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Semantic code search, which aims to retrieve code snippets relevant to a given natural language query, has attracted many research efforts with the purpose of accelerating software development. The huge amount of online publicly available code repositories has prompted the employment of deep learning techniques to build state-of-the-art code search models. Particularly, they leverage deep neural networks to embed codes and queries into a unified semantic vector space and then use the similarity between code's and query's vectors to approximate the semantic correlation between code and the query. However, most existing studies overlook the code's intrinsic structural logic, which indeed contains a wealth of semantic information, and fails to capture intrinsic features of codes. In this paper, we propose a new deep learning architecture, COSEA, which leverages convolutional neural networks with layer-wise attention to capture the valuable code's intrinsic structural logic. To further increase the learning efficiency of COSEA, we propose a variant of contrastive loss for training the code search model, where the ground-truth code should be distinguished from the most similar negative sample. We have implemented a prototype of COSEA. Extensive experiments over existing public datasets of Python and SQL have demonstrated that COSEA can achieve significant improvements over state-of-the-art methods on code search tasks.