is chosen…
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  • Cracking of GSO Single Crystal Induced by Thermal Stress
  • Abstract Quantitative estimation of the failure of a gadolinium orthosilicate (Gd2SiO5, hereafter abbreviated as GSO) single crystal induced by thermal stress was investigated. A GSO cylindrical test specimen was heated in a silicone oil bath, then subjected to large thermal stress by room temperature silicone oil. Cracking occurred during cooling. The transient heat conduction analysis was performed to obtain temperature distribution in the test specimen at the time of cracking, using the surface temperatures measured in the test. Then the thermal stress was calculated using the temperature profile of the test specimen obtained from the heat conduction analysis. It is found…
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  • Strength Evaluation of Electronic Plastic Packages Using Stress Intensity Factors of V-Notch
  • Abstract In electronic devices, the corners of joined dissimilar materials exist between plastic resin and a die pad or a chip. Failure of the plastic resin is often caused from these corners during the assembly process or the operation of products. The strength evaluation of the corner is important to protect the failure of plastic packages. To evaluate the singular stress field around a corner, we utilize the stress intensity factors of the asymptotic solution for a corner of joined dissimilar materials. We show that the accurate stress intensity factor can be analyzed by the displacement extrapolation method using the displacement…
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  • Effect of Growth Direction on Twin Formation in GaAs Crystals Grown by the Vertical Gradient Freeze Method
  • Abstract Twins in growing crystals are due to excessive thermal stresses induced by the temperature gradients developed during the growth process. Twinning is an important defect in advanced semiconductor crystals such as GaAS and InP. The objective of this study is to develop a computational model to predict the twin formation in the Gallium Arsenide (GaAs) crystals grown by the vertical gradient freeze method (VGF). A quantitative quasi-steady state thermal stress model is developed here for predicting the twinning formation in GaAs grown by VGF. The thermoelastic stresses in VGF grown crystal are calculated from a two-dimensional finite element analysis. Deformation…
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  • Modelling and Validation of Contribions to Stress in the Shallow Trench Isolation Process Sequence
  • Abstract This work is based upon a careful rendering of mechanics and mathematics to describe the phenomena that influence the stress engendered by the Shallow Trench Isolation process. The diffusion-reaction problem is posed in terms of fundamental mass balance laws. Finite strain kinematics is invoked to model the large expansion of SiO2, dielectrics are modelled as viscoelastic solids and annealing-induced density relaxation of SiO2 is incorporated as a history-dependent process. A levelset framework is used to describe the moving Si/SiO2 interface. Sophisticated finite element methods are employed to solve the mathematical equations posed for each phenomenon. These include the incorporation of…
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  • A Methodology and Associated CAD Tools for Support of Concurrent Design of MEMS
  • Abstract Development of micro-electro-mechanical systems (MEMS) products is currently hampered by the need for design aids, which can assist in integration of all domains of the design. The cross-disciplinary character of microsystems requires a top-down approach to system design which, in turn, requires designers from many areas to work together in order to understand the effects of one sub-system on another. This paper describes current research on a methodology and tool-set which directly support such an integrated design process.
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