[60]  Clemens Heitzinger and Leila Taghizadeh. The stochastic driftdiffusionPoisson system for modeling nanoscale devices and a multilevel MonteCarlo method. In Proc. 24th International Conference on Transport Theory (ICTT 2015), Taormina, Italy, 711 September 2015. Accepted for publication. [ bib ] 
[59]  Clemens Heitzinger and Leila Taghizadeh. Existence and uniqueness for the StokesNernstPlanckdriftdiffusionPoisson system for modeling nanowire sensors and nanopores. In Proc. 24th International Conference on Transport Theory (ICTT 2015), Taormina, Italy, 711 September 2015. Accepted for publication. [ bib ] 
[58]  Amirreza Khodadadian and Clemens Heitzinger. The signaltonoise ratio due to biological noise in fieldeffect sensors calculated using the stochastic Poisson equation and polynomialchaos expansion. In Proc. 13th US National Congress on Computational Mechanics, San Diego, CA, 2630 July 2015. Accepted for publication. [ bib ] 
[57]  Gregor MitschaEibl, Andreas ButtingerKreuzhuber, Gerhard Tulzer, and Clemens Heitzinger. Nonlinear coupling of the DriftDiffusionPoisson and Stokes systems for nanopore simulations. In Proc. 13th US National Congress on Computational Mechanics, San Diego, CA, 2630 July 2015. Accepted for publication. [ bib ] 
[56]  Amirreza Khodadadian and Clemens Heitzinger. Ionic currents through transmembrane proteins calculated by a transport equation for confined structures. In Proc. 4th International Conference on Computational and Mathematical Biomedical Engineering (CMBE 2015), Cachan, France, 29 June  1 July 2015. Accepted for publication. [ bib ] 
[55]  G. Tulzer, C. Ringhofer, and C. Heitzinger. Simulation of the currents through nanopore sensors. In Proc. VI International Conference on Coupled Problems in Science and Engineering (Coupled Problems 2015), Venice, Italy, 1820 May 2015. Accepted for publication. [ bib ] 
[54]  Gerhard Tulzer and Clemens Heitzinger. Noise and fluctuations in nanowire biosensors. In Proc. 8th Vienna International Conference on Mathematical Modelling (MATHMOD 2015), pages 761765, Vienna, Austria, February 2015. [ bib  PDF ] 
[53]  Clemens Heitzinger and Gerhard Tulzer. Julia and the numerical homogenization of PDEs. In Proceedings of the First Workshop for High Performance Technical Computing in Dynamic Languages (HPTCDL 2014), pages 3640, New Orleans, LA, November 2014. IEEE Press. [ bib  DOI  at publisher ] 
[52]  Amirreza Khodadadian and Clemens Heitzinger. Using the stochastic PoissonBoltzmann equation to quantify noise in nanowire bio and gas sensors. In Proc. 11th World Congress on Computational Mechanics (WCCM XI), pages A4187/12, Barcelona, Spain, 2025 July 2014. [ bib ] 
[51]  Clemens Heitzinger and Christian Ringhofer. Transport in confined structures as a multiscale problem and numerical results for nanopores. In Proc. SIAM Annual Meeting 2014, page 6, Chicago, IL, 711 July 2014. [ bib ] 
[50]  Clemens Heitzinger and Gerhard Tulzer. Various strategies for the numerical stochastic homogenization of the stochastic Poisson and Helmholtz equations. In Proc. SIAM Annual Meeting 2014, page 15, Chicago, IL, 711 July 2014. [ bib ] 
[49]  Clemens Heitzinger. Transport through confined structures as a multiscale problem. In Oberwolfach Reports, number 2 in volume 11, pages 16501653, 2014. [ bib  DOI ] 
[48]  Clemens Heitzinger. The stochastic Poisson and PoissonBoltzmann equations applied to quantifying noise and fluctuations in nanoscale sensors. In Proc. 18th European Conference on Mathematics for Industry (ECMI 2014), pages 150151, Taormina, Italy, 913 June 2014. [ bib ] 
[47]  Gerhard Tulzer and Clemens Heitzinger. MonteCarlo and quasiMonteCarlo approaches for the numerical stochastic homogenization of elliptic partial differential equations. In Proc. 11th International Conference on Monte Carlo and QuasiMonte Carlo Methods in Scientific Computing (MCQMC2014), page 168, Leuven, Belgium, 611 April 2014. [ bib ] 
[46]  Amirreza Khodadadian and Clemens Heitzinger. QuasiMonteCarlo methods for the linear and nonlinear stochastic PoissonBoltzmann equations. In Proc. 11th International Conference on Monte Carlo and QuasiMonte Carlo Methods in Scientific Computing (MCQMC2014), page 167, Leuven, Belgium, 611 April 2014. [ bib ] 
[45]  Clemens Heitzinger and Amirreza Khodadadian. Uncertainty quantification in nanowire sensors using the stochastic nonlinear PoissonBoltzmann equation. In Proc. SIAM Conference on Uncertainty Quantification (SIAM UQ14), page 87, Savannah, Georgia, USA, 31 March  3 April 2014. [ bib ] 
[44]  Gerhard Tulzer, Stephan Steinhauer, Elise Brunet, Giorgio Mutinati, Anton Köck, and Clemens Heitzinger. Noiselevel analysis of metaloxide nanowire gassensor signals for selective gas detection. In Proc. International Conference on OneDimensional Nanomaterials (ICON 2013), page 161, Annecy, France, 2326 September 2013. [ bib ] 
[43]  Amirreza Khodadadian and Clemens Heitzinger. Simulation of nanowire sensors using the stochastic PoissonBoltzmann equation. In Proc. 2nd International Conference on Mathematical Modeling in Physical Sciences (ICMSQUARE 2013), pages 1920, Prague, Czech Republic, 15 September 2013. [ bib ] 
