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AMC M
Bergische Universitat Wuppertal
Fachbereich Mathematik und Naturwissenschaften
Institute of Mathematical Modelling, Analysis andComputational Mathematics (IMACM)
Preprint BUW-IMACM 15/03
E.J.W. ter Maten, M. Gunther, P. Putek, P. Benner, L. Feng,J. Schneider, H.-G. Brachtendorf, K. Bittner, F. Deleu,
A. Wieers, R. Janssen, T. Kratochvıl, T. Gotthans, R. Pulch,Q. Liu, P. Reynier, W. Schoenmaker, P. Meuris, S. Schops,
H. De Gersem, C. Tischendorf, C. Strohm
nanoCOPS:Nanoelectronic COupled Problem Solutions
(Public Progress Report)
January 2015
http://www.math.uni-wuppertal.de
nanoCOPS: Nanoelectronic COupledProblem Solutions
AbstractThe FP7 project nanoCOPS derives new methodsfor simulation during development of designs of in-tegrated products. It covers advanced simulationtechniques for electromagnetics with feed-back cou-plings to/from electronic circuits, heat and stress.First progress is reported here.
IntroductionThe FP7 project nanoCOPS1 (Nanoelectronic COupled Prob-lem Solutions) did start on November 1, 2013. Leading ex-perts from industry and science in Europe develop and sharenew simulation methods to create and improve designs of in-tegrated products. It brings specialists together from variousfields: in circuit design, in the semiconductor development,in simulation techniques for electromagnetics and in appliedmathematics in research and in software development. In to-tal there are twelve research institutions and companies in theproject. The European Consortium supports the work underthe 7th Research Framework Programme with a total of 3.5million euros for three years.
The research project aims to solve complex problems in na-noelectronics. For example, in a so-called "Power-MOS" tran-sistor (see Fig. 1), an electronic component that in many prod-ucts shows up and which is responsible for the energy effi-ciency, electrical, thermal and stress interactions are key itemsfor simulations during the design phase. With nanoCOPSsuch new and accurate transistors can be developed in an effi-cient way. In addition a long lifetime performance in qualityis point of attention.
Figure 1: Typical layout of the power transistor (stretched invertical direction) showing its complex geometry.
In a second example, RF-circuitry in wireless communica-tion, for reducing signal interference in mobile products (tele-phone, wireless, mobile television, navigation, etc.), but alsoin pacemakers, one has to efficiently simulate signals withvery different frequencies, asking for multirate time integra-tion techniques that even can deal with analogue-digital sig-nals. Also here interaction occurs between electronic circuits,electromagnetic fields and heat production.
1http://www.fp7-nanocops.eu.
Figure 2: Block diagram of a low-IF or zero-IF receiver ar-chitecture with an image reject filter and a quadrature mixerstage. The schematic also displays the power spectral density(PSD) at different stages. Moreover it shows the realization ofthe image reject filter by a polyphase RC circuit and the sym-bolic representation of the crosstalk by a lumped LC network(reduced-order model).
In both examples the coupled interactions and the ef-fect of ageing of components are recent topics in research.NanoCOPS develops methods to predict probabilities in theperformance of the integrated functionality.
NanoCOPS combines advanced mathematical methods likemultirate time integration, co-simulation, uncertainity quan-tification and model reduction with methods to solve problemsin which electromagnetic effects, electronic circuits, heat de-velopment and material stress effects are coupled.
In nanoCOPS participate: Bergische Universität Wuppertal(Coordinator), Technische Universität Darmstadt, HumboldtUniversität zu Berlin, Ernst-Moritz-Arndt-Universität Greifs-wald, Max Planck Institut für Dynamik komplexer techni-scher Systeme in Magdeburg (all Germany), FachhochschuleOberösterreich in Hagenberg im Mühlkreis (Austria), BrnoUniversity of Technology (Czech Republic), Katholieke Uni-versiteit Leuven, MAGWEL NV (Leuven), ON Semiconduc-tor (Oudenaarde) (last three in Belgium), NXP Semiconduc-tors (Eindhoven, the Netherlands), and ACCO Semiconductor(Louveciennes, France). Hence, seven universities, one re-search institute, two major semiconductor companies and twosmall or medium enterprises (SMEs).
