Query: Element Edge Based Discretization for TCAD Device Simulation

Candidate papers:

abstract: Technology computer aided design (TCAD) semiconductor device simulators solve partial differential equations (PDE) using the finite volume method (FVM) or related methods. While this approach has been in use over several decades, its methods continue to be extended, and are still applicable for investigating novel devices. In this paper, we present an element edge based (EEB) FVM discretization approach suitable for capturing vector field effects. Drawing from a 2D approach in the literature, we have extended this method to 3D. We implemented this method in a TCAD semiconductor device simulator, which uses a generalized PDE (GPDE) approach to simulate de vices with the FVM. We describe how our EEB method is compatible with the GPDE approach, allowing the modeling of vector effects using scripting. This method is applied to solve polarization effects in a 3D ferro capacitor, and a 2D ferroelectric field effect transistor. An example for field dependent mobility in a 3D MOSFET is also presented.
title: Element Edge Based Discretization for TCAD Device Simulation
venue: IEEE Transactions on Electron Devices
year: 2021

abstract: In this article, a novel edge domain decomposition (EDD) method is proposed to solve 3 D nonlinear finite element (FE) problems of electromagnetic devices and transient field circuit co simulation. The method applies reduced magnetic vector potential formulation to discretize the physical problem based on 3 D edge elements, and the solution region is divided into many sub domains that only contain one edge unknown. The solution of lightweight nonlinear sub domain systems can be massively parallelized, and the neighbor to neighbor communication scheme eliminates the need to assemble the global FE matrix. This article also introduces an indirect coupling scheme to handle large eddy currents to interface the EDD FE system with external circuits. The abovementioned algorithms are then implemented on a many core GPU for transient field circuit co simulation. The result shows an auto gauging property, and the comparison with a commercial FE software indicates a speedup of over 43 times with relative error less than 2%
author_names: Jiacong Li

Peng Liu

Venkata R Dinavahi
title: Matrix Free Edge Domain Decomposition Method for Massively Parallel 3 D Finite Element Simulation With Field Circuit Coupling
venue: IEEE Transactions on Magnetics
year: 2020

abstract: We present a charge conservative electromagnetic particle in cell (EM PIC) algorithm optimized for the analysis of vacuum electronic devices (VEDs) with cylindrical symmetry (axisymmetry) We exploit the axisymmetry present in the device geometry, fields, and sources to reduce the dimensionality of the problem from 3D to 2D. Further, we employ 'transformation optics' principles to map the original problem in polar coordinates with metric tensor diag(1,r2,1) to an equivalent problem on a Cartesian metric tensor diag(1,1,1) with an effective (artificial) inhomogeneous medium introduced. The resulting problem in the meridian (rz) plane is discretized using an unstructured 2D mesh considering TEph polarized fields. Electromagnetic field and source (node based charges and edge based currents) variables are expressed as differential forms of various degrees, and discretized using Whitney forms. Using leapfrog time integration, we obtain a mixed E B finite element time domain scheme for the full discrete Maxwell's equations. We achieve a local and explicit time update for the field equations by employing the sparse approximate inverse (SPAI) algorithm. Interpolating field values to particles' positions for solving Newton Lorentz equations of motion is also done via Whitney forms. Particles are advanced using the Boris algorithm with relativistic correction. A recently introduced charge conserving scatter scheme tailored for 2D unstructured grids is used in the scatter step. The algorithm is validated considering cylindrical cavity and space charge limited cylindrical diode problems. We use the algorithm to investigate the physical performance of VEDs designed to harness particle bunching effects arising from the coherent (resonance) Cerenkov electron beam interactions within micro machined slow wave structures.
author_names: Dong-Yeop Na

Yuri A Omelchenko

Haksu Moon

Ben-Hur Viana Borges

Fernando Lisboa Teixeira
title: Axisymmetric charge conservative electromagnetic particle simulation algorithm on unstructured grids: Application to microwave vacuum electronic devices
venue: J. Comput. Phys.
year: 2017

abstract: Rice seed rope planting has the advantages of water saving, energy saving and it can precisely control the rate and hill space of seeds, fertilizer and herbicide or pesticide, and simplify the sowing process as well. To solve the problem of ditching and rope laying the influence of cutting edge curve of trench opener on trench resistance is studied in this paper. Three kinds of furrow opener curves are put forward: exponential, parabola and circular. The mechanical model of the seeder was established and simulation analysis of furrow opener based on discrete element method, therefore, the edge curve equation of the soil cutting and seed rope guiding device was optimized. The simulation test results show that the exponential opener has the minimum working resistance 6.71 N; and the parabola opener has a higher working resistance 7.87 N; the circle opener has the highest resistance 9.59 N. This study may provide the basis for design of the rice seed rope planter.
author_names: Dan Liu

