In radio frequency (RF) circuits the lumped model assumptions are often not valid anymore. To circumvent this problem, mixed-level circuit/electro-magnetic/device simulation allows the use of Maxwell's and semiconductor equations for the critical devices and lumped models for the ambient circuitry. Besides AC, DC, periodic steady state and transient analysis, the multirate partial differential equation technique is employed for RF circuitry, based on a spline/wavelet expansion of the waveforms. The novel technique is demonstrated for RF circuits with on-chip inductors, transmission lines and baluns, modeled as 3D devices.

This paper presents a new transient electro-thermal (ET) simulation method for fast 3D chip-level analysis of power electronics with field solver accuracy. The metallization stacks are meshed and solved with 3D field solver using nonlinear temperature-dependent parameters, and the active devices are modeled with nonlinear tabular compact models to avoid time-consuming TCAD simulation. The main contributions include: 1) A tightly-coupled formulation that solves the electrical and thermal systems simultaneously to enable a more natural characterization of ET interaction and faster convergence for strong ET coupling; 2) A specialized exponential-integrator-Newton-Krylov (EI-NK) transient solver to address the numerical challenges arising from the tightly-coupled ET simulation. Numerical experiments show that the proposed method out-performs the existing implicit time stepping with the Newton's method and the exponential integrator with an explicit nonlinear approximation.

This paper presents a new transient electro-thermal simulation method for fast 3-D chip-level analysis of power electronics with field solver accuracy. The metallization stack and substrate are meshed and solved with 3-D field solver using nonlinear temperature-dependent electrical and thermal parameters, and the active transistors are modeled with table models to avoid time-consuming technology computer-aided design simulation. Two contributions are made to enhance the physical relevance and the computational performance: 1) the capacitive effects, including interconnect parasitic capacitance and gate capacitance of power devices with nonlinear dependence on bias and temperature, are explicitly accounted for and 2) a specialized nonlinear exponential integrator (EI) method is developed to address the considerably different time scales between electrical and thermal sectors. The EI-based transient solver allows the electrical system to step with much larger time steps than in conventional methods, thus the time step gap between the electrical and the thermal simulation is largely reduced.

We present a full physical simulation picture of the electromagnetic phenomena combining electromagnetic (EM) fields and carrier transport in semiconductor devices (TCAD) in the transient regime. The simulation tool computes the EM fields in a self-consistent way and the resulting magnetic fields are incorporated in the computation of the current sources that get modified by the Lorentz force (LF).

We report recent progress in developing a numerically efficient formulation for electromagnetic-technology computer-aided design cosimulation for fast-transient computations. The difficulties underlying the currently existing transient formulation stemming from the vector potential-scalar potential (A-V) framework are analyzed. A time-domain electric field-scalar potential (E-V) framework is then developed via equation and variable transformations. This results in better-conditioned systems that are friendly to iterative solutions at fast switching times. Numerical examples show that the proposed E-V solver renders a useful tool for addressing multidomain simulation.

We present a formulation of transient field solving that allows for the inclusion of semiconducting materials whose dynamic responses are prescribed by drift-diffusion modeling. The robustness and the feasibility is demonstrated by applying the scheme to compute accurately the large-signal response of an integrated inductor.

We present a fast time-domain multiphysics simulation framework that combines full-wave electromagnetism (EM) and carrier transport in semiconductor devices (TCAD). The proposed framework features a division of linear and nonlinear components in the EM-TCAD coupled system. The former is extracted and handled independently with high efficiency by a matrix exponential approach assisted with Krylov subspace method. The latter is treated by ordinary Newton's method yet with a much sparser Jacobian matrix that leads to substantial speedup in solving the linear system of equations. More convenient error management and adaptive control are also available through the linear and nonlinear decoupling.

This paper presents an effective formulation tailored for electromagnetic-technology computer-aided design coupled simulations for extremely-high-frequency ranges and beyond (>;50 GHz). A transformation of variables is exploited from the starting A-V formulation to the E-V formulation, combined with adopting the gauge condition as the equation for scalar potential. The transformation significantly reduces the cross-coupling between electric and magnetic systems at high frequencies, providing therefore much better convergence for iterative solution. The validation of such transformations is ensured through a careful analysis of redundancy in the coupled system and material properties. Employment of the advanced matrix permutation technique further alleviates the extra computational cost introduced by the variable transformation. Numerical experiments confirm the accuracy and efficiency of the proposed E-V formulation.

This is the second paper in a series on the simulation of on-chip high-frequency effects. A computer-aided approach in three dimensions is advocated, describing high-frequency effects such as current redistribution due to the skin-effect or eddy currents and the occurrence of slow-wave modes. The electromagnetic environment is described by an electric scalar potential and a magnetic vector potential as well as a ghost field. The latter one guarantees a stable numerical implementation. This paper deals with the software implementation, the treatment of interfaces and domain boundaries, scaling considerations, numbering schemes, and solver requirements. Some illustrative examples are shown.

This paper presents a new method to discretize the equations for the physical modeling of semiconductor devices and back-end patterns. The method assembles planes in two dimensions and cubes in three dimensions and allows for adaptive meshing without the occurrence of spurious nodes due to mesh smoothing. Whereas the applications that are discussed focus on the design of microelectronic devices, the method is generally applicable to all fields of engineering where ab initio physical modeling is required.

In order to design on-chip interconnect structures in a flexible way, a computer-aided design approach is advocated in three dimensions, describing high-frequency effects such as current redistribution due to the skin effect or eddy currents and the occurrence of slow-wave modes. The electromagnetic environment is described by a scalar electric potential and a magnetic vector potential. These potentials are not uniquely defined and in order to obtain a consistent discretization scheme, a gauge transformation field is introduced. The displacement current is taken into account to describe current redistribution and a small-signal analysis solution scheme is proposed based upon existing techniques for fields in semiconductors.

One of the problems while simulating heterojunction devices is the poor numerical stability due to the broad number range for concentrations and currents in the different materials. However, it is not obvious which scaling to apply as more than one material is involved. This paper presents a unified scaling system which circumvents the problem. This includes not only the extension of the general de Mari scaling but also an extra scaling with respect to local carrier concentrations. The idea provides a way to deal with the great number range of e.g., the carrier concentrations at heterojunctions. The developed algorithm is very efficient as the new scaling system can also be applied for bulk nodes without altering it. Finally, some examples prove the technique to be very stable and promising for future development.>