Kinetic and thermodynamic modelling of ternary nanowire growth

Among nanoscale structures of different shapes and dimensions nanowires are one of the most promising because of its truly unique properties different from their bulk counterparts. The energy quantization, perfect defect-free structure, and the possibility to grow them within the miscibility gap in combination with the benefits of bottom-up design and the possibility of integration on silicon substrates make nanowires ideal candidates for applications in optoelectronics, biotechnology and energy harvesting. Today the research focus shifts toward the investigation of more complex materials, namely ternary and quaternary nanowires. For the majority of applications, a critical step in the nanowire-based device design is the ability to control the composition and crystal structure of ternary III-V nanowires. Such tuning is impossible without understanding of the underlying growth mechanism. Theoretical modelling may provide insight into the growth processes and help to assess optimal growth conditions. Moreover, simulation of nanowire growth allows one to reduce the number of experiments, which is essential in view of its high cost.
In this perspective, a set of models that encompass a variety of aspects of ternary nanowire formation including their composition and crystal structure has been developed. Within the modelling both thermodynamic and kinetic approaches have been used.
The first model is based on two-component nucleation theory and describes the formation of the critical nucleus from a quaternary liquid. An analytic expression that links the compositions of the ternary nucleus and liquid particle is derived. The nucleus composition of four materials systems is discussed in details. Next, we explain how the surface energy influences the miscibility gap and the liquid-solid composition dependence during nucleation from a liquid melt.
The second model is based on the consideration of the incorporation rates of binary species into the monolayer and describes the evolution of the solid composition from the nucleated-limited composition to the kinetic one. The kinetic steady state regime is used to fit an experimental data set, namely the liquid-solid composition dependence obtained during growth of InxGa1-xAs nanowires in an environmental transmission electron microscope.
Finally, a model which describes the composition dependence of the zinc blende – wurtzite polytypism in ternary nanowires growing by the vapor-liquid-solid mechanism is developed.

In a rapidly globalizing world, the progress and success in the electronics industry are inextricably linked to the miniaturization of electronics. The smaller the size of an electronic device, the more such devices can be fit into the same area. For example, the current type of transistor, invented in 1947, was 40 micrometers long, while IBM announced in May 2021 a chip with 2 nanometer transistors. The difference in the length scale is 20000 times (the same as the difference between the length of a Pharaoh ant and an African bush elephant). Somewhere in between, humanity made a step into the nanoscale world. The prefix “nano” comes from ancient Greek for “dwarf” and denotes 1/1 000 000 000, or one billionth.
In addition to a higher packing density of the electronic chips, which results in higher performance and lower energy use, the transition to nanoscale enables the materials to exhibit unique properties directly connected to its small size. When the size is small enough, that is on the nanometer scale, quantum mechanical effects start to dominate and one such effect is that the motion of electrons get restricted and this is known as quantum confinement. Considering the size, there are three main types of nanostructures, namely 0-dimensional with quantum confinement in all three spatial directions, 1-dimensional, with quantum confinement in two directions, and 2-dimensional with quantum confinement in one direction. The 0-dimensional nanostructures are known as quantum dots, the 1-dimensional ones as quantum wires or nanowires, and the 2-dimensional ones as quantum wells. Even if nanostructures cannot be seen with the naked eyes, their influence is more and more perceptible: they incorporate into our daily life and change it. For example, a regular customer can buy a high-resolution TV with quantum dots or glossy printing paper with ceramic nanoparticles.
Among the nanostructures of different shapes and dimensions, the nanowires are of particular interest and importance. They are whisker-like crystals with the radius of 10-100 nanometers and the length of a few micrometers. Despite there are no nanowire-based devices in today’s industry, many prototypes have been developed such as solar cells, sensors, transistors, light emitting diodes and silicon nanowire-based batteries announced by Tesla. Such a variety of applications can be explained by the possibility of controlled growth of nanowires, including their morphology (the radius and length), chemical composition (sort and number of atoms which form a nanowire) and crystal structure (the arrangement of the atoms in the crystal). This allows one to tune the optical and electrical properties of nanowires. For example, combining two binary compounds, such as indium arsenide (InAs) and gallium arsenide (GaAs), one may obtain ternary InGaAs nanowires whose properties are a combination of those of the binary compounds (InAs and GaAs). To be more specific, the properties of ternary nanowires are determined by the ratio of the number of the InAs and GaAs units in the solid. In this perspective, an important question arises: how to make a nanowire with a given chemical composition?
To answer this question, we should understand the underlying growth mechanism and know how to control the process using experimental conditions such as temperature and fluxes. The most popular way to fabricate nanowires is by so called vapor-liquid-solid growth. Within this approach, the fluxes of atomic species are directed towards a sample surface containing liquid metal droplets. Then, atoms dissolve into the liquid droplets, and when the concentration of atoms exceeds the solubility limit, it is energetically favourable for crystalline material to form. This formation process takes place at the contact area between the sample surface and the liquid drop. Continuing this process, a nanowire takes form, one atomic layer after another, until the fluxes of atomic species from the vapor are turned off.
Now, when we understand the principle behind nanowire formation, we would like to know how the composition of the liquid drop is related to the composition of the vapor, and how the composition of the solid nanowire is related to the liquid. If we know this, we can predict, on average, which atom will incorporate into the nanowire depending on the conditions.
One of the purposes of this thesis is to find the relationships between these compositions using a variety of models, which are based on different assumptions and limiting steps. Another purpose is to explain the crystal structure of ternary nanowires. The research procedure is the following. When considering nanowire growth, I assume the most critical elementary processes, which I translate into equations. Then I solve these equations and analyse their solutions under the variation of different, experimentally relevant parameters, such as concentrations and nanowire growth temperature.