Semiconductor nanostructure properties. Molecular Dynamic Simulations

The need for research is based on the fact that development of non-planar semiconductor nanosystems and nanomaterials with controlled properties is an important scientific and industrial problem. So, final scientific and technological problem is the creation of adequate modern methods and software for growth and properties simulation and optimization of various III-V (GaAs, InAs, InP, InGaAs etc.) nanostructures (e.g. nanowires) with controlled surface morphology, crystal structure, optical, transport properties etc. Accordingly, now we are developing a specialized computer code for atomistic simulation of structural (distribution of atoms and impurities, elastic and force constants, strain distribution etc.) and thermodynamic (mixing energy, interaction energy, surface energy etc.) properties of the nanostructures. Some simulation results are shown too.


Introduction
Nanowires based on semiconductor materials have recently drawn much attention due to their importance for nanoscale electronics and photonics [1]- [6]. These nanowires are usually fabricated via the Vapor-Liquid-Solis (VLS) growth mechanism [7] developed long ago for micrometer scale "whiskers" [8,9]. Using modern epitaxy techniques such as MOCVD [5,7,10] or MBE [11,12], nanowires or nanowhiskers (NWs) with diameters of several tens nanometers and length up to tens microns can be obtained. The fundamental principle underlying the VLS mechanism is the catalytic effect of a liquid metal droplet (Au, for example) assisting the NW growth from a supersaturated liquid alloy [8]. The integration of NWs components into working devices requires a high degree of control that is still lacking, and many fundamental questions concerning NW nucleation and growth remain to be answered (for instance, chemical potential in the droplet, NW and droplet surface energies, solid-liquid or/and liquid-vapor interface energies etc).
The Vapor-Liquid-Solid mechanism of NWs nucleation and growth are usually investigated using continuous medium theories of crystal growth [13]- [17]. It should be noted, that many parameters (for example, chemical potentials, surface energies, interface energies etc) have not been determined experimentally or using some continuous medium theories and their effect on nanostructures growth is

Valence Force Field Simulations
Sometimes ago, we have derived a statistical model of ternary A III B V alloys by using a new methodology, based on numerical calculations of their configuration partition function [38][39][40]. This statistical model allows calculating chemical potentials, mixing energy, mixing enthalpy, mixing entropy, phase diagrams etc. To find the mean mixing energy and the density of states in an alloy, the VFF simulations have been carried out with the Keating potential. The use of multiple computation runs (Nexp) is found to improve the representative statistics of the VFF computations, which is necessary for an accurate prediction of the mixing energy dispersion. The computational runs were Thus, this developed earlier optimized VFF method and this new methodology can be applied also to nanostructures, and not only to bulk materials. To do this, the boundary conditions for surface atoms of a modeling structure should be changed from periodic boundary conditions on free surface condition because it is no longer necessary to reduce the contribution of the surface atoms. In other aspects the simulation method is the same. The initial atomic positions are chosen to match those of a virtual crystal with the lattice constant dependent on the alloy composition via the Vegard law (the socalled "strained" modelling crystal). Both anions and cations are then allowed to relax lowering the distortion energy of the domain determined from the interatomic potential. The relaxation is allowed until the total distortion energy was converged with a relative accuracy of 10 5 − . After minimizing the distortion energy we get the so-called "relaxed" modelling crystal.

Some Simulation Results
As an example, some surface energy numerical calculations will be shown here. Surface energy E surf quantifies the disruption of intermolecular bonds that occurs when a surface is created. In the physics of solids, surfaces must be intrinsically less energetically favourable than the bulk of a material (the molecules on the surface have more energy compared with the molecules in the bulk of the material), otherwise there would be a driving force for surfaces to be created, removing the bulk of the material. The surface energy may be calculated as the excess energy at the surface of a material compared to the bulk E surf =( E PBC −E FBC )/S free , where E PBC is the energy of the modelling crystals with the periodic boundary conditions (PBC), E FBC is the energy of the modelling crystals with the free surface boundary conditions (FBC), and S free is the free surface area (here is the surface area of the cubic of side L). Table 1 shows the values of free surface area of cubic crystals with a different number of atoms. It must be remembered that ab initio calculations and simulations can be held only for crystals with atoms of less than 1000 whereas a III-V cubic crystal with a side of less than 10 nm composed of about 32000 atoms.    We can see in Figure 3 surface energy as a function of number of atoms and/or free surface area, computed for zinc-blend InAs (111) by Valence Force Field (see Section 3). It can be seen that the surface energy of the "strained" crystals (see Figure 3a) does not vary with the free surface area of the crystals and is 0.47±0.01 J/m 2 . In the case of the "relaxed" crystals ( Figure 3b) surface energy is a function of the free surface area. A similar behaviour of the surface energy is also observed for other materials, such as GaAs (111) (see Figure 4).  In Figure 3 and Figure 4 it can be seen a good agreement simulations with experiments and other calculations [41][42][43] for small number of atoms. However, apparently small number of atoms of modelling crystals is not enough to estimate surface energy of real nanosystems, especially of systems like nanoneedls, quantum dots etc (in this case we can not apply periodic boundary conditions). So, firstly, necessary to consider information about the free surface area and geometry of the system, for which the data obtained experimentally and/or calculated; secondly, the need to develop new methods for calculating (theoretical and numerical) of the surface energy of different materials and systems.

Conclusions
Accordingly, now we are developing a computer program for simulation of structural (distribution of atoms and impurities, elastic constants, strain distribution, etc.) and thermodynamic (surface energy, elastic energy, mixing energy, mixing enthalpy, mixing entropy, etc.) properties of new and practically important nanomaterials -low-dimensional nanostructures (e.g. nanowires, nanoneedles etc.) based on III-V, II-VI and IV semiconductors.
Numerical (operational) parameters of simulations and software packages can significantly affect simulation results (quality of energy relaxation). Small number of atoms of modelling crystals is not enough to estimate surface energy of real nanosystems, especially of systems like nanoneedls, quantum dots etc (in this case we can not apply periodic boundary conditions). To compare simulations, calculations and experimental results correctly one should know additional information (free surface area, geometry, simulation parameters etc.)