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This is a simulation of the Poisson's equation on a 3D structure consisting of several geometry groups and materials forming a FinFET transistor with a mesh consisting of hundreds of thousands tetrahedrons. Because NanoFEM platform consists almost entirely of open source software components, others could eventually build similar solutions including, but not limited to TCAD device simulations after reading and reviewing the NanoFEM platform design and components.

Such consideration suggests that the typical business model of TCAD, based on software companies that develop the codes and sell licenses and support, has become inefficient and very costly for customers.

In the medium term, the situation can worsen, since codes will become largely more complex, as devices enter the nanometer scale. However, our proposal might be interesting for other researchers, who effort to design and implement general simulation frameworks and projects based on the finite element method.

The finite element method is currently one of most often used techniques for numerical solutions of partial differential equations on complex modelled domains.

Finite element method has become a defacto industry standard for solving wide variety of multi-disciplinary engineering problems. There are many applications using this method, such as solid mechanics, fluid mechanics, heat transfer, acoustics, electromagnetics and computational fluid dynamics.

For numerical computation using the finite element method on general 3D modelled objects, we need to provide a suitable mesh representation of the continuum. This means to find a suitable discretization of continuous domain to simple volume cell elements e. Using the finite element basis, discrete algebraic systems are assemblied into sparse matrices and then solved.

Computed characteristics are determined in the nodes of the elements. Computation of general partial differential equations using the finite element method is rather complex to design and implement, and solid understanding of mathematics, numerical methods and computer engineering is required for designing and implementing new performance optimal solutions of real problems based on this method. One of important advantages of FEM is availability of software tools, pre- and post-processors as well as software components based on this method.

This allows for instance to automatically generate meshes on arbitrary structures, and there are some good open source meshers for FEM. The wide availability of such tools suggests that finite element method is in practice considerably more often used then similar methods, such as e. One of disadvantages of these tools is that users cannot develop their own code for new methods of device simulations, which is important for research and innovation.

There currently exist some open source or freely available tools for device simulation sometimes only for non-commercial usage or provided without source code : Archimedes 2D Quantum Monte Carlo simulator for semiconductor devices 2. Pre-processing and post-processing for these free tools is limited.

It is very complex to create a code for generation of 3D finite element mesh on arbitrary structures and therefore it is better to rely on existing meshers.

During analysis of our NanoFEM platform project we took into consideration various open source meshers libraries. From these, NETGEN [Schoberl97] and TetGen [Si06] seemed to be advanced in terms of stability, generality, quality, previous usage in other scientific projects and also suitability for our purpose. Some freely available open source environments for general finite element method analysis provide collection of components for tasks such as geometry modelling, meshing, visualization, common data structures, sometimes also an extensible framework for simulation modules and finite element solvers.

Gmsh [Geuzaine09] has some interesting features, such as integration of NETGEN and TetGen, geometry editor although very basic and with only limited interactive features and post-processing. There is support for different regions using physical volumes. The user interface seem to be very non-standard and rather inconvenient. Gmsh is using a text format of mesh and data fields, for which it is easy to write a parser.

Calculix 3. A graphical user interface seem to be less advanced than in Gmsh or even Salome Platform. It solves wide variety of mechanical, thermal, coupled thermomechanical, contact and field problems. Salome Platform 3. Geometry editor is much more advanced than the one provided with Gmsh, and there is Python functionality for this editor as well as for practically all other operations available through graphical user interface of Salome.

CORBA 3. Components can define their own user interface. With Salome Platform we have a much more advanced and powerful simulation environment, that we would have with other solutions and components that we have tested. ORCAN [Treibig06] is a software with some features similar to Salome Platform, namely in component based architecture and set of modules for geometry modelling, meshing, visualization of results and automatic generation of user interface for components.

There are also linear algebra solvers and material database. However, it is not as complete and mature as Salome Platform and is no longer actively maintained or developed since We have decided to select Salome Platform, version 3.

We also decided to make selection of a suitable free finite element solver, that would make implementing equations running on semiconductor devices easier and faster, then if we would implement a new solver by ourselves. We have reviewed many software solutions, libraries and projects, which address solving partial differential equations using the finite element method. We applied various evaluation criteria, such as ongoing development, quality of documentation, fitness for devices simulations, number of developers, community around the project, available features, generality, easiness of use, extendibility and references from other scientific projects using it.

For pre-processing, i. This way, we can use an advanced geometry editor and automatic finite element mesher on arbitrary 3D structures defined in the geometry editor. Geometry for the solved case can be defined either in a graphical user interface or using Python scripts. Quality tetrahedral meshes necessary for FEM simulations are created automatically, and we can define separate geometry and mesh groups. For visualization and post-processing, we can use advanced visualization features with 2D and 3D plots and graphs.

Salome Platform provides also functionality for exchanging data between codes and solvers in memory, CORBA to allow communication of modules on remote servers, and persistent data storage of all data based upon HDF format 4. Because of Salome implementation and because we use nano structures with very small dimensions, we had to multiply all the coordinates of modelled geometry by the scaling factor e. If we would use a smaller scaling factor 10 3 or 10 6 , we would obtain errors namely when generating a mesh or during visualization in Salome Platform.

By using Salome Platform, we save lot of work and effort, which otherwise would be necessary to design and implement the mentioned features. In order to implement equations, which would run on a device with finite element method as easy as possible, we are using a finite element library DOLFIN. This library offers many advantages and makes coding both easily and powerful.

It supports iterative and direct solvers LU decomposition 4. This solves an important desire when designing simulations for the devices: possibility for easy testing of various provided equations, without necessity for manually programming the finite elements.

A required equation has to be coded to the variational form format with bilinear and linear components and and then coded using a code with Python language syntax.

Enigma Enigma is the GSS workflow, automation and productivity framework, which is designed to deliver a powerful and flexible environment for rapid design- technology co-optimisation DTCO. It provides its users with the capability to quickly evaluate technology changes and their impact on device and circuit performance and yield, and to automatically generate PDK-quality statistical compact models based on predictive TCAD simulations.

Garand Garand is an advanced 3D TCAD simulation tool suite specifically designed for the efficient modelling of statistical variability and reliability in contemporary and future CMOS transistors. It contains both Drift Diffusion and Monte-Carlo simulation modules and provides density gradient quantum corrections for both electrons and holes.

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Please read through the documentation carefully for important changes in Cumulative Data Set cross-sectional samples from all years.



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