The various devices (transistors, resistors, etc.) in an integrated semiconductor circuit have very highly coupled or correlated parametric inter-relationships. Adding to the complexity, are changes in the parametric values as the sizes and spacings between the devices change. This coupling is not in the form of interaction fields or forces but rather takes place through the correlation of parameters between different devices. These parametric correlations occur because of the processing of the semiconductor wafers through ...
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The various devices (transistors, resistors, etc.) in an integrated semiconductor circuit have very highly coupled or correlated parametric inter-relationships. Adding to the complexity, are changes in the parametric values as the sizes and spacings between the devices change. This coupling is not in the form of interaction fields or forces but rather takes place through the correlation of parameters between different devices. These parametric correlations occur because of the processing of the semiconductor wafers through its manufacturing stages. The devices on each wafer have many n-type or p-type doped semiconductor layers in common because of being processed at the same temperature, or in the same gaseous environments, or in the same implantation sessions. In addition, each doped layer has variations over its different regions. All this results in very complex parametric interrelationships between the various devices within the integrated circuit. In turn these have very influential effects on the variation of key circuit characteristics. In spite of the tremendous importance of knowing and predicting these relationships, accurate methods of predicting these complex relationships between devices have evaded the semiconductor industry. The current methods used, such as statistically independent Monte Carlo simulation and Corner Models, either severely underestimate or severely overestimate the variation of key integrated circuit characteristics of interest. Either way, the current methods are very inaccurate. In order to meet this challenge, the methods covered in this dissertation have been developed and applied to the case at hand. They are based on applications of probability, statistics, stochastic, and random field theory, and various computer algorithms. Many of the concepts developed here can be applied to other complex correlated systems not necessarily involving semiconductors.
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