机器学习在分子束外延生长的应用进展

doi:10.16553/j.cnki.issn1000-985x.2024.0272

摘要/Abstract

摘要： 最近几年，人工智能在材料领域得到广泛应用，机器学习在分子束外延（MBE）技术中的应用引人关注。基于原位反射高能电子衍射（RHEED）及相关物性的智能识别和反馈的MBE技术，能够显著提升生长材料的质量和生长效率，有望实现薄膜的MBE智能外延。本综述聚焦机器学习MBE中的应用研究，首先介绍了MBE中常用的机器学习算法模型，阐述了机器学习在优化MBE生长条件中的应用，着重总结了不同材料体系（半导体薄膜和量子结构材料、氧化物材料和二维材料等）基于RHEED图像机器学习的研究进展，并就存在的问题和未来的发展策略进行了总结展望。

关键词: 分子束外延; 机器学习; 反射高能电子衍射; Ⅲ-Ⅴ族半导体材料; 人工智能

Abstract: In recent years， artificial intelligence has been widely applied in the field of materials， and the application of machine learning in molecular beam epitaxy （MBE） has attracted attention. Intelligent recognition and feedback based on in-situ reflection high-energy electron diffraction （RHEED） and related material properties in MBE technology can significantly improve the quality and efficiency of material growth， leading to the realization of intelligent epitaxy of epitaxial films. This article focuses on the application of machine learning in MBE. It first introduces commonly used machine learning algorithm models in MBE， and explains the application of machine learning in optimizing growth conditions and specifically summarizes the research progress on machine learning based on RHEED images for different material systems （semiconductor thin films and quantum structure materials， oxide materials， and two-dimensional materials）. A summary and outlook were provided on the existing problems and future development strategies.

Key words: molecular beam epitaxy; machine learning; reflection high-energy electron diffraction; Ⅲ-Ⅴ semiconductor material; artificial intelligence

中图分类号:

O484.1

杨再洪, 周灿, 范柳燕, 张燕辉, 陈泽中, 陈平平. 机器学习在分子束外延生长的应用进展[J]. 人工晶体学报, 2025, 54(6): 924-934.

YANG Zaihong, ZHOU Can, FAN Liuyan, ZHANG Yanhui, CHEN Zezhong, CHEN Pingping. Research Progress on Application of Machine Learning in Molecular Beam Epitaxy Growth[J]. Journal of Synthetic Crystals, 2025, 54(6): 924-934.

图/表 11

图1 机器学习的流程

Fig.1 Process of machine learning

表1 MBE技术中常见的机器学习算法模型

Table 1 Common machine learning algorithm models in MBE technology

Algorithmic model	Peculiarity	Reference
Random forest	It can process a large amount of data and high-dimensional features， is not easy to overfit， and is robust to missing data. But the training time is long， and the interpretability of the model is relatively poor.	［21⁃22］
K-means clustering	Simple， easy to understand and implement， suitable for large-scale datasets. But it is sensitive to the initial clustering center and converges to the local optimal solution.	［23］
Hierarchical clustering	Ability to organize and present information clearly， making complex concepts and relationships easier to understand and remember. But it can be an oversimplification of complex realities， leading to some information being overlooked or misunderstood.	［24］
Nonnegative matrix factorization	The latent features in the data can be extracted.But the computational complexity is high， and it is easy to fall into the local optimal solution.	［25］
Convolutional neural network	It can effectively process two-dimensional data such as images and videos， and has the characteristics of parameter sharing and local connection， which is suitable for extracting spatial features. But the training time is long， the model is poorly interpretable， and it is easy to overfit and other problems.	［26⁃27］
Support vector machine	Able to process high-dimensional data， has good generalization ability， performs well for small-sample data.But has high computational complexity for large-scale datasets， and is sensitive to missing data.	［28］
Principal components analysis	It can reduce data dimensions， remove noise and redundant information， improve model efficiency， and more. But some information may be lost， sensitivity to outliers， etc.	［29］
Uniform manifold approximation and projection	It has a good ability to express the data of nonlinear structure， and has a fast calculation speed. But the processing capacity for ultra-large-scale data is relatively weak.	［30］
Logistic regression	It is suitable for binary classification problems， which is fast to computation， easy to explain and implement.But it is not suitable for nonlinear relationships and is susceptible to outliers.	［31］
Naive bayes	The model is simple， computationally efficient， and performs well with small-scale data. But the conditional independence of the input data is more stringent， and when the assumption is not true， the classification results will be affected.	［32⁃33］

