Publications-journals.bib

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@article{Mitscha-BaudePREhigh-throughput,
  author = {Gregor Mitscha-Baude AND Benjamin Stadlbauer AND Stefan Howorka AND Clemens Heitzinger},
  title = {High-throughput simulations of protein transport through confined space},
  page = {1-18},
  note = {\textit{In preparation}}
}
@article{StadlbauerPREmodeling,
  author = {Benjamin Stadlbauer AND Gregor Mitscha-Baude AND Clemens Heitzinger},
  title = {Modeling single-molecule stochastic transport in nanopore sensors},
  pages = {1-7},
  note = {\textit{In preparation}}
}
@article{HeitzingerPREstochastic,
  author = {Clemens Heitzinger AND Markus Schmuck AND Christoph Schwab},
  title = {Stochastic two-scale convergence and covariance equation for elliptic multiscale {PDE}s},
  pages = {1-26},
  note = {\textit{In preparation}}
}
@article{CossettiniPREBayesian,
  author = {Andrea Cossettini AND Jose Morales Escalante AND Paolo Scarbolo AND Benjamin Stadlbauer AND Leila Taghizadeh AND Luca Selmi AND Clemens Heitzinger},
  title = {{Bayesian} inversion of physical and geometrical parameters for nanocapacitor array biosensors},
  page = {1-23},
  note = {\textit{In preparation}}
}
@article{TaghizadehPREBayesian,
  author = {Leila Taghizadeh AND Benjamin Stadlbauer AND Jose Morales Escalante AND Clemens Heitzinger},
  title = {{Bayesian} inversion for electrical impedance tomography},
  pages = {1-15},
  note = {\textit{In preparation}}
}
@article{AbaszadehPREmeshless,
  author = {Mostafa Abbaszadeh AND Mehdi Dehghan AND Amirreza Khodadadian AND Clemens Heitzinger},
  title = {A meshless local procedure for {2D} stochastic elliptic interface problems},
  pages = {1-25},
  note = {\textit{Submitted for publication}}
}
@article{KhodadadianPREBayesian,
  author = {Amirreza Khodadadian AND Benjamin Stadlbauer AND Clemens Heitzinger},
  title = {{Bayesian} inversion for nanowire field-effect sensors},
  pages = {1-16},
  note = {\textit{Submitted for publication}}
}
@article{DehghanPREproper,
  author = {Mehdi Dehghan AND Mostafa Abbaszadeh AND Amirreza Khodadadian AND Clemens Heitzinger},
  title = {Proper orthogonal decomposition-local discontinuous Galerkin ({POD}-{LDG}) method for solving generalized {Swift}-{Hohenberg} equations},
  pages = {1-20},
  note = {\textit{Submitted for publication}}
}
@article{KhodadadianPREadaptive,
  author = {Amirreza Khodadadian AND Maryam Parvizi AND Clemens Heitzinger},
  title = {An adaptive multilevel {Monte-Carlo} algorithm for the stochastic drift-diffusion-{Poisson} system},
  pages = {1-26},
  note = {\textit{Submitted for publication}}
}
@article{HeitzingerPREhomogenization,
  author = {Clemens Heitzinger AND Jose Morales Escalante},
  title = {Homogenization of boundary layers in the {Boltzmann}-{Poisson} system},
  pages = {1-26},
  note = {\textit{Submitted for publication}}
}
@article{KhodadadianPREmultilevel,
  author = {Amirreza Khodadadian AND Maryam Parvizi AND Mostafa Abbaszadeh AND Mehdi Dehghan AND Clemens Heitzinger},
  title = {A multilevel {Monte Carlo} finite element method for the stochastic {Cahn-Hilliard-Cook} equation},
  pages = {1-16},
  note = {\textit{Submitted for publication}}
}
@article{TaghizadehPREbiofilm,
  author = {Leila Taghizadeh AND Elisabeth Presterl AND Clemens Heitzinger},
  title = {A biofilm model including quorum sensing},
  pages = {1-12},
  note = {\textit{Submitted for publication}}
}
@article{BlankrotPREefficient,
  author = {Boaz Blankrot AND Clemens Heitzinger},
  title = {Efficient computational design and optimization of dielectric metamaterial devices},
  pages = {1-18},
  journal = {J.~Comput.\ Phys.},
  url = {http://arxiv.org/abs/1804.09489},
  note = {\textit{Submitted for publication}}
}
@article{HeitzingerPRElocal,
  author = {Clemens Heitzinger AND Leila Taghizadeh},
  title = {Existence and local uniqueness for the stochastic drift-diffusion-{Poisson} system},
  pages = {1-24},
  note = {\textit{Submitted for publication}}
}
@article{HeitzingerPREuniqueness,
  author = {Clemens Heitzinger AND Leila Taghizadeh},
  title = {Existence and local uniqueness for the {Stokes}-{Nernst}-{Planck}-drift-diffusion-{Poisson} system modeling nanopore and nanowire sensors},
  pages = {1-25},
  note = {\textit{Submitted for publication}}
}
@article{Abbaszadeh2019direct,
  author = {Mostafa Abbaszadeh AND Amirreza Khodadadian AND Maryam Parvizi AND Mehdi Dehghan AND Clemens Heitzinger},
  title = {A direct meshless local collocation method for solving stochastic {Cahn-Hilliard-Cook} and stochastic {Swift-Hohenberg} equations},
  journal = {Engineering Analysis with Boundary Elements},
  volume = 98,
  pages = {253-264},
  year = 2019,
  url = {https://doi.org/10.1016/j.enganabound.2018.10.021},
  pdf = {Papers/Abbaszadeh2019direct.pdf},
  doi = {10.1016/j.enganabound.2018.10.021},
  abstract = {In this study, the direct meshless local Petrov–Galerkin
                  (DMLPG) method has been employed to solve the
                  stochastic Cahn–Hilliard–Cook and Swift–Hohenberg
                  equations. First of all, we discretize the temporal
                  direction by a finite difference scheme. In order to
                  obtain a fully discrete scheme the direct meshless
                  local collocation method is used to discretize the
                  spatial variable and the Euler–Maruyama method is
                  used for time discretization. The used method is a
                  truly meshless technique. In order to illustrate the
                  efficiency and accuracy of the explained numerical
                  technique, we study two stochastic models with their
                  applications in biology and engineering, i.e., the
                  stochastic Cahn–Hilliard–Cook equation and a
                  stochastic Swift–Hohenberg model.}
}
@article{Heitzinger2018existence,
  author = {Clemens Heitzinger AND Michael Leumüller AND Gudmund Pammer and Stefan Rigger},
  title = {Existence, uniqueness, and a comparison of two non-intrusive methods for the stochastic nonlinear {Poisson-Boltzmann} equation},
  journal = {SIAM/ASA Journal on Uncertainty Quantification},
  volume = 6,
  number = 3,
  pages = {1019-1042},
  year = 2018,
  url = {https://epubs.siam.org/doi/pdf/10.1137/17M1127375},
  pdf = {Papers/Heitzinger2018existence.pdf},
  doi = {10.1137/17M1127375},
  abstract = {The stochastic nonlinear Poisson–Boltzmann equation
                  describes the electrostatic potential in a random
                  environment in the presence of free charges and has
                  applications in many fields. We show the existence
                  and uniqueness of the solution of this nonlinear
                  model equation and investigate its regularity with
                  respect to a random parameter. Three popular
                  nonintrusive methods, a stochastic Galerkin method,
                  a discrete projection method, and a collocation
                  method, are presented for its numerical solution. It
                  is nonintrusive in the sense that solvers and
                  preconditioners for the deterministic equation can
                  be reused as they are. By comparing these methods,
                  it is found that the stochastic Galerkin method and
                  the discrete projection method require comparable
                  computational effort and our results suggest that
                  they outperform the collocation method.}
}
@article{Blankrot2018ParticleScattering,
  author = {Boaz Blankrot AND Clemens Heitzinger},
  title = {{ParticleScattering}: solving and optimizing multiple-scattering problems in {Julia}},
  journal = {Journal of Open Source Software},
  volume = 3,
  number = 25,
  pages = {691/1--3},
  month = may,
  year = 2018,
  url = {http://dx.doi.org/10.21105/joss.00691},
  pdf = {Papers/Blankrot2018ParticleScattering.pdf},
  doi = {10.21105/joss.00691},
  abstract = {ParticleScattering is a Julia (Bezanson et al.\ 2017) package
                  for computing the electromagnetic fields scattered
                  by a large number of two-dimensional particles, as
                  well as optimizing particle parameters for various
                  applications. Such problems naturally arise in the
                  design and analysis of metamaterials, including
                  photonic crystals (Jahani and Jacob 2016). Unlike
                  most solvers for these problems, ours does not
                  require a periodic structure and is scalable to a
                  large number of particles. In particular, this
                  software is designed for scattering problems
                  involving TM plane waves impinging on a collection
                  of homogeneous dielectric particles with arbitrary
                  smooth shapes. Our code performs especially well
                  when the number of particles is substantially larger
                  than the number of distinct shapes, where particles
                  are considered indistinct if they are identical up
                  to rotation.}
}
@article{Khodadadian2018three-dimensional,
  author = {Amirreza Khodadadian AND Leila Taghizadeh AND Clemens Heitzinger},
  title = {Three-dimensional optimal multi-level {Monte-Carlo} approximation of the stochastic drift-diffusion-{Poisson} system in nanoscale devices},
  journal = {J.~Comput.\ Electron.},
  volume = 17,
  number = 1,
  pages = {76-89},
  month = mar,
  year = 2018,
  url = {https://doi.org/10.1007/s10825-017-1118-0},
  pdf = {Papers/Khodadadian2018three-dimensional.pdf},
  doi = {10.1007/s10825-017-1118-0},
  abstract = {The three-dimensional stochastic drift-diffusion-Poisson
                  system is used to model charge transport through
                  nanoscale devices in a random
                  environment. Applications include nanoscale
                  transistors and sensors such as nanowire
                  field-effect bio- and gas sensors. Variations
                  between the devices and uncertainty in the response
                  of the devices arise from the random distributions
                  of dopant atoms, from the diffusion of target
                  molecules near the sensor surface, and from the
                  stochastic association and dissociation processes at
                  the sensor surface. Furthermore, we couple the
                  system of stochastic partial differential equations
                  to a random-walk-based model for the association and
                  dissociation of target molecules. In order to make
                  the computational effort tractable, an optimal
                  multi-level Monte–Carlo method is applied to
                  three-dimensional solutions of the deterministic
                  system. The whole algorithm is optimal in the sense
                  that the total computational cost is minimized for
                  prescribed total errors. This comprehensive and
                  efficient model makes it possible to study the
                  effect of design parameters such as applied voltages
