An Instructional Two-Dimensional Diffraction Laboratory Using Patterns Created with Electron-Beam Lithography
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An Instructional Two-Dimensional Diffraction Laboratory Using Patterns Created with Electron-Beam Lithography Colin Inglefield, Royce Anthon1 Physics Department, Weber State University Ogden, UT 84408-2508, U.S.A. 1 Physics Department, University of Utah Salt Lake City, UT 84112-0830, U.S.A. ABSTRACT An instructional laboratory in two-dimensional diffraction is discussed. The experiment is appropriate for undergraduate students in materials science, solid-state physics (as was the case with our group), modern physics, or optics. The experiment is performed using visible light from a laser incident on a 2D lattice of gold dots deposited with electron beam lithography on a glass substrate. The pattern is microscopic with a lattice constant on the same order of magnitude as the wavelength of light used. Students observe the diffraction pattern, and then quantitatively determine the positions of maxima. These data are used by the students to reconstruct the (real space) microscopic lattice. The students can simulate the experiment with software that computes reciprocal lattice and diffraction patterns for an arbitrary 2D lattice. INTRODUCTION The elastic scattering of waves from periodic structures (crystalline solids, diffraction gratings, etc.) is a topic covered in several courses in the undergraduate curriculum in materials science or physics. Most of these students, at a minimum, get some laboratory experience with diffraction gratings, structures that are periodic in one dimension. The three dimensional case of particular importance is the scattering of X rays from a crystalline solid [1]. The most important two-dimensional example, from a research perspective, is likely the scattering of electrons from crystalline surfaces [2]. These topics, or at least X-ray diffraction from crystalline solids, are normally covered at some point in the lecture component of an undergraduate curriculum. However, an X-ray diffraction or an electron diffraction apparatus may be prohibitively expensive or complicated for use in a teaching laboratory. Several computer simulations are available to demonstrate the X-ray techniques used by crystallographers [3], but such simulations do not have the same value as a true laboratory experience. Also, the three-dimensional nature of any real solid complicates the analysis for undergraduate students significantly. Microwave diffraction demonstration/teaching equipment is available for demonstrating all of these phenomena on a centimeter scale but it is fairly expensive and has limited precision [4]. In this paper we present a tabletop experiment with a two-dimensional array with lattice constants on the same order (~1 µm) as the wavelength of visible light. The two dimensional array is more complex than the somewhat trivial case of the1D diffraction grating and will allow the students to work with the mathematical formalism used by x-ray crystallographers (Miller indices, etc.). At the same time the two-dimensional pattern avoids some of the potential complications of a 3D lattice. I
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