Publications in Refereed Conference Proceedings

Federated Learning (FL) decouples model training from the need for direct access to the data and allows organizations to collaborate with industry partners to reach a satisfying level of performance without sharing vulnerable business information. The performance of a machine learning algorithm is highly sensitive to the choice of its hyperparameters. In an FL setting, hyperparameter optimization poses new challenges. In this work, we investigated the impact of different hyperparameter optimization approaches in an FL system. In an effort to reduce communication costs, a critical bottleneck in FL, we investigated a local hyperparameter optimization approach that – in contrast to a global hyperparameter optimization approach – allows every client to have its own hyperparameter configuration. We implemented these approaches based on grid search and Bayesian optimization and evaluated the algorithms on the MNIST data set using an i.i.d. partition and on an Internet of Things (IoT) sensor based industrial data set using a non-i.i.d. partition.

We use the stochastic drift-diffusion-Poisson system to model charge transport in nanoscale devices. This stochastic transport equation makes it possible to describe device variability, noise, and fluctuations. We present---as theoretical results---an existence and local uniqueness theorem for the weak solution of the stochastic drift-diffusion-Poisson system based on a fixed-point argument in appropriate function spaces. We also show how to quantify random-dopant effects in this formulation. Additionally, we have developed an optimal multi-level Monte-Carlo method for the approximation of the solution. The method is optimal in the sense that the computational work is minimal for a given error tolerance.

A 3d simulator for nanowire field-effect sensors and transistors including fast varying charge concentrations at an interface is presented. This simulator is based on a system of partial differential equations calculating the electrostatic potential of the whole device and the charge concentrations in the semiconducting nanowire. Therefore, three domains need to be modeled. The nanowire is described by the drift-diffusion-Poisson system, the Poisson-Boltzmann equation is used for the simulation of an aqueous solution, and the Poisson equation holds in the remaining oxide. Such devices can be used as gas sensors, and by functionalization of the nanowire surface, i.e., by attaching probe molecules, they can also be used for the detection of biomolecules in aqueous solutions. Binding of target molecules to the surface induces a field effect due to changes of charges in a small layer around the surface. This effect is responsible for the sensor response and hence is of paramount importance. A homogenization method resulting in two jump conditions is implemented which splits the computation into the charge of the boundary layer and into the remaining device. In order to take into account the geometry of the devices, 3d simulations are necessary and hence a parallelization technique has been developed. To include the jump conditions of the homogenization method, a novel finite-element tearing and interconnecting (FETI) method has been developed. With this simulator it is possible to solve the three dimensional and heterogeneous system of partial differential equations with discontinuities in feasible time using realizable computer power. As a result, sensitivity in terms of geometrical and physical properties can be predicted and sensors can be improved.

Biologically sensitive field-effect transistors (BioFETs) are a promising technology for detecting pathogens, antigen-antibody complexes, and tumor markers. A BioFET is studied for a biotin-streptavidin complex. Biotin-streptavidin is used in detection and purification of various biomolecules. The link between the Angstrom scale of the chemical reaction and the micrometer scale of the field effect device is realized by homogenized interface conditions.

We use the stochastic linearized Poisson-Boltzmann equation to model the fluctuations in nanowire field-effect biosensors due to changes in the orientation of the biomolecules. Different orientations of the biomolecules with respect to the sensor surface due to Brownian motion have different probabilities. The probabilities of the orientations are calculated from their electrostatic free energy. The structure considered here is a cross section through a rectangular silicon nanowire lying on a an oxide surface with a back-gate contact. The oxide surface of the nanowire is functionalized by biomolecules in an electrolyte with an electrode. Various combinations of PNA (peptide nucleic acid), single-stranded DNA, and double-stranded DNA are simulated to discuss the various states of a DNA sensor. A charge-transport models yields the current through the transducer that compares well with measurements.

In this work the properties of a biotin-streptavidin BioFET have been studied numerically with homogenized boundary interface conditions as the link between the oxide of the FET and the analyte which contains the bio-sample. The biotin-streptavidin reaction pair is used in purification and detection of various biomolecules; the strong streptavidin-biotin bond can also be used to attach biomolecules to one another or onto a solid support. Thus this reaction pair in combination with a FET as the transducer is a powerful setup enabling the detection of a wide variety of molecules with many advantages that stem from the FET, like no labeling, no need of expensive read-out devices, the possibility to put the signal amplification and analysis on the same chip, and outdoor usage without the necessity of a lab.