Haobin Dong

Baofeng Zhang

Jiahan You
title: Design of Seed Rope Guiding Opener Based on DEM
year: 2021

abstract: We propose an approach based on sensitivity analysis to evaluate threshold voltage variability of nanoscale MOSFETs due to line edge roughness (LER) and to random discrete dopants (RDD) It requires a very limited number of TCAD simulations, corresponding to computational load much smaller than that required for statistical simulations. We apply our approach to 45 nm CMOS technology, and show that with only few tens of device simulations one can obtain results comparable to those of statistical simulations, with an improved understanding of the impact of physical parameters on the variability of electrical characteristics.
author_names: Valentina Bonfiglio

Giuseppe Iannaccone
title: Evaluation of threshold voltage dispersion in 45 nm CMOS technology with TCAD based sensitivity analysis
venue: 2010 14th International Workshop on Computational Electronics
year: 2010

abstract: Subsoiling, as an important mode of conservation tillage, can break plowpan and increase permeability and water retention ability of soil which increase the crop yield. Subsoiler, as a key component of subsoiling, significantly effects on the tillage resistance. Reduction of working resistance of subsoiler can decrease output power of tractor and then further reduce the cost of subsoiling operation. The existing subsoilers have problem of overlarge subsoiling resistance. The conventional methods to resolve such problem include optimal design of the structural parameters of subsoiler and application of oscillation subsoiling device, but those methods not only make the structure of subsoiler more complex, but also increase the cost of agricultural production. Based on biomimetics principles, the upper surface outline of the claw of the house mouse (mus musculus) which has exponential function curve feature, was applied to the structural design of cutting soil edge of subsoiler shaft. Accordingly, the bionic subsoiler which has exponential function curve feature was designed and manufactured. The comparative experiments were conducted using the two types of subsoilers which have exponential function curve shape and parabola type in tillage depth at 300mm and 350mm with the forward velocitys of 0.5m/s and 1.0m/s in the indoor soil bin. The horizontal tillage resistances of the two types of subsoilers were measured using remote measuring system of agricultural machinery dynamic parameters under different experimental conditions. The results showed that the horizontal tillage resistances increased with the increase of tillage depth and forward velocity. The horizontal tillage resistances of bionic anti drag subsoiler (BAS) were obviously less than those of parabola type subsoiler (PTS) under same experimental conditions and the reduction was in the range of 8.5 38.2% It indicated that the cutting soil edge of shaft with exponential function curve structure has remarkable anti drag property. The simulations of tillage processes of the two types of subsoilers were conducted using discrete element method (DEM) the stress fields and velocity fields were obtained under different simulation conditions. The results showed that the directions of stress fields and velocity fields of the two types of subsoilers have forward and upward variation trend, but the directionality of contact stress of PTS was nonuniform compared with BAS, and such results lead to an increase in soil disturbance. The intensities of stress field and velocity field of BAS were obviously less than those of PTS under same experimental conditions, The results of simulation were consistent with the results of tillage experiments, indicating that the bionic subsoiler with exponential function curve feature has significant anti drag property. The exponential function curve can be applied to the structural design of cutting soil edge of subsoiler aiming to reduce tillage resistance.
author_names: Jin Zhang

Jin Tong

Yunhai Ma
title: Simulation of Bionic Anti Drag Subsoiler with Exponential Curve Feature Using Discrete Element Method
year: 2013

abstract: Nowadays, device simulators are essential tools for designing VLSI devices and much effort is being made to improve their user interfaces. For example, unified systems have been developed which allow consecutive process and device simulations, and multi window based simulation environments have been constructed which assist users to operate simulators. Optimizing discretization mesh, however, is still left to users and this reduces the practicality of device simulators. The adaptive meshing technique resolves this problem by refining the mesh automatically according to the discretization error. Adaptive mesh generation consists of 1) solving semiconductor device equations, 2) evaluating an discretization error indicator, and 3) refining the mesh elements with the large indicator value. These steps are repeated while some element retains the large indicator value. It is crucial to select appropriate indicators for ensuring the precision in calculated device characteristics on the adapted mesh. Although several indicators were already proposed [1 4] more reliable and simpler indicator is desirable especially for the current continuity equation. In this paper, simple error indicators are incorporated into the typical adaptive mesh device simulator HFIELDS [3] and their practicality is examined. In HFIELDS, the discretization mesh is adaptively generated by using the curvature 3 of electrostatic potential (or quasi Fermi potentials q5n,q5p) as an error indicator. The indicator b' is estimated simply by "(1 2) 2 (d z) z 2. To limit p( is almost equivalent to limiting the spatial change of V$ and this reduces the discretization error in the Poisson equation effectively. In the case of the current continuity equation, to limit p(4) is not effective since current density is proportional to V4 times carrier density and carrier density varies by several orders of magnitude. Therefore, another indicator shouid be introduced that either takes account of the carrier density or directly estimates the error in current density. In the case of MOSFETs simulation, lateral current density varies abruptly near the Si surface along the vertical direction, and this spatial variation in current density can be used as an error indicator. When the discretization mesh is based on box grid, such an indicator is useful as where 5 1 and Jz are current densities along two parallel edges of a box. Essentially, the indicator 7r examines the uniformity of current density normal to the control volume boundary. Although 7, can be evaluated easily, it is well defined only for the
author_names: K Tanaka

