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Large language models (LLMs) with Transformer architectures have become phenomenal in natural language processing, multimodal generative artificial intelligence, and agent-oriented artificial intelligence. The self-attention module is the most dominating sub-structure inside Transformer-based LLMs. Computation using general-purpose graphics processing units (GPUs) inflicts reckless demand for I/O bandwidth for transferring intermediate calculation results between memories and processing units. To tackle this challenge, this work develops a fully customized vanilla self-attention accelerator, AttentionLego, as the basic building block for constructing spatially expandable LLM processors. AttentionLego provides basic implementation with fully-customized digital logic incorporating Processing-In-Memory (PIM) technology. It is based on PIM-based matrix-vector multiplication and look-up table-based Softmax design. The open-source code is available online: https://bonany.cc/attentionleg., Comment: for associated source codes, see https://bonany.cc/attentionleg