Recently, STM measurements of cleaved, self assembled quantum dots (SAQDs) have provided important information on the morphology and composition of these buried semiconductor islands. It is also now becoming possible to use STM techniques to image the electronic charge density within the SAQDs. At low bias voltages, the tunnelling current measured during cross-sectional scanning tunnelling spectroscopy (XSTS) experiments contains direct information on the 0D bound electronic states of the cleaved quantum dots. In this paper we present a numerical simulation of an XSTS experiment. The calculated tunnelling currents between an STM tip and the bound states inside a physically realistic model of a cleaved SAQD are compared to experimental results and qualitative agreement is found. The calculation of the tunnelling current is split into two stages. First the bound electron states of the cleaved quantum dot are calculated by exact diagonalisation of the Hamiltonian in a simple harmonic oscillator basis set. The calculation is performed within the single-band effective mass approximation including the position dependence of the effective mass and, most crucially, the effect of the deformations of the cleaved dot structure and the strain field within the system. The strains and deformations of the heterostructure are found with a continuum, finite element model. The calculation method is completely general, however, in this paper we apply it to the InGaAs dot structure reported by Bruls et al. Second, the Tersoff-Hamann approximation is used to calculate the tunnelling probability between the bound electronic states and the STM tip at different tip positions and bias voltages. The calculated STM signal is compared to experimental data and reasonable agreement is obtained. The method may be used to obtain additional physical information about the buried SAQDs, for example, details on the lateral variations in the composition
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