Metamaterial-Inspired Model for Electron Waves in Bulk Semiconductors

Based on an analogy with electromagnetic metamaterials, we develop an effective medium description for the propagation of electron matter waves in bulk semiconductors with a zinc-blende structure. It is formally demonstrated that even though departing from a different starting point, our theory gives results for the energy stationary states consistent with Bastard’s envelope-function approximation in the long-wavelength limit. Using the proposed approach, we discuss the time evolution of a wave packet in a bulk semiconductor with a zero-gap and linear energy–momentum dispersion. Disciplines Electrical and Computer Engineering Comments Silveirinha, M. & Engheta, N. (2012). Metamaterial-inspired model for electron waves in bulk semiconductors. Physical Review B, 86(24), 245302. doi: 10.1103/PhysRevB.86.245302 ©2012 American Physical Society This journal article is available at ScholarlyCommons: http://repository.upenn.edu/ese_papers/622 PHYSICAL REVIEW B 86, 245302 (2012) Metamaterial-inspired model for electron waves in bulk semiconductors Mário G. Silveirinha1,2,* and Nader Engheta1 1Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA 2Department of Electrical Engineering, Instituto de Telecomunicações, University of Coimbra, Coimbra 3030-290, Portugal (Received 15 May 2012; revised manuscript received 29 August 2012; published 5 December 2012) Based on an analogy with electromagnetic metamaterials, we develop an effective medium description for the propagation of electron matter waves in bulk semiconductors with a zinc-blende structure. It is formally demonstrated that even though departing from a different starting point, our theory gives results for the energy stationary states consistent with Bastard’s envelope-function approximation in the long-wavelength limit. Using the proposed approach, we discuss the time evolution of a wave packet in a bulk semiconductor with a zero-gap and linear energy–momentum dispersion. DOI: 10.1103/PhysRevB.86.245302 PACS number(s): 73.21.Cd, 42.70.Qs, 73.23.−b, 73.22.−f