                  and the geometry of the devices on the expected
                  value of the current.}
}
@article{Heitzinger2018cubature,
  author = {Clemens Heitzinger AND Gudmund Pammer AND Stefan Rigger},
  title = {Cubature formulas for multisymmetric functions and applications to stochastic partial differential equations},
  journal = {SIAM/ASA Journal on Uncertainty Quantification},
  volume = 6,
  number = 1,
  pages = {213-242},
  year = 2018,
  url = {http://doi.org/10.1137/17M1125418},
  pdf = {Papers/Heitzinger2018cubature.pdf},
  doi = {10.1137/17M1125418},
  abstract = {The numerical solution of stochastic partial differential
                  equations and numerical Bayesian estimation is
                  computationally demanding. If the coefficients in a
                  stochastic partial differential equation exhibit
                  symmetries, they can be exploited to reduce the
                  computational effort. To do so, we show that
                  permutation-invariant functions can be approximated
                  by permutation-invariant polynomials in the space of
                  continuous functions as well as in the space of
                  $p$-integrable functions defined on $[0, 1]^s$ for
                  $1 \le p < \infty$. We proceed to develop a
                  numerical strategy to compute cubature formulas that
                  exploit permutation-invariance properties related to
                  multisymmetry groups in order to reduce
                  computational work. We show that in a certain sense
                  there is no curse of dimensionality if we restrict
                  ourselves to multisymmetric functions, and we
                  provide error bounds for formulas of this
                  type. Finally, we present numerical results,
                  comparing the proposed formulas to other integration
                  techniques that are frequently applied to
                  high-dimensional problems such as quasi-Monte Carlo
                  rules and sparse grids.}
}
@article{Khodadadian2018optimal,
  author = {Amirreza Khodadadian AND Leila Taghizadeh AND Clemens Heitzinger},
  title = {Optimal multilevel randomized quasi-{Monte-Carlo} method for the stochastic drift-diffusion-{Poisson} system},
  journal = {Computer Methods in Applied Mechanics and Engineering (CMAME)},
  volume = 329,
  pages = {480-497},
  month = feb,
  year = 2018,
  url = {https://doi.org/10.1016/j.cma.2017.10.015},
  pdf = {Papers/Khodadadian2018optimal.pdf},
  doi = {10.1016/j.cma.2017.10.015},
  abstract = {In this paper, an optimal multilevel randomized
                  quasi-Monte-Carlo method to solve the stationary
                  stochastic drift–diffusion-Poisson system is
                  developed. We calculate the optimal values of the
                  parameters of the numerical method such as the mesh
                  sizes of the spatial discretization and the numbers
                  of quasi-points in order to minimize the overall
                  computational cost for solving this system of
                  stochastic partial differential equations. This
                  system has a number of applications in various
                  fields, wherever charged particles move in a random
                  environment. It is shown that the computational cost
                  of the optimal multilevel randomized
                  quasi-Monte-Carlo method, which uses randomly
                  shifted low-discrepancy sequences, is one order of
                  magnitude smaller than that of the optimal
                  multilevel Monte-Carlo method and five orders of
                  magnitude smaller than that of the standard
                  Monte-Carlo method. The method developed here is
                  applied to a realistic transport problem, namely the
                  calculation of random-dopant effects in nanoscale
                  field-effect transistors.}
}
@article{Heitzinger2017analysis,
  author = {Clemens Heitzinger AND Leila Taghizadeh},
  title = {Analysis of the drift-diffusion-{Poisson}-{Boltzmann} system for nanowire and nanopore sensors in the alternating-current regime},
  journal = {Commun.\ Math.\ Sci.},
  volume = 15,
  number = 8,
  pages = {2303-2325},
  year = 2017,
  url = {http://dx.doi.org/10.4310/CMS.2017.v15.n8.a8},
  pdf = {Papers/Heitzinger2017analysis.pdf},
  doi = {10.4310/CMS.2017.v15.n8.a8},
  abstract = {The basic analytical properties of the
                  drift-diffusion-Poisson-Boltzmann system in the
                  alternating-current (AC) regime are shown. The
                  analysis of the AC case differs from the
                  direct-current (DC) case and is based on extending
                  the transport model to the frequency domain and
                  writing the variables as periodic functions of the
                  frequency in a small-signal approximation. We first
                  present the DC and AC model equations to describe
                  the three types of material in nanowire field-effect
                  sensors: The drift-diffusion-Poisson system holds in
                  the semiconductor, the Poisson-Boltzmann equation
                  holds in the electrolyte, and the Poisson equation
                  provides self-consistency. Then the AC model
                  equations are derived. Finally, existence and local
                  uniqueness of the solution of the AC model equations
                  are shown. Real-world applications include nanowire
                  field-effect bio- and gas sensors operating in the
                  AC regime, which were only demonstrated
                  experimentally recently. Furthermore, nanopore
                  sensors are governed by the system of model
                  equations and the analysis as well.}
}
@article{Khodadadian2017optimal,
  author = {Amirreza Khodadadian AND Kiarash Hosseini AND Ali Manzour-ol-Ajdad AND Marjan Hedayati AND Reza Kalantarinejad AND Clemens Heitzinger},
  title = {Optimal design of nanowire field-effect troponin sensors},
  journal = {Computers in Biology and Medicine},
  volume = 87,
  pages = {46-56},
  month = aug,
  year = 2017,
  url = {https://doi.org/10.1016/j.compbiomed.2017.05.008},
  pdf = {Papers/Khodadadian2017optimal.pdf},
  doi = {10.1016/j.compbiomed.2017.05.008},
  abstract = {We propose a design strategy for affinity-based biosensors
                  using nanowires for sensing and measuring biomarker
                  concentration in biological samples. Such sensors
                  have been shown to have superior properties compared
                  to conventional biosensors in terms of LOD (limit of
                  detection), response time, cost, and size. However,
                  there are several parameters affecting the
                  performance of such devices that must be
                  determined. In order to solve the design problem, we
                  have developed a comprehensive model based on
                  stochastic transport equations that makes it
                  possible to optimize the sensing behavior.}
}
@article{Mitscha-Baude2017adaptive,
  author = {Gregor Mitscha-Baude AND Andreas Buttinger-Kreuzhuber AND Gerhard Tulzer AND Clemens Heitzinger},
  title = {Adaptive and iterative methods for simulations of nanopores with the {PNP}--{Stokes} equations},
  journal = {J.~Comput.\ Phys.},
  volume = 338,
  pages = {452-476},
  month = jun,
  year = 2017,
  url = {http://dx.doi.org/10.1016/j.jcp.2017.02.072},
  pdf = {Papers/Mitscha-Baude2017adaptive.pdf},
  doi = {10.1016/j.jcp.2017.02.072},
  abstract = {We present a 3D finite element solver for the nonlinear
                  Poisson--Nernst--Planck (PNP) equations for
                  electrodiffusion, coupled to the Stokes system of
                  fluid dynamics. The model serves as a building block
                  for the simulation of macromolecule dynamics inside
                  nanopore sensors. The source code is released online
                  at github.com/mitschabaude/nanopores.  We add to
                  existing numerical approaches by deploying
                  goal-oriented adaptive mesh refinement. To reduce
                  the computation overhead of mesh adaptivity, our
                  error estimator uses the much cheaper
                  Poisson--Boltzmann equation as a simplified model,
                  which is justified on heuristic grounds but shown to
                  work well in practice. To address the nonlinearity
                  in the full PNP–Stokes system, three different
                  linearization schemes are proposed and investigated,
                  with two segregated iterative approaches both
                  outperforming a naive application of Newton’s
                  method. Numerical experiments are reported on a
                  real-world nanopore sensor geometry.  We also
                  investigate two different models for the interaction
                  of target molecules with the nanopore sensor through
                  the PNP--Stokes equations. In one model, the
                  molecule is of finite size and is explicitly built
                  into the geometry; while in the other, the molecule
                  is located at a single point and only modeled
                  implicitly -- after solution of the system -- which
                  is computationally favorable. We compare the
                  resulting force profiles of the electric and
                  velocity fields acting on the molecule, and conclude
                  that the point-size model fails to capture important
                  physical effects such as the dependence of charge
                  selectivity of the sensor on the molecule radius.}
}
@article{Taghizadeh2017optimal,
  author = {Leila Taghizadeh AND Amirreza Khodadadian AND Clemens Heitzinger},
  title = {The optimal multilevel {Monte-Carlo} approximation of the stochastic drift-diffusion-{Poisson} system},
  journal = {Computer Methods in Applied Mechanics and Engineering (CMAME)},
  volume = 318,
  pages = {739-761},
  year = 2017,
  url = {http://dx.doi.org/10.1016/j.cma.2017.02.014},
  pdf = {Papers/Taghizadeh2017optimal.pdf},
  doi = {10.1016/j.cma.2017.02.014},
  abstract = {Existence and local-uniqueness theorems for weak solutions
                  of a system consisting of the
                  drift-diffusion-Poisson equations and the
                  Poisson-Boltzmann equation, all with stochastic
                  coefficients, are presented. For the numerical
                  approximation of the expected value of the solution
                  of the system, we develop a multi-level Monte-Carlo
                  (MLMC) finite-element method (FEM) and we analyze
                  its rate of convergence and its computational
                  complexity. This allows to find the optimal choice
                  of discretization parameters. Finally, numerical
                  results show the efficiency of the method.
