|
Journal of Physical Studies 22(3), Article 3701 [8 pages] (2018)
DOI: https://doi.org/10.30970/jps.22.3701 ELECTRON SPECTRUM IN OPEN DOUBLE-BARRIER NANOSTRUCTURE WITH SMOOTH POSITION-DEPENDENT POTENTIAL AND EFFECTIVE MASSJu. O. Seti, M. V. Tkach
Fedkovych Chernivtsi National University, |
 |
Solutions of Schrödinger equation are obtained and the scattering $S$-matrix is analytically calculated using the model of smooth position-dependent electron effective mass and potential energy, which linearly depend on the coordinate in the near-interface regions between the wells and the barriers of the plane open symmetrical double-barrier resonant tunnelling nanostructure. The effect of the size of the near-interface region on the resonance energies and widths of sub-barrier electron quasi-stationary states are studied for the nanostructure with In$_{0.53}$Ga$_{0.47}$As wells and In$_{0.52}$Al$_{0.48}$As barriers. It is established that the increase in the size of the near-interface region leads to: i) a high-energy shift of resonance energies of all sub-barrier states, ii) a bigger or smaller resonance width of the ground state, depending on the potential well width, iii) an increase in the resonance width of all excited sub-barrier states. The results obtained for the spectral parameters in the model under study are analyzed against those of other simplified models: the step-like potential energy and either abrupt or smooth effective mass at nanostructure interfaces. It is shown that in the interval of physically correct sizes of the near-interface regions in the models of smooth position-dependent effective mass and potential energy, the magnitudes of resonance energies differ from those obtained in the other two simplified models by not more than at $3\%$ and the resonance widths -- by not more than at $18\%$, respectively.
PACS number(s): 72.10.-d, 73.21.-b, 03.65.Ca