Publications in journals

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.

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.

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.

In recent years DNA-sensors, and generally biosensors, with semiconducting transducers were fabricated and characterized. Although the concept of so-called BioFETs was proposed already two decades ago, its realization has become feasible only recently due to advances in process technology. In this paper a comprehensive and rigorous approach to the simulation of silicon-nanowire DNAFETs at the feature-scale is presented. It allows to investigate the feasibility of single-molecule detectors and is used to elucidate the performance that can be expected from sensors with nanowire diameters in the deca-nanometer range. Finally the computational challenges for the simulation of silicon-nanowire DNA-sensors are discussed.

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.

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.

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.

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.

We propose a novel parameter-free quantum potential scheme for use in conjunction with particle-based simulations. The method is based on a perturbation theory around thermodynamic equilibrium and leads to an effective potential scheme in which the size of the electron depends upon its energy. The approach has been tested on the example of a MOS-capacitor by retrieving the correct sheet electron density. It has also been used in simulations of a 25 nm n-channel nanoscale MOSFET with high substrate doping density. We find that the use of the quantum potential approach gives rise to a threshold voltage shift of about 220 mV and drain current degradation of about 30%.

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.

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.

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-κ materials, which suffer from integration problems.

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.

We evaluate optimization techniques to reduce the necessary user interaction for inverse modeling applications as they are used in the technology computer-aided design field. Four optimization strategies are compared. Two well-known global optimization methods, simulated annealing and genetic optimization, a local gradient-based optimization strategy, and a combination of a local and a global method. We rate the applicability of each method in terms of the minimal achievable target value for a given number of simulation runs and in terms of the fastest convergence. A brief overview over the three used optimization algorithms is given. The optimization framework that is used to distribute the workload over a cluster of workstations is described. The actual comparison is achieved by means of an inverse modeling application that is performed for various settings of the optimization algorithms. All presented optimization algorithms are capable of evaluating several targets in parallel. The best optimization strategy that is found is used in the calibration of a model for silicon self-interstitial cluster formation and dissolution.

Numerically solving the nonlinear Schrödinger equation and being able to treat arbitrary space dependent potentials permits many application in the realm of quantum mechanics. The long-term stability of a numerical method and its conservation properties is an important feature since it assures that the underlying physics of the solution are respected and it ensures that the numerical result is correct also for small time spans. In this paper we describe symplectic integrators for the nonlinear Schrödinger equation with arbitrary potentials and perform numerical experiments comparing different approaches and highlighting their respective advantages and disadvantages.

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.

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.

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 0.1μm wide and 7μm deep, high aspect ratio trenches.

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.

The SIESTA framework is an extensible tool for optimization and inverse modeling of semiconductor devices including dynamic load balancing for taking advantage of several, loosely connected workstations. Two gradient-based and two evolutionary computation optimizers are currently available through a uniform interface and can be combined at will. At a real world inverse modeling example, we demonstrate that evolutionary computation optimizers provide several advantages over gradient-based optimizers, due to the specific properties of the objective functions in TCAD applications. Furthermore, we shortly discuss some issues arising in inverse modeling and conclude with a comparison of gradient-based and evolutionary computation optimizers from a TCAD point of view.

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.