Diffraction of ballistic electrons by semiconductor gratings: Rigorous analysis, approximate analyses, and device design

A rigorous coupled-wave analysis is developed to model ballistic electron diffraction by semiconductor gratings with periodic effective mass and for potential energy variations. This analysis includes expressions for diffracted angles, evanescent and propagating orders, the Bragg condition, and diffraction efficiencies. Two approximate diffraction regimes, Bragg and Raman-Nath, are defined in which the rigorous coupled-wave equations (RCWEs) can be solved analytically, and the approximations required, the approximate solutions, and the restrictions placed on the grating parameters for each regime are given. It is shown that both the Bragg regime and the Raman-Nath regime are achievable with physically fabricated semiconductor grating structures. In addition, it is shown that both narrow and broad angular and energy selectivities can be achieved through control of the effective thickness of the grating. These results are used in the design of a two-dimensional electron gas (2-DEG) switch and a 2-DEG broadcast device