                  Applications are, among others, noise and
                  fluctuations in nanoscale transistors, in
                  field-effect bio- and gas sensors, and in
                  nanopores.}
}
@article{Khodadadian2016basis,
  author = {Amirreza Khodadadian AND Clemens Heitzinger},
  title = {Basis adaptation for the stochastic nonlinear {Poisson}-{Boltzmann} equation},
  journal = {J.~Comput.\ Electron.},
  volume = 15,
  number = 4,
  pages = {1393-1406},
  year = 2016,
  url = {http://link.springer.com/article/10.1007%2Fs10825-016-0922-2},
  pdf = {Papers/Khodadadian2016basis.pdf},
  doi = {10.1007/s10825-016-0922-2},
  abstract = {A basis-adaptation method based on polynomial chaos
                  expansion is used for the stochastic nonlinear
                  Poisson–Boltzmann equation. The uncertainty in this
                  numerical approach is motivated by the
                  quantification of noise and fluctuations in
                  nanoscale field-effect sensors. The method used here
                  takes advantage of the properties of the nonlinear
                  Poisson–Boltzmann equation and shows an exact and
                  efficient approximation of the real
                  solution. Numerical examples are motivated by the
                  quantification of noise and fluctuations in nanowire
                  field-effect sensors as a concrete example. Basis
                  adaptation is validated by comparison with the full
                  solution, and it is compared to optimized
                  multi-level Monte-Carlo method, and the model
                  equations are validated by comparison with
                  experiments. Finally, various design parameters of
                  the field-effect sensors are investigated in order
                  to maximize the signal-to-noise ratio.}
}
@article{Geiersbach2016optimal,
  author = {Caroline Geiersbach AND Clemens Heitzinger AND Gerhard Tulzer},
  title = {Optimal approximation of the first-order corrector in multiscale stochastic elliptic {PDE}},
  journal = {SIAM/ASA J.\ Uncertainty Quantification},
  volume = 4,
  number = 1,
  pages = {1246-1262},
  year = 2016,
  url = {http://epubs.siam.org/toc/sjuqa3/4/1},
  pdf = {Papers/Geiersbach2016optimal.pdf},
  doi = {10.1137/16M106011X},
  abstract = {This work addresses the development of an optimal
                  computational scheme for the approximation of the
                  first-order corrector arising in the stochastic
                  homogenization of linear elliptic PDEs in divergence
                  form. Equations of this type describe, for example,
                  diffusion phenomena in materials with a
                  heterogeneous microstructure, but require enormous
                  computational efforts in order to obtain reliable
                  results. We derive an optimization problem for the
                  needed computational work with a given error
                  tolerance, then extract the governing parameters
                  from numerical experiments, and finally solve the
                  obtained optimization problem. The numerical
                  approach investigated here is a stochastic sampling
                  scheme for the probability space connected with a
                  finite-element method for the discretization of the
                  physical space.}
}
@article{Bernardi2016serum,
  author = {Martin Hermann Bernardi AND Daniel Schmidlin AND Robin Ristl AND Clemens Heitzinger AND Arno Schiferer AND Thomas Neugebauer AND Thomas Wrba AND Michael Hiesmayr AND Wilfred Druml AND Andrea Lassnigg},
  title = {Serum creatinine back-estimation in cardiac surgery patients: misclassification of {AKI} using existing formulae and a data-driven model},
  journal = {Clin. J. Am. Soc. Nephrol. (CJASN)},
  volume = 11,
  number = 3,
  pages = {395-404},
  year = 2016,
  pdf = {Papers/Bernardi2016serum.pdf},
  doi = {10.2215/CJN.03560315},
  note = {(CJASN 2014 impact factor: 4.613; this publication was awarded
                  the Science Price 2017 by ÖGARI (Austrian Society
                  for Anesthesiology, Reanimation, and Intensive
                  Medicine).)},
  abstract = {Conclusions:
                  bSCr values back-estimated using currently available
                  eGFR formulae are inaccurate and cannot correctly
                  classify AKI stages. Our model eSCr improves the
                  prediction of AKI but to a still inadequate extent.}
}
@article{Tulzer2016Brownian-motion,
  author = {Gerhard Tulzer AND Clemens Heitzinger},
  title = {Brownian-motion based simulation of stochastic reaction-diffusion systems for affinity based sensors},
  journal = {Nanotechnology},
  volume = 27,
  number = 16,
  pages = {165501/1--9},
  year = 2016,
  url = {http://dx.doi.org/10.1088/0957-4484/27/16/165501},
  pdf = {Papers/Tulzer2016Brownian-motion.pdf},
  doi = {10.1088/0957-4484/27/16/165501},
  abstract = {In this work, we develop a 2D algorithm for stochastic
                  reaction-diffusion systems describing the binding
                  and unbinding of target molecules at the surfaces of
                  affinity-based sensors. In particular, we simulate
                  the detection of DNA oligomers using
                  silicon-nanowire field-effect biosensors. Since
                  these devices are uniform along the nanowire, two
                  dimensions are sufficient to capture the kinetic
                  effects features. The model combines a stochastic
                  ordinary differential equation for the binding and
                  unbinding of target molecules as well as a diffusion
                  equation for their transport in the liquid. A
                  Brownian-motion based algorithm simulates the
                  diffusion process, which is linked to a
                  stochastic-simulation algorithm for association at
                  and dissociation from the surface. The simulation
                  data show that the shape of the cross section of the
                  sensor yields areas with significantly different
                  target-molecule coverage. Different initial
                  conditions are investigated as well in order to aid
                  rational sensor design. A comparison of the
                  association/hybridization behavior for different
                  receptor densities allows optimization of the
                  functionalization setup depending on the
                  target-molecule density.}
}
@article{Khodadadian2015transport,
  author = {Amirreza Khodadadian AND Clemens Heitzinger},
  title = {A transport equation for confined structures applied to the {OprP}, {Gramicidin~A}, and {KcsA} channels},
  journal = {J.~Comput.\ Electron.},
  volume = 14,
  number = 2,
  pages = {524-532},
  year = 2015,
  url = {http://link.springer.com/article/10.1007/s10825-015-0680-6},
  pdf = {Papers/Khodadadian2015transport.pdf},
  doi = {10.1007/s10825-015-0680-6},
  abstract = {A transport equation for confined structures is used to
                  calculate the ionic currents through various
                  transmembrane proteins.  The transport equation is a
                  diffusion-type equation where the concentration of
                  the particles depends on the one-dimensional
                  position in the confined structure and on the local
                  energy.  The computational significance of this
                  continuum model is that the $(6+1)$-dimensional
                  Boltzmann equation is reduced to a
                  $(2+1)$-dimensional diffusion-type equation that can
                  be solved with small computational effort so that
                  ionic currents through confined structures can be
                  calculated quickly.  The applications here are three
                  channels, namely OprP, Gramicidin~A, and KcsA. In
                  each case, the confinement potential is estimated
                  from the known molecular structure of the channel.
                  Then the confinement potentials are used to
                  calculate ionic currents and to study the effect of
                  parameters such as the potential of mean force, the
                  ionic bath concentration, and the applied voltage.
                  The simulated currents are compared with
                  measurements, and very good agreement is found in
                  each case.  Finally, virtual potassium channels with
                  selectivity filters of varying length are simulated
                  in order to discuss the optimality of the filter.}
}
@article{Tulzer2015fluctuations,
  author = {Gerhard Tulzer AND Clemens Heitzinger},
  title = {Fluctuations due to association and dissociation processes at nanowire-biosensor surfaces and their optimal design},
  journal = {Nanotechnology},
  volume = 26,
  number = 2,
  pages = {025502/1--9},
  year = 2015,
  url = {http://stacks.iop.org/0957-4484/26/i=2/a=025502},
  pdf = {Papers/Tulzer2015fluctuations.pdf},
  doi = {10.1088/0957-4484/26/2/025502},
  abstract = {In this work, we calculate the effect of the binding and
                  unbinding of molecules at the surface of a nanowire
                  biosensor on the signal-to-noise ratio of the
                  sensor. We model the fluctuations induced by
                  association and dissociation of target molecules by
                  a stochastic differential equation and extend this
                  approach to a coupled diffusion-reaction
                  system. Where possible, analytic solutions for the
                  signal-to-noise ratio are given. Stochastic
                  simulations are performed wherever closed forms of
                  the solutions cannot be derived. Starting from
                  parameters obtained from experimental data, we
                  simulate DNA hybridization at the sensor surface for
                  different target molecule concentrations in order to
                  optimize the sensor design.}
}
@article{Heitzinger2014hierarchies,
  author = {Clemens Heitzinger AND Christian Ringhofer},
  title = {Hierarchies of transport equations for nanopores -- Equations derived from the {Boltzmann} equation and the modeling of confined structures},
  journal = {J.~Comput.\ Electron.},
  volume = 13,
  number = 4,
  pages = {801-817},
  year = 2014,
  url = {http://link.springer.com/article/10.1007/s10825-014-0586-8},
  pdf = {Papers/Heitzinger2014hierarchies.pdf},
  doi = {10.1007/s10825-014-0586-8},
  abstract = {We review transport equations and their usage for the
                  modeling and simulation of nanopores.  First, the
                  significance of nanopores and the experimental
                  progress in this area are summarized. Then the
                  starting point of all classical and semiclassical
                  considerations is the Boltzmann transport equation
                  as the most general transport equation. The
                  derivation of the drift-diffusion equations from the
                  Boltzmann equation is reviewed as well as the
                  derivation of the Navier-Stokes equations. Nanopores
                  can also be viewed as a special case of a confined
                  structure and hence as giving rise to a multiscale
                  problem, and therefore we review the derivation of a
                  transport equation from the Boltzmann equation for
                  such confined structures. Finally, the state of the
                  art in the simulation of nanopores is summarized.},
  note = {\textit{Invited review paper.}}
}
@article{Heitzinger2014multiscale,
  author = {Clemens Heitzinger AND Christian Ringhofer},
  title = {Multiscale Modeling of Fluctuations in Stochastic Elliptic {PDE} Models of Nanosensors},
  journal = {Commun.\ Math.\ Sci.},
  volume = 12,
  number = 3,
  pages = {401-421},
  year = 2014,
  url = {http://dx.doi.org/10.4310/CMS.2014.v12.n3.a1},
  pdf = {Papers/Heitzinger2014multiscale.pdf},
  doi = {10.4310/CMS.2014.v12.n3.a1},
  abstract = {In this work, the multiscale problem of modeling
                  fluctuations in boundary layers in stochastic
                  elliptic partial differential equations is solved by
                  homogenization.  A homogenized equation for the
                  covariance of the solution of stochastic elliptic
                  PDEs is derived.  In addition to the homogenized
                  equation, a rate for the covariance and variance as
                  the cell size tends to zero is given.  For the
                  homogenized problem, an existence and uniqueness
                  result and further properties are shown.  The
                  multiscale problem stems from the modeling of the
                  electrostatics in nanoscale field-effect sensors,
                  where the fluctuations arise from random charge
                  concentrations in the cells of a boundary layer.
                  Finally, numerical results and a numerical
                  verification are presented.}
}
@article{Brinkman2014convergent,
  author = {Daniel Brinkman AND Clemens Heitzinger AND Peter Markowich},
  title = {A convergent {2D} finite-difference scheme for the {Dirac}-{Poisson} system with magnetic potential and the simulation of graphene},
  journal = {J.~Comput.\ Phys.},
  volume = {257A},
  pages = {318-332},
  year = 2014,
  url = {http://dx.doi.org/10.1016/j.jcp.2013.09.052},
  doi = {10.1016/j.jcp.2013.09.052},
  abstract = {We present a convergent finite-difference scheme of second
                  order in both space and time for the 2D
                  electromagnetic Dirac equation.  We apply this
                  method in the self-consistent Dirac-Poisson system
                  to the simulation of graphene.  The model is
                  justified for low energies, where the particles have
                  wave vectors sufficiently close to the Dirac points.
                  In particular, we demonstrate that our method can be
                  used to calculate solutions of the Dirac-Poisson
                  system where potentials act as beam-splitters or
                  Veselago lenses.}
}
@article{Tulzer2013kinetic,
  author = {Gerhard Tulzer AND Stefan Baumgartner AND Elise Brunet AND Giorgio C. Mutinati AND Stephan Steinhauer AND Anton Köck AND Paolo E. Barbano AND Clemens Heitzinger},
  title = {Kinetic Parameter Estimation and Fluctuation Analysis of {CO} at {SnO$_2$} Single Nanowires},
  journal = {Nanotechnology},
  volume = 24,
  number = 31,
  pages = {315501/1--10},
  month = aug,
  year = 2013,
  url = {http://iopscience.iop.org/0957-4484/24/31/315501/},
  pdf = {Papers/Tulzer2013kinetic.pdf},
  doi = {10.1088/0957-4484/24/31/315501},
  abstract = {In this work, we present calculated numerical values for the
                  kinetic parameters governing adsorption/desorption
                  processes of carbon monoxide at tin dioxide
                  single-nanowire gas sensors.  The response of such
                  sensors to pulses of 50ppm carbon monoxide in
                  nitrogen is investigated at different temperatures
                  to extract the desired information.  A rate-equation
                  approach is used to model the reaction kinetics,
                  which results in the problem of determining
                  coefficients in a coupled system of nonlinear
                  ordinary differential equations.  The numerical
                  values are computed by inverse-modeling techniques
                  and are then used to simulate the sensor response.
                  With our model, the dynamic response of the sensor
                  due to the gas–surface interaction can be studied in
                  order to find the optimal setup for detection, which
                  is an important step towards selectivity of these
                  devices.  We additionally investigate the noise in
                  the current through the nanowire and its changes due
                  to the presence of carbon monoxide in the sensor
                  environment.  Here, we propose the use of a wavelet
                  transform to decompose the signal and analyze the
                  noise in the experimental data.  This method
                  indicates that some fluctuations are specific for
                  the gas species investigated here.}
}
@article{Baumgartner2013one-level,
  author = {Stefan Baumgartner AND Clemens Heitzinger},
  title = {A one-level {FETI} method for the drift-diffusion-{Poisson} system with discontinuities at an interface},
  journal = {J.~Comput.\ Phys.},
  volume = 243,
  pages = {74-86},
  month = jun,
  year = 2013,
  doi = {10.1016/j.jcp.2013.02.043},
  url = {http://dx.doi.org/10.1016/j.jcp.2013.02.043},
  abstract = {A 3d FETI method for the drift-diffusion-Poisson system
                  including discontinuities at a 2d interface is
                  developed.  The motivation for this work is to
                  provide a parallel numerical algorithm for a system
                  of PDEs that are the basic model equations for the
                  simulation of semiconductor devices such as
                  transistors and sensors.  Moreover, discontinuities
                  or jumps in the potential and its normal derivative
                  at a 2d surface are included for the simulation of
                  nanowire sensors based on a homogenized model.
