A multi-scale random-walk thermal-analysis methodology for complex IC-interconnect systems

We have developed and demonstrated a 3D multi-scale thermal-analysis methodology for multiple and stacked-chip configurations. This approach employs a global-local problem-domain discretization in conjunction with the floating RW (random walk) method. Emphasis has been placed on capturing complex thermal effects due to interconnect layers. We have analyzed a hypothetical stacked-chip geometry derived from a Stanford interconnect test chip. 2D gdsII layout data was automatically processed and converted into a 3D problem domain. On a 400 MHz Apple PowerBook G3^TM, execution time was about three minutes per temperature data point. Temperature at each evaluated point was computed with 1000 RWs, yielding a 1-σ statistical error of about 5%. Based on heuristic formulas that we have deduced, a local window of ±20 μm relative to the RW start point achieved a reasonable global-local discretization error