Bruce Whitefield

Wafer sampling by regression for systematic wafer variation detection

In-line measurements are used to monitor semiconductor manufacturing processes for excessive variation using statistical process control (SPC) chart techniques. Systematic spatial wafer variation often occurs in a recognizable pattern across the wafer that is characteristic of a particular manufacturing step. Visualization tools are used to associate these patterns with specific manufacturing steps preceding the measurement. Acquiring the measurements is an expensive and slow process. The number of sites measured on a wafer must be minimized while still providing sufficient data to monitor the process. We address two key challenges to effective wafer-level monitoring. The first challenge is to select a small sample of inspection sites that maximize detection sensitivity to the patterns of interest, while minimizing the confounding effects of other types of wafer variation. The second challenge is to develop a detection algorithm that maximizes sensitivity to the patterns of interest without exceeding a user-specified false positive rate. We propose new sampling and detection methods. Both methods are based on a linear regression model with distinct and orthogonal components. The model is flexible enough to include many types of systematic spatial variation across the wafer. Because the components are orthogonal, the degree of each type of variation can be estimated and detected independently with very few samples. A formal hypothesis test can then be used to determine whether specific patterns are present. This approach enables one to determine the sensitivity of a sample plan to patterns of interest and the minimum number of measurements necessary to adequately monitor the process.

Factors Affecting Thickness Variation of

Thin oxide films have been grown by wet oxidation on 200 mm silicon wafers at atmospheric pressure in three different furnaces. The effects of temperature tilt, purge flow rate to oxidation flow rate ratio, reactant mole fraction, and oxidation time on axial and radial thickness distributions have been studied. Two of the furnaces share a similar design while the third furnace has a different fluid flow configuration and torch design. The two similar furnaces show virtually identical axial profiles in average thickness after both the pre-oxidation steps and the combined oxidation-purge steps. Under conditions of a standardized run recipe, the wafer-averaged oxide thickness decreases monotonically by about 3 Å down the axis of the boat. Depletion of water due to oxide formation can account for only about 20% of this decrease in oxide growth. A reduction in the concentration of steam due to adsorption and condensation during the oxidation period, which is then reversed during the purge period, is proposed as a significant cause of those thinner oxide films. Thickness variations within single wafers are also significant, with thickness being highest at the side of a wafer corresponding to the furnace outlet and monotonically decreasing to the opposite side.

{\rm SiO}_{2}

We describe a new method of estimating the systematic spatial variation across wafers. Current methods for this task share some common deficiencies. For example, few of these techniques are able to decompose the systematic variation into components that can be assigned to different types of tools. Most of these methods are also sensitive to outliers and require that the outliers be manually removed before the model can be estimated. Almost none of the previous methods can account for high-frequency effects caused by reticle non-uniformity. Our method is based on a linear regression model with various components to account for the systematic variation that occurs in practice. Polynomial components model the smooth variation caused by tools that cannot process the wafer uniformly. Reticle components model the variation that occurs due to non-uniformities in the microlithography and etch tools. To generate distinct patterns, we apply QR orthogonalization to the systematic patterns prior to regression. To limit the effects of outliers, we employ robust regression. We demonstrate the performance of our technique with an example on data collected from production wafers.