# Publications-journals.bib

@comment{{This file has been generated by bib2bib 1.99}}

@comment{{Command line: bib2bib -ob Publications-journals.bib -c '($type = "ARTICLE" or$type = "INCOLLECTION") and (not hide : "true") and (not hide_online : "true")' /Users/Clemens/Documents/CV/Publications.bib}}

@comment{{submitted to IEEE Trans. on Neural Networks and Learning Systems)
}}

@article{MoralesPREstochastic,
author = {Jose A. Morales Escalante AND Clemens Heitzinger},
title = {Stochastic {Galerkin} Methods for the {Boltzmann}-{Poisson} system},
pages = {1-25},
note = {\textit{Submitted for publication}}
}

@article{BoeckPREsuperhuman,
author = {Markus Böck AND Julien Malle AND Daniel Pasterk AND Hrvoje Kukina AND Ramin Hasani AND Clemens Heitzinger},
title = {Superhuman performance for sepsis treatment by distributional reinforcement learning},
pages = {1-17},
note = {\textit{In review}}
}

@article{BoeckPREspeedy,
author = {Markus Böck AND Clemens Heitzinger},
title = {Speedy Categorical Distributional Reinforcement Learning and Complexity Analysis},
pages = {1-16},
note = {\textit{Submitted for publication}}
}

@article{BlankrotPRErobust,
author = {Boaz Blankrot AND Clemens Heitzinger},
title = {On the robust optimization of photonic structures for asymmetric light transmission},
note = {\textit{Submitted for publication}}
}

@article{TaghizadehPREanalysis,
title = {Analysis of the stochastic drift-diffusion-{Poisson} system with applications in nanoscale devices},
note = {\textit{Submitted for publication}}
}

@article{Mitscha-Baude2021protein,
author = {Gregor Mitscha-Baude AND Benjamin Stadlbauer AND Stefan Howorka AND Clemens Heitzinger},
title = {Protein transport through nanospace illuminated by high-throughput simulations},
journal = {ACS Nano},
volume = 15,
pages = {9900-9912},
year = 2021,
url = {https://doi.org/10.1021/acsnano.1c01078},
pdf = {Papers/Mitscha-Baude2021protein.pdf},
doi = {10.1021/acsnano.1c01078},
abstract = {The transport of molecules through nanoscale confined space
is relevant in biology, biosensing, and industrial
filtration. Microscopically modeling transport
through nanopores is required for a fundamental
understanding and guiding engineering, but the short
duration and low replica number of existing
simulation approaches limit statistically relevant
insight. Here we explore protein transport in
nanopores with a high-throughput computational
method that realistically simulates hundreds of up
to seconds-long protein trajectories by combining
Brownian dynamics and continuum simulation and
integrating both driving forces of electroosmosis
and electrophoresis. Ionic current traces are
computed to enable experimental comparison. By
examining three biological and synthetic nanopores,
mechanism of protein transport and additionally
reveals insight that is inaccessible from
experiments yet relevant for pore design. The
discovery of extremely frequent unhindered passage
can guide the improvement of biosensor pores to
enhance desired biomolecular recognition by
pore-tethered receptors. Similarly, experimentally
invisible nontarget adsorption to pore walls
highlights how to improve recently developed DNA
nanopores. Our work can be expanded to
pressure-driven flow to model industrial
nanofiltration processes.}
}

@article{Abbaszadeh2021local,
title = {Application of direct meshless local {Petrov}-{Galerkin} method for numerical solution of stochastic elliptic interface problems},
journal = {Numerical Methods for Partial Differential Equations},
volume = {TBD},
pages = {TBD},
year = 2021,
url = {https://doi.org/10.1002/num.22742},
doi = {10.1002/num.22742},
abstract = {A truly meshless numerical procedure to simulate stochastic
elliptic interface problems is developed. The
meshless method is based on the generalized moving
least squares approximation. This method can be
implemented in a straightforward manner and has a
very good accuracy for solving this kind of
problems. Several realistic examples are presented
to investigate the efficiency of the new
procedure. Furthermore, compared with other meshless
methods that have been developed, the present
technique needs less CPU time.},
note = {\textit{At press}}
}

