- 99-127 Daniel Bessis, G. Andrei Mezincescu
- Design of semiconductor heterostructures with preset electron reflectance
by inverse scattering techniques
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Apr 23, 99
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Abstract. We present the application of the inverse scattering method to the design
of semiconductor heterostructures having a preset dependence of the
(conduction) electrons' reflectance on the energy. The electron dynamics
are described by either the effective mass Schroedinger, or by the
(variable mass) BenDaniel and Duke equations. The problem of phase
(re)construction for the complex transmission and reflection coefficients
is solved by a combination of Pade approximant techniques, obtaining
reference solutions with simple analytic properties.
Reflectance-preserving transformations allow bound state and reflection
resonance management. The inverse scattering problem for the Schroedinger
equation is solved using an algebraic approach due to Sabatier.
This solution can be mapped unitarily onto a family of BenDaniel and
Duke type equations. The boundary value problem for the nonlinear
equation which determines the mapping is discussed in some detail.
The chemical concentration profile of heterostructures whose self consistent
potential yields the desired reflectance is solved completely in the
case of Schroedinger dynamics and approximately for Ben-Daniel and Duke
dynamics. The Appendix contains a brief digest of results from
scattering and inverse scattering theory for the one-dimensional
Schr\"odinger equation which are used in the paper.