The importance of the industrial use casesThe carefully defined Industrial Use Cases in the nanoCOPSproject are of critical importance to MAGWEL in order to getthe solutions accepted in industry via a track record of silicon-demonstrated predictive quality. Comparison with experimen-tal results pinpoints to the range of application but also bringsinto the front stage weaknesses in model assumptions that canbe corrected for in a next iteration. Moreover, the IndustrialUse Cases introduce requirements for usability in a produc-tion environment that differs strongly from a research envi-ronment. Ease of use and robustness of the proposed solutionnow will be an important criterion to accept the tools for com-modity use.
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NXP Semiconductors observes an increasing complexityof wireless systems in terms of frequency bands, modula-tion schemes, signal paths and signal co-existence results ina serious design flow and thus becoming a design automa-tion (EDA) challenge. At the moment, no existing commer-cial EDA tools can perform simulations of single chip high-GHz modules. The current EDA tools and design flows arefar behind the requirements of circuit designers, leading to aproductivity gap. Within nanoCOPS the key ingredients (forMultirate/Multi-tone Simulation, for Model Order Reduction,for Reliability and for Uncertainty Quantification) will be de-veloped as prototype software and tested on Industrial UseCases to provide solutions to the gaps in the software suites ofcommercial vendors. NXP will use this to improve its designmethodology.
The industrial use cases solved by the new techniquesfrom nanoCOPS include practical and important contribu-tions applicable to approximately 30% of the products de-veloped by ON Semiconductor’s automotive business unit.Based on the findings in nanoCOPS, we look for extensionsof the tool capabilities to detect and assess important relia-bility problems including thermo-mechanical induced passi-vation cracks, bond-wire fusing and electro-migration. Earlydetection of such reliability risks are of utmost importance inthe ever increasing power densities that devices have to endureand the high quality and reliability requirements the automo-tive industry requires. Adequate detection and prediction willstrongly affect overall cost and time to market, key differen-tiators in the automotive market.
ObjectivesDesigns in nanoelectronics often lead to large-size simulationproblems and include strong feedback couplings. Industry de-mands the provisions of variability to guarantee quality andyield. It also requires the incorporation of higher abstractionlevels to allow for system simulation in order to shorten thedesign cycles, while at the same time preserving accuracy.
To meet market demands, the scientific challenges are to:
• create efficient and robust simulation techniques for stronglycoupled systems, that exploit the different dynamics of sub-systems and that allow designers to predict reliability and age-ing;
• include a variability capability such that robust design and op-timization, worst case analysis, and yield estimation with tinyfailures are possible (including large deviations like 6-sigma);
• reduce the complexity of the sub-systems while ensuring thatthe operational and coupling parameters can still be varied andthat the reduced models offer higher abstraction models that areefficient to simulate.
Achieving solutions to these challenges will have consider-able industrial impact. The overall objective of nanoCOPSis to advance a methodology for circuit and systems-levelmodelling simulation based on best practice rules to deal withcoupled electromagnetic field-circuit-heat problems aswell as coupled electro-thermal-stress problems that arisein nanoelectronic designs. The new methods developed willbe robust and allow for strong feedback coupling when inte-grating systems to increase the performance of both existingdevices and when integrating systems to produce new devices.
With the new techniques it will be possible to efficiently an-alyze the effects due to variability. Our methods are designedto solve reliability questions arising from manufacturabil-ity. They will facilitate robust design as well as enable worstcase analysis. They can also be used to study effects due toageing. Ageing causes variations in parameters over a long-term period, which cannot be predicted exactly and thus aretypically uncertain. In this project variability due to ageingwill be addressed. The challenges in doing this for an Inte-grated Circuit (IC) are that each device has its own electricaland thermal conditions, which are changing over time (age-ing). Here, each device has its own required life-time. Hence,one of the aims of this project is to construct probability dis-tributions or probability density functions, respectively, fromwhich the true statistics can be approximated at a sufficientdegree of accuracy.
The new Model Order Reduction techniques will be appli-cable to both coupled systems and parameterized subsystems.New design procedures for systems of components with vari-ous levels of abstraction will be developed.