表1 MBE技术中常见的机器学习算法模型

Table 1 Common machine learning algorithm models in MBE technology

Algorithmic model	Peculiarity	Reference
Random forest	It can process a large amount of data and high-dimensional features， is not easy to overfit， and is robust to missing data. But the training time is long， and the interpretability of the model is relatively poor.	［21⁃22］
K-means clustering	Simple， easy to understand and implement， suitable for large-scale datasets. But it is sensitive to the initial clustering center and converges to the local optimal solution.	［23］
Hierarchical clustering	Ability to organize and present information clearly， making complex concepts and relationships easier to understand and remember. But it can be an oversimplification of complex realities， leading to some information being overlooked or misunderstood.	［24］
Nonnegative matrix factorization	The latent features in the data can be extracted.But the computational complexity is high， and it is easy to fall into the local optimal solution.	［25］
Convolutional neural network	It can effectively process two-dimensional data such as images and videos， and has the characteristics of parameter sharing and local connection， which is suitable for extracting spatial features. But the training time is long， the model is poorly interpretable， and it is easy to overfit and other problems.	［26⁃27］
Support vector machine	Able to process high-dimensional data， has good generalization ability， performs well for small-sample data.But has high computational complexity for large-scale datasets， and is sensitive to missing data.	［28］
Principal components analysis	It can reduce data dimensions， remove noise and redundant information， improve model efficiency， and more. But some information may be lost， sensitivity to outliers， etc.	［29］
Uniform manifold approximation and projection	It has a good ability to express the data of nonlinear structure， and has a fast calculation speed. But the processing capacity for ultra-large-scale data is relatively weak.	［30］
Logistic regression	It is suitable for binary classification problems， which is fast to computation， easy to explain and implement.But it is not suitable for nonlinear relationships and is susceptible to outliers.	［31］
Naive bayes	The model is simple， computationally efficient， and performs well with small-scale data. But the conditional independence of the input data is more stringent， and when the assumption is not true， the classification results will be affected.	［32⁃33］

图2 （a）RHEED图案；（b）AFM照片；（c）θ-2θ扫描XRD图谱；（d）具有50~52的RRR的SrRuO3薄膜的截面HAADF-STEM图像；（e）图（d）中界面附近的放大图像；（f）图（e）中界面附近的放大图像［34］

Fig.2 （a） RHEED pattern；（b） AFM image；（c） θ-2θ scanned XRD pattern；（d） cross-sectional HAADF-STEM image of the SrRuO3 thin film with the RRR of 50~52；（e） magnified image near the interface in Fig.（d）；（f） magnified image near the interface in Fig.（e）［34］

图3 不同条件下外延生长TiN薄膜的电阻率随温度的变化关系［35］

Fig.3 Change relationship between of epitaxial TiN films with temperature under different conditions［35］

图4 机器学习在RHEED中应用的总体框架［37］

Fig.4 Overarching framework for the application of machine learning in RHEED［37］

图5 在两次不同脱氧运行中实现7×7 RHEED模式的概率［38］

Fig.5 Probability of achieving 7×7 RHEED pattern in two different deoxidation runs［38］

图6 包括卷积神经网络和全连接层的RHEED模式多类分类别模型［42］

Fig.6 RHEED model multiclass classification model includes convolutional neural network and fully connected layer［42］

图7 高密度量子点的受控生长过程［43］

Fig.7 Controlled growth process of high-density quantum dots［43］

图8 （a）对于TbScO3上的SrTiO3，K均值聚类高达K=7；（b）每个聚类中的平均代表图像；（c）每个K值绘制的K均值最小化函数［45］

Fig.8 （a） K-means clustering up to K = 7 for SrTiO3 on TbScO3；（b） mean representative images in each cluster；（c） K-means minimization function plotted for each value of K［45］

图9 LAO的NMF等级为4。（a）~（d）四个簇的相应系数图；（e）~（h）四个簇的相应基础图［47］

Fig.9 NMF with rank 4 for LAO. （a）~（d） corresponding coefficient plots for the four clusters；（e）~（h） corresponding basis plots for the four clusters［47］

图10 PCA结果。（a）RHEED视频的6个PC。PC1显示石墨烯的衍射信号，PC2包含石墨烯和ReSe 2层两者的信号，PC3-6仅示出了ReSe2层的2D生长的信号；（b）相应的得分图；（c）原始RHEED图像强度；（d）~（e）修改后的RHEED视频的强度图。蓝色和橙色线分别表示ReSe2薄膜的（0，0）和（2，0）衍射条纹（如插图所示）［50］

Fig.10 PCA results. （a） Six PCs of the RHEED video for the 3UC-thick-ReSe2 thin film， PC1 shows the diffraction signal of graphene， PC2 contains the signals of both the graphene and -ReSe2 layers， PC3-6 show the signal of only the 2D growth of ReSe2 layer；（b） corresponding score plots；（c） original RHEED video；（d）~（e） modified RHEED video. Blue and orange lines denote the （0，0） and （2，0） diffraction streaks of the ReSe2 thin film （shown in the inset）， respectively［50］

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