Wim Schoenmaker

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.

Renormalization group meshes and the discretization of TCAD equations

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.

Statistical Modeling based on extensive TCAD simulations Proposed methodology for extraction of Fast/Slow models and Statistical models

Determination of fast/slow models and/or statistical models as a function of process dispersions are very challenging for designing new circuits. The present paper describes a methodology to extract fast/slow models and statistical models based on extensive process/device simulation. Also, AC parameters are extracted such as drain to gate overlap capacitance of MOS transistors as a function of process parameters variations. With the help of Principle Component Analysis, it is possible to get an uncorrected set of parameter that represent electrical and SPICE parameters dispersions. This leads to a more easy analysis for providing statistical models.

Simulation of substrate currents

Recently a new approach was presented to determine the high-frequency response of on-chip passive components and interconnects. The method solves the electric scalar and magnetic vector potentials in a prescribed gauge. The latter one is included by introducing an additional independent scalar field, whose field equation needs to be solved. This additional field is a mathematical aid that allows for the construction of a gauge-conditioned, regular matrix representation of the curl-curl operator acting on edge elements. This paper reports on the convergence properties of the new method and shows the first results of this new calculation scheme for VLSI-based structures at high frequencies. The high-frequent behavior of the substrate current, the skin effect and current crowding is evaluated.

Quantum transport in submicron devices

The paper presents both conceptual and computational features of quantum transport in semiconductor nanostructures. The results comprise microelectronic structures (MOSFETs, heterojunction devices) where the quantum effects count as well as nanometer-sized semiconductor structures.

Optimization of Inductive Coupling between Qbit Rings

We are investigating inductive coupling optimization schemes and quantization effects for microscopic metal rings as a possible basis for a quantum bit (qbit). Faraday induction is proposed to provide electromagnetic coupling between the rings, therefore acting as an information carrier. Quantizing this information will produce distinguishable ring states that can be denoted by |0〉 and |1〉, representing the logic states of the qbit. We have set up simulation case studies with the aim of reducing signal loss between the rings. Further, different quantization mechanisms are investigated analytically. A combination of the two concepts can in theory be used to design qbits, consisting of metal rings with I/O facilities.

Open Versus Closed Systems

Quantum transport in open systems is obscured by the fact that the number of carriers is not well defined. We cannot even define an expectation values for the number of particles, since particles permanently leaving the device, whereas others enter. Crudely speaking, we imagine a device connected to two or more leads, and that carriers enter the device by one lead and leave the device through another lead. This picture suggests that we can discriminate or distinguish particle by their location in space. However, quantum-mechanical treatment should avoid any attempt to distinguish identical particles and therefore it is not appropriate to associate some carriers with restricted parts (the leads) of the system and others with the device. Another drawback of open systems is that the Hilbert space (or classically, the phase space) cannot be constructed. Again, this shortcoming is not due to the fact that we do not know the number of particles, but to the fact that particles are leaving and entering the system.

Wigner Distribution Functions

A popular method to include quantum effects into the calculation of the characteristics of submicron devices is based on the Wigner functions. The underlying idea is that quantum transport can be catched into generalized transport equations that are in the spirit of the Boltzmann transport equation, suitable extended with terms that represent quantum corrections.

Ab-initio Electrodynamic Modeling of On-Chip Back-End Structures

The geometrical structure of electrodynamics is reviewed following the analogy with gravity. It is found that the vector potentials that represent magnetic fields can be identified as connections. As a consequence, these potentials should be assigned to the links of discretization grids. A ghost field is introduced to guarantee numerical stability in the solution scheme of solving electromagnetic field problems for interconnects and on-chip passives.

Ghost Field Gauging Used in Electrodynamic Simulation

Recently, a new approach was presented to determine the high-frequency response of on-chip passives and interconnects. The method solves the electric scalar and magnetic vector potentials in a prescribed gauge. The latter one is included by introducing an additional independent scalar field, whose field equation needs to be solved. This additional field is a mathematical aid that allows for the construction of a gauge-conditioned, regular matrix representation of the curl-curl operator acting on edge elements. This paper reports on the convergence properties of the new method and shows the first results of this new calculation scheme for VLSI-based structures at high frequencies.