Model Reduction for Circuit Simulation

by Benner, Peter; Hinze, Michael; ter Maten, E. Jan W.

• ISBN13: 9789400700888
• ISBN10: 9400700881
• Format: Hardcover
• Copyright: 2011-03-29
• Publisher: Springer Verlag

Summary

Simulation plays a major role in computer aided design of integratedcircuits (ICs). Mathematical models describe the dynamical processesand interactions of electrical devices. Verification of a circuit'sbehaviour by means of solving these model equations in time andfrequency domain is a mandatory task in the design process. Thestructures' sizes are decreasing, the packing density increases andso do the driving frequencies. This requires to use refined models andtake into account secondary, parasitic effects. The very highdimensional problems that emerge in this way may be solvable with the help of computer algebra in an unreasonable amount of timeonly. Clearly, this conflicts with the short time-to-market demands inindustry. Model-Order-Reduction (MOR) presents a way out of thisdilemma. Redundancies are resolved, less relevant quantities arereplaced by the most significant ones. In this way, the problem'scomplexity is reduced, keeping the main characteristics. Solving lowerdimensional problems one can get statements on the circuit'sperformance more quickly. With Model Reduction for Circuit Simulation we survey the state of the art in the challenging research field of model order reduction for ICs, and also address its future research directions. Special emphasis is taken on aspects stemming from miniturizations to the nano scale. Contributions cover complexity reduction using e.g., balanced truncation, Krylov-techniques or POD approaches. For semiconductor applications a focus is on generalising current techniques to differential-algebraic equations, on including design parameters, on preserving stability, and on including nonlinearity by means of piecewise linearisations along solution trajectories (TPWL) and interpolation techniques for nonlinear parts.Furthermore the influence of interconnects and powergrids on the physical properties of the device is considered, and also top-down system design approaches in which detailed block descriptions are combined with behavioural models.  MOR faces the same requests as those appearing with Response Surface Modeling (RSM) techniques for Robust Design, with emphasis on parameterization, parameter screening, and nonlinearity. Further topics consider MOR and the combination of approaches from optimization and statistics, and the inclusion of PDE models with emphasis on MOR for the resulting Partial Differential Algebraic systems. It is a proven fact that semiconductor industries see MOR as akey tool for simulations of nano-technology designs, with high demandof well educated experts in the field. This implies that timely education is needed. The current number of books in this area is very limited, so that this volume helps to fill a gap in providing the state of the art material, and to stimulate further research in the area of MOR for ICs. Furthermore, the methods which currently are being developed have also relevance in other application areas such as mechanical multibody systems, and systems arising in chemistry and to biology. Furthermore, Model Reduction for Circuit Simulation  reflects and documents the vivid interaction between three active research projects in this area, namely the EU-Marie Curie Action ToK project O-MOORE-NICE (members in Belgium, The Netherlands and Germany), the EU-Marie Curie Action RTN-project COMSON (members in The Netherlands, Italy, Germany, and Romania), and the German federal project System reduction in Nano electronics (SyreNe).