@article{Heitzinger2021homogenization,
author = {Clemens Heitzinger AND Jose A. Morales Escalante},
title = {Homogenization of boundary layers in the {Boltzmann}-{Poisson} system},
journal = {Multiscale Modeling and Simulation (MMS)},
volume = 19,
number = 1,
pages = {506-532},
year = 2021,
url = {https://doi.org/10.1137/18M1193888},
pdf = {Papers/Heitzinger2021homogenization.pdf},
doi = {10.1137/18M1193888},
abstract = {We homogenize the Boltzmann--Poisson system where the
background medium is given by a periodic
permittivity and a periodic charge
concentration. The domain is the half-space with a
periodic charge concentration on the boundary. Hence
the domain consists of cells in ${\mathbb{R}}^3$
that are periodically repeated in two dimensions and
unbounded in the third dimension. We obtain formal
results for this homogenization problem. We prove
the existence and uniqueness of the solution of the
Laplace and Poisson problems in the fast variables
with periodic and surface charge boundary conditions
generating an electric field at infinity, obtaining
formal solutions for the potential in terms of
Magnus expansions for the case where the diagonal
permittivity matrix depends on the vertical fast
variable. Further on, splitting the potential into a
stationary part and a self-consistent part,
performing the two-scale homogenization expansions
for the Poisson and the Boltzmann equations, and
applying a solvability condition, we arrive at the
drift-diffusion equations for the boundary-layer
problem.}
}

@article{Karimi2021optimal,
title = {Optimal {Bayesian} experimental design for electrical impedance tomography in medical imaging},
journal = {Computer Methods in Applied Mechanics and Engineering (CMAME)},
volume = 373,
pages = {113489/1--17},
year = 2021,
url = {https://doi.org/10.1016/j.cma.2020.113489},
pdf = {Papers/Karimi2021optimal.pdf},
doi = {10.1016/j.cma.2020.113489},
abstract = {Optimal design of electronic devices such as sensors is
essential since it results in more accurate output
at the shortest possible time. In this work, we
develop optimal Bayesian inversion for electrical
impedance tomography (EIT) technology in order to
improve the quality of medical images generated by
EIT and to put this promising imaging technology
into practice. We optimize Bayesian experimental
design by maximizing the expected information gain
in the Bayesian inversion process in order to design
optimal experiments and obtain the most informative
data about the unknown parameters. We present
optimal experimental designs including optimal
frequency and optimal electrode configuration, all
of which result in the most accurate estimation of
the unknown quantities to date and high-resolution
EIT medical images, which are crucial for diagnostic
purposes. Numerical results show the efficiency of
the proposed optimal Bayesian inversion method for
the EIT inverse problem.}
}

@article{Abbaszadeh2020reduced,
author = {Mostafa Abbaszadeh AND Mehdi Dehghan AND Amirreza Khodadadian AND Nima Noii AND Clemens Heitzinger AND Thomas Wick},
title = {A reduced-order variational multiscale interpolating element free {Galerkin} technique based on proper orthogonal decomposition for solving {Navier-Stokes} equations coupled with a heat transfer equation: nonstationary incompressible {Boussinesq} equations},
journal = {J.~Comput.\ Phys.},
volume = 426,
pages = {109875/1--27},
year = 2020,
url = {https://doi.org/10.1016/j.jcp.2020.109875},
doi = {10.1016/j.jcp.2020.109875},
abstract = {In the recent decade, meshless methods have been handled for
solving some PDEs due to their easiness. One of the
most efficient meshless methods is the element free
Galerkin (EFG) method. The test and trial functions
of the EFG are based upon the special
basis. Recently, some modifications have been
developed to improve the EFG method. One of these
improvements is the variational multiscale EFG
(VMEFG) procedure. In the current article, the shape
functions of interpolating moving least squares
(IMLS) approximation are applied to the variational
multiscale EFG technique to numerical study the
Navier–Stokes equations coupled with a heat transfer
equation such that this model is well-known as
two-dimensional nonstationary Boussinesq
equations. In order to reduce the computational time
of simulation, we employ a reduced order model (ROM)
based on the proper orthogonal decomposition (POD)
technique. In the current paper, we developed a new
reduced order model based on the meshless numerical
procedure for solving an important model in fluid
mechanics. To illustrate the reduction in CPU time
as well as the efficiency of the proposed method, we
investigate two-dimensional cases.}
}