In summary, our solutions are• to develop advanced co-simulation/multirate/monolithic tech-
niques, combined with envelope/wavelet approaches;• to produce new generalized techniques from Uncertainty Quan-
tification (UQ) for coupled problems, tuned to the statisticaldemands from manufacturability;
• to develop enhanced, parameterized Model Order Reductiontechniques for coupled problems and for UQ.
Figure 3: Schematic of a coupled problem (consisting oftwo sub-problems), including uncertainties. In nanoCOPS,those problems will be efficiently solved in time domain andprobability space with exploitation of their multirate (differ-ent time steps) and multiscale behaviour (different discretiza-tions). The discretized models will lead to different reducedmodels by techniques from MOR. Parameterized MOR willguarantee the ability to properly deal with the uncertainties inparameters, geometries, and coupling quantities.
The whole interplay of the various mathematical ap-proaches is graphically indicated in Fig. 3.All the new algorithms produced will be implemented andtransferred to the SME partner MAGWEL. Validation willbe conducted on industrial designs provided by our industrialpartners. These industrial end-users provide feedback duringthe project life-time and contribute to measurements andprovide material data and process data. A thorough com-parison to measurements on real devices is being made todemonstrate the industrial applicability.
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Project ProgressRecently the Project Prgress after 9 months was presented inBrussels. Here we give an impression.
FH Oberösterreich focused on the development of a toolwhich enables the co-simulation and monolithic/holistic sim-ulation of a circuit/device system or electrical-thermal systembased on the multirate envelope approach for different timescales. Different time scales arise from the co-simulation ofbaseband signals and modulated or bandpass signals, as wellas from electro-thermal couplings due to self-heating. Theapproach is based on the multirate envelope technique whichreformulates the system of ordinary Differential-AlgebraicEquations (DAEs) by a system of Multirate Partial DAEs(MPDAEs). By separating the time scales an enormous speed-up can be obtained. One generates a time solution that de-pends on two time parameters, representing the two differenttime scales. The actual solution can be reconstructed by aspecial curve over the colored surface in Fig. 4.
Figure 4: Multirate solution of a 3 MHz Colpitts oscillator.Shown is a surface solution as a function of two different timeparameters, one in milli seconds, the other in micro seconds.
The Universität Greifswald and the Bergische Univer-sität Wuppertal cooperated on methods for UncertaintyQuantification and applied the approaches to address varia-tions of material properties as well as in the geometry.For an electromagnetic-thermal coupled problem, includinga randomly varying electric conductivity, the mean and stan-dard variations could be efficiently determined for a time de-pendent ("transient") simulation, both for the currents in thetransistor as well as for the temperature, see Fig. 5.
As an additional example, because of prior knowledge, ro-bust topology optimization for a Permanent Magnet (PM) mo-tor was done (which is not of nano scale), where uncertaintiesof both iron and magnet material parameters in rotor poleswere considered. The model of a PM machine, with eitherinput variation or a material random field, is shown in Fig. 6.In this example, the quantities that are assumed as uncertainare the reluctivity of the iron and the PM poles as well as themagnetic permeability of the air-gap all with variations around10%. This example told us that geometrical variations are yetmore difficult to treat by the methods because of re-meshingof the problem.
TU Darmstadt, KU Leuven and ON Semiconductorworked on bond-wire modelling. Reporting is done in a sepa-rate contribution in this Newsletter.
Figure 5: Simplified Power Transistor for which the variabil-ity of currents and temperature, due to varying values of theelectric conductivity, was determined. This was done muchfaster than with normal Monte Carlo methods.
Figure 6: The concept of stochastic forward model for therobust topology optimization.
The Humboldt Universität zu Berlin and MAGWEL de-veloped and tested a Python-C++ interface for a coupled EM-circuit simulation, see Fig. 7. It allows a monolithic transientsimulation of lumped circuit equations (arising from the Mod-ified Nodal Analysis), coupled with the electromagnetic fieldequations (in vector potential formulation). The simulationhas as bottleneck a huge dimensional, non-symmetric Jaco-bian where standard direct and iterative linear solvers fail.However, one can exploit a certain Jacobian block structurethat allows a hybrid linear solving combining direct and itera-tive methods. Details were shown at ECMI-2014 in Taormina.
