Mechanical characterization of polysilicon : a stochastic, deep learning-based approach

In this work, a deep-learning-based approach is proposed to address the multi-scale characterization of polysilicon movable structures of micro-electro-mechanical systems, based on data assimilation from two-dimensional stochastically representative images of polycrystalline films. The material’s representations are digitally generated via Voronoi tessellations in conjunction with a Monte Carlo procedure, exploited to quantify the stochastic effects associated with the grain arrangements, i.e. the stochastic variables governing the topology of the grain boundary network and the lattice orientation of each grain. A dataset of microstructures is collected and a convolutional neural network-based model is trained to ultimately provide the appropriate scattering in the value of the overall stiffness (in terms e.g. of Young’s modulus) of the grain aggregates. In an initial phase, focused on hyperparameter tuning and training, a certain number of representative images are employed to learn the underlaying microstructure-property mappings. For this, finite element simulations provide the ground-truth data required for the training. After this, the regression model is used to perform predictions of the Young’s modulus over unseen microstructures. In this way, the intended task of capturing the dispersion of the values around the mean is easily accomplished afterwards, by computing the statistical indicator of interest (i.e. the standard deviation) from a set of predictions. Finally, the accuracy of the proposed approach is assessed on microstructures characterized by specific values of the ratio between the absolute dimension of the polycrystalline aggregate and the target in-plane grain size. In particular, the sets gathered for training and validation, feature a value of 4 for this ratio, while values of 6 and 10 are considered for the generation of two test sets. This allow to investigate whether or not the size effects are correctly captured and to explore the generalization capability of the model. The results demonstrate that the relevant property predictions are characterized by standard deviations featuring absolute percentage errors as low as 5.7% (ratio = 10 case) and 4.8% (ratio = 6 case). This indicates the effectiveness of the proposed approach for providing accurate statistical characterization of the considered polysilicon aggregates. Moreover, for the case of ratio = 10, the model is able not only to accomplish the aforementioned statistical description, but also, to reconstruct the one-to-one correspondence between microstructural arrangements and the relevant elastic property. This is qualitatively observed by the linear dispersion of the data shown in the respective parity plot, and evidenced by the low value of mean square error (MSE) achieved. Hence, the main contribution of this work is that the proposed approach allows for an easy multiscale exploration of the size effects, representing a feasible alternative to standard numerical homogenization approaches for the mechanical characterization of polycrystalline films. This is accomplished by handling single-size input images, independently of the representative length scale of the material under consideration, a feature that potentiates the ability of the model to emulate the scale-dependent solution in a straight-forward data-driven manner.