@article{Taghizadeh2020uncertainty,
title = {Uncertainty quantification in epidemiological models for the {COVID-19} pandemic},
journal = {Computers in Biology and Medicine},
volume = 125,
number = 104011,
pages = {1-11},
year = 2020,
url = {https://doi.org/10.1016/j.compbiomed.2020.104011},
doi = {10.1016/j.compbiomed.2020.104011},
abstract = {Mathematical modeling of epidemiological diseases using
differential equations are of great importance in
order to recognize the characteristics of the
diseases and their outbreak.  The procedure of
modeling consists of two essential components: the
first component is to solve the mathematical model
numerically, the so-called forward modeling.  The
second component is to identify the unknown
parameter values in the model, which is known as
inverse modeling and leads to identifying the
epidemiological model more precisely.  The main goal
of this paper is to develop the forward and inverse
modeling of the coronavirus (COVID-19) pandemic
using novel computational methodologies in order to
accurately estimate and predict the pandemic.  This
leads to governmental decisions support in
implementing effective protective measures and
prevention of new outbreaks.  To this end, we use
the logistic equation and the SIR
(susceptible-infected-removed) system of ordinary
differential equations to model the spread of the
COVID-19 pandemic.  For the inverse modeling, we
propose Bayesian inversion techniques, which are
robust and reliable approaches, in order to estimate
the unknown parameters of the epidemiological
models.  We deploy an adaptive Markov-chain
Monte-Carlo (MCMC) algorithm for the estimation of a
posteriori probability distribution and confidence
intervals for the unknown model parameters as well
as for the reproduction number.  We perform our
analyses on the publicly available data for Austria
to estimate the main epidemiological model
parameters and to study the effectiveness of the
protective measures by the Austrian government.  The
estimated parameters and the analysis of fatalities
provide useful information for decision makers and
makes it possible to perform more realistic
forecasts of future outbreaks.  According to our
Bayesian analysis for the logistic model, the growth
rate and the carrying capacity are estimated
respectively as 0.28 and 14974.  Moreover for the
parameters of the SIR model, namely the transmission
rate and recovery rate, we estimate 0.36 and 0.06,
respectively.  Additionally, we obtained an average
infectious period of 17 days and a transmission
period of 3 days for COVID-19 in Austria.  We also
estimate the reproduction number over time for
Austria. This quantity is estimated around 3 on
March 26, when the first recovery was reported.
Then it decays to 1 at the beginning of April.
Furthermore, we present a fatality analysis for
COVID-19 in Austria, which is also of importance for
governmental protective decision making.  According
to our analysis, the case fatality rate (CFR) is
estimated as 4\% and a prediction of the number of
fatalities for the coming 10 days is also presented.
Additionally, the ICU bed usage in Austria indicates
that around 2\% of the active infected individuals
are critical cases and require ICU beds.  Therefore,
if Austrian governmental protective measures would
not have taken place and for instance if the number
of active infected cases would have been around five
times larger, the ICU bed capacity could have been
exceeded.}
}

@article{AdeliSadabad2020frequency,
title = {Frequency dependence of dielectrophoresis fabrication of single-walled carbon nanotube field-effect transistors},
journal = {J.~Comput.\ Electron.},
volume = 19,
number = 4,
pages = {1516-1526},
year = 2020,
url = {https://doi.org/10.1007/s10825-020-01562-x},
doi = {10.1007/s10825-020-01562-x},
abstract = {A new theoretical model for the dielectrophoretic (DEP)
fabrication of single-walled carbon nanotubes
(SWCNTs) is presented. A different frequency
interval for the alignment of wide-energy-gap
semiconductor SWCNTs is obtained, exhibiting a
considerable difference from the prevalent
model. Two specific models are study, namely the
spherical model and the ellipsoid model, to estimate
the frequency interval. Then, the DEP process is
performed and the obtained frequencies (from the
spherical and ellipsoid models) are used to align
the SWCNTs. These empirical results confirm the
theoretical predictions, representing a crucial step
towards the realization of carbon nanotube
field-effect transistors (CNT-FETs) via the DEP
process based on the ellipsoid model.}
}