                  Using the FETI method, these jump conditions can be
                  included with the usual numerical properties and the
                  original Farhat-Roux FETI method is extended to the
                  drift-diffusion-Poisson equations including
                  discontinuities.  We show two numerical
                  examples. The first example verifies the correct
                  implementation including the discontinuities on a 2d
                  grid divided into eight subdomains.  The second
                  example is 3d and shows the application of the
                  algorithm to the simulation of nanowire sensors with
                  high aspect ratios.  The Poisson-Boltzmann equation
                  and the drift-diffusion-Poisson system with jump
                  conditions are solved on a 3d grid with real-world
                  boundary conditions.}
}
@article{Baumgartner2013predictive,
  author = {Stefan Baumgartner AND Clemens Heitzinger AND Aleksandar Vacic AND Mark A. Reed},
  title = {Predictive Simulations and Optimization of Nanowire Field-Effect {PSA} Sensors Including Screening},
  journal = {Nanotechnology},
  volume = 24,
  number = 22,
  pages = {225503/1--9},
  month = jun,
  year = 2013,
  url = {http://stacks.iop.org/0957-4484/24/225503},
  pdf = {Papers/Baumgartner2013predictive.pdf},
  doi = {10.1088/0957-4484/24/22/225503},
  abstract = {We apply our self-consistent PDE model for the electrical
                  response of field-effect sensors to the 3D
                  simulation of nanowire PSA (prostate-specific
                  antigen) sensors.  The charge concentration in the
                  biofunctionalized boundary layer at the
                  semiconductor-electrolyte interface is calculated
                  using the PROPKA algorithm, and the screening of the
                  biomolecules by the free ions in the liquid is
                  modeled by a sensitivity factor.  This comprehensive
                  approach yields excellent agreement with
                  experimental current-voltage characteristics without
                  any fitting parameters.  Having verified the
                  numerical model in this manner, we study the
                  sensitivity of nanowire PSA sensors by changing
                  device parameters, making it possible to optimize
                  the devices and revealing the attributes of the
                  optimal field-effect sensor.}
}
@article{Tulzer2012inverse,
  author = {Gerhard Tulzer AND Stefan Baumgartner AND Elise Brunet AND Giorgio C. Mutinati AND Stephan Steinhauer AND Anton Köck AND Clemens Heitzinger},
  title = {Inverse modeling of {CO} reactions at {SnO$_2$} nanowire surfaces for selective detection},
  journal = {Procedia Engineering},
  volume = 47,
  pages = {809-812},
  year = 2012,
  url = {http://dx.doi.org/10.1016/j.proeng.2012.09.270},
  doi = {10.1016/j.proeng.2012.09.270},
  pdf = {Papers/Tulzer2012inverse.pdf},
  abstract = {Nanowire gas sensors show high sensitivity towards various
                  gases and offer great potential to improve present
                  gas sensing. In this work, we investigate
                  experimental results achieved with an undoped single
                  SnO$_2$ nanowire sensor device for CO pulses in N$_2$
                  atmosphere at different operating temperatures. We
                  calculated the reaction parameters according to the
                  mass action law including frequency factors,
                  activation energies, and numbers of intrinsic as
                  well as extrinsic surface sites. With the values
                  obtained, we then calculated the surface charge of
                  the nanowire sensor by solving the corresponding
                  differential equations. The simulated results agree
                  very well with the experimental values at an
                  operating temperature of 200°C and hence provide
                  good understanding of the chemical reaction. This
                  can be used to simulate the current through the
                  transducer and consequently the sensitivity of the
                  device, and the parameters provided here are useful
                  for computational procedures to provide
                  selectivity.}
}
@incollection{Baumgartner2012modeling,
  author = {Stefan Baumgartner AND Martin Vasicek AND Clemens Heitzinger},
  title = {Modeling and Simulation of Nanowire Based Field-Effect Biosensors},
  booktitle = {Chemical Sensors: Simulation and Modeling.  Volume 2: Conductometric-Type Sensors},
  pages = {447-469},
  year = 2012,
  editor = {G. Korotcenkov},
  publisher = {Momentum Press},
  doi = {10.5643/9781606503140/ch12},
  pdf = {Papers/baumgartner2012modeling.pdf},
  abstract = {A book chapter.  Contents:\\ 1. Introduction\\
                  2. Homogenization\\ 3. The biofunctionalized
                  boundary layer\\ 4. The current through the nanowire
                  transducer\\ 5. Summary}
}
@article{Punzet2012determination,
  author = {Manuel Punzet AND Dieter Baurecht AND Franz Varga AND Heidrun Karlic AND Clemens Heitzinger},
  title = {Determination of surface concentrations of individual molecule-layers used in nanoscale biosensors by in-situ {ATR-FTIR} spectroscopy},
  journal = {Nanoscale},
  volume = 4,
  number = 7,
  pages = {2431-2438},
  year = 2012,
  url = {http://pubs.rsc.org/en/Content/ArticleLanding/2012/NR/c2nr12038k},
  doi = {10.1039/C2NR12038K},
  pdf = {Papers/Punzet2012determination.pdf},
  abstract = {For the development of nanowire sensors for chemical and
                  medical detection purposes, the optimal
                  functionalization of the surface is a mandatory
                  component. Quantitative ATR-FTIR spectroscopy was
                  used in-situ to investigate the step-by-step layer
                  formation of typical functionalization protocols and
                  to determine the respective molecule surface
                  concentrations. BSA, anti-TNF-$\alpha$ and anti-PSA
                  antibodies were bound via 3-(trimethoxy)butylsilyl
                  aldehyde linkers to silicon-oxide surfaces in order
                  to investigate surface functionalization of
                  nanowires. Maximum determined surface concentrations
                  were $7.17\times 10^{-13}$ mol cm$^{-2}$ for BSA,
                  $1.7\times 10^{-13}$ mol cm$^{-2}$ for
                  anti-TNF-$\alpha$ antibody, $6.1\times 10^{-13}$ mol
                  cm$^{-2}$ for anti-PSA antibody, $3.88\times 10^{-13}$
                  mol cm$^{-2}$ for TNF-$\alpha$ and
                  $7.0\times 10^{-13}$ mol cm$^{-2}$ for
                  PSA. Furthermore we performed antibody-antigen
                  binding experiments and determined the specific
                  binding ratios. The maximum possible ratios of 2
                  were obtained at bulk concentrations of the antigen
                  in the $\mu$g ml$^{-1}$ range for TNF-$\alpha$ and
                  PSA.},
  ignored_note = {(2011 impact factor of \textit{Nanoscale:} 5.914.)}
}
@article{Baumgartner2012existence,
  author = {Stefan Baumgartner AND Clemens Heitzinger},
  title = {Existence and local uniqueness for 3d self-consistent multiscale models for field-effect sensors},
  journal = {Commun.\ Math.\ Sci.},
  volume = 10,
  number = 2,
  pages = {693--716},
  year = 2012,
  url = {http://www.intlpress.com/CMS/2012/issue10-2/},
  pdf = {Papers/baumgartner2012existence.pdf},
  abstract = {We present existence and local uniqueness theorems for a
                  system of partial differential equations modeling
                  field-effect nano-sensors.  The system consists of
                  the Poisson(-Boltzmann) equation and the
                  drift-diffusion equations coupled with a homogenized
                  boundary layer.  The existence proof is based on the
                  Leray-Schauder fixed-point theorem and a maximum
                  principle is used to obtain a-priori estimates for
                  the electric potential, the electron density, and
                  the hole density.  Local uniqueness around the
                  equilibrium state is obtained from the
                  implicit-function theorem.  Due to the multiscale
                  problem inherent in field-effect biosensors, a
                  homogenized equation for the potential with
                  interface conditions at a surface is used.  These
                  interface conditions depend on the surface-charge
                  density and the dipole-moment density in the
                  boundary layer and still admit existence and local
                  uniqueness of the solution when certain conditions
                  are satisfied.  Due to the geometry and the boundary
                  conditions of the physical system, the
                  three-dimensional case must be considered in
                  simulations.  Therefore a finite-volume
                  discretization of the 3d self-consistent model was
                  implemented to allow comparison of simulation and
                  measurement.  Special considerations regarding the
                  implementation of the interface conditions are
                  discussed so that there is no computational penalty
                  when compared to the problem without interface
                  conditions.  Numerical simulation results are
                  presented and very good quantitative agreement with
                  current-voltage characteristics from experimental
                  data of biosensors is found.},
  pdf = {Papers/baumgartner2012existence.pdf}
}
@article{Baumgartner2011optimization,
  author = {Stefan Baumgartner AND Martin Vasicek AND Alena Bulyha AND Clemens Heitzinger},
  title = {Optimization of nanowire {DNA} sensor sensitivity using self-consistent simulation},
  journal = {Nanotechnology},
  volume = 22,
  number = 42,
  pages = {425503/1--8},
  month = oct,
  year = 2011,
  url = {http://stacks.iop.org/0957-4484/22/425503},
  pdf = {Papers/baumgartner2011optimization.pdf},
  doi = {10.1088/0957-4484/22/42/425503},
  abstract = {In order to facilitate the rational design and the
                  characterization of nanowire field-effect sensors,
                  we have developed a model based on self-consistent
                  charge-transport equations combined with interface
                  conditions for the description of the
                  biofunctionalized surface layer at the
                  semiconductor/electrolyte interface. Crucial
                  processes at the interface, such as the screening of
                  the partial charges of the DNA strands and the
                  influence of the angle of the DNA strands with
                  respect to the nanowire, are computed by a
                  Metropolis Monte Carlo algorithm for charged
                  molecules at interfaces. In order to investigate the
                  sensing mechanism of the device, we have computed
                  the current–voltage characteristics, the
                  electrostatic potential and the concentrations of
                  electrons and holes. Very good agreement with
                  measurements has been found and optimal device
                  parameters have been identified. Our approach
                  provides the capability to study the device
                  sensitivity, which is of fundamental importance for
                  reliable sensing.},
  ignored_note = {(2011 impact factor of \textit{Nanotechnology:} 3.979.)}
}
@article{Baumgartner2011analysis,
  author = {Stefan Baumgartner AND Martin Vasicek AND Clemens Heitzinger},
  title = {Analysis of Field-Effect Biosensors Using Self-Consistent {3D} Drift-Diffusion and {Monte-Carlo} Simulations},
  volume = 25,
  pages = {407-410},
  journal = {Procedia Engineering},
  year = 2011,
  url = {http://dx.doi.org/10.1016/j.proeng.2011.12.101},
  pdf = {Papers/baumgartner2011analysis.pdf},
  doi = {10.1016/j.proeng.2011.12.101},
  abstract = {Field-effect biosensors based on nanowires enjoy
                  considerable popularity due to their high
                  sensitivity and direct electrical readout. However,
                  crucial issues such as the influence of the
                  biomolecules on the charge-carrier transport or the
                  binding of molecules to the surface have not been
                  described satisfactorily yet in a quantitative
                  manner. In order to analyze these effects, we
                  present simulation results based on a 3D macroscopic
                  transport model coupled with Monte-Carlo simulations
                  for the bio-functionalized surface layer. Excellent
                  agreement with measurement data has been found,
                  while detailed study of the influence of the most
                  prominent biomolecules, namely double-stranded DNA
                  and single-stranded DNA, on the current through the
                  semiconductor transducer has been carried out.}
}
@article{Heitzinger2011transport,
  author = {Clemens Heitzinger AND Christian Ringhofer},
  title = {A transport equation for confined structures derived from the {Boltzmann} equation},
  journal = {Commun.\ Math.\ Sci.},
  volume = 9,
  number = 3,
  pages = {829-857},
  year = 2011,
  pdf = {Papers/heitzinger2011transport.pdf},
  abstract = {A system of diffusion-type equations for transport in 3d
                  confined structures is derived from the Boltzmann
                  transport equation for charged particles.  Transport
                  takes places in confined structures and the scaling
                  in the derivation of the diffusion equation is
                  chosen so that transport and scattering occur in the
                  longitudinal direction and the particles are
                  confined in the two transversal directions.  The
                  result are two diffusion-type equations for the
                  concentration and fluxes as functions of position in
                  the longitudinal direction and energy.  Entropy
                  estimates are given.  The transport coefficients
                  depend on the geometry of the problem that is given
                  by arbitrary harmonic confinement potentials.  An
                  important feature of this approach is that the
                  coefficients in the resulting diffusion-type
                  equations are calculated explicitly so that the six
                  position and momentum dimensions of the original 3d
                  Boltzmann equation are reduced to a 2d problem.
