Electrical Engineering Applications

1 Semiconductor Device Analysis.- 1.1 Introduction.- 1.2 The Basic Semiconductor Equations.- 1.3 Two Well Known Approximations.- 1.4 A Particular Application: The MOS Transistor.- 1.5 Some Further Applications.- 1.6 Conclusion.- References.- 2 Thermal Analysis of Semiconductor Devices.- 2.1 Introduction.- 2.2 Review of Previous Works.- 2.3 The Boundary Element Method.- 2.3.1 The Boundary Integral Formulation.- 2.3.2 Modeling Using the Boundary Element Method.- 2.3.3 Accuracy of the Boundary Element Method.- 2.4 Applications.- 2.4.1 Two and Three Dimensional Models of Semiconductor Devices.- 2.4.2 The Effect of Die-Bond Voids on Device Performance.- Summary.- Acknowledgement.- References.- 3 Applications of Boundary Elements in Corrosion Engineering.- 3.1 Introduction.- 3.1.1 Corrosion.- 3.2 Prediction Techniques.- 3.3 Theoretical Foundations of Cathodic Protection and Galvanic Corrosion.- 3.4 Mathematical Aspects.- 3.4.1 Numerical Solution.- 3.5 Electrode Kinetics.- 3.6 Coupling of the System.- 3.7 Polarisation.- 3.8 Systems Approach.- 3.9 Example 1: Comparison of BE Results with Cathodic Protection Experiment on a Plate.- 3.10 Example 2: Cathodic Protection of Underground Pipelines.- 3.11 Example 3: Analysis of Galvanic Corrosion (A Comparison with FE Analysis).- 3.12 Example 4: Analysis of a Galvanic Corrosion Due to a Chemical Cleaning Process.- 3.13 Example 5: Analysis of a Jacket Type Offshore Platform.- 3.14 Conclusions.- Acknowledgements.- References.- 4 Application of BEM to Galvanic Corrosion and Cathodic Protection.- 4.1 Introduction.- 4.2 Electrochemical Aspects.- 4.3 Mathematical Model.- 4.4 Boundary Element Formulation.- 4.5 Iterative Solution Procedures.- 4.6 Infinite Problems.- 4.7 Applications.- 4.7.1 Comparison with Theoretical Results.- 4.7.2 Effect of Externally Impressed Polarization.- 4.7.3 Comparison with Experimental Data.- 4.7.4 Estimation of Maximum Current Density.- 4.7.5 Three-Dimensional Problems.- 4.7.6 Infinite Problems.- 4.8 Concluding Remarks.- Acknowledgements.- References.- 5 Capacitance of Transducers for Displacement Measurement.- 5.1 Introduction.- 5.2 Calculation of Capacitance by the Boundary Element Method.- 5.2.1 Green Solution and Capacitance.- 5.2.2 Boundary Element Method.- 5.2.3 Two-Dimensional Case.- 5.2.4 Calculation of Conductance or Resistance in an Infinite Area by Ihe Boundary Element Method.- 5.3 Numerical Results.- 5.3.1 Curve of Change of Capacitance.- 5.3.2 Effect of the Gap Between the Two Electrodes.- 5.3.3 Effect of Width of Teeth.- 5.3.4 Effect of Filing a Dielectric Between Electrodes.- 5.4 Experimental Results.- 5.4.1 Experimental Equipment.- 5.4.2 Curve of Change of Capacitance.- 5.4.3 Effect of the Gap Between the Two Electrodes.- 5.4.4 Effect of Width of Teeth.- 5.5 Conclusions.- Acknowledgement.- References.- 6 Electroplating.- 6.1 Introduction.- 6.2 Mathematical Formulation.- 6.3 Boundary Element Formulation.- 6.4 Solution of the Nonlinear System.- 6.5 Development of a One-dimensional Model.- 6.6 Numerical Examples.- 6.6.1 Example 1.- 6.6.2 Example 2.- 6.6.3 Example 3.- 6.7 Conclusions.- Acknowledgement.- References.- 7 Simulation of an Electrochemical Plating Process.- 7.1 Introduction.- 7.2 Equations.- 7.3 Boundary Element Method.- 7.4 Experiment.- 7.4.1 Plating Cell.- 7.4.2 Tank Discretization.- 7.4.3 Node Movement.- 7.4.4 Parameters.- 7.5 Results.- 7.6 Conclusions.- Acknowledgements.- References.- 8 Electrochemical Cell Design.- 8.1 Introduction.- 8.2 Fundamental Equations.- 8.2.1 Transport of Charge.- 8.2.2 Transport of Mass.- 8.3 Boundary Conditions.- 8.3.1 Insulators.- 8.3.2 Electrodes.- 8.3.2.1 Electrode Reactions.- 8.3.2.2 Resistances Involved by Coatings.- 8.3.2.3 Concentration Overpotentials.- 8.3.2.4 Resistive Electrodes.- 8.4 Types of Distributions, the Wagner Number.- 8.5 Electrode Shape Change and Moving Boundaries.- 8.6 Solution of the Potential Model.- 8.6.1 Discretization of the BEM.- 8.6.1.1 Two-Dimensional Problems.- 8.6.1.2 Axìsymmetrical Problems.- 8.6.2 Solution of the Non-linear System.- 8.6.3 Solution of Resistive Electrodes.- 8.6.4 Repetitive Geometries.- 8.6.5 Examples.- 8.6.6 Comparison with Measurements.- 8.7 Solution of Electrode Shape Changes.- 8.7.1 Discretization with Respect to Time.- 8.7.1.1 Electrode Shape Change Next to an Insulator.- 8.7.1.2 Electrochemical Machining.- 8.7.2 Examples.- 8.7.3 Comparison with Measurements.- References.- 9 Inverse Problems and Some Applications.- 9.1 Introduction.- 9.2 Fields of Application of Inverse Problems.- 9.3 Application of Boundary Element Methods.- 9.4 Numerical Simulation.- 9.4.1 The Inverse Electrocardiography Problem.- 9.4.1.1 Fundamentals of an Electrocardiogram.- 9.4.1.2 Boundary Element Model.- 9.4.1.3 Numerical Experiments.- 9.4.1.4 On Ill-Conditioning and Regularization Problems.- 9.4.2 Boundary Determination in Impedance Plethysmography.- 9.4.2.1 On Impedance CT and Plethysmography.- 9.4.2.2 Influence Coefficient Approach and Lead Theory Approach.- 9.4.2.3 Numerical Experiments.- 9.4.2.4 Some Mathematical Background.- 9.4.2.5 Other Approaches and Applications.- 9.5 Improvement of the Boundary Determination Capability.- 9.5.1 Efficiency and Convergence.- 9.5.2. Boundary Determination Based on Dual Complementary Formulation.- 9.5.2.1 Lead Theory in Single Medium Field.- 9.5.2.2 Dual and Complementary Expressions.- 9.5.2.3 Boundary Element Discretization.- 9.5.3 Dual and Complementary Energy Expressions.- 9.5.4 Numerical Simulation.- 9.5.4.1 Electric Potential-nondestructive Testing.- 9.5.4.2 Impedance Plethysmography.- References.