Optimal relaxation of I/O electrical requirements under packaging uncertainty by stochastic methods

Fast and accurate evaluation of system failure rate is performed using stochastic collocation methods. First, we demonstrate that variability in I/O performance, such as driven voltage and slew rate, will impact failure probability of the link. For instance, higher slew rates will lead to increased levels of crosstalk between signals. Crosstalk above a certain threshold can be an indicator of system failure. Then, we demonstrate that by defining an upper bound for failure probability, an optimally relaxed set of I/O performance metrics can be generated corresponding to a stochastic interconnect model. This can be achieved by minimizing a cost function formulated with some performance metric, if these metrics are random variables. Lastly, we demonstrate that, if more information about the packaging design becomes available, the randomness of the interconnect model can be reduced, leading to a more relaxed set of I/O performance metrics. The method proposed in [1] is then be used to verify that the packaging design will meet the tolerated failure probability.