[Show abstract][Hide abstract] ABSTRACT: This work deals with the stochastic simulation of a nanowire biosensor surface and the surrounding liquid domain for DNA detection. The objective is an analysis of the fluctuations and of the biological noise induced by the inherent randomness of the hybridization process at the surface. We consider a coupled system of diffusion-reaction equations to model the movement of DNA oligomers as well as the hybridization processes at the functionalized surface of the sensor. Since analytical solutions cannot be derived, numerical investigation is necessary. Here, we present an algorithm different from the already published one in Tulzer and Heitzinger (2014) and show the non-monotonic behaviour of the variance in certain regimes. The variance determines the detection limit, which is an important quantity for optimal sensor design.
[Show abstract][Hide abstract] 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.
No preview · Article · Jun 2015 · Journal of Computational Electronics
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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.
No preview · Article · Dec 2014 · Journal of Computational Electronics
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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.
No preview · Article · Jan 2014 · Journal of Computational Physics
[Show abstract][Hide abstract] 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).
Full-text · Article · Jan 2014 · Communications in mathematical sciences
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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.
No preview · Article · Jun 2013 · Journal of Computational Physics
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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.
Preview · Article · May 2013 · Proceedings of SPIE - The International Society for Optical Engineering
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] ABSTRACT: Metal-oxide gas sensors are advantageous for various purposes due to their physical and chemical as well as electrical properties. However, a lack of selectivity remains the central issue in this field. A quantitative understanding of the processes at the semiconductor surface is crucial to overcome these difficulties. In this work, we determine numerical values for the parameters governing the interaction of H2 with the device to obtain quantitative information regarding the influence of the atmosphere on the sensor. With the computed values, simulations regarding the surface charge can be performed to understand the sensor behavior under different ambient conditions.
[Show abstract][Hide abstract] 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 SnO2 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 degrees 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. (C) 2012 Elsevier Ltd....Selection and/or peer-review under responsibility of the Symposium Cracoviense Sp. z.o.o.
Preview · Article · Dec 2012 · Procedia Engineering
[Show abstract][Hide abstract] 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.
Preview · Article · Jun 2012 · Communications in mathematical sciences
[Show abstract][Hide abstract] 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.