Device-level simulation capabilities have been developed to self-consistently model the Si-nanowire (NW) biosensor systems. Our numerical study demonstrates that by introducing electro-diffusion current flow in the electrolyte solutions, the electrostatic screening of the biological charge can be significantly suppressed; an improvement of the sensed signal strength by more than approximately 10 times is indicated. Based on such an operation principle, the screening-induced performance limits on Si-NW biosensors can be overcome.

In this paper a bottom-up approach for modeling field-effect Biosensors (BioFETs) is developed. Starting from the given positions of charged atoms, of a given molecule, the charge and the dipole moment of a single molecule are calculated. This charge and dipole moment are used to calculate the mean surface density and mean dipole moment at the biofunctionalized surface, which are introduced into homogenized interface conditions linking the Angstrom-scale of the molecule with the micrometer-scale of the FET. By considering a single-stranded to double-stranded DNA reaction, we demonstrate the capability of a BioFET to detect a certain DNA and to resolve the DNA orientation.

We have developed a topography simulation method which combines advanced level-set techniques for surface evolution with Monte Carlo flux calculation. The result is an algorithm with an overall complexity and storage requirement scaling like O(N logN) with surface disretization. The calculation of particle trajectories is highly optimized, since spatial partitioning is used to accelerate ray tracing. The method is demonstrated on Si etching in SF₆/O₂ plasma.

Experiments for silicon biosensors with gate lengths in the range of 200nm to 500nm have not been extensively carried out. In this paper, simulations were performed for gate lengths proportionally smaller and greater than regular experimental gate lengths. The sensitivity of the biosensors was simulated using a 2D drift-diffusion model in cylindrical coordinates using the Prophet simulator. In this study simulated conductance results and the respective experimental values are compared. The good agreement between simulation and experiment enables us to predict and optimize the sensitivity of the DNA sensors.

The sensitivity was studied in terms of conductance by varying the gate length, probe spacing, binding efficiency and angle of probe from normal.

Electrons and holes captured in self-assembled quantum dots (QDs) are subject to symmetry breaking that cannot be represented in with continuum material representations. Atomistic calculations reveal symmetry lowering due to effects of strain and piezo-electric fields. These effects are fundamentally based on the crystal topology in the quantum dots. This work studies these two competing effects and demonstrates the fine structure splitting that has been demonstrated experimentally can be attributed to the underlying atomistic structure of the quantum dots.

Self-assembled quantum dots (DQ) can be grown as stacks where the QD distance can be controlled with atomic layer control. This distance determines the interaction of the artificial atom states to form artificial molecules. The design of QD stacks becomes complicated since the structures are subject to inhomogeneous, long-range strain and growth imperfections such as non-identical dots and inter-diffused interfaces. This study presents simulations of stacks consistent of three QDs in their resulting inhomogeneous strain field. The simulations are performed with NEMO 3-D which uses the valence force field method to compute the strain and the empirical sp3d5s* tight binding method to compute the electronic structure. Strain is shown to provide a very interesting mixing between states and preferred ordering of the ground state in the top-most or bottom most quantum dot subject to growth asymmetries.

Conventional SOI DNAFET devices, being able to detect single-nucleotide polymor phisms, are simulated in a comprehensive approach. These devices can be fabricated in high-density arrays and offer advantages compared to optical detection methods. The influence of device parameters like doping concentration and the size of the exposed sensor area is investigated.

