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A FEM dataset of Ge film profiles and elastic energies for machine learning approximation of strain state and morphological evolution

Daniele Lanzoni1*, Fabrizio Rovaris1*, Luis Martín-Encinar2*, Andrea Fantasia1*, Roberto Bergamaschini1*, Francesco Montalenti1*

1 Dipartimento di Scienza dei Materiali, Università di Milano-Bicocca, 20125, Milano, Italy

2 Dpto. de Electricidad y Electrónica, E.T.S.I. de Telecomunicación, Universidad de Valladolid, 47011, Valladolid, Spain

* Corresponding authors emails: d.lanzoni@campus.unimib.it, fabrizio.rovaris@unimib.it, luis.martin.encinar@uva.es, a.fantasia1@campus.unimib.it, roberto.bergamaschini@unimib.it, francesco.montalenti@unimib.it
DOI10.24435/materialscloud:5r-9j [version v1]

Publication date: Apr 18, 2024

How to cite this record

Daniele Lanzoni, Fabrizio Rovaris, Luis Martín-Encinar, Andrea Fantasia, Roberto Bergamaschini, Francesco Montalenti, A FEM dataset of Ge film profiles and elastic energies for machine learning approximation of strain state and morphological evolution, Materials Cloud Archive 2024.59 (2024), https://doi.org/10.24435/materialscloud:5r-9j


Machine Learning (ML) can be conveniently applied to continuum materials simulations, allowing for the investigation of larger systems and longer timescales, pushing the limits of tractable systems. Here we provide a comprehensive dataset of strained Ge films on Si and their corresponding strain states, which can be used to train a ML model capable of such acceleration. Approximately 80k 2D cases are included, reporting the profiles h(x) and the corresponding elastic energy densities and strain fields. The profiles are conveniently sampled using Perlin-noise and pure-sine waves. A 100nm-large computational domain is considered. The mechanical equilibrium problem is solved using Finite Element Method (FEM). Ge is modeled as an isotropic material and an eigenstrain of 3.99% is used, as in Ge/Si(001). The database has been exploited for training a (fully) Convolutional Neural Network (CNN) which maps the free surface profile h(x) to the corresponding energy density. If plugged into the proper time-dependent Partial Differential Equation, this term can be used to accelerate continuum simulations of the morphological evolution of strained films while retaining FEM-level accuracy. Tests of the reliability of such CNN model are also provided in the repository, together with the output of surface morphology minimization procedures and morphological evolution simulations during coarsening and growth. In the latter, evolution by surface diffusion has been considered as an important case, but applications to other mechanisms are possible. Generalization examples to larger computational cells with respect to those in the dataset are also available.

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File name Size Description
1.2 KiB README file outlining folder structure. Additional details can be found in specific README files in subfolders
4.2 GiB FEM calculation dataset
164.8 MiB Output of morphological evolution simulations (annealing and growth) using the NN approximation. Corresponding FEM calculations are also provided for some cases.
278.8 KiB Minimization of free surface profiles using the NN approximation and the corresponding FEM calculations
1.4 MiB Generalization tests on profiles not present in the dataset. Corresponding FEM calculations are also provided


Files and data are licensed under the terms of the following license: Creative Commons Attribution 4.0 International.
Metadata, except for email addresses, are licensed under the Creative Commons Attribution Share-Alike 4.0 International license.

External references

D. Lanzoni, F. Rovaris, L. Martín-Encinar, A. Fantasia, R. Bergamaschini, F. Montalenti "Simulation of the Evolution of Strained Films via Convolutional Neural Networks: tackling large sizes and long time scales with FEM accuracy" (in preparation)


Machine Learning Continuum Models Convolutional Neural Network Finite Element Method Strained films Surface evolution Thin films Elastic energy Germanium

Version history:

2024.59 (version v1) [This version] Apr 18, 2024 DOI10.24435/materialscloud:5r-9j