Robust Optimization of Test-Access Architectures Under Realistic Scenarios

3-D integration using through-silicon vias offers many benefits, such as high bandwidth, low power, and small footprint. However, test complexity and test cost are major concerns for 3-D ICs. Recent work on the optimization of 3-D test architectures to reduce test cost suffer from the drawback that they ignore potential uncertainties in input parameters; they consider only a single point in the input-parameter space. In realistic scenarios, the assumed values for parameters such as test power and pattern count of logic cores, which are used for optimizing the test architecture for a die, may differ from the actual values that are known only after the design stage. In a 3-D setting, a die can be used in multiple stacks with different properties. As a result, the originally designed test architecture is no longer optimal, which leads to an undesirable increase in the test cost. We propose an optimization approach that takes uncertainties in input parameters into account and provides a solution that is efficient in the presence of input-parameter variations. We formulate a mathematical model for the robust test-architecture optimization problem, and propose an efficient heuristic to solve the problem even for large designs in reasonable time. The proposed optimization framework is evaluated using the ITC'02 SoC benchmarks and we show that robust solutions are superior to single-point solutions in terms of average test time when there are uncertainties in the values of input parameters.