PARAMETRIC MODELING OF PHOTOELECTRON EFFECTS IN X-RAY-LITHOGRAPHY

In the energy range of interest for x-ray lithography, absorption of x rays by atoms results in the emission of photoelectrons and Auger secondaries, as well as the generation of a shower of low-energy electrons. The development of accurate models for the image formation in x-ray lithography requires that this mechanism be included. The electronic processes produce a redistribution of the x-ray energy over a finite volume. The interaction of the electrons with the medium is complex, and can be treated in the framework of a response theory (dielectric function). A simplified model can be obtained by separating elastic and inelastic interactions. The elastic interactions are treated with atomic Mott cross sections, and the inelastic interactions by a continuous slowing down approximation based on the dielectric response function. The model accounts for all the physical interactions of interest, and includes tabulated values for epsilon from published data. These models were incorporated in a Monte Carlo simulation code and have successfully benchmarked it with published results of Murata et al. [Optik 84, 163 (1990)]. The low efficiency of the Monte Carlo method motivates the need to parameterize the energy redistribution results from the simulation. This parameterization was performed, for a given material, in two steps: First, as a function of the photoelectron initial kinetic energy and then as a function of the photon energy. Parameterization as a function of the photoelectron initial kinetic energy is interpreted as a response of the medium to a particular electron. The parameterization as a function of the photon energy is the weighted sum of individual electron responses, according to the electrons emitted. Both can be used as point-spread functions as appropriate.