Computational Electrodynamics is a vast research field with a wide variety of tools. In physics the principle of gauge invariance plays a pivotal role as a guide towards a sensible formulation of the laws of nature as well as computing the properties of elementary particles using the lattice formulation of gauge theories, yet the gauge principle has played a much less pronounced role in performing computation in classical electrodynamics. In this work the author will demonstrate that starting from the gauge formulation of electrodynamics using the electromagnetic potentials leads to computational tools that can very well compete with the conventional electromagnetic field-based tools. Once accepting the formulation based on gauge fields, the computational code is very transparent due to the mimetic mapping of the electrodynamic variables on the computational grid. Although the illustrations and applications originate from microelectronic engineering, the method has a much larger range of applicability. Therefore this book is of interest to everyone having interest in computational electrodynamics. The volume is organized as follows: In part 1, a detailed introduction and overview is presented of the Maxwell equations as well as the derivation of the current and charge densities is different materials. Semiconductors are responding to electromagnetic fields in a non-linear way and the induced complications are discussed in detail. In part 2, the transition of the theory of electrodynamics, using the gauge potentials, to a formulation that can serve as the gateway to computational code is presented. In part 3, the feasibility and success of the methods of part 2 are demonstrated by a collection of microelectronic device designs. Part 4 focuses on a set of topical themes that brings the reader to the frontier of research in building the simulation tools using the gauge principle in computational electrodynamics. Technical topics discussed in the book include:Electromagnetic Field EquationsConstitutive RelationsDiscretization and Numerical AnalysisFinite Element and Finite Volume MethodsDesign of Integrated Passive Components

Purpose: LinzFrame is a circuit and device simulatorCircuit and device simulator with emphasis on radio frequency circuits (RF) applications. Slowly changing amplitudes are modulated by a carrier signal at a very high center frequency. These waveforms are referred to as multi-tone signals. RF devices are often distributed elements, i.e. their behavior cannot be adequately represented by terminal voltages and currents. Design/Methodology: Besides SPICE-like analysis features LinzFrame offers several techniques dedicated to RF circuits. Among them are the multi-tone Harmonic Balance (HB), periodic steady state shooting method, a toolbox for autonomous circuits (oscillators), and multi-rate envelope methods. Besides transient analysis based on the BDF formulas, a toolbox for a spline-wavelet approximation has been developed. This technique combines the advantages of variable time step techniques (such as BDF) with a compact representation of signals by a set of basis functions (such as HB). In contrary to HB a spline-wavelet representation of signals with variable refinements allows for a representation of signals with sharp slew rates without the unwanted Gibbs phenomenon. In recent time, the simulator has been extended to a circuit-device mixed-level simulator by coupling the circuit simulator to a TCAD simulator. This feature enables the co-simulation of device and circuit levels, where the critical devices are simulated and optimized in full 3D, such as distributed elements. Originality/Value: LinzFrameLinzFrame enables the holistic (strong) coupling of a circuit and a device simulator, enabling either modeling of the circuit/device as lumped (concentrated) model or as a full 3D model, depending on the needed accuracy. Moreover it circumvents the prohibitive run-time of conventional transient analysis by several multi-rate techniques dedicated to RF circuits/devices.

An important outcome of the validation activities is the formulation of methodologies to address coupled problems in EDA. This chapter describes typical coupled problems arising in the field of activities of the industrial partners. It also highlights the challenges and makes the link to some test cases. In order to address these challenges and solve the design problems illustrated by the test cases, several design flows were put in place based on outcomes of the project activities. We describes these flows as well as the tools set-up in order to support them. Finally, the recommended usage of these flows is proposed.

We overview reliability related activities like ageing and life time prediction. We want to predict the number of thermal stress cycles an IC can handle before showing passivation cracks. For this a sufficient model for electro-migration was used that can be applied to an IC with multiple drivers and knowing a required thermal profile. At first state-of-the-art reliability concepts are reviewed. Next a new framework is introduced that aims at simplifying and speeding-up the process of assessing the reliability of complex application profiles.

This chapter discusses a number of techniques to solve the discrete systems of equations that result from the coupling of the circuit and electromagnetic field equations. We briefly summarize the modified nodal analysis for the lumped modeling of circuits. Then we discuss the coupling relations for including EM models into the circuit simulation systems and combine them with the spatially discretized Maxwell equations. Finally, we apply an adaptive time stepping scheme to the resulting coupled differential-algebraic equation system and in particular focus on a number of technical steps to find the solutions of the discretized coupled equations.

The Test Set for the Power-MOS Devices and RF-Circuitry, as described in Chapter [11], and the Measurements for RF-Amplifiers, Bond Wire Fusing and MOS Power Cells (see Chapter [18]) were used to validate simulation results of coupled problems by comparing with measurements, as well as by comparing to outcomes with other simulation tools (when possible, mostly without full coupling).