Semiconductor manufacturing is an intricate process involving thousands of process steps. The manufacturing data generated from this industry poses a unique data science challenge because of its volume and complexity. A major portion of this data comprises of images encompassing high-resolution scans of silicon wafers to microscopic circuitry images. Traditionally, machine learning approaches in semiconductor manufacturing have predominantly been supervised. However, this method entails a significant drawback, requiring users to possess complete labels for data and continually update them—an impractical task due to the sheer volume and complexity of the data. This paper introduces Deep Topological Data Analysis (DTDA) and Self-Supervised Learning (SSL) as an alternative paradigm, focusing on combining unsupervised and self-supervised approaches. The combined approach offers a distinct advantage by automatically extracting patterns from the data and highlighting crucial anomalies for users. DTDA extracts and analyzes the shape-based, topological features of data, which is particularly useful in identifying patterns and anomalies in complex images. SSL, on the other hand, leverages vast amounts of unlabeled data through algorithms that learn to understand and represent data without explicit external supervision. Implementing these methods in semiconductor manufacturing can lead to significant advancements by automatically classifying and analyzing the images for rapidly identifying defects, predicting failures, and optimizing manufacturing processes. We demonstrate the effectiveness of our approach through unsupervised image segmentation applied to two prominent public wafer map datasets in semiconductor manufacturing: MixedWM38 and WM811K. These datasets present distinct challenges owing to the substantial volume and diverse range of defects they contain. These datasets are thus frequently utilized by researchers and data scientists for validating approaches that can automatically conduct defect detection and classification.