                  Finally, numerical results are given and discussed.
                  Applications of this work include the simulation of
                  charge transport in nanowires, nanopores, ion
                  channels, and similar structures.}
}
@article{Bulyha2011algorithm,
  author = {Alena Bulyha AND Clemens Heitzinger},
  title = {An algorithm for three-dimensional {Monte-Carlo} simulation of charge distribution at biofunctionalized surfaces},
  journal = {Nanoscale},
  volume = 3,
  number = 4,
  pages = {1608-1617},
  year = 2011,
  doi = {10.1039/C0NR00791A},
  url = {http://pubs.rsc.org/en/content/articlelanding/2011/nr/c0nr00791a},
  pdf = {Papers/bulyha2011algorithm.pdf},
  abstract = {In this work, a Monte-Carlo algorithm in the
                  constant-voltage ensemble for the calculation of 3d
                  charge concentrations at charged surfaces
                  functionalized with biomolecules is presented.  The
                  motivation for this work is the theoretical
                  understanding of biofunctionalized surfaces in
                  nanowire field-effect biosensors (BioFETs).  This
                  work provides the simulation capability for the
                  boundary layer that is crucial in the detection
                  mechanism of these sensors; slight changes in the
                  charge concentration in the boundary layer upon
                  binding of analyte molecules modulate the
                  conductance of nanowire transducers.  The simulation
                  of biofunctionalized surfaces poses special
                  requirements on the Monte-Carlo simulations and
                  these are addressed by the algorithm.  The
                  constant-voltage ensemble enables us to include the
                  right boundary conditions; the DNA strands can be
                  rotated with respect to the surface; and several
                  molecules can be placed in a single simulation box
                  to achieve good statistics in the case of low ionic
                  concentrations relevant in experiments.  Simulation
                  results are presented for the leading example of
                  surfaces functionalized with PNA and with single-
                  and double-stranded DNA in a sodium-chloride
                  electrolyte.  These quantitative results make it
                  possible to quantify the screening of the
                  biomolecule charge due to the counter-ions around
                  the biomolecules and the electrical double layer.
                  The resulting concentration profiles show a
                  three-layer structure and non-trivial interactions
                  between the electric double layer and the
                  counter-ions.  The numerical results are also
                  important as a reference for the development of
                  simpler screening models.},
  ignored_note = {(2011 impact factor of \textit{Nanoscale:} 5.914.)}
}
@article{Heitzinger2010calculation,
  author = {Clemens Heitzinger AND Yang Liu AND Norbert Mauser AND Christian Ringhofer AND Robert W. Dutton},
  title = {Calculation of Fluctuations in Boundary Layers of Nanowire Field-Effect Biosensors},
  journal = {J. Comput. Theor. Nanosci.},
  volume = 7,
  number = 12,
  pages = {2574-2580},
  year = 2010,
  doi = {10.1166/jctn.2010.1644},
  pdf = {Papers/heitzinger2010calculation.pdf},
  abstract = {Fluctuations in the biofunctionalized boundary layers of
                  nanowire field-effect biosensors are investigated by
                  using the stochastic linearized Poisson-Boltzmann
                  equation. The noise and fluctuations considered here
                  are due to the Brownian motion of the biomolecules
                  in the boundary layer, i.e., the various
                  orientations of the molecules with respect to the
                  surface are associated with their probabilities. The
                  probabilities of the orientations are calculated
                  using their free energy. The fluctuations in the
                  charge distribution give rise to fluctuations in the
                  electrostatic potential and hence in the current
                  through the semiconductor transducer of the sensor,
                  both of which are calculated. A homogenization
                  result for the variance and covariance of the
                  electrostatic potential is presented. In the
                  numerical simulations, a cross section of a silicon
                  nanowire on a flat surface including electrode and
                  back-gate contacts is considered. The
                  biofunctionalized boundary layer contains
                  single-stranded or double-stranded DNA oligomers,
                  and varying values of the surface charge, of the
                  oligomer length, and of the electrolyte ionic
                  strength are investigated.}
}
@article{Heitzinger2010multiscale,
  author = {Clemens Heitzinger AND Norbert Mauser AND Christian Ringhofer},
  title = {Multiscale Modeling of Planar and Nanowire Field-Effect Biosensors},
  journal = {SIAM J.~Appl.\ Math.},
  volume = 70,
  number = 5,
  pages = {1634-1654},
  year = 2010,
  doi = {10.1137/080725027},
  pdf = {Papers/Heitzinger2010multiscale.pdf},
  abstract = {Field-effect nanobiosensors (or BioFETs, biologically
                  sensitive field-effect transistors) have recently
                  been demonstrated experimentally and have thus
                  gained interest as a technology for direct,
                  label-free, real-time, and highly sensitive
                  detection of biomolecules. The experiments have not
                  been accompanied by a quantitative understanding of
                  the underlying detection mechanism. The modeling of
                  field-effect biosensors poses a multiscale problem
                  due to the different length scales in the sensors:
                  the charge distribution and the electric potential
                  of the biofunctionalized surface layer changes on
                  the Angstrom length scale, whereas the exposed
                  sensor area is measured in micrometers squared. Here
                  a multiscale model for the electrostatics of planar
                  and nanowire field-effect sensors is developed by
                  homogenization of the Poisson equation in the
                  biofunctionalized boundary layer. The resulting
                  interface conditions depend on the surface charge
                  density and dipole moment density of the boundary
                  layer. The multiscale model can be coupled to any
                  charge transport model and hence makes the
                  self-consistent quantitative investigation of the
                  physics of field-effect sensors possible. Numerical
                  verifications of the multiscale model are
                  given. Furthermore a silicon nanowire biosensor is
                  simulated to elucidate the influence of the surface
                  charge density and the dipole moment density on the
                  conductance of the semiconductor transducer. The
                  numerical evidence shows that the conductance varies
                  exponentially as a function of both charge and
                  dipole moment. Therefore the dipole moment of the
                  surface layer must be included in biosensor
                  models. The conductance variations ob- served in
                  experiments can be explained by the field effect,
                  and they can be caused by a change in dipole moment
                  alone.}
}
@article{Ringhofer2008multi-scale,
  author = {Christian Ringhofer AND Clemens Heitzinger},
  title = {Multi-Scale Modeling and Simulation of Field-Effect Biosensors},
  journal = {ECS Transactions},
  volume = 14,
  number = 1,
  pages = {11-19},
  year = 2008,
  doi = {10.1149/1.2956012},
  url = {http://ecsdl.org/vsearch/servlet/VerityServlet?KEY=ECSTF8&smode=strresults&sort=rel&maxdisp=25&threshold=0&pjournals=ECSTF8&possible1=heitzinger&possible1zone=article&OUTLOG=NO&viewabs=ECSTF8&key=DISPLAY&docID=1&page=1&chapter=0},
  pdf = {http://ecsdl.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=ECSTF8000014000001000011000001&idtype=cvips&prog=search},
  abstract = {BioFETs (biologically sensitive field-effect transistors)
                  are field-effect biosensors with semiconducting
                  transducers. Their device structure is similar to a
                  MOSFET, except that the gate structure is replaced
                  by an aqueous solution containing the analyte. The
                  detection mechanism is the conductance modulation of
                  the transducer due to binding of the analyte to
                  surface receptors. The main advantage of BioFETs,
                  compared to currently available technology, is
                  label-free operation. We present a quantitative
                  analysis of BioFETs which is centered around
                  multi-scale models. The technique for solving the
                  multi-scale problem used here is the derivation of
                  interface conditions for the Poisson equation that
                  include the effects of the quasi-periodic
                  biofunctionalized boundary layer. The multi-scale
                  model enables self-consistent simulation and can be
                  used with any charge transport model. Hence it
                  provides the foundation for understanding the
                  physics of the sensors by continuum models.}
}
@article{Heitzinger2008modeling,
  author = {Clemens Heitzinger AND Rick Kennell AND Gerhard Klimeck AND Norbert Mauser AND Michael McLennan AND Christian Ringhofer},
  title = {Modeling and Simulation of Field-Effect Biosensors ({BioFETs}) and Their Deployment on the {nanoHUB}},
  journal = {J. Phys.: Conf. Ser.},
  volume = 107,
  pages = {012004/1--12},
  year = 2008,
  doi = {10.1088/1742-6596/107/1/012004},
  url = {http://www.iop.org/EJ/abstract/1742-6596/107/1/012004},
  pdf = {http://www.iop.org/EJ/article/1742-6596/107/1/012004/jpconf8_107_012004.pdf},
  abstract = {BioFETs (biologically active field-effect transistors) are
                  biosensors with a semiconductor transducer. Due to
                  recent experiments demonstrating detection by a
                  field effect, they have gained attention as
                  potentially fast, reliable, and low-cost biosensors
                  for a wide range of applications. Their advantages
                  compared to other technologies are direct,
                  label-free, ultra-sensitive, and (near) real-time
                  operation. We have developed 2D and 3D multi-scale
                  models for planar sensor structures and for nanowire
                  sensors. The multi-scale models are indispensable
                  due to the large difference in the characteristic
                  length scales of the biosensors: the charge
                  distribution in the biofunctionalized surface layer
                  varies on the Angstrom length scale, the diameters
                  of the nanowires are several nanometers, and the
                  sensor lengths measure several micrometers. The
                  multi-scale models for the electrostatic potential
                  can be coupled to any charge transport model of the
                  transducer. Conductance simulations of nanowire
                  sensors with different diameters provide numerical
                  evidence for the importance of the dipole moment of
                  the biofunctionalized surface layer in addition to
                  its surface charge. We have also developed a web
                  interface to our simulators, so that other
                  researchers can access them at the nanohub and
                  perform their own investigations.}
}
@article{Heitzinger2007finite,
  author = {Clemens Heitzinger AND Christian Ringhofer AND Siegfried Selberherr},
  title = {Finite Difference Solutions of the Nonlinear {Schrödinger} Equation and their Conservation of Physical Quantities},
  journal = {Commun.\ Math.\ Sci.},
  volume = 5,
  number = 4,
  pages = {779-788},
  month = dec,
  year = 2007,
  url = {http://www.intlpress.com/CMS/p/2007/issue5-4/CMS-5-4-A2-Heitzinger.pdf},
  pdf = {http://www.intlpress.com/CMS/p/2007/issue5-4/CMS-5-4-A2-Heitzinger.pdf},
  abstract = {The solutions of the nonlinear Schrödinger equation are of
                  great importance for ab initio calculations. It can
                  be shown that such solutions conserve a countable
