Clemens Heitzinger

Vienna University of Technology, Wien, Vienna, Austria

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Publications (80)60.01 Total impact

  • Clemens Heitzinger, Christian Ringhofer
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    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.
    Journal of Computational Electronics 12/2014; 13(4). · 1.37 Impact Factor
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    Clemens Heitzinger, Thomas Binder, Siegfried Selberherr
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    ABSTRACT: The SIESTA (Simulation Environment for Semiconduc-tor Technology Analysis) framework is an extensible tool for optimization and inverse modeling of semiconductor de-vices including dynamic load balancing for taking advantage of several, loosely connected workstations. Because of the increasing computational power available today, the use of evolutionary computation optimizers which usually require a large number of evaluations of the objective functions be-comes feasible even for problems with computationally very expensive objective functions. After a brief introduction to the SIESTA framework and its capabilities, we compare the performance of its optimizers at a real world parameter ex-traction problem and find that for certain problems genetic algorithms and simulated annealing perform better than gra-dient based optimization.
    11/2014;
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    Clemens Heitzinger, Christian Ringhofer
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    ABSTRACT: In this work, the multiscale problem of modeling fluctuations in boundary layers in stochastic elliptic partial differential equations is solved by homogenization. Homogenized equations for the covariance and variance of the solution of stochastic elliptic PDEs are derived. In addition to the homogenized equations, a scaling law for the covariance and variance as the cell size tends to zero is given. For the homogenized problems, existence and uniqueness results and a priori bounds are given and further properties are proven. The multiscale problem stems from the modeling of the electrostatics in nanoscale field-effect sensors, where the fluctuations arise from randomly distributed charge concentrations in the cells of a boundary layer. Finally, numerical results and a spectral approximation are presented. AMS subject classifications. 35B27 Homogenization; equations in media with periodic structure, 35J05 Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation, 35Q92 PDEs in connection with biology and other natural sciences, 62P30 Applications in engineering and industry, 82D80 Nanostructures and nanoparticles, 92C50 Medical applications (general).
    Communications in mathematical sciences 01/2014; 12(3). · 1.00 Impact Factor
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    ABSTRACT: In this work, we present calculated numerical values for the kinetic parameters governing adsorption/desorption processes of carbon monoxide at tin dioxide single-nanowire gas sensors. The response of such sensors to pulses of 50 ppm 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.
    Nanotechnology 07/2013; 24(31):315501. · 3.67 Impact Factor
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    ABSTRACT: One of the challenging issues for semiconductor circuit design is how to overcome RC delays in the interconnect layers. To reduce the overall dielectric constant, it is important to develop a low -k barrier/et ch stop film that can prevent the metal lines, usually made of aluminum, from interacting with other materials in multi - level interconnect schemes. An additional requirement for a barrier/etch stop film is high etch selectivity with respect to the ILD (inter- layer dielectric). Silicon nitride has been generally accepted as a first generation barrier. However, its k- value is high and when used in conjunction with a lower k dielectric, the overall k-value of the stack is significantly impacted. Here voids may serve a beneficial purpose, where they can lower the overall capacitance. In this paper the simulation of backend and interconnect capacitance is considered. The backend stack is built up using topography simulation of deposition, etching, and CMP (chemical mechanical planarization) processes in different metal lines. We present results for a 100nm CMOS process. We show that the influence of void formation between interconnect lines strongly impacts the whole interconnect stack performance. Our tool for the topography simulations is called ELSA (enhanced level set applications) whose outputs are used by the capacitance extraction tool called RAPHAEL. The results of RAPHAEL are made available to the circuit designer in turn and are used in SPICE.
    06/2013;
  • Stefan Baumgartner, Clemens Heitzinger
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    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.
    Journal of Computational Physics 06/2013; 243:74–86. · 2.49 Impact Factor
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    ABSTRACT: Experiments of As-doped poly-silicon deposition have shown that under certain process conditions step coverages ¢ ¤ £ can be achieved. We have developed a new model for the simulation of As-doped poly-silicon deposition, which takes into account surface coverage dependent sticking coefficients and surface coverage dependent As incorporation and desorption rates. The additional introduction of Langmuir type time-dependent surface coverage enabled the reproduction of the bottom-up filling of the trenches. In addition the rigorous treatment of the time-dependent surface coverage allows to trace the in-situ doping of the deposited film. Simulation results are shown for poly-Si deposition into 0.1 ¥ ¦ wide and 7 ¥ ¦ deep, high aspect ratio trenches.
    05/2013;
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    Clemens Heitzinger, Siegfried Selberherr
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    ABSTRACT: Our Simulation Environment for Semiconductor Technology Analysis (Siesta) is a flexible, user programmable tool for optimization and inverse modeling of semiconductor devices. It is easily customizable through an interactive, object-oriented and functional scripting language. Dynamic load balancing enables to take advantage of a cluster of hosts with minimal requirements on the software infrastructure. Our approach combines the advantages of gradient based and evolutionary algorithm optimizers into one framework. Gradient based optimizers are well-suited for finding local extrema. Evolutionary algorithm optimizers add the capability of finding global extrema and thus make unattended optimizations without guessing starting values possible. Experiments can be interactively set up and tested. Bindings for the most common simulation tools are provided, and new bindings can easily be integrated taking advantage of the object-oriented and functional design. Results of experiments are saved in an object database and can be interactively retrieved as starting points for further computations or for visualizations. The user may impose arbitrary constraints (as functions defined on the parameter space) on the set in which solutions are searched. Evaluating the constraints before any simulation tool is called and getting rid of useless combinations of parameter values saves computation time and eliminates the risk of the simulation tools being called with input values that might lead to unforeseen behavior. The combination of gradient based and evolutionary algorithm optimizers enables many new optimization strategies and includes convenient handling of results.