FIGURE 7: OVERVIEW FLOW FOR MONOLITHIC COUPLED SIMULATION.
MAGWEL and ON Semiconductor co-operated onelectro-thermal simulation in order to guarantee industrial ac-ceptance. An important highlight of this work is that the elec-
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trothermal simulation tool is very flexible concerning the var-ious device technologies since the nano-scale transistor archi-tecture is incorporated via compact models. Therefore, it ispossible to couple the large scale (millimeter) structures andthe small scale (sub-micron) of the finger architecture in a sin-gle simulation. The computation deals with the coupling ofthe electrical response and, moreover, the thermal response ina first-principle field solving. Fig. 8 illustrates today’s capa-bilities of the tool.
Figure 8: Analysis of a power MOS (left figure) resulting intoan asymmetric current density due to thermally induced con-ductance variations in the metallic interconnect (right figure).
In the nanoCOPS project, the main responsibilities of theMax Planck Institute in Magdeburg are to develop efficientparameterized/parametric MOR (pMOR) methods and tech-niques for fast simulation of electro-thermal coupled modelsand to develop pMOR methods for fast Uncertainty Quantifi-cation (UQ) of nanoelectronic, electro-thermal models withrandom variables or stochastic processes; and the compactnetlist generation based on the reduced order models. By sucha "netlist", these models can be used by a circuit simulator. Ina separate contribution in this Newsletter pMOR methods forelectro-thermal coupled models are described. The MP In-stitute has accumulated experience in MOR for fast UQ ofelectromagnetic problems, see Fig. 9, which will contribute todeveloping efficient parameterized MOR methods for fast UQof nanoelectronic, electro-thermal models in the nanoCOPSproject. Compact netlist generation will start once code inMATLAB for MOR is ready for transformation into C++.
Figure 9: Relative error of the expectation of the electricalfield in a coplanar waveguide.
The industrial partners NXP Semiconductors, ON Semi-conductor, and ACCO Semiconductors did provide threedata sets with measurements. One data set (NXP) involvedthe currents of a PMOS/NMOS transistor. The other two datasets (ON and ACCO) did include many material properties forall dies on a wafer and for multiple wafers, where sparse mea-surements appeared. F.i., NXP provided measurements on thecurrents of an NMOS and of a PMOS device for a certaintechnology. For the moment, the main task was to analyze thecorrelations between the two measured properties. Fig. 10 (a)shows these measurements. Fig. 10 (b) depicts random sam-ples drawn from an approximating normal distribution. Also
a 3-sigma ellipse is shown illustrating the mean and the co-variance matrix. Multivariate normal distributions are a spe-cial class of "elliptically contoured distributions". The datawas analyzed statistically by Universität Greifswald and Ber-gische Universiät Wuppertal. We observed that the measure-ments have fatter tails.
Figure 10: Measurements in the NXP example (a) and randomsamples taken from an approximating normal distribution (b).The variables x1 and x2 are the currents of an NMOS and of aPMOS device, respectively. In both cases also a 3σ ellipse isshown.
Additionally NXP Semiconductors did compile a large setof test examples. For an example, see Fig 11.
Figure 11: An 8-shaped inductor, an excellent test case todemonstrate the quality of the software for EM solving.
The Brno University of Technology, together with ONSemiconductor and ACCO Semiconductor, did set up aplan for measurements. With ON Semiconductor this cur-rently concentrates on the bond wire testing. The encapsulatedbond wires have already been delivered and the individualbond wires are just to be tested at room temperature. Beforethat, some informative x-rays have been acquired, as visible inFig. 12 (left). The location of fusing gaps will be monitoredafter the test of the package is completed. Each measurementsequence will be controlled by a program, which begins withkeeping constant the current and frequency, defining a numberof the pulses (in descending order) and after each pulse trainis finished, the procedure loop ends with adjusting the dutycycle.With ACCO Semiconductor the set-up of measuring parts ofa Power Amplifier has been started.
