Ulrich Kaempf

Statistical Significance Of Defect density Estimates

The yield of functional circuits or specially designed test structures is commonly used by process engineers to estimate the types and densities of defects that occur during the fabrication of integrated circuits. Systematic defects and defects that can be spatially correlated occur mainly during the development phase of a new process, and often show discernable and repeatable patterns when their electrical pass/fail data is displayed in the form of wafer maps. These patterns can be identified visually, and the correct conclusion can be drawn with a reasonable confidence. In contrast, defects that dominate a mature and well controlled process are mostly random and uncorrelated in nature, resulting in wafer maps that show failed circuits in a uniform random distribution across the wafer. Due to the randomness of such a yield distribution, the estimate of defect density can only be made within certain confidence limits. It is essential for the process and yield improvement engineer to understand these limits to properly estimate the defect density as obtained from yield information. It is equally important for the designer of test structures to understand the statistical relationship between yield and defect density in order to optimize the layout of the structure.

The Wheatstone bridge as an alignment test structure

A new test structure for the electrical measurement of level-to-level registration is introduced. This structure, based on the Wheatstone bridge measurement principle, offers improved accuracy over the conventional U-shaped test structure. With the described Wheatstone bridge method, the registration error (misalignment) is directly proportional to a single voltage. In contrast, the misalignment of the U-shaped structure is calculated from the difference of two voltages, an operation that can result in poor precision. The paper describes a two-by-twelve contact pad module, which includes two Wheatstone bridge structures to measure the misalignment in the X- and Y-directions, two calibration structures to determine the zero- and full-scale accuracy, and a Van der Pauw structure to measure the sheet resistance of the conducting material as required for the alignment measurement. The mathematical expressions are derived, and actual test results are discussed.