An Overview of Modeling Approaches for Compositional Control in III-V Ternary Nanowires

Self-Consistent Model for the Compositional Profiles in Vapor-Liquid-Solid III-V Nanowire Heterostructures Based on Group V Interchange

Due to the very efficient relaxation of elastic stress on strain-free sidewalls, III-V nanowires offer almost unlimited possibilities for bandgap engineering in nanowire heterostructures by using material combinations that are attainable in epilayers. However, axial nanowire heterostructures grown using the vapor-liquid-solid method often suffer from the reservoir effect in a catalyst droplet. Control over the interfacial abruptness in nanowire heterostructures based on the group V interchange is more difficult than for group-III-based materials, because the low concentrations of highly volatile group V atoms cannot be measured after or during growth. Here, we develop a self-consistent model for calculations of the coordinate-dependent compositional profiles in the solid and liquid phases during the vapor-liquid-solid growth of the axial nanowire heterostructure Ax0B1-x0C/Ax1B1-x1C with any stationary compositions x0 and x1. The only assumption of the model is that the growth rates of both binaries AC and BC are proportional to the concentrations of group V atoms A and B in a catalyst droplet, requiring high enough supersaturations in liquid phase. The model contains a minimum number of parameters and fits quite well the data on the interfacial abruptness across double heterostructures in GaP/GaAsxP1-x/GaP nanowires. It can be used for any axial III-V nanowire heterostructures obtained through the vapor-liquid-solid method. It forms a basis for further developments in modeling the complex growth process and suppression of the interfacial broadening caused by the reservoir effect.

Circumventing the Uncertainties of the Liquid Phase in the Compositional Control of VLS III-V Ternary Nanowires Based on Group V Intermix

Control over the composition of III-V ternary nanowires grown by the vapor-liquid-solid (VLS) method is essential for bandgap engineering in such nanomaterials and for the fabrication of functional nanowire heterostructures for a variety of applications. From the fundamental viewpoint, III-V ternary nanowires based on group V intermix (InSbxAs1-x, InPxAs1-x, GaPxAs1-x and many others) present the most difficult case, because the concentrations of highly volatile group V atoms in a catalyst droplet are beyond the detection limit of any characterization technique and therefore principally unknown. Here, we present a model for the vapor-solid distribution of such nanowires, which fully circumvents the uncertainties that remained in the theory so far, and we link the nanowire composition to the well-controlled parameters of vapor. The unknown concentrations of group V atoms in the droplet do not enter the distribution, despite the fact that a growing solid is surrounded by the liquid phase. The model fits satisfactorily the available data on the vapor-solid distributions of VLS InSbxAs1-x, InPxAs1-x and GaPxAs1-x nanowires grown using different catalysts. Even more importantly, it provides a basis for the compositional control of III-V ternary nanowires based on group V intermix, and it can be extended over other material systems where two highly volatile elements enter a ternary solid alloy through a liquid phase.

Composition of Vapor-Liquid-Solid III-V Ternary Nanowires Based on Group-III Intermix

Compositional control in III-V ternary nanowires grown by the vapor-liquid-solid method is essential for bandgap engineering and the design of functional nanowire nano-heterostructures. Herein, we present rather general theoretical considerations and derive explicit forms of the stationary vapor-solid and liquid-solid distributions of vapor-liquid-solid III-V ternary nanowires based on group-III intermix. It is shown that the vapor-solid distribution of such nanowires is kinetically controlled, while the liquid-solid distribution is in equilibrium or nucleation-limited. For a more technologically important vapor-solid distribution connecting nanowire composition with vapor composition, the kinetic suppression of miscibility gaps at a growth temperature is possible, while miscibility gaps (and generally strong non-linearity of the compositional curves) always remain in the equilibrium liquid-solid distribution. We analyze the available experimental data on the compositions of the vapor-liquid-solid AlxGa1-xAs, InxGa1-xAs, InxGa1-xP, and InxGa1-xN nanowires, which are very well described within the model. Overall, the developed approach circumvents uncertainty in choosing the relevant compositional model (close-to-equilibrium or kinetic), eliminates unknown parameters in the vapor-solid distribution of vapor-liquid-solid nanowires based on group-III intermix, and should be useful for the precise compositional tuning of such nanowires.