DisseminationAn extensive list of presentations at Conferences and Work-shops and a first list of scientific papers can be found online on
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Figure 12: Left: X-rays of available SOIC24 samples (ONSemiconductor) with bond wires. Right: Single-cell exper-imental measurement (Brno UT), input pulses (upper trace)and voltage drops across sensing resistor (lower trace) andfour wire currents.
the project website, http://www.fp7-nanocops.eu. Here,we first summarize the Outreach at ECMI-2014, ACOMEN-2014, and SCEE-2014 conferences.
• At ECMI-2014, 18th European Conference on Mathematics forIndustry, June 9-13, 2014, Taormina, Sicily, eleven presenta-tions have been given by nanoCOPS partners. As part of the1st nanoCOPS Workshop, a special Minisymposium "Simula-tion Issues for Nanoelectronic Coupled Problems" was orga-nized with five public talks.
• At ACOMEN-2014, 6th International Conference on AdvancedComputational Methods in Engineering, June 23-28, 2014,Ghent, Belgium, nanoCOPS partners were involved in five pre-sentations.
• At SCEE-2014, Scientific Computing in Electrical Engineer-ing, July 22-25, 2014, Wuppertal, Germany, twelve nanoCOPSpresentations were given, of which one from partner TU Darm-stadt was an Invited Talk.
We also recall a presentation at SIAM UQ-2014, Conf. on Un-certainty Quantification, March 31 - April 3, 2014, Savannah,Georgia, USA (which is major conference in this field). Al-ready two papers have been published in IEEE Journals. Onepaper did recently appear in COMPEL and another one willappear soon in the International Journal for Uncertainty Quan-tification. An online publication was in Radioengineering.For the (peer reviewed) ECMI-2014 proceedings several con-tributions have been submitted. Submissions to proceedingsACOMEN-2014 and SCEE-2014 are currenty being made.
Acknowledgement
Figure 13: The Collaborative Project nanoCOPS, Nano-electronic COupled Problems Solutions, is supported by theEuropean Union in the FP7-ICT-2013-11 Program underGrant Agreement Number 619166. Website: http://www.fp7-nanocops.eu.
Conclusion and next PhaseNanoCOPS is ready for entering a new phase in the project:now emphasis will be put on implementation in C++ that willhave to be glued into library modules. The software will allowfor interaction with the existing software of MAGWEL. Dur-ing this phase the algorithms will be further developed basedon test and validation outcomes. Comparison will be madeagainst measurements.
E. Jan W. ter Maten, Michael Günther, Piotr PutekBergische Universität WuppertalGaußstrasse 20, D-42119 WuppertalGermany{terMaten,Guenther,Putek}@math.uni-wuppertal.de
Peter Benner, Lihong Feng, Judith SchneiderMax Planck Institut für Dynamik komplexer technischerSysteme, Magdeburg, Germany{Benner,Feng,Judith.Schneider}@mpi-magdeburg.mpg.de
Hans-Georg Brachtendorf, Kai BittnerFH Oberösterreich, Hagenberg im Mühlkreis, Austria{Hans-Georg.Brachtendorf,Kai.Bittner}@fh-hagenberg.at
Frederik Deleu, Aarnout WieersON Semiconductor, Oudenaarde, Belgium{Frederik.Deleu,Aarnout.Wieers}@onsemi.com
Rick JanssenNXP Semiconductors, Eindhoven, the [email protected]
Tomás Kratochvíl, Tomás GötthansBrno University of Technology, Czech Republic{KratoT,Gotthans}@feec.vutbr.cz
Roland Pulch, Qingzhe LiuErnst-Moritz-Arndt-Universität Greifswald, Germany{PulchR,LiuQ}@uni-greifswald.de
Pascal ReynierACCO Semiconductor, Louveciennes, [email protected]
Wim Schoenmaker, Peter MeurisMAGWEL NV, Leuven, Belgium{Wim.Schoenmaker,Peter.Meuris}@magwel.com
Sebastian Schöps, Herbert De GersemTechnische Universität Darmstadt, [email protected], [email protected]
Caren Tischendorf, Christian StrohmHumboldt Universität zu Berlin, Germany{Caren.Tischendorf,StrohmCh}@math.hu-berlin.de
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