    Proceedings of SPIE - The International Society for Optical Engineering 05/2013; · 0.20 Impact Factor
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    ABSTRACT: We describe a technique to generate structurally aligned triangular grids. The main advantage of this method is the adjustable propagating speed of the front in different parts of the simulation domain in order to achieve different densities of triangles in each part of the simulation domain. This feature is usually needed in semiconductor device simulation. Other advantages of this technique are twofold: firstly, the grid can be very well adapted to the structures, and secondly, the grid elements fulfill desirable requirements like Delaunay triangulation and the minimum angle criterion. The technique is based on viewing the boundary of the simulation domain as a front which is propagated structurally at different speeds. A smooth propagation is achieved by the level set method by viewing the front as the zero level set of a higher dimensional function whose equation of motion is described by a partial differential equation.
    05/2013;
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    ABSTRACT: An essential task for any finite element method is to provide appropriate resolution of the mesh to resolve the initial solution. We present a computational method for anisotropic tetrahedral mesh refinement according to an adjustable discretization error. The initial attribute profile is given by an analytical function which is twice continously differentiable. Anisotropy is taken into ac-count to reduce the amount of elements compared to pure isotropic meshes. By the proposed method the spatial resolution in three-dimensional unstructured tetrahedral meshes used for diffusion simulation is locally increased and the accuracy of the discretization improved.
    05/2013;
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    C Heitzinger, S Selberherr
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    ABSTRACT: The optimization of computationally expensive objective functions requires ap-proximations that preserve the global properties of the function under investigation. The RSM approach of using multivariate polynomials of degree two can only pre-serve the local properties of a given function and is therefore not well-suited for global optimization tasks. In this paper we discuss generalized Bernstein polyno-mials that provide faithful approximations by converging uniformly to the given function. Apart from being useful for optimization tasks, they can also be used for solving design for manufacturability problems.
    05/2013;
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    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.
    Nanotechnology 05/2013; 24(22):225503. · 3.67 Impact Factor
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    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-α 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 × 10(-13) mol cm(-2) for BSA, 1.7 × 10(-13) mol cm(-2) for anti-TNF-α antibody, 6.1 × 10(-13) mol cm(-2) for anti-PSA antibody, 3.88 × 10(-13) mol cm(-2) for TNF-α and 7.0 × 10(-13) mol cm(-2) for PSA. Furthermore we performed antibody-antigen binding experiments and determined the specific binding ratios. The maximum possible ratio of 2 was obtained at bulk concentrations of the antigen in the μg ml(-1) range for TNF-α and PSA.
    Nanoscale 03/2012; 4(7):2431-8. · 6.74 Impact Factor
  • Procedia Engineering 01/2012; 47:809-812.
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    Stefan Baumgartner, Clemens Heitzinger
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    ABSTRACT: We present existence and local uniqueness theorems for a system of partial differ-ential 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 exis-tence 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 sim-ulations. Therefore a finite-volume discretization of the 3d self-consistent model was implemented to allow comparison of simulation and measurement. Special considerations regarding the imple-mentation 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.
    Communications in mathematical sciences 01/2012; 10(2). · 1.00 Impact Factor
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    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.
    International Journal of Nanoscience 11/2011; 04(03).
  • S Baumgartner, M Vasicek, A Bulyha, C Heitzinger
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    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.
    Nanotechnology 09/2011; 22(42):425503. · 3.67 Impact Factor
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    Alena Bulyha, Clemens Heitzinger
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    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.
    Nanoscale 02/2011; 3(4):1608-17. · 6.74 Impact Factor
  • Alena Bulyha, Clemens Heitzinger, Norbert J. Mauser
    ERCIM News. 01/2011; 2011:40-41.
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    Clemens Heitzinger, Christian Ringhofer
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    ABSTRACT: In memoriam Naoufel Ben Abdallah. 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.
    Communications in mathematical sciences 01/2011; 9(3). · 1.00 Impact Factor

Publication Stats

304 Citations
60.01 Total Impact Points

Institutions

  • 2002–2014
    • Vienna University of Technology
      • Institute of Microelectronics
      Wien, Vienna, Austria
  • 2013
    • University of Cambridge
      • Department of Applied Mathematics and Theoretical Physics
      Cambridge, England, United Kingdom
    • AIT Austrian Institute of Technology
      Wien, Vienna, Austria
  • 2008–2012
    • University of Vienna
      • • Institut für Biophysikalische Chemie
      • • Faculty of Mathematics
      Wien, Vienna, Austria
  • 2008–2011
    • Wolfgang Pauli Institute Vienna
      Wien, Vienna, Austria
  • 2003–2011
    • Arizona State University
      • School of Electrical, Computer and Energy Engineering
      Phoenix, Arizona, United States
  • 2007
    • Purdue University
      • School of Electrical and Computer Engineering
      West Lafayette, Indiana, United States
  • 2002–2004
    • IST Austria
      Klosterneuberg, Lower Austria, Austria