Coherence and imaging properties of non-ideal patterned multilayer structures

Abstract

Several topics concerning the imaging properties of patterned multilayer mask structures are addressed. Using the split-step beam propagation method in conjunction with linear systems theory, the reflected electric field from a patterned multilayer structure is calculated. This calculation accounts for the finite thickness of the pattern structure and the angular dependence of the multilayer reflector. A coherence mapping relationship is developed for a patterned multilayer structure placed in the object plane of an optical system. It is shown that both the spatial period of the pattern structure as well as the angular dependence of the multilayer reflector determines when a simulation must include angular dependence in the coherence mapping. If the illumination system is non-telecentric, a spatially dependent variation of the image irradiance occurs over the field of view of the optical system. A source with a finite spectral bandwidth causes a substantial irradiance decrease in the final image, due to the spectral dependence of the multilayer structure. In an effort to analyze the effects of roughness in short-wavelength imaging systems, the theory of speckle in partially coherent imaging systems is expanded to include the effects of a pattern structure, as well as imaging system aberrations. Including a pattern structure causes the partially developed speckle to manifest itself as a line edge roughness (LER) in images printed in a binary photoresist. It is shown that the LER can increase as the system becomes more incoherent. It is also shown that defocus causes LER produced in the image plane to dramatically increase. An iterative algorithm is developed to calculate the reflected electric field from a rough multilayer structure, which uses no first-order phase approximation and includes the effects of diffraction within the structure. The iterative algorithm is used with the coherence theory developed in this dissertation to analyze the imaging properties of a patterned multilayer structure. Including the effects of the multilayer structure and the thick pattern in the simulation results in an increase in LER, a slight shift in the ideal focus position and an asymmetry in LER for off-axis illumination.