@article{Khodadadian2020estimation,
author = {Amirreza Khodadadian AND Nima Noii AND Maryam Parvizi AND Mostafa Abbaszadeh AND Thomas Wick AND Clemens Heitzinger},
title = {A {Bayesian} estimation method for variational phase-field fracture problems},
journal = {Computational Mechanics},
volume = 66,
pages = {827-849},
year = 2020,
url = {https://doi.org/10.1007/s00466-020-01876-4},
doi = {10.1007/s00466-020-01876-4},
abstract = {In this work, we propose a parameter estimation framework
for fracture propagation problems. The fracture
problem is described by a phase-field
method. Parameter estimation is realized with a
Bayesian approach. Here, the focus is on
uncertainties arising in the solid material
parameters and the critical energy release rate. A
reference value (obtained on a sufficiently refined
mesh) as the replacement of measurement data will be
chosen, and their posterior distribution is
obtained. Due to time- and mesh dependencies of the
problem, the computational costs can be high. Using
Bayesian inversion, we solve the problem on a
relatively coarse mesh and fit the parameters. In
several numerical examples our proposed framework is
curves, that are usually the target functions, are
matched with the reference values.}
}

@article{Khodadadian2020adaptive,
title = {An adaptive multilevel {Monte-Carlo} algorithm for the stochastic drift-diffusion-{Poisson} system},
journal = {Computer Methods in Applied Mechanics and Engineering (CMAME)},
volume = 368,
pages = {113163/1--23},
year = 2020,
url = {https://doi.org/10.1016/j.cma.2020.113163},
doi = {10.1016/j.cma.2020.113163},
abstract = {We present an adaptive multilevel Monte Carlo algorithm for
solving the stochastic drift–diffusion–Poisson
system with non-zero recombination rate. The
a-posteriori error is estimated to enable
goal-oriented adaptive mesh refinement for the
spatial dimensions, while the a-priori error is
estimated to guarantee linear convergence of the
$H^1$ error. In the adaptive mesh refinement,
efficient estimation of the error indicator gives
rise to better error control. For the stochastic
dimensions, we use the multilevel Monte Carlo method
to solve this system of stochastic partial
differential equations. Finally, the advantage of
the technique developed here compared to uniform
mesh refinement is discussed using a realistic
numerical example.}
}

@article{Abbaszadeh2020error,
title = {Error analysis of the interpolating element free {Galerkin} method to solve the non-linear extended {Fisher}-{Kolmogorov} equation},
journal = {Computers and Mathematics with Applications},
volume = 80,
pages = {247-262},
year = 2020,
url = {https://doi.org/10.1016/j.camwa.2020.03.014},
doi = {10.1016/j.camwa.2020.03.014},
abstract = {Nonlinear partial differential equations (PDEs) play an
important role in the modeling of the natural
phenomena as they have great significance in
real-world applications. This investigation proposes
a new algorithm to find the numerical solution of
the nonlinear extended Fisher–Kolmogorov
equation. Firstly, the time variable is discretized
by a second-order finite difference scheme. The rate
of convergence and stability of the semi-discrete
formulation are studied by the energy method. The
existence and uniqueness of the solution of the weak
form based on the proposed technique have been
proved in detail. Furthermore, the interpolating
element free Galerkin approach based on the
interpolation moving least-squares approximation is
employed to derive a fully discrete scheme. Finally,
the error estimate of the full-discrete plan is
proposed and its convergence order is $O(\tau^2 + \delta^{m+1})$ in which $\tau$, $\delta$ and $m$
denote the time step, the radius of the weight
function and smoothness of the exact solution of the
main problem, respectively.}
}

@article{Taghizadeh2020inversion,
author = {Leila Taghizadeh AND Ahmad Karimi AND Benjamin Stadlbauer AND Wolfgang J. Weninger AND Eugenijus Kaniusas AND Clemens Heitzinger},
title = {{Bayesian} inversion for electrical-impedance tomography in medical imaging using the nonlinear {Poisson}-{Boltzmann} equation},
journal = {Computer Methods in Applied Mechanics and Engineering (CMAME)},
volume = 365,
pages = {112959/1--16},
year = 2020,
url = {https://doi.org/10.1016/j.cma.2020.112959},
doi = {10.1016/j.cma.2020.112959},
abstract = {We develop an electrical-impedance tomography (EIT) inverse
model problem in an infinite-dimensional setting by
introducing a nonlinear elliptic PDE as a new EIT
forward model. The new model completes the standard
linear model by taking the transport of ionic charge
into account, which was ignored in the standard
equation. We propose Bayesian inversion methods to
extract electrical properties of inhomogeneities in
the main body, which is essential in medicine to
screen the interior body and detect tumors or
determine body composition. We also prove
well-definedness of the posterior measure and
well-posedness of the Bayesian inversion for the
presented nonlinear model. The new model is able to
distinguish between liquid and tissues and the
state-of-the-art delayed-rejection
adaptive-Metropolis (DRAM) algorithm is capable of
analyzing the statistical variability in the
measured data in various EIT experimental
designs. This leads to design a reliable device with
higher resolution images which is crucial in
medicine for diagnostic purposes. We first test the
validation of the presented nonlinear model and the
proposed inverse method using synthetic data on a
simple square computational domain with an
inclusion. Then we establish the new model and
robustness of the proposed inversion method in
solving the ill-posed and nonlinear EIT inverse
problem by presenting numerical results of the
corresponding forward and inverse problems on a
real-world application in medicine and
healthcare. The results include the extraction of
electrical properties of human leg tissues using
measurement data.}
}