P Ciampohni

Anna Pierantoni

Giorgio Baccarani
title: Comparison Between A Posteriori Error Indicators For Adaptive Mesh Generation In Semiconductor Device Simulation
venue: [Proceedings] 1993 International Workshop on VLSI Process and Device Modeling (1993 VPAD)
year: 1993

abstract: Technology scaling increasingly emphasizes complexity and non ideality of the electrical behavior of semiconductor devices and boosts interest on alternatives to the conventional planar MOSFET architecture. TCAD simulation tools are fundamental to the analysis and development of new technology generations. However, the increasing device complexity is reflected in an augmented dimensionality of the problems to be solved. The trade off between accuracy and computational cost of the simulation is especially influenced by domain discretization: mesh generation is therefore one of the most critical steps and automatic approaches are sought. Moreover, the problem size is further increased by process variations, calling for a statistical representation of the single device through an ensemble of microscopically different instances. The aim of this thesis is to present multi disciplinary approaches to handle this increasing problem dimensionality in a numerical simulation perspective. The topic of mesh generation is tackled by presenting a new Wavelet based Adaptive Method (WAM) for the automatic refinement of 2D and 3D domain discretizations. Multiresolution techniques and efficient signal processing algorithms are exploited to increase grid resolution in the domain regions where relevant physical phenomena take place. Moreover, the grid is dynamically adapted to follow solution changes produced by bias variations and quality criteria are imposed on the produced meshes. The further dimensionality increase due to variability in extremely scaled devices is considered with reference to two increasingly critical phenomena, namely line edge roughness (LER) and random dopant fluctuations (RD) The impact of such phenomena on FinFET devices, which represent a promising alternative to planar CMOS technology, is estimated through 2D and 3D TCAD simulations and statistical tools, taking into account matching performance of single devices as well as basic circuit blocks such as SRAMs. Several process options are compared, including resist and spacer defined fin patterning as well as different doping profile definitions. Combining statistical simulations with experimental data, potentialities and shortcomings of the FinFET architecture are analyzed and useful design guidelines are provided, which boost feasibility of this technology for mainstream applications in sub 45 nm generation integrated circuits.
author_names: Emanuele Baravelli
title: TCAD approaches to multidimensional simulation of advanced semiconductor devices
year: 2008

abstract: The mapping of the current induced by a focused electron beam in a scanning electron microscope (SEM) has been used to localize electrically stressed regions in the AlGaN/GaN on Si Schottky barrier diode (SBD) structures cross sectioned by the focused ion beam (FIB) technique. We have shown that homogeneously distributed electron beam induced current (EBIC) intensity detected below the Schottky contact at 0 V changes with increasing reverse voltage {V}_{R} and peaks at the edges of a field plate region. The build up of local microavalanches at high electric voltages has been indicated by overexposed EBIC signal at areas following the edges of the field plate structure. Interpretation of EBIC measurements is supported by electro physical modeling and simulations employing the 2 D finite element method in Synopsys TCAD Sentaurus. The simulations prove that the electric field intensity in the SBD locally reaches values sufficiently high to trigger multiplication of the excessive carriers generated by an electron beam, which helps one to visualize and localize critical regions in GaN based power electronic devices by the EBIC method.
author_names: Juraj Priesol

Alexander Satka

Ales Chvala

Steve Stoffels

Brice De Jaeger

Stefaan Decoutere
title: Identification of Electrically Stressed Regions in AlGaN/GaN on Si Schottky Barrier Diode Using EBIC Technique
venue: IEEE Transactions on Electron Devices
year: 2021

abstract: A 3D drift diffusion device simulation tool with quantum corrections has been applied to study the off current, threshold voltage and sub threshold slope variability induced by the metal gate granularity using a Voronoi approach, and line edge roughness using Fourier synthesis, in a 25?nm Si FinFET. The discretization based on the finite element method allows for an accurate description of the 3D geometry. We have simulated 4000 variations of the device to study the metal gate granularity using four different metal grain sizes. The results for the threshold voltage variability ranged from 8.6?mV, for a 3?nm grain size, to 25.9?mV, for a 10?nm grain size. The effect of the grain size was studied and we found an inverse square root dependence of the variability for the three figures of merit. The mean threshold voltage and sub threshold slope have monotonous decrease with the decrease in metal grain size suggesting that the device power consumption and switching speed can be improved by reducing the grain size. The corresponding threshold voltage variability can reach up to 8.2?mV when RMS 3?nm and the correlation length is 50?nm.
author_names: Guillermo Indalecio

Manuel Aldegunde

Natalia Seoane

Karol Kalna

Antonio J Garcia-Loureiro
title: Statistical study of the influence of LER and MGG in SOI MOSFET
year: 2014