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Tunneling Through Finite Quantum Dot Superlattices

  • Research Article - Computer Engineering and Computer Science
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Abstract

From first principles, we arrive at a generalized Tsu–Esaki formula for current per unit-cell in the case of one-dimensional, time-independent, open-system charge-transport along the growth direction of stacked layers of self-assembled quantum dots with perfect, transverse Bravais-lattice layout. We rigorously derive, using symmetry considerations, great simplifications to the final formula and identify significant computational benefits that would make modeling and simulation for such a complex problem not only feasible but also efficient. We allow an arbitrary sequence of quantum dot layers with or without intervening spacer and wetting layers. While the symmetry does suggest that final expressions for transmission coefficients should have simple form, the split, open boundary conditions as well as lack of longitudinal symmetry cast doubt on this. Employing a multiple sequential scattering view of processes within the heterostructure layers and using a limiting argument, we prove that the device behaves as a diffraction grating which distributes incident-carrier wavefunction-phases into specific patterns of reflected and transmitted phases which forms the basis for our conclusions.

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Authors and Affiliations

  1. Intel Corp, Santa Clara, CA, USA

    M. Rajagopalan

  2. Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA

    P. Mazumder

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  1. M. Rajagopalan
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  2. P. Mazumder
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Correspondence to P. Mazumder.

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Rajagopalan, M., Mazumder, P. Tunneling Through Finite Quantum Dot Superlattices. Arab J Sci Eng 39, 1863–1879 (2014). https://doi.org/10.1007/s13369-013-0806-8

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  • DOI: https://doi.org/10.1007/s13369-013-0806-8

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