## 1 Introduction
Self-supervised learning is a type of machine learning where a model learns to represent data in a way that is useful for downstream tasks without requiring direct supervision or labeled data [18]. Instead, the model is trained on an auxiliary task designed to capture meaningful patterns in the data. This approach is advantageous when labeled data are scarce or expensive, as it allows the model to learn from large amounts of  
Figure 1: Relationship between wafer, die, and chip. Figure 2: Examples of several WBMs with specific defect patterns. unlabeled data. Based on the pretext task for visual features in images, self-supervised learning approaches can be classified into three categories: generation-based [19; 20; 21; 22; 23], context-based [24; 25; 26; 27; 28; 29], and contrastive-based [30; 31; 32; 33; 34; 35; 36]. In WBM yield, [PERSON] and [PERSON] [2] proposed a self-supervised learning-based framework that uses unlabeled data to learn rich visual representations beforehand to realize a data-efficient WBM GFA classification. [PERSON] and [PERSON] [37] proposed a dynamic WBM clustering method using pseudo-labels. [PERSON] [38] proposed an end-to-end wafer defect classifier that unites the few-shot learning and self-supervised learning algorithms in the training period, which opens up a new line. The existing research on WBM self-supervised learning effectively leverages unlabeled data and enhances classification performance. However, it still requires a substantial amount of labeled data for fine-tuning. Improving the feature representation ability of the model is the critical way to reduce the demand for labeled data. A more effective self-supervised learning method is needed to utilize the information in unlabeled data fully, enhance the model's feature representation ability, and improve its classification performance with limited labeled data. To this end, this study introduced momentum contrastive learning [32] for self-supervised pretraining on unlabeled WBMs. Contrastive learning is a branch of self-supervised learning that learns representations by maximizing the agreement between different views of the same data point and has been shown to achieve state-of-the-art performance in many computer vision tasks, especially in low-data regimes. Momentum contrastive learning is a variant of contrastive learning in which a momentum encoder is introduced to improve the quality of learned representations. The momentum encoder is updated using an exponential moving average of the parameters from the primary encoder, which encourages the momentum encoder to capture the global structure of the data while the primary encoder focuses on capturing local features. By leveraging the momentum encoder, momentum contrastive learning performs better than standard contrastive learning in various computer vision tasks. After momentum contrastive learning, we proposed a low-data fine-tuning method for WBM defect classification. Thanks to [PERSON] [38], we reference it to use a prototypical few-shot learning approach. Moreover, different to [38], the prototypical network is only performed in the fine-tuning period in the proposed framework. By comparing with other existing methods, the proposed method outperforms the comparative methods regarding classification performance with real-world WBM data. The results indicate that introducing momentum contrastive learning improves the performance of supervised learning and makes it possible to achieve classification with only a small amount of labeled data. The contributions of the article are as follows:  
1. Momentum contrastive learning is introduced for the unlabeled WBMs pretraining, enhancing the feature representation ability and improving WBM defect classification accuracy. 2. We propose a two-step method where the prototype network is fine-tuned after contrastive learning pretraining, improving low-data fine-tuning performance. 3.