Ronald L. Allen

Spectral ellipsometry on patterned wafers

Ellipsometry has seen only limited application to the post-deposition pattern etch process despite the fact that physical parameters such as groove width, depth and pitch are as critical to product performance as the more basic thin film parameters traditionally analyzed using ellipsometry. This paper presents initial theoretical results pertaining to modeling the reflectance from a 1D etched pattern on a semiconductor substrate. To analyze the samples effects upon the incident beam polarization, we formulate the zeroth-order reflection coefficients for the orthogonal p and s polarization states and construct models of ellipsometric parameters (Psi and Delta) for a rectangular-groove surface pattern, emphasizing the effect of groove geometry upon these quantities.

TimeScale Signal Transforms

This chapter develops both continuous and discrete scale-based transforms. The topics include the continuous wavelet transform; further development of the idea of frames, covered earlier; the concept of multiresolution analysis; orthogonal wavelets; discrete wavelet transforms; and, finally, the construction of multiresolution analyses and orthogonal wavelets. Wavelet decomposition furnishes an alternative approach for describing signal structure.

FrequencyDomain Signal Analysis

Frequency-domain signal analysis covers a wide variety of techniques involving the Fourier transformation of the signal. The signals frequency domain representation is then manipulated, decomposed, segmented, classified, and interpreted. One central idea is that of a filter: a linear, translation-invariant system that allows one band of frequencies to appear in the output and suppresses the others. Where signal elements of interest occupy a restricted spectrum, filters invariably enter into the early processing of candidate signals. In other ways - often purely theoretical - frequency-domain analysis is important. For example, in this chapter we substantiate the methods of matched filtering and scale-space decomposition, and the Fourier transform plays a crucial role.