[42]  Clemens Heitzinger. Deterministic and stochastic homogenization problems with new applications in nanotechnology. In Oberwolfach Reports, number 1 in volume 10, pages 823826, 2013. [ bib  DOI ] 
[41]  Gerhard Tulzer, Stefan Baumgartner, Elise Brunet, Giorgio Mutinati, Stephan Steinhauer, Anton Köck, and Clemens Heitzinger. Modeling H_{2} adsorption processes at SnO_{2} nanowire surfaces: Parameter estimation and simulation. In Proc. 6th International Conference on Biomedical Electronics and Devices (BIODEVICES 2013), pages 265268, Barcelona, Spain, 1114 February 2013. [ bib  PDF ] 
[40]  Gerhard Tulzer, Stefan Baumgartner, Elise Brunet, Giorgio Mutinati, Stephan Steinhauer, Anton Köck, and Clemens Heitzinger. Characteristics of CO and H_{2} detection with single nanowire gas sensors. In Proc. 5th Szeged International Workshop on Advances in Nanoscience 2012 (SIWAN 2012), pages 3637, Szeged, Hungary, 2427 October 2012. [ bib ] 
[39]  Gerhard Tulzer, Stefan Baumgartner, Elise Brunet, Giorgio C. Mutinati, Stephan Steinhauer, Anton Köck, and Clemens Heitzinger. Inverse modeling of CO reactions at SnO_{2} nanowire surfaces for selective detection. In Proc. Eurosensors XXVI 2012, pages W2C4/14, Krakow, Poland, 912 September 2012. (Most prestigious European sensors conference.). [ bib ] 
[38]  Stefan Baumgartner and Clemens Heitzinger. Modeling and simulation of nanowire fieldeffect transistors. In Proc. Computational Methods in Applied Mathematics (CMAM 2012), pages 1213, Berlin, Germany, 30 July  3 August 2012. [ bib ] 
[37]  Gerhard Tulzer, Stefan Baumgartner, Elise Brunet, Giorgio Mutinati, Stephan Steinhauer, Anton Köck, and Clemens Heitzinger. Inverse modeling of CO adsorption processes at semiconductor nanowire surfaces for selective gas detection. In Proc. Computational Methods in Applied Mathematics (CMAM 2012), pages 5455, Berlin, Germany, 30 July  3 August 2012. [ bib ] 
[36]  Gerhard Tulzer, Stefan Baumgartner, Elise Brunet, Giorgio C. Mutinati, Stephan Steinhauer, Anton Köck, and Clemens Heitzinger. Calculation of gas surfacereaction parameters at SnO_{2} nanowire surfaces. In Proc. 9th International Conference on Nanosciences and Nanotechnologies (NN12), page 59, Thessaloniki, Greece, 36 July 2012. [ bib ] 
[35]  Stefan Baumgartner, Martin Vasicek, and Clemens Heitzinger. Parallel simulation of nanowire fieldeffect transistors. In Proc. 15th International Workshop on Computational Electronics (IWCE 15), pages 245246, Madison, WI, May 2012. [ bib ] 
[34]  Elise Brunet, Gerhard Tulzer, Stephan Steinhauer, Giorgio Mutinati, Anton Köck, Martin Vasicek, and Clemens Heitzinger. Fabrication and simulation of SnO_{2} nanowire gas sensors. In Proc. 3rd International Congress on Nanotechnology in Medicine and Biology (BioNanoMed 2012), page 8, Krems, Austria, March 2012. [ bib ] 
[33]  Stefan Baumgartner, Martin Vasicek, and Clemens Heitzinger. Selfconsistent simulation of nanowire fieldeffect biosensors. In Proc. 3rd International Congress on Nanotechnology in Medicine and Biology (BioNanoMed 2012), page C6, Krems, Austria, March 2012. [ bib ] 
[32] 
Stefan Baumgartner, Martin Vasicek, and Clemens Heitzinger.
Advanced modeling and simulation of nanowire fieldeffect sensors.
In Proc. 7th Vienna International Conference on Mathematical
Modelling (MATHMOD 2012), pages 240245, Vienna, Austria, February 2012.
[ bib 
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A 3d simulator for nanowire fieldeffect sensors and transistors including fast varying charge concentrations at an interface is presented. This simulator is based on a system of partial differential equations calculating the electrostatic potential of the whole device and the charge concentrations in the semiconducting nanowire. Therefore, three domains need to be modeled. The nanowire is described by the driftdiffusionPoisson system, the PoissonBoltzmann equation is used for the simulation of an aqueous solution, and the Poisson equation holds in the remaining oxide. Such devices can be used as gas sensors, and by functionalization of the nanowire surface, i.e., by attaching probe molecules, they can also be used for the detection of biomolecules in aqueous solutions. Binding of target molecules to the surface induces a field effect due to changes of charges in a small layer around the surface. This effect is responsible for the sensor response and hence is of paramount importance. A homogenization method resulting in two jump conditions is implemented which splits the computation into the charge of the boundary layer and into the remaining device. In order to take into account the geometry of the devices, 3d simulations are necessary and hence a parallelization technique has been developed. To include the jump conditions of the homogenization method, a novel finiteelement tearing and interconnecting (FETI) method has been developed. With this simulator it is possible to solve the three dimensional and heterogeneous system of partial differential equations with discontinuities in feasible time using realizable computer power. As a result, sensitivity in terms of geometrical and physical properties can be predicted and sensors can be improved.