@article{Taghizadeh2020Bayesian,
author = {Leila Taghizadeh AND Ahmad Karimi AND Elisabeth Presterl AND Clemens Heitzinger},
title = {{Bayesian} inversion for a biofilm model including quorum sensing},
journal = {Computers in Biology and Medicine},
volume = 117,
pages = {103582/1--11},
year = 2020,
url = {https://doi.org/10.1016/j.compbiomed.2019.103582},
doi = {10.1016/j.compbiomed.2019.103582},
abstract = {We propose a mathematical model based on a system of partial
differential equations (PDEs) for biofilms. This
model describes the time evolution of growth and
degradation of biofilms which depend on
environmental factors. The proposed model also
includes quorum sensing (QS) and describes the
cooperation among bacteria when they need to resist
against external factors such as antibiotics. The
applications include biofilms on teeth and medical
implants, in drinking water, cooling water towers,
food processing, oil recovery, paper manufacturing,
and on ship hulls. We state existence and uniqueness
of solutions of the proposed model and implement the
mathematical model to discuss numerical simulations
of biofilm growth and cooperation. We also determine
the unknown parameters of the presented biofilm
model by solving the corresponding inverse
problem. To this end, we propose Bayesian inversion
techniques and the delayed-rejection
simultaneous extraction of multiple parameters from
the measurements. These quantities cannot be
determined directly from the experiments or from the
computational model. Furthermore, we evaluate the
presented model by comparing the simulations using
the estimated parameter values with the measurement
data. The results illustrate a very good agreement
between the simulations and the measurements.}
}

@article{Abbaszadeh2020analysis,
title = {Analysis and application of the interpolating element free {Galerkin} ({IEFG}) method to simulate the prevention of groundwater contamination with application in fluid flow},
journal = {Journal of Computational and Applied Mathematics},
volume = 368,
pages = {112453/1--17},
year = 2020,
url = {https://doi.org/10.1016/j.cam.2019.112453},
doi = {10.1016/j.cam.2019.112453},
abstract = {We develop a meshless numerical procedure to simulate the
groundwater equation (GWE). The used technique is
based on the interpolating element free Galerkin
(IEFG) method. The interpolating moving least
squares (IMLS) approximation produces a set of
functions such that they are well-known as shape
functions. The IEFG technique employs the shape
functions of IMLS approximation. The shape functions
of IMLS approximation vanish on the boundary and
also they satisfy the property of the Kronecker
Delta function. Thus, Dirichlet boundary conditions
can be exactly imposed. In this paper, we check the
unconditional stability and convergence of the
proposed numerical scheme based on the energy
method. The numerical results confirm the
theoretical analysis.}
}

@article{Stadlbauer2020modeling,
author = {Benjamin Stadlbauer AND Gregor Mitscha-Baude AND Clemens Heitzinger},
title = {Modeling single-molecule stochastic transport for {DNA} exo-sequencing in nanopore sensors},
journal = {Nanotechnology},
volume = 31,
number = 7,
pages = {075502/1--7},
year = 2020,
url = {https://doi.org/10.1088/1361-6528/ab513e},
doi = {10.1088/1361-6528/ab513e},
abstract = {We present a simulation framework for computing the
probability that a single molecule reaches the
recognition element in a nanopore sensor. The model
consists of the Langevin equation for the diffusive
motion of small particles driven by external forces
and the Poisson-Nernst-Planck-Stokes equations to
compute these forces. The model is applied to
examine DNA exo-sequencing in $\alpha$-hemolysin,
whose practicability depends on whether isolated DNA
monomers reliably migrate into the channel in their
correct order. We find that, at moderate voltage,
migration fails in the majority of trials if the
exonuclease which releases monomers is located
farther than 1 nm above the pore entry. However, by
tuning the pore to have a higher surface charge,
applying a high voltage of 1 V and ensuring the
exonuclease stays close to the channel, success
rates of over 95\% can be achieved.}
}

