Electron transport through triangular potential barriers with doping-induced disorder

Abstract

Electron transport through single-, double-, and triple-barrier structures created by the insertion of suitably $\ensuremath{\delta}$-doped layers in GaAs is investigated. The results are compared with experiments on barriers of similar shape, but obtained by linear grading of the Al fraction x in ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ structures. In the case of the doping-induced space-charge potential it is found that the effective barrier height for transport is much lower than expected from a simple model, in which uniform distribution of the doping charge within the doped layers is assumed. This reduction is quantitatively explained by taking into account the random distribution of the acceptor atoms within the $\ensuremath{\delta}p$-doped layers, which results in large spatial fluctuations of the barrier potential. The transport turns out to be dominated by small regions around the energetically lowest saddle points of the random space-charge potential. Additionally, independent on the dimensionality of the transport [three-dimensional (3D) to 3D in the single barrier, from 3D through 2D to 3D in the double barrier, and from 3D through 2D through 2D to 3D in the triple-barrier structure], fingerprints of 2D subband resonances are neither experimentally observed nor theoretically expected in the doping-induced structures. This is attributed to the disorder-induced random spatial fluctuations of the subband energies in the n layers which are uncorrelated for neighboring layers. Our interpretations of the temperature-dependent current-voltage characteristics are corroborated by comparison with the experimental and theoretical results obtained from the corresponding fluctuation-free ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ structures. Quantitative agreement between theory and experiment is observed in both cases.