Modelling of Electron States in Quantum -Wire Systems - Influence of Stochastic Effects on the Confining Potential

Authors: Mikhail Vladimirovich Deryabin, Morten Willatzen

Abstract:

In this work, we address theoretically the influence of red and white Gaussian noise for electronic energies and eigenstates of cylindrically shaped quantum dots. The stochastic effect can be imagined as resulting from crystal-growth statistical fluctuations in the quantum-dot material composition. In particular we obtain analytical expressions for the eigenvalue shifts and electronic envelope functions in the k . p formalism due to stochastic variations in the confining band-edge potential. It is shown that white noise in the band-edge potential leaves electronic properties almost unaffected while red noise may lead to changes in state energies and envelopefunction amplitudes of several percentages. In the latter case, the ensemble-averaged envelope function decays as a function of distance. It is also shown that, in a stochastic system, constant ensembleaveraged envelope functions are the only bounded solutions for the infinite quantum-wire problem and the energy spectrum is completely discrete. In other words, the infinite stochastic quantum wire behaves, ensemble-averaged, as an atom.

Keywords: cylindrical quantum dots, electronic eigen energies, red and white Gaussian noise, ensemble averaging effects.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1072998

References:

[1] T. Ando, A. Fowler, and F. Stern, Rev. Mod. Phys. 54, 437 (1992).
[2] V. Ya Prinz, D. Grutzmacher, A. Beyer, C. David, and B. Ketterer, Nanotechnology 12, S1 (2001).
[3] O.G. Schmidt and K. Eberl, Nature (London) 410, 168 (2001).
[4] S. Matsutani and H. Tsuru, J. Phys. Soc. Jpn. 60, 3640 (1991).
[5] S. Tanda, T. Tsuneta, Y. Okajima, K. Inagaki, K. Yamaya and N. Hatakenaka, Nature 417, 397 (2002).
[6] K. T. Shimizu,W. K. Woo, B. R. Fisher, H. J. Eisler, andM. G. Bawendi, Phys. Rev. Lett. 89, 117401 (2002).
[7] X. Duan, C. Niu, V. Sahi, J. Chen, J. W. Parce, S. Empedocles, and J. L. Goldman, Nature 425, 274 (2003).
[8] N. Van Kampen, "Stochastic processes in physics and chemistry," North Holland Personal Library (2001).
[9] F.J. Poulin and M. Scott, Nonl. Process. in Geophys., 12, 871-876 (2005).
[10] G. Bastard, "Wave Mechanics Applied to Semiconductor Heterostructures," Les Editions de Physique, Les Ulis (1988).
[11] P. Moon and D.E. Spencer, "Field Theory Handbook," Second Edition, Springer-Verlag, Berlin (1988).
[12] L.C. Lew Yan Voon and M. Willatzen, J. Phys. Cond. Matt., 14, 13667- 13678 (2002).