Popular growth models include:[1][2] They are studied for their fractal properties, scaling behavior, critical exponents, universality classes, and relations to chaos theory, dynamical system, non-equilibrium / disordered / complex systems.
Popular tools include statistical mechanics, renormalization group, rough path theory, etc.
Kinetic Monte Carlo (KMC) is a form of computer simulation in which atoms and molecules are allowed to interact at given rate that could be controlled based on known physics.
This simulation method is typically used in the micro-electrical industry to study crystal surface growth, and it can provide accurate models surface morphology in different growth conditions on a time scales typically ranging from micro-seconds to hours.
Experimental methods such as scanning electron microscopy (SEM), X-ray diffraction, and transmission electron microscopy (TEM), and other computer simulation methods such as molecular dynamics (MD), and Monte Carlo simulation (MC) are widely used.
First, the model tries to predict where an atom would land on a surface and its rate at particular environmental conditions, such as temperature and vapor pressure.
In order to land on a surface, atoms have to overcome the so-called activation energy barrier.
The frequency of passing through the activation barrier can by calculated by the Arrhenius equation:
First, they would diffuse on the surface and find other atoms to make a cluster, which will be discussed below.
The desorption is described exactly as in the absorption process, with the exception of a different activation energy barrier.
For example, if all positions on the surface of the crystal are energy equivalent, the rate of growth can be calculated from Turnbull formula:
Multiscale modeling techniques have also been developed to deal with overlapping time scales.
The interest of growing a smooth and defect-free surface requires a combination set of physical conditions throughout the process.
Such conditions are bond strength, temperature, surface-diffusion limited and supersaturation (or impingement) rate.
Bond strength and temperature certainly play important roles in the crystal grow process.
This behavior results in many isolated cluster formations with a variety of size yielding a rough surface.
Conclusion: high bond strength and low temperature is preferred to grow a smoothed surface.
Conclusion: low impingement rate helps creating smoother surface.
With the control of all growth conditions such as temperature, bond strength, diffusion, and saturation level, desired morphology could be formed by choosing the right parameters.