# Molecular Dynamics Simulations

**Introduction**

The first Molecular Dynamics (MD) simulations appeared nearly at the same time as the first computers. With this technique the motion of atoms and molecules under predefined conditions, such as temperature, pressure, stress, external forces, *etc.* is simulated. MD simulations can therefore be used to study dynamical processes at the nanoscale and to calculate a broad range of properties, *e.g.* phase diagrams, diffusion coefficients, or various response functions, as well as static quantities such as radial distribution functions, diffraction spectra, coordination numbers, elastic moduli, *etc.*

MD essentially utilizes the numerical solution of Newton’s equations of motion for a set of atoms from a given initial configuration. This is commonly achieved via numerical integration by discretizing time into small intervals called the time step. The interactions between atoms, *i.e.* the interatomic forces, can be calculated based on various methods, ranging from density functional theory (DFT) to classical potentials. These forces determine the acceleration of the atoms and allow the positions and velocities to propagate toward the next time step. Repeating this procedure many times yields a series of snapshots, describing the trajectory of the system in phase space, which can be analyzed to extract the desired properties.

Before setting up the simulation you need to decide what type of calculation you are interested in. Should the total energy be conserved, as in an isolated system? Should the temperature be kept constant to mimic the coupling of the system to a heat bath? Is the system exposed to any external pressure or stress? Based on these considerations, a suitable set of simulation parameters should be selected: Time step size, number of integration steps (duration of simulation), integration algorithm, initial temperature, constraints, *etc.*

Often MD calculations are performed together with *ab initio* simulations which can, for instance, be used to develop realistic potentials to describe the atomic interactions when the system is too large or the necessary trajectory is too long for DFT calculations. The results of MD simulations can also be used as input for high-level *ab initio* simulations to calculate properties such as absorption spectra, photo-luminescence, electron delocalization, magnetic properties, Raman and infrared spectra, material work functions and much more.

The ultimate test for the validity of any atomic simulation is always its comparison to experimental measurements. In this sense, a very fruitful synergy can be established based on the suggestion and interpretation of experiments.

In the following, we present some concrete examples showing the power of MD simulations (for more details please see AIP Conference Proceedings 963 (1), 224-249, 2007).

**Example #1: Deposition of hydrogenated silicon clusters for efficient epitaxial growth **Epitaxial silicon thin films grown from the deposition of plasma-born hydrogenated silicon nanoparticles using plasma-enhanced chemical vapor deposition have widely been investigated due to their potential applications in photovoltaic and nano-electronic device technologies. However, the optimal experimental conditions and the underlying growth mechanisms leading to high-speed epitaxial growth of thin silicon films from hydrogenated silicon nanoparticles remain far from being understood. In this example, extensive molecular dynamics simulations were performed to study the epitaxial growth of silicon thin films resulting from the deposition of plasma-born hydrogenated silicon clusters at low substrate temperatures under realistic reactor conditions. There is strong evidence that a temporary phase transition of the substrate area around the cluster impact site to the liquid state is necessary for the epitaxial growth to take place. We predict further that a non-normal incidence angle for the cluster impact significantly facilitates the epitaxial growth of thin crystalline silicon films.

**Example #2: Controlled growth of silicon nanoclusters in a plasma reactor**Using a powerful multilevel simulation approach, we ‘‘visualize’’ the complete growth dynamics of hydrogenated silicon nanostructures under realistic experimental conditions of a plasma reactor. For the early stages of the synthesis, we demonstrate for the first time how precise control of atomic hydrogen not only permits one to choose between the production of amorphous and crystalline nanoparticles, but also to ‘‘steer’’ the growth toward the formation of elementary ‘‘building blocks’’ for the synthesis of hexagonal silicon nanowires.

(a) The electron density is calculated from the total self-consistent field density mapped with the corresponding electrostatic potential in atomic units for isomer (d) depicted above; the shown color differences correspond to a permanent dipole moment of 1.9 D (Debye units); (b) contour plots are shown resulting from a longitudinal cut through the center of the structure; (c), (d), and (e) demonstrate typical contour plots resulting from transversal cuts through the Si19H12 structure (see Phys. Rev. Lett. http://dx.doi.org/10.1103/PhysRevLett.95.165502)

**Example #3: Hydrogen-induced healing of cluster-damaged silicon surfaces**

A silicon surface which was partly damaged by the violent impact of hydrogenated silicon clusters has been treated by atomic hydrogen. After the exposure with hydrogen atoms, we observe that the ill-defined silicon surface is rearranged to its initial crystalline structure and that the silicon atoms of the deposited cluster are now incorporated in the crystalline structure of the repaired substrate surface.

The structural change of a damaged silicon surface after exposure to only 12 H-atoms; due to the reaction with the H-atoms, the surface temperature increased locally to around 1600 K. The blue atoms represent the silicon atoms found in epitaxial positions.

The Radial Distribution Function (RDF) of the local surface region after H-treatment and after cooling down to 573 K is compared to the RDF of this region before the H-exposure and with the RDF of bulk c-Si at 573 K. (see Chem Phys Lett: dx.doi.org/10.1016/j.cplett.2014.07.034)

### Example #4: Terahertz and Gigahertz Emission from an All-Silicon Nanocrystal

Based on first-principles calculations, we predict the use of pure silicon nanocrystals as nano-oscillators in the giga- and terahertz region. Small- and large-amplitude, one-dimensional vibrations are observed. The former are spontaneously excited thermally at frequencies around 3 THz. Large-amplitude vibrations originate from oscillations between the inversion geometries of the nanocrystal and can be caused either classically by an external excitation or by quantum tunneling. The latter causes a ground-state splitting of 4.2 GHz, suggesting the use of the proposed nanocrystals as laser elements in a configuration analogous to that of the ammonia maser.

Blue line: longitudinal scan showing potential wells “seen” by the inner silicon atom. The symmetric and anti- symmetric wave functions are shown schematically. The energy splitting is not drawn to scale (see PRL 112, 197401, DOI: 10.1103/PhysRevLett.112.197401).