Statistical multilot characterization of spatial thickness variations in LPCVD oxide nitride polysilicon and thermal oxide films

摘要

This paper describes a method for the statistical characterization and modeling of spatial variations of thin film thickness across a wafer lot over multiple furnace runs. The method uses experimental thickness data to construct a simplified Karhunen-Loeve model that captures both deterministic and random nonuniformity variations. The model uses simple quadratic interpolation functions and a reduced number of random variables and permits calculations of distribution functions over different lot populations (wafer, die, point, etc.) The main advantage of this model is the retention of spatial correlations that are essential for the accurate prediction of parametric yield. The characterization method was applied to several thin films using a data set of 35,000 thickness measurements of LPCVD oxide, nitride, and polycrystalline silicon as well as thermal oxide. Run-to-run distributions for the random variables were estimated using three-year (1995 - 1997) historical rate data logged at the UM Solid State Electronics Laboratory. Comparisons are presented depicting probability density functions extracted from the model and a Monte Carlo based estimator are in good agreement.