[31]  Stefan Baumgartner, Martin Vasicek, and Clemens Heitzinger. Analysis of fieldeffect biosensors using selfconsistent 3D driftdiffusion and MonteCarlo simulations. In Proc. Eurosensors XXV 2011, pages 1275/14, Athens, Greece, September 2011. (Most prestigious European sensors conference.). [ bib  PDF ] 
[30]  Stefan Baumgartner, Martin Vasicek, Alena Bulyha, Nathalie Tassotti, and Clemens Heitzinger. Design investigations of nanowire fieldeffect biosensors using selfconsistent 3d driftdiffusion and MonteCarlo simulations. In Proc. 8th International Conference on Nanosciences and Nanotechnologies (NN11), page 88, Thessaloniki, Greece, July 2011. [ bib  PDF ] 
[29] 
Thomas Windbacher, Viktor Sverdlov, Siegfried Selberherr, Clemens Heitzinger,
Norbert Mauser, and Christian Ringhofer.
Simulation of fieldeffect biosensors (BioFETs) for
biotinstreptavidin complexes.
In AIP Conf. Proc. (Physics of Semiconductors: 29th
International Conference on the Physics of Semiconductors), volume 1199,
pages 507508. AIP, January 2010.
[ bib 
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Biologically sensitive fieldeffect transistors (BioFETs) are a promising technology for detecting pathogens, antigenantibody complexes, and tumor markers. A BioFET is studied for a biotinstreptavidin complex. Biotinstreptavidin is used in detection and purification of various biomolecules. The link between the Angstrom scale of the chemical reaction and the micrometer scale of the field effect device is realized by homogenized interface conditions.

