Abstract
For the first time to our knowledge, the Kane’s (k, p)-theory describing the electron mass renormalization in bulk semiconductors, is modified for thin (a few nanometers thick) quantum wires. It is shown that the longitudinal electron effective mass increases with quantum numbers of transverse motion. This leads to unique features of the electron spectrum in the wire under two conditions: (i) the band structure of a wire material is covariant, which makes impossible hole localization and (ii) the wire radius should be small enough. As a result, dispersion curves of electrons localized on wires intersect, and the associated energy subbands cross. Therefore, a longitudinal electric pulse easily creates population inversion. This can be a theoretical basis for the new principle of operation of quantum amplifiers and generators.
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Notes
Here we do not consider the effects of the “intrinsic anisotropy” of the effective mass, associated with the difference between principal values of effective mass tensors in bulk semiconductors. It is clear that this will only amplify awkwardness and mask the essence of the phenomenon under study.
It can be slightly corrected by the Coulomb interaction of localized electrons, since holes cannot be localized at the wire; therefore, the excess negative charge of the wire is not compensated. For the system of quantum dots, this leads to the constraint on the probability of populating vacant levels [9].
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Funding
This work was supported by the Russian Foundation for Basic Research, project no. 20-07-00983A and the Ministry of Higher Education and Science of the Russian Federation, project no. FSFS-2020-0025.
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Translated by A. Kazantsev
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Mandel’, A.M., Oshurko, V.B., Pershin, S.M. et al. EFFECT OF SIZE QUANTIZATION SUBBAND CROSSING IN THIN QUANTUM WIRES. Bull. Lebedev Phys. Inst. 47, 296–299 (2020). https://doi.org/10.3103/S1068335620100073
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DOI: https://doi.org/10.3103/S1068335620100073