                  number of quantities, the simplest being the local
                  norm square conservation law. Numerical solutions of
                  high quality, especially for long time intervals,
                  must necessarily obey these conservation laws. In
                  this work we first give the conservation laws that
                  can be calculated by means of Lie theory and then
                  critically compare the quality of different finite
                  difference methods that have been proposed in
                  geometric integration with respect to conservation
                  laws. We find that finite difference schemes derived
                  by writing the Schrödinger equation as an
                  (artificial) Hamiltonian system do not necessarily
                  conserve important physical quantities better than
                  other methods.}
}
@article{Heitzinger2007effective,
  author = {Clemens Heitzinger AND Christian Ringhofer},
  title = {An Effective Quantum Potential for Particle-Particle Interactions in Three-dimensional Semiconductor Device Simulations},
  journal = {J.~Comput.\ Electron.},
  volume = 6,
  number = 4,
  pages = {401-408},
  year = 2007,
  doi = {10.1007/s10825-007-0148-4},
  url = {http://dx.doi.org/10.1007/s10825-007-0148-4},
  pdf = {http://www.springerlink.com/content/x2m56hq080724k05/fulltext.pdf},
  abstract = {The classical Coulomb potential and force can be calculated
                  efficiently using fast multi-pole methods. Effective
                  quantum potentials, however, describe the physics of
                  electron transport in semiconductors more
                  precisely. Such an effective quantum potential was
                  derived previously for the interaction of an
                  electron with a barrier for use in particle-based
                  Monte Carlo semiconductor device simulators. The
                  method is based on a perturbation theory around
                  thermodynamic equilibrium and leads to an effective
                  potential scheme in which the size of the electron
                  depends upon its energy and which is
                  parameter-free. Here we extend the method to
                  electron-electron interactions and show how the
                  effective quantum potential can be evaluated
                  efficiently in the context of many-body
                  problems. Finally several examples illustrate how
                  the momentum of the electrons changes the classical
                  potential.}
}
@article{Heitzinger2007computational,
  author = {Clemens Heitzinger AND Gerhard Klimeck},
  title = {Computational Aspects of the Three-Dimensional Feature-Scale Simulation of Silicon-Nanowire Field-Effect Sensors for {DNA} Detection},
  journal = {J.~Comput.\ Electron.},
  volume = 6,
  number = {1-3},
  pages = {387-390},
  year = 2007,
  doi = {10.1007/s10825-006-0139-x},
  url = {http://www.springerlink.com/content/k888322550q77216/?p=3775349bb29e4462a47731b834eecf5b&pi=2},
  pdf = {http://www.springerlink.com/content/k888322550q77216/fulltext.pdf},
  abstract = {In recent years DNA-sensors, and generally biosensors, with
                  semiconducting transducers were fabricated and
                  characterized. Although the concept of so-called
                  BioFETs was proposed already two decades ago, its
                  realization has become feasible only recently due to
                  advances in process technology. In this paper a
                  comprehensive and rigorous approach to the
                  simulation of silicon-nanowire DNAFETs at the
                  feature-scale is presented. It allows to investigate
                  the feasibility of single-molecule detectors and is
                  used to elucidate the performance that can be
                  expected from sensors with nanowire diameters in the
                  deca-nanometer range. Finally the computational
                  challenges for the simulation of silicon-nanowire
                  DNA-sensors are discussed.}
}
@article{Heitzinger2007Monte,
  author = {Clemens Heitzinger AND Christian Ringhofer AND Shaikh Ahmed AND Dragica Vasileska},
  title = {{3D} {Monte-Carlo} Device Simulations Using an Effective Quantum Potential Including Electron-Electron Interactions},
  journal = {J.~Comput.\ Electron.},
  volume = 6,
  number = {1-3},
  pages = {15-18},
  year = 2007,
  doi = {10.1007/s10825-006-0058-x},
  url = {http://www.springerlink.com/content/k5550m151310078v/?p=3775349bb29e4462a47731b834eecf5b&pi=0},
  pdf = {http://www.springerlink.com/content/k5550m151310078v/fulltext.pdf},
  abstract = {Effective quantum potentials describe the physics of
                  quantum-mechanical electron transport in
                  semiconductors more than the classical Coulomb
                  potential. An effective quantum potential was
                  derived previously for the interaction of an
                  electron with a barrier for use in particle-based
                  Monte Carlo semiconductor device simulators. The
                  method is based on a perturbation theory around
                  thermodynamic equilibrium and leads to an effective
                  potential scheme in which the size of the electron
                  depends upon its energy and which is
                  parameter-free. Here we extend the method to
                  electron-electron interactions and show how the
                  effective quantum potential can be evaluated
                  efficiently in the context of many-body
                  problems. The effective quantum potential was used
                  in a three-dimensional Monte-Carlo device simulator
                  for calculating the electron-electron and
                  electron-barrier interactions. Simulation results
                  for an SOI transistor are presented and illustrate
                  how the effective quantum potential changes the
                  characteristics compared to the classical
                  potential.}
}
@article{Wessner2006anisotropic,
  author = {Wilfried Wessner AND Johann Cervenka AND Clemens Heitzinger AND Andreas Hössinger AND Siegfried Selberherr},
  title = {Anisotropic Mesh Refinement for the Simulation of Three-Dimensional Semiconductor Manufacturing Processes},
  journal = {IEEE Trans.\ Computer-Aided Design of Integrated Circuits and Systems},
  volume = 25,
  number = 10,
  pages = {2129-2139},
  month = oct,
  year = 2006,
  doi = {10.1109/TCAD.2005.862750},
  url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?arnumber=1677696&isnumber=35285&punumber=43&k2dockey=1677696@ieeejrns&query=%28heitzinger+%3Cin%3E+metadata%29+%3Cand%3E+%2843+%3Cin%3E+punumber%29&pos=0},
  pdf = {http://ieeexplore.ieee.org/iel5/43/35285/01677696.pdf?tp=&isnumber=35285&arnumber=1677696&punumber=%3Cb%3E%3Cfont%20color=990000%3E43%3C/font%3E%3C/b%3E},
  doi = {10.1109/TCAD.2005.862750},
  abstract = {This paper presents an anisotropic adaptation strategy for
                  three-dimensional unstructured tetrahedral meshes,
                  which allows us to produce thin mostly anisotropic
                  layers at the outside margin, i.e., the skin of an
                  arbitrary meshed simulation domain. An essential
                  task for any modern algorithm in the finite-element
                  solution of partial differential equations,
                  especially in the field of semiconductor process and
                  device simulation, the major application is to
                  provide appropriate resolution of the partial
                  discretization mesh. The start-up conditions for
                  semiconductor process and device simulations claim
                  an initial mesh preparation that is performed by
                  so-called Laplace refinement. The basic idea is to
                  solve Laplace’s equation on an initial coarse mesh
                  with Dirichlet boundary conditions. Afterward, the
                  gradient field is used to form an anisotropic metric
                  that allows to refine the initial mesh based on
                  tetrahedral bisection.}
}
@article{Heitzinger2005method,
  author = {Clemens Heitzinger AND Alireza Sheikholeslami AND Jong-Mun Park AND Siegfried Selberherr},
  title = {A Method for Generating Structurally Aligned Grids for Semiconductor Device Simulation},
  journal = {IEEE Trans.\ Computer-Aided Design of Integrated Circuits and Systems},
  volume = 24,
  number = 10,
  pages = {1485-1491},
  month = oct,
  year = 2005,
  url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?arnumber=1512368&isnumber=32384&punumber=43&k2dockey=1512368@ieeejrns&query=%28heitzinger+%3Cin%3E+metadata%29+%3Cand%3E+%2843+%3Cin%3E+punumber%29&pos=1},
  pdf = {http://ieeexplore.ieee.org/iel5/43/32384/01512368.pdf?tp=&isnumber=32384&arnumber=1512368&punumber=%3Cb%3E%3Cfont%20color=990000%3E43%3C/font%3E%3C/b%3E},
  doi = {10.1109/TCAD.2005.852297},
  abstract = {The quality of the numeric approximation of the partial
                  differential equations governing carrier transport
                  in semiconductor devices depends particularly on the
                  grid. The method of choice is to use structurally
                  aligned grids since the regions and directions
                  therein that determine device behavior are usually
                  straightforward to find as they depend on the
                  distribution of doping. Here, the authors present an
                  algorithm for generating structurally aligned grids
                  including anisotropy with resolutions varying over
                  several orders of magnitude. The algorithm is based
                  on a level set approach and permits to define the
                  refined resolutions in a flexible manner as a
                  function of doping. Furthermore, criteria on grid
                  quality can be enforced. In order to show the
                  practicability of this method, the authors study the
                  examples of a trench gate metal-oxide-semiconductor
                  field-effect transistor (TMOSFET) and a radio
                  frequency silicon-on-insulator lateral double
                  diffused metal-oxide-semiconductor (RF SOI LDMOS)
                  power device using the device simulator MINIMOS NT,
                  where simulations are performed on a grid generated
                  by the new algorithm. In order to resolve the
                  interesting regions of the TMOSFET and the RF SOI
                  LDMOS power device accurately, several regions of
                  refinement were defined where the grid was grown
                  with varying resolutions.}
}
@article{Vasileska2005quantum,
  author = {Dragica Vasileska AND Hasanur Khan AND Shaikh Ahmed AND Christian Ringhofer AND Clemens Heitzinger},
  title = {Quantum and {Coulomb} Effects in Nanodevices},
  journal = {International Journal of Nanoscience},
  volume = 4,
  number = 3,
  pages = {305-361},
  month = jun,
  year = 2005,
  url = {http://www.worldscinet.com/ijn/04/0403/S0219581X05003164.html},
  pdf = {http://www.worldscinet.com/ijn/04/preserved-docs/0403/S0219581X05003164.pdf},
  abstract = {In state-of-the-art devices, it is well known that quantum
                  and Coulomb effects play significant role on the
                  device operation. In this paper, we demonstrate that
                  a novel effective potential approach in conjunction
                  with a Monte Carlo device simulation scheme can
                  accurately capture the quantum-mechanical size
                  quantization effects. We also demonstrate, via
                  proper treatment of the short-range Coulomb
                  interactions, that there will be significant
                  variation in device design parameters for devices
                  fabricated on the same chip due to the presence of
                  unintentional dopant atoms at random locations
                  within the channel.}
}
@article{Ahmed2005quantum,
  author = {Shaikh Ahmed AND Dragica Vasileska AND Clemens Heitzinger AND Christian Ringhofer},
  title = {Quantum Potential Approach to Modeling Nanoscale {MOSFETs}},
  journal = {J.~Comput.\ Electron.},
  volume = 4,
  number = {1-2},
  pages = {57-61},
  year = 2005,
  url = {http://www.springerlink.com/content/q0745k8845157147/?p=3775349bb29e4462a47731b834eecf5b&pi=4},
  pdf = {http://www.springerlink.com/content/q0745k8845157147/fulltext.pdf},
  abstract = {We propose a novel parameter-free quantum potential scheme
                  for use in conjunction with particle-based
                  simulations. The method is based on a perturbation