[28] 
Clemens Heitzinger, Norbert Mauser, Christian Ringhofer, Yang Liu, and
Robert W. Dutton.
Modeling and simulation of orientationdependent fluctuations in
nanowire fieldeffect biosensors using the stochastic linearized
PoissonBoltzmann equation.
In Proc. Simulation of Semiconductor Processes and Devices
(SISPAD 2009), pages 8690, San Diego, CA, USA, September 2009.
(Acceptance rate 57%.).
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We use the stochastic linearized PoissonBoltzmann equation to model the fluctuations in nanowire fieldeffect biosensors due to changes in the orientation of the biomolecules. Different orientations of the biomolecules with respect to the sensor surface due to Brownian motion have different probabilities. The probabilities of the orientations are calculated from their electrostatic free energy. The structure considered here is a cross section through a rectangular silicon nanowire lying on a an oxide surface with a backgate contact. The oxide surface of the nanowire is functionalized by biomolecules in an electrolyte with an electrode. Various combinations of PNA (peptide nucleic acid), singlestranded DNA, and doublestranded DNA are simulated to discuss the various states of a DNA sensor. A chargetransport models yields the current through the transducer that compares well with measurements.

[27]  M. Punzet, H. Karlic, F. Varga, C. Heitzinger, and D. Baurecht. Quantitative evaluation of surface modifications used for BioFETs by FTIRATR spectroscopy. In Proc. 4th International Workshop on Vibrational Spectroscopy of Thin Films, Potsdam, Germany, 35 June 2009. [ bib ] 
[26] 
Thomas Windbacher, Viktor Sverdlov, Siegfried Selberherr, Clemens Heitzinger,
Norbert Mauser, and Christian Ringhofer.
Study of the properties of biotinstreptavidin sensitive BioFETs.
In Proc. International Conference on Biomedical Electronics and
Devices (BIODEVICES 2009), pages 2430, Porto, Portugal, January 2009.
[ bib 
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In this work the properties of a biotinstreptavidin BioFET have been studied numerically with homogenized boundary interface conditions as the link between the oxide of the FET and the analyte which contains the biosample. The biotinstreptavidin reaction pair is used in purification and detection of various biomolecules; the strong streptavidinbiotin bond can also be used to attach biomolecules to one another or onto a solid support. Thus this reaction pair in combination with a FET as the transducer is a powerful setup enabling the detection of a wide variety of molecules with many advantages that stem from the FET, like no labeling, no need of expensive readout devices, the possibility to put the signal amplification and analysis on the same chip, and outdoor usage without the necessity of a lab.

[25] 
Yang Liu, Klas Lilja, Clemens Heitzinger, and Robert W. Dutton.
Overcoming the screeninginduced performance limits of nanowire
biosensors: a simulation study on the effect of electrodiffusion flow.
In IEDM 2008 Technical Digest, pages 491494, San Francisco,
CA, USA, December 2008.
(Most prestigious electrondevices conference; acceptance rate
˜33%.).
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Devicelevel simulation capabilities have been developed to selfconsistently model the Sinanowire (NW) biosensor systems. Our numerical study demonstrates that by introducing electrodiffusion current flow in the electrolyte solutions, the electrostatic screening of the biological charge can be significantly suppressed; an improvement of the sensed signal strength by more than approximately 10 times is indicated. Based on such an operation principle, the screeninginduced performance limits on SiNW biosensors can be overcome.

[24] 
Thomas Windbacher, Viktor Sverdlov, Siegfried Selberherr, Clemens Heitzinger,
Norbert Mauser, and Christian Ringhofer.
Simulation of fieldeffect biosensors (BioFETs).
In Proc. Simulation of Semiconductor Processes and Devices
(SISPAD 2008), pages 193196, Hakone, Japan, September 2008.
(Acceptance rate 70%.).
[ bib 
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In this paper a bottomup approach for modeling fieldeffect Biosensors (BioFETs) is developed. Starting from the given positions of charged atoms, of a given molecule, the charge and the dipole moment of a single molecule are calculated. This charge and dipole moment are used to calculate the mean surface density and mean dipole moment at the biofunctionalized surface, which are introduced into homogenized interface conditions linking the Angstromscale of the molecule with the micrometerscale of the FET. By considering a singlestranded to doublestranded DNA reaction, we demonstrate the capability of a BioFET to detect a certain DNA and to resolve the DNA orientation.

[23] 
Otmar Ertl, Clemens Heitzinger, and Siegfried Selberherr.
Efficient coupling of MonteCarlo and levelset methods for
topography simulation.
In Proc. Simulation of Semiconductor Processes and Devices
(SISPAD 2007), pages 417420, Vienna, Austria, September 2007.
(Acceptance rate 55%.).
[ bib 
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We have developed a topography simulation method which combines advanced levelset techniques for surface evolution with Monte Carlo flux calculation. The result is an algorithm with an overall complexity and storage requirement scaling like O(N logN) with surface disretization. The calculation of particle trajectories is highly optimized, since spatial partitioning is used to accelerate ray tracing. The method is demonstrated on Si etching in SF_{6}/O_{2} plasma.

[22] 
Sriraman Damodaran, Selvakumaran Vadivelmurugan, QuocThai Do, Clemens
Heitzinger, Yang Liu, Robert Dutton, and Gerhard Klimeck.
Investigation of the conductance of silicon nanowire biosensors using
the 2D driftdiffusion model.
In Proc. 10th NSTI Nanotech Conference 2007 (NSTI Nanotech
2007), pages 1374/13, Santa Clara, CA, USA, May 2007.
[ bib 
PDF ]
Experiments for silicon biosensors with gate lengths in the range of 200nm to 500nm have not been extensively carried out. In this paper, simulations were performed for gate lengths proportionally smaller and greater than regular experimental gate lengths. The sensitivity of the biosensors was simulated using a 2D driftdiffusion model in cylindrical coordinates using the Prophet simulator. In this study simulated conductance results and the respective experimental values are compared. The good agreement between simulation and experiment enables us to predict and optimize the sensitivity of the DNA sensors.

