Formulation and heuristic algorithms for multi-chip module substrate testing

Multi-chip module (MCM) substrates are designed for packing two or more semiconductor chips. On these substrates, there are open faults in the wiring, which are electrical disconnections. We must therefore test the substrates to detect open faults, and it is essential to establish an efficient method of testing them. One type of test method uses two probes. Two probes, each touching one edge (end) of an inter-chip wiring, are used to check for the presence of faults. Testing is complete when we have confirmed that no faults exist on the MCM substrate. The objective is to minimize the time to complete testing, that is, our aim is to design efficient routes for the two probes. In this paper, we propose a novel approach of formulating the routing problem as a shortest path problem with covering constraints (SPCC) and we also propose three algorithms for the SPCC. In computational experiments, we show that our formulation and algorithms outperform the existing method.

Graphical abstractFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights► We propose a novel approach to MCM substrate testing. ► We formulate MCM substrate testing as a shortest path problem with covering constraints. ► We propose three heuristic algorithms for MCM substrate testing. ► Experiments show that our formulation and algorithms outperform the existing methods.