Electron Wave Filters from Inverse Scattering Theory
Abstract
Semiconductor heterostructures with prescribed energy dependence of the transmittance can be designed by combining: a) Pad\'e approximant reconstruction of the S-matrix; b) inverse scattering theory for Schro\"dinger'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 AlcGa1-cAs filter with the high energy peak more than twice narrower than the other.
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