[21] 
Shaikh Ahmed, Muhammad Usman, Clemens Heitzinger, Rajib Rahman, Andrei Schliwa,
and Gerhard Klimeck.
Symmetry breaking and fine structure splitting in zincblende quantum
dots: Atomistic simulations of longrange strain and piezoelectric field.
In AIP Conf. Proc., volume 893, pages 849850. AIP, April
2007.
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Electrons and holes captured in selfassembled quantum dots (QDs) are subject to symmetry breaking that cannot be represented in with continuum material representations. Atomistic calculations reveal symmetry lowering due to effects of strain and piezoelectric fields. These effects are fundamentally based on the crystal topology in the quantum dots. This work studies these two competing effects and demonstrates the fine structure splitting that has been demonstrated experimentally can be attributed to the underlying atomistic structure of the quantum dots.

[20] 
Muhammad Usman, Shaikh Ahmed, Marek Korkusinski, Clemens Heitzinger, and
Gerhard Klimeck.
Strain and electronic structure interactions in realistically scaled
quantum dot stacks.
In AIP Conf. Proc., volume 893, pages 847848. AIP, April
2007.
[ bib 
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Selfassembled quantum dots (DQ) can be grown as stacks where the QD distance can be controlled with atomic layer control. This distance determines the interaction of the artificial atom states to form artificial molecules. The design of QD stacks becomes complicated since the structures are subject to inhomogeneous, longrange strain and growth imperfections such as nonidentical dots and interdiffused interfaces. This study presents simulations of stacks consistent of three QDs in their resulting inhomogeneous strain field. The simulations are performed with NEMO 3D which uses the valence force field method to compute the strain and the empirical sp3d5s* tight binding method to compute the electronic structure. Strain is shown to provide a very interesting mixing between states and preferred ordering of the ground state in the topmost or bottom most quantum dot subject to growth asymmetries.

[19] 
Clemens Heitzinger and Gerhard Klimeck.
Investigation of conventional DNAFETs for genomewide detection of
polymorphisms.
In Proc. Eurosensors XX 2006, volume 1, pages 448449,
Göteborg, Sweden, September 2006.
[ bib 
PDF ]
Conventional SOI DNAFET devices, being able to detect singlenucleotide polymor phisms, are simulated in a comprehensive approach. These devices can be fabricated in highdensity arrays and offer advantages compared to optical detection methods. The influence of device parameters like doping concentration and the size of the exposed sensor area is investigated.

[18] 
Gerhard Klimeck, Michael McLennan, Matteo Mannino, Marek Korkusinski, Clemens
Heitzinger, Rick Kennell, and Steven Clark.
NEMO 3D and nanoHUB: Bridging research and education.
In Proc. 6th IEEE Conference on Nanotechnology (IEEENANO
2006), volume 2, pages 441444, Cincinnati, OH, USA, June 2006. IEEE.
[ bib 
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The 3D Nanoelectronic Modeling Tool (NEMO 3D) is an electronic structure simulation code for the analysis of quantum dots, quantum wells, nanowires, and impurities. NEMO 3D uses the Valence Force Field (VFF) method for strain and the empirical tight binding (ETB) for the electronic structure calculations. Various ETB models are available, ranging from single s orbitals (single band effective mass), over sp^{3}s* to sp^{3}d^{5}s* models, with and without explicit representation of spin. The code is highly optimized for operation on cluster computing systems. Simulations of systems of 64 million atoms (strain) and 21 million atoms have been demonstrated. This implies that every atom is accounted for in simulation volumes of (110nm)^{3} and (77nm)^{3}, respectively. Such simulations require parallel execution on 64 itanium2 CPUs for around 12 hours. A simple effective mass calculation of an isolated quantum dot, in contrast, requires about 20 seconds on a single CPU. NEMO 3D therefore offers the opportunity to engage both educators and advanced researchers, utilizing a single code. nanoHUB.org is the community web site hosted by the Network for Computational Nanotechnology (NCN) dedicated to bridge education, research, and development for the whole nanoscience and nanotechnology community. This paper reviews the mission of the NCN exemplified by the development and deployment of the NEMO 3D tool.

[17] 
Alireza Sheikholeslami, Farnaz Parhami, Rene Heinzl, Elaf AlAni, Clemens
Heitzinger, Fuad Badrieh, Helmut Puchner, Tibor Grasser, and Siegfried
Selberherr.
Applications of threedimensional topography simulation in the design
of interconnect lines.
In Proc. Simulation of Semiconductor Processes and Devices
(SISPAD 2005), pages 187190, Tokyo, Japan, September 2005.
(Acceptance rate 57%.).
[ bib 
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We present an analysis of deposition of silicon nitride and silicon dioxide layers into threedimensional interconnect structures. The investigations have been performed using our general purpose topography simulator ELSA (Enhanced Level Set Applications). We predict void formation and its characteristics, which play an important role for the formation of cracks which are observed during the passivation of layers covering IC chips.

