To overcome the memory and power wall problems on a high performance microprocessor for supercomputer systems, the reduction in memory access latencies and its power consumptions is urgently required. Recently, a 2.5D integration technology, which can integrate multiple chips on a silicon die by using vertical interconnects, are expected as key technologies to overcome these problems. Under this situation, this paper explores the design space of a processor and memory module for vector supercomputers using a vertical integration technology. In this study, both a processor and a memory of vector supercomputers are integrated in one silicon die as a single module, and its performance and power are evaluated by leading scientific applications. The evaluation results demonstrated that the 2.5D integration reduces the energy consumption by 83% compared to the conventional PCB implementation.