Fully Automated Identification of Two-Dimensional Material Samples

Thin nanomaterials are key constituents of modern quantum technologies and materials research. The identification of specimens of these materials with the properties required for the development of state-of-the-art quantum devices is usually a complex and tedious human task. In this work, we provide a neural-network-driven solution that allows for accurate and efficient scanning, data processing, and sample identification of experimentally relevant two-dimensional materials. We show how to approach the classification of imperfect and imbalanced data sets using an iterative application of multiple noisy neural networks. We embed the trained classifier into a comprehensive solution for end-to-end automatized data processing and sample identification.

Figure 1

The collection and processing of data. (a) A typical microscope image of $\mathrm{hBN}$. (b) Examples of the preprocessed images: the first column depicts examples picked up by our preprocessing algorithm that are not $\mathrm{hBN}$ flakes, whereas the second column shows hBN flakes labeled as “good”. (c) A schematic illustration of the architecture of the neural network that is used: the convolutional layers are followed by pooling and are connected to the dense layer—the two-neuron output layer outputs probabilities for a given flake being suitable (“good”) or unsuitable (“bad”) for further processing.

Figure 2

The application of the multiple networks. The iterative procedure filters out bad flakes on the concrete example of a small set of 944 flakes. The rectangle on the left of each network is its input and the rectangle on the right of the network is its number of flakes classified by the network to be good. The dark green ovals denote the number of good flakes present in each step according to the human operator’s labeling. The input of the algorithm is $944$ flakes, out of which $108$ are labeled as good by a human operator. The first iteration of the networks classifies $224$ flakes as suitable for further processing. Out of these, $98$ are actually labeled as good by a human expert. Therefore, the network misses ten good flakes in this first step. In the second step of the iterative algorithm, we input the $224$ flakes selected by our first model into the second neural network. The second network classifies $160$ flakes as suitable, out of which $87$ are labeled as good by a human operator. In the second step, the model misses an additional $11$ good flakes. Finally, we run the last neural network on the output of the second neural network. The model now selects $150$ flakes as suitable, out of which $86$ are labeled as good. In this last step, the algorithm misses one good flake from the set of good flakes identified in the previous step.

Figure 3

The loss and accuracy of the three models used in the iterative algorithm. The networks are trained using a training set of ${10}^5$ labeled flakes. Panels (a), (b), and (c) show the evaluation loss in orange and the corresponding evaluation accuracy in blue for the three models used in the algorithm as shown in Fig. 2.

Figure 4

Validation by a human operator. The first 25 flakes of the set for human validation are shown with their evaluation by three different operators: 23 flakes are denoted to be suitable by at least one operator, while two flakes are dismissed by all three operators. While the user-to-user variation is significant, the algorithm provides flakes that are mostly considered suitable by at least one operator.

Figure 5

Testing the performance of the network on different materials: (a) an example of a graphite wafer; (b) examples of bad (left) and good (right) graphite flakes; (c) the results of the application of our protocol to $1200$ flakes obtained by scanning a single wafer. The test set of $1200$ flakes contains $132$ flakes labeled as “good” by a human operator. The three iterations of the protocol propose that $185$ flakes are suitable, out of which $109$ are actually good (as labeled by a human operator). This result shows that approximately $60\mathrm{\%}$ of the flakes suggested by the model are indeed suitable. In total, the network identifies $83\mathrm{\%}$ of the “good” flakes in the set while missing $17\mathrm{\%}$.

Figure 6

Testing the performance of the network on bilayer graphene: (a) examples of preprocessed data containing bilayer-graphene flakes; (b) the results of the application of our protocol on $3800$ flakes obtained by scanning a single wafer.