Electron wave filters from inverse scattering theory

¹ Service de Physique Théorique, C.E. Saclay - 91191 Gif-sur-Yvette Cedex, France
² Center for Theoretical Study of Physical Systems, Clark, Atlanta University, Atlanta, GA 30314, USA
³ Istituto di Scienze Matematiche e Fisiche, Università di Milano sede di Como, Via Lucini 3, 22100 Como, Italy
⁴ Institutul de Fizica şi Tehnologia Materialelor, C.P. MG-7, Bucureşti - Măgurele, Romania
⁵ Facultatea de Fizică, Universitatea Bucureşti, C.P. MG-11, Bucureşti - Măgurele, Romania

Received: 12 August 1996
Accepted: 26 November 1996

Abstract

Semiconductor heterostructures with prescribed energy dependence of the transmittance can be designed by combining: a) Padé approximant reconstruction of the S-matrix; b) inverse scattering theory for Schrödinger's equation; c) a unitary transformation which takes into account the variable mass effects. The resultant continuous concentration profile can be digitized into an easily realizable rectangular-wells structure. For illustration, we give the specifications of a 2 narrow band-pass 12-layer filter with the high-energy peak more than twice narrower than the low-energy one.