Decision-Theoretical Model for Failures Which are Tackled by Countermeasures

Abstract

In semiconductor manufacturing, it is necessary to guarantee the reliability of the produced devices. Latent defects have to be screened out by means of burn-in (that is, stressing the devices under accelerated life conditions) before the items are delivered to the customers. In a burn-in study, a sample of the stressed devices is investigated on burn-in relevant failures with the aim of proving a target failure probability level. In general, zero failures are required; if burn-in related failures occur, countermeasures are implemented in the production process, and the burn-in study actually has to be restarted. Countermeasure effectiveness is assessed by experts. In this paper, we propose a statistical model for assessing the devices' failure probability level, taking account of the reduced risk of early failures after the implementation of the countermeasures. Based on that, the target ppm-level can be proven when extending the running burn-in study by a reduced number of additional inspections. Therefore, a restart of the burn-in study is no longer required. A Generalized Binomial model is applied to handle countermeasures with different amounts of effectiveness. The corresponding probabilities are efficiently computed, exploiting a sequential convolution algorithm, which also works for a larger number of possible failures. Furthermore, we discuss the modifications needed in case of uncertain effectiveness values, which are modeled by means of Beta expert distributions. For the more mathematically inclined reader, some details on the model's decision-theoretical background are provided. Finally, the proposed model is applied to reduce the burn-in time, and to plan the additional sample size needed to continue the burn-in studies also in the case of failure occurrences.