@article{Khodadadian2020Bayesian,
title = {{Bayesian} inversion for nanowire field-effect sensors},
journal = {J.~Comput.\ Electron.},
volume = 19,
pages = {147-159},
year = 2020,
url = {https://doi.org/10.1007/s10825-019-01417-0},
doi = {10.1007/s10825-019-01417-0},
abstract = {Nanowire field-effect sensors have recently been developed
for label-free detection of biomolecules. In this
work, we introduce a computational technique based
on Bayesian estimation to determine the physical
parameters of the sensor and, more importantly, the
properties of the analyte molecules. To that end, we
first propose a PDE-based model to simulate the
device charge transport and electrochemical
behavior. Then, the adaptive Metropolis algorithm
with delayed rejection is applied to estimate the
posterior distribution of unknown parameters, namely
molecule charge density, molecule density, doping
concentration, and electron and hole mobilities. We
determine the device and molecules properties
simultaneously, and we also calculate the molecule
density as the only parameter after having
determined the device parameters. This approach
makes it possible not only to determine unknown
parameters, but it also shows how well each
parameter can be determined by yielding the
probability density function (pdf).}
}

@article{Lenzi2019reliability,
author = {E.K. Lenzi AND L.R. Evangelista AND L. Taghizadeh AND D. Pasterk AND R.S. Zola AND T. Sandev AND C. Heitzinger AND I. Petreska},
title = {The reliability of {Poisson–Nernst–Planck} anomalous models for impedance spectroscopy},
journal = {Journal of Physical Chemistry~B},
volume = 123,
number = 37,
pages = {7885-7892},
year = 2019,
url = {https://doi.org/10.1021/acs.jpcb.9b06263},
pdf = {Papers/Lenzi2019reliability.pdf},
doi = {10.1021/acs.jpcb.9b06263},
abstract = {We investigate possible connections between two different
implementations of the Poisson-Nernst-Planck (PNP)
anomalous models used to analyze the electrical
response of electrolytic cells. One of them is built
in the framework of the fractional calculus and
considers integro-differential boundary conditions
also formulated by using fractional derivatives; the
other one is an extension of the standard PNP model
presented by Barsoukov and Macdonald, which can also
be related to equivalent circuits containing
constant phase elements (CPEs). Both extensions may
be related to an anomalous diffusion with
subdiffusive characteristics through the
electrical conductivity and are able to describe the
experimental data presented here. Furthermore, we
apply the Bayesian inversion method to extract the
parameter of interest in the analytical formulas of
impedance. To resolve the corresponding inverse
problem, we use the delayed-rejection
adaptive-Metropolis algorithm (DRAM) in the context
of Markov-chain Monte Carlo (MCMC) algorithms to
find the posterior distributions of the parameter
and the corresponding confidence intervals.}
}

@article{Taghizadeh2019existence,
author = {Leila Taghizadeh AND Clemens Heitzinger},
title = {Existence and local uniqueness for the {Stokes}-{Nernst}-{Planck}-drift-diffusion-{Poisson} system modeling nanopore and nanowire sensors},
journal = {Commun.\ Math.\ Sci.},
volume = 17,
number = 8,
pages = {2089-2112},
year = 2019,
url = {https://dx.doi.org/10.4310/CMS.2019.v17.n8.a2},
doi = {10.4310/CMS.2019.v17.n8.a2},
abstract = {This work gives analytical results for a system of transport
equations which is the underlying mathematical model
for nanopore sensors and for all types of
affinity-based nanowire sensors. This model consists
of the Poisson equation for the electrostatic
potential ensuring self-consistency and including
interface conditions stemming from a homogenized
boundary layer, the drift-diffusion equations
describing the transport of charge carriers in the
sensor, the Nernst–Planck equations describing the
transport of ions, and the Stokes equations
describing the flow of the background medium
water. We present existence and local uniqueness
theorems for this stationary, nonlinear, and fully
coupled system. The existence proof is based on the
Schauder fixed-point theorem and local uniqueness
around equilibrium is obtained from the
implicit-function theorem. The maximum principle is
used to obtain a priori estimates for the
solution. Due to the multiscale problem inherent in
affinity-based field-effect sensors, a homogenized
equation for the potential with interface conditions
at a surface is used.}
}

