- General information
- Subprojects
- SP 6 (Hamburg)
- Partners
- Activities

Mathematics for Innovations in Industry and Services

--MoreSim4Nano--

- Subproject leader:
**Prof. Dr. Michael Hinze, University of Hamburg**

This subproject uses the ansatz, to provide parametric robust homologous models for nonlinear nano-electric structures with methods of simulation based model reduction (POD, RB method) using suitable mathematical models. Homologous models for a nano electric structure are obtained using simulations of the full nonlinear coupled model (GMOR). Thus the adaption of the approximation level of the structure simulation to the precision of the network simulation is left to the MOR method. Due to the small scale and the high density of conductors there is need for the provision for quantum effects and EM effects where appropriate.

The whole system consists of a network of nano electrial structures. Depending on scale, structures are described by either instationary drift diffusion (DD) or quantum drift diffusion (QDD) models. EM effects are included if necessary using Maxwells equations. Currently solving the resulting highly nonlinear PDAE systems is a great challenge. Starting point are numerical methods for the simulation of circuits with highly resolved 2-dimensional DD models. Simulation based reduction with snapshot POD is used, which in the project SyreNe have promised results for MOR nonlinear circuits with semiconductors. Combined with greedy methods this enables to construct robust homologous models for the relevant frequency domain.

The parametric reduction method will be designed for networks with some nano electric structures.

Validation on a basic circuit:

- quantum effects, instationary QDD model.

extend the syrene simulation software QDD. - instationary DD model of EM effects using maxwells equations

This gives information about principle options of the MOR for coupled systems and allows to compare the ansatz from this SP and the SP4 and SP5.

Milestones:

- [Months 1-12] Mathematical modelling of circuits with nanoelectrical structures with regard to EM-effects, problem-adapted scaling and discretization of the resulting PDAE systems.
- [Months 7-24] Parametric MOR with snapshot POD and greedy approach for a prototypic nanoelectrical structure, described with a 1D QDD model.
- [Months 18-32] Parametric MOR for a basis network with prototypic semiconductor structures will be modelled with an instationary DD model with coupling of EM effects with Maxwell equations.
- [Months 25-36] Parametric MOR for a basic network with prototypic semiconductor structures, with regard to quantum and EM effects simultaneous where appropriate.
- [Months 13-36] Analysis of PDAE systems and transfer of the a posteriori analysis to the residual based greedy approach of the nonlinear systems where appropriate.

- quantum effects, instationary QDD model.