The 3-D Nanoelectronic Modeling Tool (NEMO 3-D) is an electronic structure simulation code for the analysis of quantum dots, quantum wells, nanowires, and impurities. NEMO 3-D uses the Valence Force Field (VFF) method for strain and the empirical tight binding (ETB) for the electronic structure calculations. Various ETB models are available, ranging from single s orbitals (single band effective mass), over sp³s* to sp³d⁵s* models, with and without explicit representation of spin. The code is highly optimized for operation on cluster computing systems. Simulations of systems of 64 million atoms (strain) and 21 million atoms have been demonstrated. This implies that every atom is accounted for in simulation volumes of (110nm)³ and (77nm)³, respectively. Such simulations require parallel execution on 64 itanium2 CPUs for around 12 hours. A simple effective mass calculation of an isolated quantum dot, in contrast, requires about 20 seconds on a single CPU. NEMO 3-D therefore offers the opportunity to engage both educators and advanced researchers, utilizing a single code. nanoHUB.org is the community web site hosted by the Network for Computational Nanotechnology (NCN) dedicated to bridge education, research, and development for the whole nanoscience and nanotechnology community. This paper reviews the mission of the NCN exemplified by the development and deployment of the NEMO 3-D tool.

We present an analysis of deposition of silicon nitride and silicon dioxide layers into three-dimensional interconnect structures. The investigations have been performed using our general purpose topography simulator ELSA (Enhanced Level Set Applications). We predict void formation and its characteristics, which play an important role for the formation of cracks which are observed during the passivation of layers covering IC chips.

The goal of this paper is to identify simulation models for the deposition of silicon dioxide layers from TEOS (tetraethoxysilane) in a CVD (chemical vapor deposition) process and to calibrate the parameters of these models by comparing simulation results to SEM (scanning electron microscope) images of deposited layers in trenches with different aspect ratios. We describe the three models used and the parameters which lead to the best results for each model which allows us to draw conclusions on the usefulness of the models.

The continued scaling of MOSFETs into the nano-scale regime requires refined models for carrier transport due to, e.g., unintentional doping in the active channel region which gives rise to threshold voltage and on-state current fluctuations. Therefore every transport simulator which is supposed to accurately simulate nano-devices must have a proper model for the inclusion of the Coulomb interactions. This paper proposes to use a 3D FMM (fast multi-pole method) (Greengard and Rokhlin, 1997; Cheng et al., 1999). The FMM is based on the idea of condensing the information of the potential generated by point sources in series expansions. After calculating expansions in a hierarchical manner, the long-range part of the potential is obtained by evaluating the series at the point in question and the short-range part is calculated by direct summation. Its computational effort is only O(n) where n is the number of particles. In summary, the use of the FMM approach for semiconductor transport simulations was validated. Simulation times are decreased significantly and effects due to electron-electron and electron-impurity interactions are observed as expected. Since the FMM algorithm operates independently of the grid used in the MC simulation, it can be easily included into existing MC device simulation codes.

We present the application of level set and fast marching methods to the simulation of surface topography of a wafer in three dimensions for deposition and etching processes. These simulations rest on many techniques, including a narrow band level set method, fast marching for the eikonal equation, extension of the speed function, transport models, visibility determination, and an iterative equation solver.

The aim of this work is to study the etching of trenches in silicon and the generation of voids during the filling of genuinely three-dimensional trench structures with silicon dioxide or nitride. The trenches studied are part of the manufacturing process of power MOSFETs, where void-less filling must be achieved. Another area of applications is capacitance extraction in interconnect structures, where the deliberate inclusion of voids serves the purpose of reducing overall capacitance. Furthermore, these simulations make it possible to analyze the variations on the feature scale depending on the position of the single trench on the wafer and in the reactor.

A method for determining higher order thermal coefficients for electrical and thermal properties of metallic interconnect materials used in semiconductor fabrication is presented. By applying inverse modeling on transient electrothermal three-dimensional finite element simulations the measurements of resistance over time of Polysilicon fuse structures can be matched. This method is intended to be applied to the optimization of Polysilicon fuses for reliability and speed.

The current challenge for TCAD is the prediction of the performance of groups of devices, backends, and -- generally speaking -- large parts of the final IC in contrast to the simulation of single devices and their fabrication. This enables one to predictively simulate the performance of the final device depending on different process technologies and parameters, which the simulation of single devices cannot achieve.

In this paper we focus on the simulation of backend, interconnect capacitance, and time delays. To that end topography simulations of deposition, etching, and CMP processes in the various metal lines are used to build up the backend stack. The output of the feature scale simulations is used as input to a capacitance extraction tool, whose results are made available directly to the circuit designer.