@article{Blankrot2019efficient,
author = {Boaz Blankrot AND Clemens Heitzinger},
title = {Efficient computational design and optimization of dielectric metamaterial structures},
journal = {IEEE Journal on Multiscale and Multiphysics Computational Techniques},
volume = 4,
number = 1,
pages = {234-244},
year = 2019,
url = {https://doi.org/10.1109/JMMCT.2019.2950569},
pdf = {Papers/Blankrot2019efficient.pdf},
doi = {10.1109/JMMCT.2019.2950569},
abstract = {Dielectric structures composed of many inclusions that
manipulate light in ways the bulk materials cannot
are commonly seen in the field of metamaterials. In
these structures, each inclusion depends on a set of
parameters such as size and orientation, which are
difficult to ascertain. We propose and implement an
optimization-based approach for designing such
metamaterials in two dimensions by using a fast
boundary element method and a multiple-scattering
solver for a given set of parameters. This approach
provides the backbone of an automated process for
the design and analysis of metamaterials that does
not rely on analytical approximations. We
demonstrate the validity of our approach with
simulations that converge to optimal parameter
values and result in substantially better
performance.}
}

@article{Stadlbauer2019Bayesian,
author = {Benjamin Stadlbauer AND Andrea Cossettini AND Jose Morales Escalante AND Paolo Scarbolo AND Leila Taghizadeh AND Clemens Heitzinger AND Luca Selmi},
title = {{Bayesian} estimation of physical and geometrical parameters for nanocapacitor array biosensors},
journal = {Journal of Computational Physics},
volume = 397,
pages = {108874/1--19},
year = 2019,
url = {https://doi.org/10.1016/j.jcp.2019.108874},
doi = {10.1016/j.jcp.2019.108874},
abstract = {Massively parallel nanosensor arrays fabricated with
low-cost CMOS technology represent powerful
platforms for biosensing in the Internet-of-Things
(IoT) and Internet-of-Health (IoH) era. They can
efficiently acquire “big data” sets of dependable
calibrated measurements, representing a solid basis
for statistical analysis and parameter estimation.
In this paper we propose Bayesian estimation methods
to extract physical parameters and interpret the
statistical variability in the measured outputs of a
dense nanocapacitor array biosensor. Firstly, the
physical and mathematical models are
presented. Then, a simple 1D-symmetry structure is
used as a validation test case where the estimated
parameters are also known a-priori. Finally, we
apply the methodology to the simultaneous extraction
of multiple physical and geometrical parameters from
measurements on a CMOS pixelated nanocapacitor
biosensor platform.}
}

@article{Khodadadian2019new,
title = {A new method for selective functionalization of silicon nanowire sensors and {Bayesian} inversion for its parameters},
journal = {Biosensors and Bioelectronics},
volume = 142,
pages = {111527/1--8},
year = 2019,
url = {https://doi.org/10.1016/j.bios.2019.111527},
pdf = {Papers/Mirsian2019new.pdf},
doi = {10.1016/j.bios.2019.111527},
abstract = {In this work, a modification procedure for the
functionalization of silicon nanowire (SiNW) is
applied in biological field effect transistor
(BioFET) system. The proposed method precedes the
silanization reaction in a manner that the only SiNW
and not its substrate is functionalized by
(3-Aminopropyl) triethoxysilane (APTES)
initiators. This method has an effective role in
increasing the sensitivity of BioFET sensors and can
be applied in commercial ones. Furthermore, we
introduce an efficient computational technique to
estimate unknown senor parameters. To that end,
Bayesian inversion is used to determine the number
of PSA target molecules bound to the receptors in
both selective and nonselective SiNWs. The approach
is coupled with the
Poisson-Boltzmann-drift-diffusion (PBDD) equations
to provide a comprehensive system to model all
biosensor interactions.},
note = {Impact factor 9.518}
}

