Synopsis van het proefschrift
«Numerical methods for on-chip passive structures»
van E. Shcherbakov MSc
This research was partly financed by the European IST project CODESTAR. The main goal of the CODESTAR project was the development of numerical algorithms dedicated for the electromagnetic simulation of passive on-chip structures resulting in a small simulation network. First a detailed analysis of the test structure is carried out using an electromagnetic field solver. The outcome of the field solver is a full net list describing the detailed characteristics of the passive structure. This net list will be too large to be useful and therefore a systematic reduction of the net list must be done (i.e. reduced-order modeling). The resulting compact equivalent lumped-element model is inserted back into the full design scheme and the design cycle can be pursued. Parallel fabrication, characterisation and evaluation of dedicated test structures is carried out, in order to validate the CODESTAR-code. The matching between experimental and CODESTAR simulation results is the measure of the project success.
The research carried out for this thesis concentrated on numerical methods to aid the simulation of passive structures using EM methods. Complexity of the electromagnetic computations in 3-d have brought out the importance of extrapolation methods for the time stepping of wave equations. In this study, several new techniques are addressed to in search for the optimal one. First of all, one can increase accuracy of computations by using two staggered grids derived from the traditional Yee sampling. Rather than simply double the number of points, a special combination of two solutions computed simultaneously allows more effective use of computer capacity and do not limit the stability time step as strict as in the traditional FDTD. Usability of the similar method in frequency domain is also investigated and tested on few examples.
Following the line of searching effective solution methods an unconditionally stable three-dimensional finite-difference time domain method is investigated where the time step used is no longer restricted by stability but by accuracy. Unlike the conventional ADI algorithms the alternation is performed in respect to mixed coordinates rather than to each respective coordinate direction. Fourier mode analysis of the unconditional stability is shown and numerical results is shown and numerical results are presented to demonstrate the effectiveness and efficiency of the method.
Apart from the research described in the above on improved spatial and temporal discretization schemes, research has been done for some specific interconnect-related topics.