Modeling of semiconductor nanostructures and semiconductor-electrolyte interfaces

The main objective of Part I is to give an overview of some of the methods that have been implemented into the nextnano3 software. Examples are discussed that give insight into doping, strain and mobility. Applications of the single-band Schroedinger equation include three-dimensional superlattices, and a qubit that is manipulated by a magnetic field. Results of the multi-band k.p method are presented for HgTe-CdTe and InAs-GaSb superlattices, and for a SiGe-Si quantum cascade structure. Particular focus is put on a detailed description of the contact block reduction (CBR) method that has been developed within our research group. By means of this approach, quantum transport in the ballistic limit in one, two and three dimensions can be calculated. I provide a very detailed description of the algorithm and present several well documented examples that highlight the key points of this method. Calculating quantum transport in three dimensions is a very challenging task where computationally efficient algorithms - apart from the CBR method - are not available yet. Part II describes the methods that I have implemented into the nextnano3 software for calculating systems that consist of a combination of semiconductor materials and liquids. These biosensors have a solid-electrolyte interface, and the charges in the solid and in the electrolyte are coupled to each other through the Poisson-Boltzmann equation. I apply this model to a silicon based protein sensor, where I solve the Schroedinger equation together with the Poisson-Boltzmann equation self-consistently, and compare theoretical results with experiment. Furthermore, I have developed a novel approach to model the charge density profiles at semiconductor-electrolyte interfaces that allows us to distinguish hydrophobic and hydrophilic interfaces. Our approach extends previous work where ion specific potentials of mean force describe the distribution of ion species at the interface. I apply this new model to recently developed graphene and diamond based solution gated field-effect transistors, and compare my calculations to experiment. All numerical examples presented in this thesis are available as input files for the nextnano3 and/or nextnano++ software. It is thus possible for other researchers to reproduce the results of all calculations of this thesis. Additionally, the respective input files can easily be modified to study variations of device characteristics, like geometry, choice of materials, doping, and many more. To date, the nextnano software has been used successfully in many master and doctoral theses, as well as in numerous scientific articles to provide either a qualitative understanding or a quantitative analysis of the electronic and optoelectronic properties of modern semiconductor nanostructures. (orig.)