                  theory around thermodynamic equilibrium and leads to
                  an effective potential scheme in which the size of
                  the electron depends upon its energy. The approach
                  has been tested on the example of a MOS-capacitor by
                  retrieving the correct sheet electron density. It
                  has also been used in simulations of a 25 nm
                  n-channel nanoscale MOSFET with high substrate
                  doping density. We find that the use of the quantum
                  potential approach gives rise to a threshold voltage
                  shift of about 220 mV and drain current degradation
                  of about 30\%.}
}
@article{Khan2004modeling,
  author = {Hasanur Khan AND Dragica Vasileska AND Shaikh Ahmed AND Christian Ringhofer AND Clemens Heitzinger},
  title = {Modeling of {FinFET}: {3D} {MC} Simulation Using {FMM} and Unintentional Doping Effects on Device Operation},
  journal = {J.~Comput.\ Electron.},
  volume = 3,
  number = {3-4},
  pages = {337-340},
  year = 2004,
  url = {http://www.springerlink.com/content/p187g1k0707k65t4/?p=3775349bb29e4462a47731b834eecf5b&pi=3},
  pdf = {http://www.springerlink.com/content/p187g1k0707k65t4/fulltext.pdf},
  abstract = {Novel device concepts such as dual gate SOI, Ultra thin body
                  SOI, FinFETs, etc., have emerged as a solution to
                  the ultimate scaling limits of conventional bulk
                  MOSFETs. These novel devices suppress some of the
                  Short Channel Effects (SCE) efficiently, but at the
                  same time more physics based modeling is required to
                  investigate device operation. In this paper, we use
                  semi-classical 3D Monte Carlo device simulator to
                  investigate important issues in the operation of
                  FinFETs. Fast Multipole Method (FMM) has been
                  integrated with the EMC scheme to replace the time
                  consuming Poisson equation solver. Effect of
                  unintentional doping for different device dimensions
                  has been investigated. Impurities at the source side
                  of the channel have most significant impact on the
                  device performance.}
}
@article{Holzer2004extraction,
  author = {Stefan Holzer AND Rainer Minixhofer AND Clemens Heitzinger AND Johannes Fellner AND Tibor Grasser AND Siegfried Selberherr},
  title = {Extraction of Material Parameters Based on Inverse Modeling of Three-Dimensional Interconnect Fusing Structures},
  journal = {Microelectronics Journal},
  volume = 35,
  number = 10,
  pages = {805-810},
  year = 2004,
  url = {http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V44-4CXTWXT-1&_user=103677&_coverDate=10%2F01%2F2004&_rdoc=5&_fmt=summary&_orig=browse&_srch=doc-info(%23toc%235748%232004%23999649989%23519251%23FLA%23display%23Volume)&_cdi=5748&_sort=d&_docanchor=&view=c&_ct=12&_acct=C000007978&_version=1&_urlVersion=0&_userid=103677&md5=50173218fbb91d7fffc427de2ce77c36},
  pdf = {http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6V44-4CXTWXT-1-K&_cdi=5748&_user=103677&_orig=browse&_coverDate=10%2F01%2F2004&_sk=999649989&view=c&wchp=dGLbVzb-zSkWA&md5=4c8af46a84181bb2cc4443bee0dda4bb&ie=/sdarticle.pdf},
  html = {http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V44-4CXTWXT-1&_user=103677&_coverDate=10%2F01%2F2004&_rdoc=5&_fmt=full&_orig=browse&_srch=doc-info(%23toc%235748%232004%23999649989%23519251%23FLA%23display%23Volume)&_cdi=5748&_sort=d&_docanchor=&view=c&_ct=12&_acct=C000007978&_version=1&_urlVersion=0&_userid=103677&md5=62e230f1069b06e7f40ebc6a2a9eb884},
  abstract = {An approach for determining higher order coefficients of the
                  electrical and thermal conductivities for different
                  materials is presented. The method is based on
                  inverse modeling using three-dimensional transient
                  electrothermal finite element simulations for
                  electrothermal investigations of complex layered
                  structures, for instance polycrystalline silicon
                  (polysilicon) fuses or other multi-layered
                  devices. The simulations are performed with a
                  three-dimensional interconnect simulator, which is
                  automatically configured and controlled by an
                  optimization framework. Our method is intended to be
                  applied to optimize devices with different material
                  compositions and geometries as well as for achieving
                  an optimum of speed and reliability.}
}
@article{Heitzinger2004feature,
  author = {Clemens Heitzinger AND Alireza Sheikholeslami AND Fuad Badrieh AND Helmut Puchner AND Siegfried Selberherr},
  title = {Feature-Scale Process Simulation and Accurate Capacitance Extraction for the Backend of a 100-nm Aluminum/{TEOS} Process},
  journal = {IEEE Trans.\ Electron Devices},
  volume = 51,
  number = 7,
  pages = {1129-1134},
  month = jul,
  year = 2004,
  url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?arnumber=1308637&isnumber=29042&punumber=16&k2dockey=1308637@ieeejrns&query=%28%28heitzinger%29%3Cin%3Emetadata%29&pos=5},
  pdf = {http://ieeexplore.ieee.org/iel5/16/29042/01308637.pdf?tp=&isnumber=29042&arnumber=1308637&punumber=16},
  doi = {10.1109/TED.2004.829868},
  abstract = {One of the challenges that technology computer-aided design
                  must meet currently is the analysis of the
                  performance of groups of components, interconnects,
                  and, generally speaking, large parts of the IC. This
                  enables predictions that the simulation of single
                  components cannot achieve. In this paper, we focus
                  on the simulation of backend processes, interconnect
                  capacitances, and time delays. The simulation flows
                  start from the blank wafer surface and result in
                  device information for the circuit designer usable
                  from within SPICE. In order to join topography and
                  backend simulations, deposition, etching, and
                  chemical mechanical planarization processes in the
                  various metal lines are used to build up the backend
                  stack, starting from the flat wafer
                  surface. Depending on metal combination,
                  line-to-line space, and line width, thousands of
                  simulations are required whose results are stored in
                  a database. Finally, we present simulation results
                  for the backend of a 100-nm process, where the
                  influence of void formation between metal lines
                  profoundly impacts the performance of the whole
                  interconnect stack, consisting of aluminum metal
                  lines, and titanium nitride local
                  interconnects. Scanning electron microscope images
                  of test structures are compared to topography
                  simulations, and very good agreement is
                  found. Moreover, charge-based capacitance
                  measurements were carried out to validate the
                  capacitance extraction, and it was found that the
                  error is smaller than four percent. These
                  simulations assist the consistent fabrication of
                  voids, which is economically advantageous compared
                  to low-$\kappa$ materials, which suffer from
                  integration problems.}
}
@article{Heitzinger2004algorithm,
  author = {Clemens Heitzinger AND Andreas Hössinger AND Siegfried Selberherr},
  title = {An Algorithm for Smoothing Three-Dimensional {Monte Carlo} Ion Implantation Simulation Results},
  journal = {Mathematics and Computers in Simulation},
  volume = 66,
  number = {2-3},
  pages = {219-230},
  month = jun,
  year = 2004,
  url = {http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V0T-4BGW348-1&_user=103677&_coverDate=06%2F29%2F2004&_rdoc=10&_fmt=summary&_orig=browse&_srch=doc-info(%23toc%235655%232004%23999339997%23506199%23FLA%23display%23Volume)&_cdi=5655&_sort=d&_docanchor=&view=c&_ct=13&_acct=C000007978&_version=1&_urlVersion=0&_userid=103677&md5=8780e2ecc4ccb01edc1293ee0931056f},
  pdf = {http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6V0T-4BGW348-1-40&_cdi=5655&_user=103677&_orig=browse&_coverDate=06%2F29%2F2004&_sk=999339997&view=c&wchp=dGLbVzW-zSkzV&md5=36c6e1eb5522ca99e2cc94028e626a46&ie=/sdarticle.pdf},
  html = {http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V0T-4BGW348-1&_user=103677&_coverDate=06%2F29%2F2004&_rdoc=10&_fmt=full&_orig=browse&_srch=doc-info(%23toc%235655%232004%23999339997%23506199%23FLA%23display%23Volume)&_cdi=5655&_sort=d&_docanchor=&view=c&_ct=13&_acct=C000007978&_version=1&_urlVersion=0&_userid=103677&md5=f4e4092bcdf02e85b59685c1aa560a92},
  abstract = {We present an algorithm for smoothing results of
                  three-dimensional Monte Carlo ion implantation
                  simulations and translating them from the grid used
                  for the Monte Carlo simulation to an arbitrary
                  unstructured three-dimensional 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 ortho-grids 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 three-dimensional real world
                  implantation example are given and compared with
                  those of a least squares fit of a multivariate
                  polynomial of degree 2, which yielded unusable
                  results.}
}
@article{Binder2004study,
  author = {Thomas Binder AND Clemens Heitzinger AND Siegfried Selberherr},
  title = {A Study on Global and Local Optimization Techniques for {TCAD} Analysis Tasks},
  journal = {IEEE Trans.\ Computer-Aided Design of Integrated Circuits and Systems},
  volume = 23,
  number = 6,
  pages = {814-822},
  month = jun,
  year = 2004,
  url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?arnumber=1302183&isnumber=28935&punumber=43&k2dockey=1302183@ieeejrns&query=%28heitzinger+%3Cin%3E+metadata%29+%3Cand%3E+%2843+%3Cin%3E+punumber%29&pos=4},
  pdf = {http://ieeexplore.ieee.org/iel5/43/28935/01302183.pdf?tp=&isnumber=28935&arnumber=1302183&punumber=%3Cb%3E%3Cfont%20color=990000%3E43%3C/font%3E%3C/b%3E},
  doi = {10.1109/TCAD.2004.828130},
  abstract = {We evaluate optimization techniques to reduce the necessary
                  user interaction for inverse modeling applications
                  as they are used in the technology computer-aided
                  design field. Four optimization strategies are
                  compared. Two well-known global optimization
                  methods, simulated annealing and genetic
                  optimization, a local gradient-based optimization
                  strategy, and a combination of a local and a global
                  method. We rate the applicability of each method in
                  terms of the minimal achievable target value for a
                  given number of simulation runs and in terms of the
                  fastest convergence. A brief overview over the three
                  used optimization algorithms is given. The
                  optimization framework that is used to distribute
                  the workload over a cluster of workstations is
                  described. The actual comparison is achieved by
                  means of an inverse modeling application that is
                  performed for various settings of the optimization
                  algorithms. All presented optimization algorithms
                  are capable of evaluating several targets in
                  parallel. The best optimization strategy that is
                  found is used in the calibration of a model for
                  silicon self-interstitial cluster formation and
                  dissolution.}
}
@article{Heitzinger2004note,
  author = {Clemens Heitzinger AND Christian Ringhofer},
  title = {A Note on the Symplectic Integration of the Nonlinear {Schrödinger} Equation},
  journal = {J.~Comput.\ Electron.},
  volume = 3,
  number = 1,
  pages = {33-44},
  year = 2004,
  url = {http://www.springerlink.com/content/h4463821jm220u5t/?p=3775349bb29e4462a47731b834eecf5b&pi=1},
  pdf = {http://www.springerlink.com/content/h4463821jm220u5t/fulltext.pdf},
  abstract = {Numerically solving the nonlinear Schrödinger equation and
                  being able to treat arbitrary space dependent
                  potentials permits many application in the realm of
                  quantum mechanics. The long-term stability of a
                  numerical method and its conservation properties is
                  an important feature since it assures that the
