Peter Meuris

Strategy for electromagnetic interconnect modeling

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.

Electromagnetic interconnects and passives modeling: software implementation issues

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.

An Effective Formulation of Coupled Electromagnetic-TCAD Simulation for Extremely High Frequency Onward

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.

Uncertainty Quantification for Robust Topology Optimization of Power Transistor Devices

In this paper, we focus on incorporating a stochastic collocation method (SCM) into a topological shape optimization of a power semiconductor device, including material and geometrical uncertainties. This results in a stochastic direct problem and, in consequence, affects the formulation of an optimization problem. In particular, our aim is to minimize the current density overshoots, since the change of the shape and topology of a device layout is the proven technique for the reduction of a hotspot area. The gradient of a stochastic cost functional is evaluated using the topological asymptotic expansion and the continuous design sensitivity analysis with the SCM. Finally, we show the results of the robust optimization for the power transistor device, which is an example of a relevant problem in nanoelectronics, but which is also widely used in the automotive industry.

Modeling of passive-active device interactions

This paper deals with the modeling of the injection of electromagnetic fields into the active devices/circuits originating from integrated passive devices. It is shown that the impact of induced electromagnetic fields can be included as modified terminal conditions of the nearby devices.

Model Order Reduction for nanoelectronics coupled problems with many inputs

This paper is concerned with Model Order Reduction (MOR) for nanoelectronics coupled problems with many inputs. Our main applications are electro-thermal coupled problems described by nonlinear quadratic differential-algebraic systems (DAEs). We present algorithms that combine the advantages of the splitting techniques for DAEs and the existing MOR methods for systems with many inputs such as sparse implicit projection (SIP) for RC/RLC networks and MOR based on the superposition principle.

Holistic coupled field and circuit simulation

Circuit simulators used in semiconductor industry are based on lumped element models described in form of net lists. In order to be able to incorporate the mutual electromagnetic influence of neighboring elements (e.g. cross talking), one needs refined models based on a sufficiently exact discretization of the full Maxwell equations. Here, we present a holistic simulation approach for lumped circuit models including 3D electromagnetic field models for specific devices.

Application of Krylov-type Parametric Model Order Reduction in Efficient Uncertainty Quantification of Electro-thermal Circuit Models

As CMOS devices scale down to the nanoscale regime, it becomes increasingly more desired to design systems robust to device variations due to the fabrication process. In robust system design, uncertainty quantification plays an indispensable role. This paper considers uncertainty quantification of power-MOS devices used in energy harvesting. Uncertainty quantification of such a system is usually computationally demanding because it requires either simulating the high-order system at many sampling points, or simulating an even larger system. This paper uses parametric model order reduction techniques to accelerate uncertainty quantification of electro-thermal systems. We embed the reduced model into two uncertainty quantification methods, namely a Latin hypercube sampling method and a stochastic collocation method. Numerical results show that for both methods, uncertainty quantification based on a reduced model not only yields accurate results, but also achieves a significant speedup.

Evaluation of Electromagnetic Coupling Between Microelectronic Device Structures Using Computational Electrodynamics

Electromagnetic coupling between devices in an microelectronic layout can become a serious design concern. In this paper, the problem of electromagnetic coupling is addressed from field computational point of view. Approximation schemes are justified by evaluating dimensionless parameters in the set up of the field equations and scale considerations of devices. The discretization scheme is reviewed and a simulation method is presented to compute the S-matrix directly by imposing boundary conditions that map directly to the experimental set up. An example demonstrates the validity of the scheme.

An index-aware parametric model order reduction method for parameterized quadratic differential–algebraic equations

Modeling of sophisticated applications, such as coupled problems arising from nanoelectronics can lead to quadratic differential algebraic equations (DAEs). The quadratic DAEs may also be parameterized, due to variations in material properties, system configurations, etc., and they are usually subject to multi-query tasks, such as optimization, or uncertainty quantification. Model order reduction (MOR), specifically parametric model order reduction (pMOR), is known as a useful tool for accelerating the simulations in a multi-query context. However, pMOR dedicated to this particular structure, has not yet been systematically studied. Directly applying the existing pMOR methods may produce parametric reduced-order models (pROMs) which are less accurate, or may be very difficult to simulate. The same problem was already observed for linear DAEs, and could be eliminated by introducing splitting MOR techniques such as the index-aware MOR (IMOR) methods. We extend the IMOR methods to parameterized quadratic DAEs, thereby producing accurate and easy to simulate index-aware parametric reduced-order models (IpROMs). The proposed approach is so far limited to index-1 one-way coupled problems, but these often appear in computational nanoelectronics. We illustrate the performance of the new approach using industrial models for nanoelectronic structures.