Modelling & Evaluation of EM Effect of Metal Fills used in IC Technology

Abstract

Nowadays, recent Integrated Circuit Technology demands a minimum metal fill inclusion across the entire die of each functional layer to have uniform planarity. It is challenging to numerically simulate the real structure using Electromagnetic (EM) solvers because the mesh size of an EM solver is inversely proportional to the number of vertices in the layout and the inclusion of these metal fills has a significant impact on these vertices and increases mesh size. It is important to understand the metal fills do have an impact on the RF performance of the component and the impact becomes stronger as the frequency increases due to the parasitics and hence we cannot neglect it. Therefore, a Design Flow Methodology is studied and analyzed to take into account the effect of metal fills without penalty in accuracy and simulation time.

The second part of the thesis focuses on two different approaches that can be used to extract the complex parameters providing the electromagnetic response of the layers, i.e. electrical permittivity and magnetic permeability. First, we describe the Quasistatic approach to extract the epsilon parameters from the capacitance and inductance. After, describing some of the limitations of this approach we focus on the Oblique Incidence Method as reported in the literature to extract the complex epsilon tensor parameters.

The third part of the thesis looks into the Design Flow Methodology that embeds the Oblique Incidence Method into the design flow for 3D EM solvers to take into account the effect of metal fills. The 2.5D EM solver takes into account a scalar number which is less accurate and hence an insight of how the solution from the Oblique Incidence Method can used to extract a scalar number for the effective parameters and therefore be implemented in 2.5D EM tools is discussed.

The fourth part of the thesis shows the validation of the Oblique Incidence Method for the 3D EM tool for two test cases which are wave propagating structure and lumped structure namely Grounded Coplanar Waveguide (CPWG) and Stacked Transformer. Validation of the Scalar Number Approaches for the 2.5D EM Tool was done for the CPWG structure.

Finally, a brief study on the Design Based Approach is conducted with different metal fill shapes and alignment by using the Oblique Incidence Method by making use of 3D EM tool. This approach provides a better understanding of the epsilon variations for different metal fill shapes and that for less epsilon variations, an accurate scalar number value can be extracted to enable 2.5D EM simulations with improved accuracy.