                  underlying physics of the solution are respected and
                  it ensures that the numerical result is correct also
                  for small time spans. In this paper we describe
                  symplectic integrators for the nonlinear Schrödinger
                  equation with arbitrary potentials and perform
                  numerical experiments comparing different approaches
                  and highlighting their respective advantages and
                  disadvantages.}
}
@article{Heitzinger2004formation,
  author = {Clemens Heitzinger AND Siegfried Selberherr},
  title = {On the Simulation of the Formation and Dissolution of Silicon Self-Interstitial Clusters and the Corresponding Inverse Modeling Problem},
  journal = {Microelectronics Journal},
  volume = 35,
  number = 2,
  pages = {167-171},
  month = feb,
  year = 2004,
  url = {http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V44-49XPJ15-1&_user=103677&_coverDate=02%2F29%2F2004&_rdoc=9&_fmt=summary&_orig=browse&_srch=doc-info(%23toc%235748%232004%23999649997%23475108%23FLA%23display%23Volume)&_cdi=5748&_sort=d&_docanchor=&view=c&_ct=16&_acct=C000007978&_version=1&_urlVersion=0&_userid=103677&md5=39083ba6722ea306c8cb62ad73740772},
  pdf = {http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6V44-49XPJ15-1-33&_cdi=5748&_user=103677&_orig=browse&_coverDate=02%2F29%2F2004&_sk=999649997&view=c&wchp=dGLbVzb-zSkzk&md5=3204cfc96191be632aed663d9be92d6d&ie=/sdarticle.pdf},
  html = {http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V44-49XPJ15-1&_user=103677&_coverDate=02%2F29%2F2004&_rdoc=9&_fmt=full&_orig=browse&_srch=doc-info(%23toc%235748%232004%23999649997%23475108%23FLA%23display%23Volume)&_cdi=5748&_sort=d&_docanchor=&view=c&_ct=16&_acct=C000007978&_version=1&_urlVersion=0&_userid=103677&md5=0a7c1dc34660e04844934633e3ddfb52},
  abstract = {The formation and dissolution of silicon self-interstitial
                  clusters is linked to the phenomenon of
                  transient-enhanced diffusion (TED) which in turn has
                  gained importance in the manufacturing of
                  semiconductor devices. Based on theoretical
                  considerations and measurements of the number of
                  self-interstitial clusters during a thermal step, a
                  model for the formation and dissolution of
                  self-interstitial clusters is presented including
                  the adjusted 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. In addition
                  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.}
}
@article{Heitzinger2003smoothing,
  author = {Clemens Heitzinger AND Andreas Hössinger AND Siegfried Selberherr},
  title = {On Smoothing Three-Dimensional {Monte Carlo} Ion Implantation Simulation Results},
  journal = {IEEE Trans.\ Computer-Aided Design of Integrated Circuits and Systems},
  volume = 22,
  number = 7,
  pages = {879-883},
  month = jul,
  year = 2003,
  url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?arnumber=1208447&isnumber=27194&punumber=43&k2dockey=1208447@ieeejrns&query=%28heitzinger+%3Cin%3E+metadata%29+%3Cand%3E+%2843+%3Cin%3E+punumber%29&pos=2},
  pdf = {http://ieeexplore.ieee.org/iel5/43/27194/01208447.pdf?tp=&isnumber=27194&arnumber=1208447&punumber=%3Cb%3E%3Cfont%20color=990000%3E43%3C/font%3E%3C/b%3E},
  doi = {10.1109/TCAD.2003.814259},
  abstract = {An algorithm for smoothing results of three-dimensional
                  (3-D) Monte Carlo ion implantation simulations and
                  translating them from the grid used for the Monte
                  Carlo simulation to an arbitrary unstructured 3-D
                  grid is presented. This algorithm is important for
                  joining various process simulation steps, where data
                  have to be smoothed or transferred from one grid to
                  another. Furthermore, it is important for
                  integrating the ion implantation simulator into a
                  process flow. One reason for using different grids
                  is that for certain Monte Carlo simulation methods,
                  using orthogrids is mandatory because of performance
                  reasons.

                  The algorithm presented sweeps a small
                  rectangular grid over the points of the new
                  tetrahedral grid and uses approximation 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 adverse effects of least squares
                  fits of polynomials of fixed degree as known from
                  the response surface method.

                  The most important
                  properties of Bernstein polynomials generalized to
                  cuboid domains are presented, including uniform
                  convergence, an asymptotic formula, and the
                  variation diminishing property. The smoothing
                  algorithm which works very fast is described and, in
                  order to show its applicability, the resulting
                  values of a 3-D 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.}
}
@article{Heitzinger2003simulation,
  author = {Clemens Heitzinger AND Wolfgang Pyka AND Naoki Tamaoki AND Toshiro Takase AND Toshimitsu Ohmine AND Siegfried Selberherr},
  title = {Simulation of Arsenic In-Situ Doping with Poly-Silicon {CVD} and its Application to High Aspect Ratio Trenches},
  journal = {IEEE Trans.\ Computer-Aided Design of Integrated Circuits and Systems},
  volume = 22,
  number = 3,
  pages = {285-292},
  month = mar,
  year = 2003,
  url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?arnumber=1182073&isnumber=26533&punumber=43&k2dockey=1182073@ieeejrns&query=%28heitzinger+%3Cin%3E+metadata%29+%3Cand%3E+%2843+%3Cin%3E+punumber%29&pos=3},
  pdf = {http://ieeexplore.ieee.org/iel5/43/26533/01182073.pdf?tp=&isnumber=26533&arnumber=1182073&punumber=%3Cb%3E%3Cfont%20color=990000%3E43%3C/font%3E%3C/b%3E},
  doi = {10.1109/TCAD.2002.807879},
  abstract = {Filling high aspect ratio trenches is an essential
                  manufacturing step for state of the art memory
                  cells. Understanding and simulating the transport
                  and surface processes enables to achieve voidless
                  filling of deep trenches, to predict the resulting
                  profiles, and thus to optimize the process
                  parameters and the resulting memory cells.

                  Experiments of arsenic doped polysilicon deposition
                  show that under certain process conditions step
                  coverages greater than unity can be achieved. We
                  developed a new model for the simulation of arsenic
                  doped polysilicon deposition, which takes into
                  account surface coverage dependent sticking
                  coefficients and surface coverage dependent arsenic
                  incorporation and desorption rates. The additional
                  introduction of Langmuir--Hinshelwood type time
                  dependent surface coverage enabled the reproduction
                  of the bottom up filling of the trenches in
                  simulations. Additionally, the rigorous treatment of
                  the time dependent surface coverage allows to trace
                  the in situ doping of the deposited film.

                  The model
                  presented was implemented and simulations were
                  carried out for different process parameters. Very
                  good agreement with experimental data was achieved
                  with theoretically deduced parameters. Simulation
                  results are shown and discussed for polysilicon
                  deposition into 0.1$\mu$m wide and 7$\mu$m deep,
                  high aspect ratio trenches.}
}
@article{Grasser2002characterization,
  author = {Tibor Grasser AND Hans Kosina AND Clemens Heitzinger AND Siegfried Selberherr},
  title = {Characterization of the Hot Electron Distribution Function Using Six Moments},
  journal = {J.~Appl.\ Phys.},
  volume = 91,
  number = 6,
  pages = {3869-3879},
  year = 2002,
  url = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JAPIAU000091000006003869000001&idtype=cvips&gifs=yes},
  pdf = {http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JAPIAU000091000006003869000001&idtype=cvips&prog=normal},
  html = {http://scitation.aip.org/journals/doc/JAPIAU-ft/vol_91/iss_6/3869_1.html},
  doi = {10.1063/1.1450257},
  abstract = {The shape of the hot electron distribution function in
                  semiconductor devices is insufficiently described
                  using only the first four moments. We propose using
                  six moments of the distribution function to obtain a
                  more accurate description of hot carrier
                  phenomena. An analytic expression for the symmetric
                  part of the distribution function as a function of
                  the even moments is given which shows good agreement
                  with Monte Carlo data for both the bulk case and
                  inside n$^+$-n-n$^+$ test structures. The influence
                  of the band structure on the parameters of the
                  distribution function is studied and proven to be of
                  importance for an accurate description.}
}
@article{Heitzinger2002extensible,
  author = {Clemens Heitzinger AND Siegfried Selberherr},
  title = {An Extensible {TCAD} Optimization Framework Combining Gradient Based and Genetic Optimizers},
  journal = {Microelectronics Journal},
  year = 2002,
  volume = 33,
  number = {1-2},
  pages = {61-68},
  url = {http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V44-44RNMMN-9&_user=103677&_coverDate=01%2F02%2F2002&_rdoc=9&_fmt=summary&_orig=browse&_srch=doc-info(%23toc%235748%232002%23999669998%23279355%23FLA%23display%23Volume)&_cdi=5748&_sort=d&_docanchor=&view=c&_ct=21&_acct=C000007978&_version=1&_urlVersion=0&_userid=103677&md5=c4fe291cc7b11174beac29f24f4f42a3},
  pdf = {http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6V44-44RNMMN-9-10&_cdi=5748&_user=103677&_orig=browse&_coverDate=01%2F02%2F2002&_sk=999669998&view=c&wchp=dGLbVtb-zSkzk&md5=455e6caec00f729b76c54e716bdecf40&ie=/sdarticle.pdf},
  html = {http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V44-44RNMMN-9&_user=103677&_coverDate=01%2F02%2F2002&_rdoc=9&_fmt=full&_orig=browse&_srch=doc-info(%23toc%235748%232002%23999669998%23279355%23FLA%23display%23Volume)&_cdi=5748&_sort=d&_docanchor=&view=c&_ct=21&_acct=C000007978&_version=1&_urlVersion=0&_userid=103677&md5=4d1c918839690f0c4321db0eff56a409},
  abstract = {The SIESTA framework is an extensible tool for optimization
                  and inverse modeling of semiconductor devices
                  including dynamic load balancing for taking
                  advantage of several, loosely connected
                  workstations. Two gradient-based and two
                  evolutionary computation optimizers are currently
                  available through a uniform interface and can be
                  combined at will. At a real world inverse modeling
                  example, we demonstrate that evolutionary
                  computation optimizers provide several advantages
                  over gradient-based optimizers, due to the specific
                  properties of the objective functions in TCAD
                  applications. Furthermore, we shortly discuss some
                  issues arising in inverse modeling and conclude with
                  a comparison of gradient-based and evolutionary
                  computation optimizers from a TCAD point of view.}
}
@article{Grasser2002accurate,
  author = {Tibor Grasser AND Hans Kosina AND Clemens Heitzinger AND Siegfried Selberherr},
  title = {Accurate Impact Ionization Model which Accounts for Hot and Cold Carrier Populations},
  journal = {Appl.\ Phys.\ Lett.},
  volume = 80,
  number = 4,
  month = jan,
  pages = {613-615},
  year = 2002,
  url = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=APPLAB000080000004000613000001&idtype=cvips&gifs=yes},
  pdf = {http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=APPLAB000080000004000613000001&idtype=cvips&prog=normal},
  html = {http://scitation.aip.org/journals/doc/APPLAB-ft/vol_80/iss_4/613_1.html},
  doi = {10.1063/1.1445273},
  abstract = {Conventional macroscopic impact ionization models which use
                  the average carrier energy as a main parameter can
                  not accurately describe the phenomenon in modern
                  miniaturized devices. Here, we present a 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 metal-oxide-semiconductor
                  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.}
}

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