@article{Dehghan2019Galerkin,
title = {{Galerkin} proper orthogonal decomposition reduced order method ({POD-ROM}) for solving the generalized {Swift}-{Hohenberg} equation},
journal = {International Journal of Numerical Methods for Heat and Fluid Flow},
volume = 29,
number = 8,
pages = {2642-2665},
year = 2019,
url = {https://doi.org/10.1108/HFF-11-2018-0647},
pdf = {Papers/Dehghan2019Galerkin.pdf},
doi = {10.1108/HFF-11-2018-0647},
abstract = {Purpose -- The current paper aims to develop a reduced order
discontinuous Galerkin method for solving the
generalized Swift–Hohenberg equation with
application in biological science and mechanical
engineering. The generalized Swift–Hohenberg
equation is a fourth-order PDE; thus, this paper
uses the local discontinuous Galerkin (LDG) method
for it.  Design/methodology/approach -- At first,
the spatial direction has been discretized by the
LDG technique, as this process results in a
nonlinear system of equations based on the time
variable. Thus, to achieve more accurate outcomes,
this paper uses an exponential time differencing
scheme for solving the obtained system of ordinary
differential equations. Finally, to decrease the
used CPU time, this study combines the proper
orthogonal decomposition approach with the LDG
method and obtains a reduced order LDG method. The
circular and rectangular computational domains have
been selected to solve the generalized
Swift–Hohenberg equation. Furthermore, the energy
stability for the semi-discrete LDG scheme has been
discussed.  Findings -- The results show that the
new numerical procedure has not only suitable and
acceptable accuracy but also less computational cost
compared to the local DG without the proper
orthogonal decomposition (POD) approach.
Originality/value -- The local DG technique is an
efficient numerical procedure for solving models in
the fluid flow. The current paper combines the POD
approach and the local LDG technique to solve the
generalized Swift–Hohenberg equation with
application in the fluid mechanics. In the new
technique, the computational cost and the used CPU
time of the local DG have been reduced.}
}

@article{Blankrot2019design,
author = {Boaz Blankrot AND Clemens Heitzinger},
title = {Design of aperiodic demultiplexers and optical diodes by optimizing photonic crystals},
journal = {OSA Continuum},
volume = 2,
number = 7,
pages = {2244-2252},
month = jul,
year = 2019,
url = {https://doi.org/10.1364/OSAC.2.002244},
pdf = {Papers/Blankrot2019design.pdf},
doi = {10.1364/OSAC.2.002244},
abstract = {We apply a previously developed approach for the automated
design of optical structures to two cases. This
approach reduces the basis of the electromagnetic
optimization. In the first case, an existing
photonic crystal demultiplexer is optimized for
higher power transmission and lower crosstalk. In
the second, new optical diodes for plane- and
cylindrical-wave incidence are designed using a
photonic crystal as a starting point. Highly
efficient and aperiodic devices are obtained in all
cases. These results indicate that aperiodic devices
produced by this automated design method can
outperform their analytically-obtained counterparts
and encourage its application to other photonic
crystal-based devices.}
}

@article{Khodadadian2019multilevel,
title = {A multilevel {Monte Carlo} finite element method for the stochastic {Cahn-Hilliard-Cook} equation},
journal = {Computational Mechanics},
volume = 64,
number = 4,
pages = {937-949},
year = 2019,
url = {https://doi.org/10.1007/s00466-019-01688-1},
doi = {10.1007/s00466-019-01688-1},
abstract = {In this paper, we employ the multilevel Monte Carlo finite
element method to solve the stochastic
Cahn–Hilliard–Cook equation. The Ciarlet–Raviart
mixed finite element method is applied to solve the
fourth-order equation. In order to estimate the mild
solution, we use finite elements for space
discretization and the semi-implicit Euler–Maruyama
method in time. For the stochastic scheme, we use
the multilevel method to decrease the computational
cost (compared to the Monte Carlo method). We
implement the method to solve three specific
numerical examples (both two- and three dimensional)
and study the effect of different noise measures.}
}

@article{Abbaszadeh2019direct,
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},
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,
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},
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,
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},
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,
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},
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},
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
existing numerical approaches by deploying
goal-oriented adaptive mesh refinement. To reduce
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,
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},
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,
title = {Basis adaptation for the stochastic nonlinear {Poisson}-{Boltzmann} equation},
journal = {J.~Comput.\ Electron.},
volume = 15,
number = 4,
pages = {1393-1406},
year = 2016,
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,
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,
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,
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
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 observed 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},
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},
abstract = {In recent years DNA-sensors, and generally biosensors, with
semiconducting transducers were fabricated and
characterized. Although the concept of so-called
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},
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,
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},
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,
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},
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,
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
}

@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,
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,
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,
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},
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
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,
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
}

@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,
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,
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},
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,
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},
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
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
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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