A Graph-Based Model of Micro-Transfer Printing for Cost-Optimized Heterogeneous 2.5D Systems

Micro-transfer printing (μTP) is a promising assembly technology that enables heterogeneous integration of dies originating from different wafers. It combines the advantages of pick-and-place in terms of flexibility with the advantages of wafer-level processing in terms of high throughput. μTP applies an elastomer stamp to transfer multiple dies from source to target wafers in parallel. Increasing the stamp size allows for the transfer of more dies at once and reciprocally shortens the manufacturing time, enabling extensive cost reductions. On the other hand, larger stamps result in a lower wafer utilization, thereby causing increases in costs. Finding the cost-optimal stamp layout is one of the key tasks when designing heterogeneous systems for μTP. There is no trivial solution to calculate the wafer utilization needed to evaluate the quality of a stamp layout. Based on a graph problem known as maximum independent set, we propose a model to determine the wafer utilization subject to the stamp and wafer layout. We demonstrate the application of our model within an economic cost function to optimize a μTP design with regard to manufacturing costs.