In an article published in the journal Nature, researchers introduced a real-time feedback control method for optimizing the density of self-assembled indium arsenic (InAs)/gallium arsenic (GaAs) quantum dots (QD) grown via molecular beam epitaxy (MBE).
a The schematic of the sample structure. The thick GaAs buffer layer is grown on an n-type GaAs substrate at 600 °C. Subsequently, the substrate is cooled to 450–500 °C for the growth of InAs QDs. b–e The 2 μm × 2 μm atomic force microscope (AFM) images of QDs with varied labels. “zero”: there are no QDs on the surface. “low”: the InAs QDs sample with density less than 1 × 1010 cm−2. “middle”: the InAs QDs sample with density range from 1 × 1010 cm−2 to 4 × 1010 cm−2. “high”: the InAs QDs sample with density higher than 4 × 1010 cm−2. f–i Corresponding reflection high-energy electron diffraction (RHEED) images with varied labels. https://www.nature.com/articles/s41467-024-47087-w
The method utilized a machine learning (ML) model trained on reflection high-energy electron diffraction (RHEED) videos to provide real-time feedback on surface morphologies during the growth process. This approach enabled precise tuning of QD densities, expediting optimization and enhancing reproducibility in semiconductor manufacturing for optoelectronic and microelectronic applications.
Background
Self-assembled QDs fabricated through MBE hold immense potential for various optoelectronic applications. However, achieving specific QD densities tailored to different applications poses a significant challenge due to the complex interplay of growth parameters during the MBE process.
Previous approaches to optimize QD density involved time-consuming trial-and-error methods, relying heavily on the expertise of MBE researchers. While ML has shown promise in predicting growth outcomes, existing methods often lack real-time feedback and overlook temporal information from in situ characterization techniques like RHEED.
The present paper addressed these gaps by proposing a real-time feedback control method based on ML, which leveraged continuous RHEED videos to predict QD density during growth. By employing a three-dimensional (3D) ResNet 50 model trained on temporal RHEED data, the system intelligently adjusted growth parameters in real-time to achieve desired QD densities.
Unlike previous approaches, this method provided immediate feedback during growth, enabling precise control over QD density without the need for post-growth analysis. The proposed approach not only streamlined the optimization process but also enhanced the reproducibility of MBE, paving the way for more efficient and reliable fabrication of QD-based devices for optoelectronic applications.
Methods
The InAs QD samples were grown on GaAs substrates using a Riber 32P MBE system with precise control over arsenic, indium, and gallium fluxes. Substrate temperature and growth rates were carefully monitored and calibrated using a C-type thermocouple and RHEED oscillations. The growth process involved substrate outgassing, deoxidation, and buffer layer deposition before QD formation in the Stranski-Krastanow growth mode.
RHEED patterns were continuously recorded during growth, and atomic force microscopy (AFM) was used for surface morphology characterization. The hardware setup included a Windows 10 computer system with a specific central processing unit (CPU), memory, graphic processing unit (GPU), and storage configurations. The model, constructed in a Jupyter Notebook environment on Ubuntu, utilized PyTorch for deep learning operations, open neural network exchange (ONNX) for model deployment, and TensorRT for inference acceleration.
The interface allowed users to set targets for desired QD density, control substrate, and cell temperatures, analyze RHEED data in real-time, and display growth status information. This comprehensive setup facilitated precise control over the MBE process and enabled real-time monitoring and adjustment of growth parameters to achieve target QD densities.
Results
The growth parameters were determined based on an existing database correlating growth parameters with QD characteristics. The sample structure included a GaAs buffer layer followed by InAs QDs. The density of QDs was varied, ranging from zero to high density, with corresponding RHEED patterns.
The RHEED patterns transitioned from streaky to spotty as the QD density increased. The program framework included pre-processing RHEED videos, utilizing a 3D ResNet 50 model for classification, and deploying the model using LabVIEW, ONNX, and TensorRT for inference acceleration.
The ResNet 50 model was chosen for its ability to handle gradient vanishing issues and extract features from raw data efficiently.
Two models were trained: the "QDs model" for detecting QD formation and the "density model" for classifying QD density. Both models showed improvement in accuracy and loss during training. When deployed, the models produced results at a rate of approximately one sample per second. A control logic was developed to adjust substrate temperature based on model outputs to achieve the desired QD density.
Controlled growth experiments demonstrated the effectiveness of the model-guided growth process. In low-density QD growth experiments, adjustments to substrate temperature were made to achieve the target density, as confirmed by RHEED patterns and AFM images. Similarly, in high-density QD growth experiments, the model accurately identified the formation of high-density QDs, guiding the decision to close the shutter at the appropriate time. These results showcased the capability of the model to control the growth process in real time based on desired QD characteristics.
Discussion
In this study, a metrology method was developed to control the growth of QDs using MBE. By analyzing RHEED videos of as-grown samples with a neural network, the post-growth density of QDs could be accurately predicted. This enabled real-time adjustment of growth parameters to achieve desired QD densities, reducing the need for trial-and-error experimentation.
Although current hardware limitations resulted in a few seconds delay in prediction, upgrading hardware could significantly reduce this time. The method showed promise for optimizing material growth processes, reducing development time, and improving epitaxial thin film quality. Future applications might include defect detection and repair during growth, highlighting the potential impact of this approach in materials science.
Conclusion
In summary, researchers introduced a real-time feedback control method for optimizing the density of self-assembled InAs/GaAs QDs grown via MBE. Utilizing ML models trained on RHEED videos, they achieved precise tuning of QD densities, expediting optimization and enhancing reproducibility in semiconductor manufacturing for various applications. This method holds promise for efficient and reliable fabrication of QD-based devices, with the potential for further advancements in defect detection and repair during growth.
Journal reference:
- Shen, C., Zhan, W., Xin, K., Li, M., Sun, Z., Cong, H., Xu, C., Tang, J., Wu, Z., Xu, B., Wei, Z., Xue, C., Zhao, C., & Wang, Z. (2024). Machine-learning-assisted and real-time-feedback-controlled growth of InAs/GaAs quantum dots. Nature Communications, 15(1), 2724. https://doi.org/10.1038/s41467-024-47087-w, https://www.nature.com/articles/s41467-024-47087-w
Mixture Differential Cryptanalysis Empowered by Machine Learning