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 ppmlevel 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. Index Terms-Bayes, burn-in, Clopper-Pearson, countermeasure, decision theory, early life failure probability, generalized binomial distribution. ACRONYMS AND ABBREVIATIONS BI burn-in CL confidence level CP Clopper-Pearson CM(s) countermeasure(s) Manuscript
In semiconductor manufacturing, it is a key to ensure reliability of the produced devices. The population's reliability level is demonstrated by means of a burn‐in study (that is investigating a large number of devices under real‐life stress conditions for product relevant fails). Burn‐in settings are based on the lifetime distribution of early fails. Typically, it is modelled as a Weibull distribution Wb(a,b) with scale parameter a > 0 and shape parameter b ∈ (0,1) motivated by a decreasing failure rate within the devices' early life. Depending on the applied burn‐in scheme, the Weibull parameters have to be estimated from time‐to‐failure and discrete failure count data, respectively. In this paper, we present advanced Bayesian estimation models for the Weibull distribution handling both data situations. First, a simplified conjugate approach using gamma‐histogram‐beta priors is presented. Further, according to the paper's main focus, an extended Bayesian concept for assessing Weibull early life failure distributions is highlighted. It is characterized by a Dirichlet prior distribution applied to the lifetime function of early fails. The proposed model simplifies the incorporation of engineering prior knowledge. Moreover, it can be extended to both discrete failure and time‐to‐failure burn‐in data. The joint posterior distribution, Bayesian estimators and compounded and joint credible regions are derived by means of Monte Carlo simulation. The principle of Bayesian learning allows to update the Weibull early life failure distribution whenever new failure data become available. Therefore, burn‐in settings can dynamically be adapted improving the efficiency of burn‐in. Copyright © 2014 John Wiley & Sons, Ltd.
Design and production of semiconductor devices for the automotive industry are characterized by high reliability requirements, such that the proper functioning of these devices is ensured over the whole specified lifetime. Therefore, manufacturers let their products undergo extensive testing procedures that simulate the tough requirements their products have to withstand. Such tests typically are highly accelerated, to test the behavior of the products over the whole lifetime. In case of drift of electrical parameters, manufacturers then need to find appropriate tolerance limits for their final electrical product tests, such that the proper functioning of their devices over the whole specified lifetime is ensured. In this study, we present a statistical model for the determination of tolerance limits that minimize yield loss. The model considers longitudinal measurements of continuous features, based on censored data from stress tests. The tolerance limits are derived from multivariate distributions where the dependence structure is described by different copulas. Based on extensive numerical testing, we are able to provide insights into the properties of our model for different drift behaviors of the devices.
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