Methods and systems for accurate measurement of deep structures having distorted geometry

Methods and systems for estimating values of geometric parameters characterizing in-plane, distorted shapes of high aspect ratio semiconductor structures based on x-ray scatterometry measurements are presented herein. A parameterized geometric model captures the scattering signature of in-plane, non-elliptical distortions in hole shape. By increasing the number of independent parameters employed to describe the in-plane shape of hole structures the model fit to the actual shape of high aspect ratio structures is improved. In one aspect, a geometrically parameterized measurement model includes more than two degrees of freedom to characterize the in-plane shape of a measured structure. In some embodiments, the geometric model includes a closed curve having three degrees of freedom or more. In some embodiments, the geometric model includes a piecewise assembly of two or more conic sections. Independent geometric model parameters are expressed as functions of depth to capture shape variation through the structure