Amy Grigg and Dr. Steve Turley, Physics and Astronomy
This paper examines a method that takes oxidation gradients into consideration when determining optical constants from reflectance and transmission measurements. The oxidation gradients were measured by two techniques using x-ray photoelectron spectroscopy: sputtering, where data are taken at various depths in the sample after removing the surface by sputtering; and variable angle scans, where depth information is obtained by placing the detector at several angles. X-ray photoelectron spectroscopy sputtering was found to give better results for our purposes. This method resulted in very good fits of theoretical data. For more details, see the author’s honors thesis.
Because of the high absorption of materials in the EUV, reflection and transmission data must be obtained in vacuum with extremely thin samples. Oxidation is often negligible in the visual spectrum due to the transparency of most oxides and the relatively thin layer of oxide. In the EUV, however, oxidation has a significant effect on the optical constants of samples, as oxides are typically opaque in the EUV and can make up a large fraction of the sample composition. The interface between the oxide and the sample itself is particularly important in modeling the sample to determine optical constants.
The reflectivity of the sample differs greatly between an abrupt interface and one that varies smoothly. The oxidation gradient of the material must be well determined experimentally in order to accurately determine the optical constants of the materials under study.
In this study, I used X-ray Photoelectron Spectroscopy (XPS) to determine the uniformity of thin-film samples and to obtain models of oxidation as a function of depth. There are two methods of accomplishing this with XPS: sputtering, where data are taken at various depths in the sample after removing the surface by sputtering; and variable angle scans, where depth information is obtained by placing the detector at several angles. For our samples, I found sputtering to be the best method for determining oxidation gradients. I also wrote a data-fitting program that takes into account the measured oxidation gradient in determining optical constants based on reflectance/transmission data.
X-ray photoelectron sputtering is shown to be the best method for determining molecular composition gradients or the uniformity of a sample with depth. Angle resolved x-ray photoelectron spectroscopy is a useful method for determining the extent of surface contamination. Both methods require deconvolution to obtain the real surface from the measured surface. The deconvolution of a sputtered depth profile is much simpler to perform, whereas obtaining the real surface of a variable angle profile requires fitting many variables at once. The sputtering method yields information about the entire sample, regardless of thickness, whereas the variable angle profile yields composition to a depth of about 80 angstroms. If both methods are used together, however, information about the shape of the real interface from sputtering may be used to better determine the depth of the variable angle scan, and a more complete picture may be obtained. This option requires further study. Further study is also required to determine the shape and roughness of the sputtered area and how this affects the depth profile.
The matlab program determines the optical constants of a stack based on measured reflectance or transmission. The fits are very good for theoretical reactance and transmission data with different amounts of random noise added. The method of approximating oxidation gradients by varying n from one layer to the next theoretically yields better fits than when the layers are approximated based on an ideal interface. Because of experimental setbacks, the program was unable to be tested with real reflectance and transmission data. Future research will include testing the program with real reflectance and transmission data, and creating a user interface for the program to make it accessible to others. The program can then be used to determine optical constants of materials, taking into account oxidation gradients of the material. The program can conceivably take into account roughness as well, by approximating the surface roughness with a multilayer varying from the n of air to the n of the material.
Thorium has high reflectance in the extreme ultraviolet, but, without a protective layer, may not be as useful for technological purposes. The oxidation of thorium is rapid and difficult to control when exposed to air. Reactively sputtered thorium dioxide, however, is a more stable, controllable, uniform material that may be more useful for technological applications.