Mueller matrix characterization using spectral reflectometry

The fast evolution of microelectronics fabrication technology demands a concurrent development in metrology capabilities. In recent years, Mueller Matrix (MM) scatterometry has been asserted as a useful tool in characterizing critical dimensions (CD) in periodical arrays of nanometer-size structures. Specifically, some symmetry properties of the measured structure can be readily extracted from the MM, allowing effective isolation of abnormal features. One example is measuring deviations of grating structures from perfect mirror symmetry, characteristic of faults in the fabrication process. The most general form of the Muller matrix requires 16 independent measurements, and requires spectral ellipsometry. However, using some very general assumptions on the reflection properties of the measured sample, one can reduce this number considerably. Such realistic assumptions are time independence of the reflection properties, and homogeneity of the sample (i.e., constant reflectivity throughout the measurement spot), as is the common case in optical CD metrology targets. We show that under these assumptions the Mueller matrix can be completely measured using spectral reflectometry. The goal of characterizing asymmetry is then further analyzed, and a new approach for such measurement, based on spectral reflectometry, is presented. Specifically, using spectral differences metrology (SDM), this approach is shown to provide a simpler means to measure the same asymmetry-dependent quantity as targeted today using MM metrology, but requires only two distinct measurements leading to improved throughput.