Impressum |
MS4N balls
Vielen Dank.
MoreSim4Nano Logo
Mathematik für Innovationen in Industrie und Dienstleistungen
MoreSim4Nano> SP 5 (Kaiserslautern)

Research network within the BMBF funded program
Mathematics for Innovations in Industry and Services


Subproject 5: Mixed numeric/symbolic MOR-methods for nanoelectronic systems regarding process variations

    Subproject leader:

    Dr. Patrick Lang, Fraunhofer-Institut für Techno- und Wirtschaftsmathematik (ITWM) Kaiserslautern

    With the trend from micro- to nanoelectronics the modeling of analog circuits via nominal systems has reached its limit. In contrast to the simulations of the nominal system, the neglect of process variations in the production and handling of semiconductor devices leads to a drastic increase of the percentage of produced circuits whose characteristics are beyond their specifications. To estimate the deviation of the circuit characteristic from the nominal one, often Monte-Carlo simulations are used, but these are computationally expensive or not applicable for complex systems and large parameter spaces. Therefore the two industry partners X-FAB, producer of nanoscale semiconductor devices, and MunEDA, provider of EDA-software, are very interested in alternative simulation techniques, which yield a reliable and efficient prognosis of the device behavior under parameter deviations.

    Starting from a netlist description, mixed symbolic/numeric reduction methods are used to generate a reduced behavioral model. The main focus of the project is the preservation of the physical parameters as well as the statistical validation of their effects onto the system behavior. The tool Analog Insydes for design and reduction of analog circuits which is developed at the ITWM is used for the realization of this work.

    Due to the fact that the model order reduction of systems with parameter uncertainties via Monte-Carlo methods leads to large computationally effort, alternative methods will be developed to yield a significant acceleration of the model order reduction process. Thereby sensitivity information of direct or adjoint sensitivity analysis will be used and a parallelization of several time consuming sub-steps will be realized. The connection of sensitivities with the system equations leads to a significant increase of the DAE so that its solution needs an efficient and robust method. Thereby structural similarities between the equations of the nominal system and the derived sensitivity equations will be used to transform the system in a form, that can be handled efficiently by DAE-solvers.


    • [Months 1-4] Verification of concept of parameter tolerances in simulation and MOR, identification of computationally intensive reduction steps.

    • [Months 5-18] Preprocessing methods for extended DAE-systems based on nominal systems and model sensitivities.

    • [Months 16-28] Hierarchical MOR regarding parameter variations.

    • [Months 22-34] Parallelization of MOR-methods, in particular reference generation, ranking method and error determination.

    • [Months 32-36] Application and verification of the methods by means of technology examples of the X-FAB, comparing the performance with simulation methods of MunEDA.
Back to TopTop
Judith Schneider, judith.schneider@mpi-magdeburg.mpg.de