Real-space electronic structure methods for modeling nanowires and atomic force microscopy imaging
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Our group develops a pseudopotential-based electronic structure code constructed within first-principles density functional theory to study various problems in chemical engineering and condensed matter physics. One of the code's unique features is that it performs calculations on a real-space grid without using an explicit basis. This makes it particularly well-suited for examining localized systems with confined dimensionalities, such as nanostructures. In the dissertation we apply our code to the study of two main topics: germanium nanowires and atomic force microscopy simulations. First we examine how the electronic properties of germanium nanowires are affected by mechanical strain. We find that applying strain can drastically influence the transport properties of nanowires by inducing band crossings that change the nature of the band gap from direct to indirect, hampering carrier mobilities. In another project we take advantage of the real-space formalism for charged systems to devise a computationally efficient method to calculate accurate doping binding energies for nanowires. We demonstrate the method on phosphorus-doped germanium nanowires. The second focus of the dissertation is atomic force microscopy simulations. Atomic force microscopy is a powerful probe-based imaging technique that can be used to visualize and characterize chemical phenomena. However, the interpretation of experimental images is not well-understood. We develop a theoretical simulation method in order to better understand the fundamental physics behind the imaging mechanism. In one study, we clarify the mechanism for imaging hydrogen bonds. Experimental findings on certain organic oligomers have reported striking images showing what appear to be direct visualizations of intermolecular bonding. We apply our simulation technique to show that tip tilting is responsible for resolving these apparent hydrogen bonds. In another study, we examine the phenomenon of contrast inversion. We find that the key factor responsible for contrast inversion is the chemical reactivity of the tip. Theoretical imaging simulations such as these can be used to guide the experimental acquisition of images and to help characterize results.