We discuss the utilized simulation tools and their integration. The topography simulations were performed by our tool called ELSA (enhanced level set applications) and the subsequent simulations by RAPHAEL. Finally simulation results for a 100nm process are presented, where the influence of void formation between metal lines profoundly impacts the performance of the whole interconnect stack.

The error of the numeric approximation of the semiconductor device equations particularly depends on the grid used for the discretization. Since the most interesting regions of the device are generally straightforward to identify, the method of choice is to use structurally aligned grids. Here we present an algorithm for generating structurally aligned grids including anisotropy and for producing grids whose resolution varies over several orders of magnitude. Furthermore the areas with increased resolution and the corresponding resolutions can be defined in a flexible manner and criteria on grid quality can be enforced.

The grid generation algorithm was applied to sample structures which highlight the features of this method. Furthermore we generated grids for the simulation of a high voltage trench gate MOSFET. In order to resolve the junction regions accurately, four regions were defined where the grid was grown in several directions with varying resolutions. Finally device simulations performed by MINIMOS NT show current voltage characteristics and the threshold voltage.

We present a computational method for locally adapted conformal anisotropic tetrahedral mesh refinement. The element size is determined by an anisotropy function which is governed by an error estimation driven ruler according to an adjustable maximum error. Anisotropic structures are taken into account to reduce the amount of elements compared to strict isotropic refinement. The spatial resolution in three-dimensional unstructured tetrahedral meshes for diffusion simulation can be dynamically increased.

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 two, which yielded unusable results.

Deposition and etching in Silicon trenches is an important step of today’s semiconductor manufacturing. Understanding the surface evolution enables to predict the resulting profiles and thus to optimize process parameters. Simulations using the radiosity modeling approach and the level set method provide accurate results, but their speed has to be considered when employing advanced models and for purposes of inverse modeling.

In this paper strategies for increasing the accuracy of deposition simulations while decreasing simulation times are presented. Two algorithms were devised: first, intertwining narrow banding and extending the speed function yields a fast and accurate level set algorithm. Second, an algorithm which coarsens the surface reduces the computational demands of the radiosity method.

Finally measurements of a typical TEOS deposition process are compared with simulation results both with and without coarsening of the surface elements. It was found that the computational effort is significantly reduced without sacrificing the accuracy of the simulations.

Deposition and etching of silicon trenches is an important manufacturing step for state of the art memory cells. Understanding and simulating the transport of gas species and surface evolution enables to achieve void-less filling of deep trenches, to predict the resulting profiles, and thus to optimize process parameters with respect to manufacturing throughput and the quality of the resulting memory cells. For the simulation of the SiO₂ deposition process from TEOS (Tetraethoxysilane), the level set method was used in addition to physical models. The level set algorithm devised minimizes computational effort while ensuring high accuracy by intertwining narrow banding and extending the speed function. In order to make the predictions of the simulation more accurate, model parameters were extracted by comparing the step coverages of the deposited layers in the simulation with those of SEM (scanning electron microscope) images.

The formation and dissolution of silicon self-interstitial clusters is linked to the phenomenon of TED (transient enhanced diffusion) 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 we were interested in finding a suitable model for the formation and dissolution of self-interstitial clusters and extracting corresponding 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. Additional 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.

Conventional macroscopic impact ionization models which use the average carrier energy as main parameter cannot accurately describe the phenomenon in modern miniaturized devices. Here we present a new 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 MOS 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.

The optimization of computationally expensive objective functions requires approximations that preserve the global properties of the function under investigation. The RSM approach of using multivariate polynomials of degree two can only preserve the local properties of a given function and is therefore not well-suited for global optimization tasks. In this paper we discuss generalized Bernstein polynomials 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.

We present simulations of a recently published SRAM memory gain cell consisting of two transistors and one MOS capacitor, representing an alternative to conventional six transistor SRAMs. Inverse modeling is used to fit a given device characteristic to measurement data. To account for de-charging due to tunneling, we use a simple, non-local tunneling model and calibrate it with data from literature. By optimization, we find values for the contact voltages in the off-region at which the retention time is a maximum.

Experiments of As-doped poly-silicon deposition have shown that under certain process conditions step coverages > 1 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 0.1μm wide and 7μm deep, high aspect ratio trenches.