[16] 
Alireza Sheikholeslami, Stefan Holzer, Clemens Heitzinger, Markus Leicht,
Oliver Häberlen, Josef Fugger, Tibor Grasser, and Siegfried Selberherr.
Inverse modeling of oxid deposition using measurements of a TEOS
CVD process.
In Proc. PhD Research in Microelectronics and Electronics 2005,
volume 2, pages 7982, Lausanne, Switzerland, July 2005.
[ bib 
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The goal of this paper is to identify simulation models for the deposition of silicon dioxide layers from TEOS (tetraethoxysilane) in a CVD (chemical vapor deposition) process and to calibrate the parameters of these models by comparing simulation results to SEM (scanning electron microscope) images of deposited layers in trenches with different aspect ratios. We describe the three models used and the parameters which lead to the best results for each model which allows us to draw conclusions on the usefulness of the models.

[15] 
Clemens Heitzinger, Christian Ringhofer, Shaikh Ahmed, and Dragica Vasileska.
Efficient simulation of the full Coulomb interaction in three
dimensions.
In Proc. 10th International Workshop on Computational
Electronics (IWCE 10), pages 2425, West Lafayette, IN, USA, October 2004.
IEEE.
[ bib 
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The continued scaling of MOSFETs into the nanoscale regime requires refined models for carrier transport due to, e.g., unintentional doping in the active channel region which gives rise to threshold voltage and onstate current fluctuations. Therefore every transport simulator which is supposed to accurately simulate nanodevices must have a proper model for the inclusion of the Coulomb interactions. This paper proposes to use a 3D FMM (fast multipole method) (Greengard and Rokhlin, 1997; Cheng et al., 1999). The FMM is based on the idea of condensing the information of the potential generated by point sources in series expansions. After calculating expansions in a hierarchical manner, the longrange part of the potential is obtained by evaluating the series at the point in question and the shortrange part is calculated by direct summation. Its computational effort is only O(n) where n is the number of particles. In summary, the use of the FMM approach for semiconductor transport simulations was validated. Simulation times are decreased significantly and effects due to electronelectron and electronimpurity interactions are observed as expected. Since the FMM algorithm operates independently of the grid used in the MC simulation, it can be easily included into existing MC device simulation codes.

[14] 
Alireza Sheikholeslami, Clemens Heitzinger, Tibor Grasser, and Siegfried
Selberherr.
Threedimensional topography simulation for deposition and etching
processes using a level set method.
In Proc. 24th IEEE International Conference on Microelectronics
(MIEL 2004), volume 1, pages 241244, Niš, Yugoslavia, May 2004.
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We present the application of level set and fast marching methods to the simulation of surface topography of a wafer in three dimensions for deposition and etching processes. These simulations rest on many techniques, including a narrow band level set method, fast marching for the eikonal equation, extension of the speed function, transport models, visibility determination, and an iterative equation solver.

[13] 
Clemens Heitzinger, Alireza Sheikholeslami, Josef Fugger, Oliver Häberlen,
Markus Leicht, and Siegfried Selberherr.
A case study in predictive threedimensional topography simulation
based on a levelset algorithm.
In H. Deligianni, S.T. Mayer, T.P. Moffat, and G.R. Stafford,
editors, Proc. 205th Meeting of the Electrochemical Society (ECS),
Electrochemical Processes in ULSI and MEMS, volume PV 200417, pages
132142, San Antonio, TX, USA, May 2004. The Electrochemical Society.
[ bib 
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The aim of this work is to study the etching of trenches in silicon and the generation of voids during the filling of genuinely threedimensional trench structures with silicon dioxide or nitride. The trenches studied are part of the manufacturing process of power MOSFETs, where voidless filling must be achieved. Another area of applications is capacitance extraction in interconnect structures, where the deliberate inclusion of voids serves the purpose of reducing overall capacitance. Furthermore, these simulations make it possible to analyze the variations on the feature scale depending on the position of the single trench on the wafer and in the reactor.

[12] 
Rainer Minixhofer, Stefan Holzer, Clemens Heitzinger, Johannes Fellner, Tibor
Grasser, and Siegfried Selberherr.
Optimization of electrothermal material parameters using inverse
modeling.
In José Franca and Paulo Freitas, editors, Proc. 33rd European
SolidState Device Research Conference (ESSDERC 2003), pages 363366,
Estoril, Portugal, September 2003. IEEE.
[ bib 
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A method for determining higher order thermal coefficients for electrical and thermal properties of metallic interconnect materials used in semiconductor fabrication is presented. By applying inverse modeling on transient electrothermal threedimensional finite element simulations the measurements of resistance over time of Polysilicon fuse structures can be matched. This method is intended to be applied to the optimization of Polysilicon fuses for reliability and speed.

