Abstract
We present a mathematical model and a tool chain for the numerical simulation of TEM images of semiconductor quantum dots (QDs). This includes elasticity theory to obtain the strain profile coupled with the Darwin–Howie–Whelan equations, describing the propagation of the electron wave through the sample. We perform a simulation study on indium gallium arsenide QDs with different shapes and compare the resulting TEM images to experimental ones. This tool chain can be applied to generate a database of simulated TEM images, which is a key element of a novel concept for model-based geometry reconstruction of semiconductor QDs, involving machine learning techniques.
Highlights
The fabrication of semiconductor quantum dots (QDs) with specific 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
The approach is based on (a) an appropriate model for the QD configuration in real space including a categorization of QD shapes and continuous parameters, (b) a database of simulated transmission electron microscopy (TEM) images covering a large number of possible QD configurations and image acquisition parameters, as well as (c) a statistical procedure for the estimation of QD properties and classification of QD types based on acquired TEM image data
We presented a tool chain for the simulation of TEM images for QDs with realistic parameterized 3D geometries
Summary
The fabrication of semiconductor quantum dots (QDs) with specific 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. We present as a first step towards MBGR: A mathematical model and a tool chain for the numerical simulation of TEM images for semiconductor QDs. We perform a simulation study on lens-shaped and pyramidal indium gallium arsenide QDs embedded in a gallium arsenide matrix and compare the resulting TEM simulations to experimental derived images. It is known that TEM images are very sensitive to strain fields around QDs and these fields are mostly responsible for the observed contrast. In order to link the contrasts in TEM images with shapes and concentration of these QDs it is crucial to combine strain calculations with TEM image simulations. By our systematic study of the influence of the shape on the image contrast, we could identify excitation conditions that allow to distinguish between lens-shaped and pyramidal QDs
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