Localized electronic states induced by the presence of two defective resonators in electronic comb-like waveguides structure

Abstract

Abstract In this paper, we use the transfer matrix method to determine the band structure and electrical transmission rate of a one-dimensional electronic comb-like waveguide system. This structure is made up of the periodicity of finite GaAs quantum wire (QWR) (segment) grafted in its extremity by a vertical Ga <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi/> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>−</mml:mo> <mml:mi>x</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> Al x As QWR (resonator). In this perfect structure, we replace the resonator situated in the middle of the periodic structure by a composed resonator made of vertical superposition of two resonators of different Al concentrations ( x 01 and x 02 ). These defective resonators induce electronic localized states, inside the electronic band gaps of the perfect structure, with higher energy values depending on the geometrical (lengths) and the physical ( x 01 , x 02 ) parameters of the defective resonators. When the length d 02 of the upper resonator composed of Al concentration <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>x</mml:mi> <mml:mrow> <mml:mn>02</mml:mn> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0.3</mml:mn> </mml:mrow> </mml:math> increases, these localized electronic states move to lower energies; conversely, when the concentration x 02 increases, they move to higher energies. We also show that there is an important effect of changing the localized states of two resonators connected in cascade with different concentrations. Our results may be relevant to the design of electronic guidance, filtering, and detection systems.