[11] 
Fuad Badrieh, Helmut Puchner, Alireza Sheikholeslami, Clemens Heitzinger, and
Siegfried Selberherr.
From feature scale simulation to backend simulation for a 100nm
CMOS process.
In José Franca and Paulo Freitas, editors, Proc. 33rd European
SolidState Device Research Conference (ESSDERC 2003), pages 441444,
Estoril, Portugal, September 2003. IEEE.
[ bib 
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The current challenge for TCAD is the prediction of the performance of groups of devices, backends, and  generally speaking  large parts of the final IC in contrast to the simulation of single devices and their fabrication. This enables one to predictively simulate the performance of the final device depending on different process technologies and parameters, which the simulation of single devices cannot achieve.

[10] 
Clemens Heitzinger, Alireza Sheikholeslami, JongMun Park, and Siegfried
Selberherr.
A method for generating structurally aligned high quality grids and
its application to the simulation of a trench gate MOSFET.
In José Franca and Paulo Freitas, editors, Proc. 33rd European
SolidState Device Research Conference (ESSDERC 2003), pages 457460,
Estoril, Portugal, September 2003. IEEE.
[ bib 
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The error of the numeric approximation of the semiconductor device equations particularly depends on the grid used for the discretization. Since the most interesting regions of the device are generally straightforward to identify, the method of choice is to use structurally aligned grids. Here we present an algorithm for generating structurally aligned grids including anisotropy and for producing grids whose resolution varies over several orders of magnitude. Furthermore the areas with increased resolution and the corresponding resolutions can be defined in a flexible manner and criteria on grid quality can be enforced.

[9] 
Wilfried Wessner, Clemens Heitzinger, Andreas Hössinger, and Siegfried
Selberherr.
Error estimated driven anisotropic mesh refinement for
threedimensional diffusion simulation.
In Proc. Simulation of Semiconductor Processes and Devices
(SISPAD 2003), pages 109112, Boston, MA, USA, September 2003. IEEE.
[ bib 
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We present a computational method for locally adapted conformal anisotropic tetrahedral mesh refinement. The element size is determined by an anisotropy function which is governed by an error estimation driven ruler according to an adjustable maximum error. Anisotropic structures are taken into account to reduce the amount of elements compared to strict isotropic refinement. The spatial resolution in threedimensional unstructured tetrahedral meshes for diffusion simulation can be dynamically increased.

[8] 
Clemens Heitzinger, Andreas Hössinger, and Siegfried Selberherr.
An algorithm for smoothing threedimensional Monte Carlo ion
implantation simulation results.
In I. Troch and F. Breitenecker, editors, Proc. 4th IMACS
Symposium on Mathematical Modelling (MathMod 2003), pages 702711, Vienna,
Austria, February 2003.
[ bib 
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We present an algorithm for smoothing results of threedimensional Monte Carlo ion implantation simulations and translating them from the grid used for the Monte Carlo simulation to an arbitrary unstructured threedimensional grid. This algorithm is important for joining various simulations of semiconductor manufacturing process steps, where data have to be smoothed or transferred from one grid to another. Furthermore different grids must be used since using orthogrids is mandatory because of performance reasons for certain Monte Carlo simulation methods. The algorithm is based on approximations by generalized Bernstein polynomials. This approach was put on a mathematically sound basis by proving several properties of these polynomials. It does not suffer from the ill effects of least squares fits of polynomials of fixed degree as known from the popular response surface method. The smoothing algorithm which works very fast is described and in order to show its applicability, the results of smoothing a threedimensional real world implantation example are given and compared with those of a least squares fit of a multivariate polynomial of degree two, which yielded unusable results.

[7] 
Clemens Heitzinger, Josef Fugger, Oliver Häberlen, and Siegfried Selberherr.
On increasing the accuracy of simulations of deposition and etching
processes using radiosity and the level set method.
In G. Baccarani, E. Gnani, and M. Rudan, editors, Proc. 32th
European SolidState Device Research Conference (ESSDERC 2002), pages
347350, Florence, Italy, September 2002. University of Bologna.
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Deposition and etching in Silicon trenches is an important step of today’s semiconductor manufacturing. Understanding the surface evolution enables to predict the resulting profiles and thus to optimize process parameters. Simulations using the radiosity modeling approach and the level set method provide accurate results, but their speed has to be considered when employing advanced models and for purposes of inverse modeling.

[6] 
Clemens Heitzinger, Josef Fugger, Oliver Häberlen, and Siegfried Selberherr.
Simulation and inverse modeling of TEOS deposition processes using
a fast level set method.
In Proc. Simulation of Semiconductor Processes and Devices
(SISPAD 2002), pages 191194, Kobe, Japan, September 2002. Business Center
for Academic Societies, Japan.
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Deposition and etching of silicon trenches is an important manufacturing step for state of the art memory cells. Understanding and simulating the transport of gas species and surface evolution enables to achieve voidless filling of deep trenches, to predict the resulting profiles, and thus to optimize process parameters with respect to manufacturing throughput and the quality of the resulting memory cells. For the simulation of the SiO_{2} deposition process from TEOS (Tetraethoxysilane), the level set method was used in addition to physical models. The level set algorithm devised minimizes computational effort while ensuring high accuracy by intertwining narrow banding and extending the speed function. In order to make the predictions of the simulation more accurate, model parameters were extracted by comparing the step coverages of the deposited layers in the simulation with those of SEM (scanning electron microscope) images.

