TEM images of InAs QDs (Courtesy of TU Berlin [1])

The growth of semiconductor quantum dots (QDs) with desired electronic properties would highly benefit from the assessment of QD geometry, distribution, and strain profile in a feedback loop between epitaxial growth and analysis of their properties. However, the reconstruction of geometric properties of semiconductor quantum dots (QDs) from imaging of bulk-like samples (thickness 100-300 nm) by transmission electron microscopy (TEM) is a difficult problem. A direct reconstruction by solving the tomography problem is not feasible due to the limited image resolution (0.5-1 nm), the highly nonlinear behavior of the dynamic electron scattering, nonlocal effects due to strain and strong stochastic influences due to uncertainties in the experiment. Here, we outline a novel concept for 3D

model-based geometry reconstruction (MBGR) of QDs from TEM images. This will include (a) an appropriate model for the QD configuration in real space including a categorization of QD shapes (e.g., pyramidal or lens-shaped) and continuous parameters (e.g., size, height), (b) a database of simulated TEM images covering a large number of possible QD configurations and image acquisition parameters (e.g. bright field/dark field, sample tilt), as well as (c) a statistical procedure for the estimation of QD properties and classification of QD types based on acquired TEM image data. To this end we need an accurate mathematical model for the numerical simulation of the TEM images.

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