[5] 
Clemens Heitzinger and Siegfried Selberherr.
A calibrated model for silicon selfinterstitial cluster formation
and dissolution.
In Proc. 23rd IEEE International Conference on Microelectronics
(MIEL 2002), pages 431434, Niš, Yugoslavia, May 2002.
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DOI 
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The formation and dissolution of silicon selfinterstitial clusters is linked to the phenomenon of TED (transient enhanced diffusion) which in turn has gained importance in the manufacturing of semiconductor devices. Based on theoretical considerations and measurements of the number of selfinterstitial clusters during a thermal step we were interested in finding a suitable model for the formation and dissolution of selfinterstitial clusters and extracting corresponding model parameters for two different technologies (i.e., material parameter sets). In order to automate the inverse modeling part a general optimization framework was used. Additional to solving this problem the same setup can solve a wide range of inverse modeling problems occurring in the domain of process simulation. Finally the results are discussed and compared with a previous model.

[4] 
Tibor Grasser, Hans Kosina, Clemens Heitzinger, and Siegfried Selberherr.
An impact ionization model including an explicit cold carrier
population.
In Proc. 5th International Conference on Modeling and Simulation
of Microsystems (MSM 2002), pages 572575, San Juan, Puerto Rico, USA,
April 2002.
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Conventional macroscopic impact ionization models which use the average carrier energy as main parameter cannot accurately describe the phenomenon in modern miniaturized devices. Here we present a new model which is based on an analytic expression for the distribution function. In particular, the distribution function model accounts explicitly for a hot and a cold carrier population in the drain region of MOS transistors. The parameters are determined by three even moments obtained from a solution of a six moments transport model. Together with a nonparabolic description of the density of states accurate closed form macroscopic impact ionization models can be derived based on familiar microscopic descriptions.

[3] 
Clemens Heitzinger and Siegfried Selberherr.
Optimization for TCAD purposes using Bernstein polynomials.
In D. Tsoukalas and C. Tsamis, editors, Proc. Simulation of
Semiconductor Processes and Devices (SISPAD 2001), pages 420423, Athens,
Greece, September 2001. Springer, Wien, New York.
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The optimization of computationally expensive objective functions requires approximations that preserve the global properties of the function under investigation. The RSM approach of using multivariate polynomials of degree two can only preserve the local properties of a given function and is therefore not wellsuited for global optimization tasks. In this paper we discuss generalized Bernstein polynomials that provide faithful approximations by converging uniformly to the given function. Apart from being useful for optimization tasks, they can also be used for solving design for manufacturability problems.

[2] 
Andreas Gehring, Clemens Heitzinger, Tibor Grasser, and Siegfried Selberherr.
TCAD analysis of gain cell retention time for SRAM applications.
In D. Tsoukalas and C. Tsamis, editors, Proc. Simulation of
Semiconductor Processes and Devices (SISPAD 2001), pages 416419, Athens,
Greece, September 2001. Springer, Wien, New York.
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We present simulations of a recently published SRAM memory gain cell consisting of two transistors and one MOS capacitor, representing an alternative to conventional six transistor SRAMs. Inverse modeling is used to fit a given device characteristic to measurement data. To account for decharging due to tunneling, we use a simple, nonlocal tunneling model and calibrate it with data from literature. By optimization, we find values for the contact voltages in the offregion at which the retention time is a maximum.

[1] 
Wolfgang Pyka, Clemens Heitzinger, Naoki Tamaoki, Toshiro Takase, Toshimitsu
Ohmine, and Siegfried Selberherr.
Monitoring arsenic insitu doping with advanced models for
polysilicon CVD.
In D. Tsoukalas and C. Tsamis, editors, Proc. Simulation of
Semiconductor Processes and Devices (SISPAD 2001), pages 124127, Athens,
Greece, September 2001. Springer, Wien, New York.
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Experiments of Asdoped polysilicon deposition have shown that under certain process conditions step coverages > 1 can be achieved. We have developed a new model for the simulation of Asdoped polysilicon deposition, which takes into account surface coverage dependent sticking coefficients and surface coverage dependent As incorporation and desorption rates. The additional introduction of Langmuir type timedependent surface coverage enabled the reproduction of the bottomup filling of the trenches. In addition the rigorous treatment of the timedependent surface coverage allows to trace the insitu doping of the deposited film. Simulation results are shown for polySi deposition into 0.1μm wide and 7μm deep, high aspect ratio trenches.

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