Kablukova E.G.   Sabelfeld K.  

A stochastic kinetic-thermodynamic model and simulation algorithm for nanowire burst nucleation and growth

Reporter: Kablukova E.G.

We suggest a kinetic-thermodynamic stochastic model of self-induced nucleation of GaN nanowires (NW)  by the molecular beam epitaxy. A remarkable feature of the nanowire  nucleation in the epitaxy method is a very long incubation time followed by a rapid, so-called burst nucleation of stable GaN islands, which then grow as nanowires. During the incubation  time, no stable nuclei appear. The rapid nucleation is achieved by a key element which is the inclusion of a concentration-dependent critical nucleus size, determined self-consistently along with the subcritical cluster population density in accordance with the thermodynamic nucleation theory [1]. In [2, 3] a nanowire growth model has been developed where diffusion of atoms, NW coalescence and rescattering of atoms between the nanowires was taken into account while the initial distribution of nanowires on the substrate was taken when the formation of new NW nuclei has been terminated  in accordance with the experimental data. We construct a stochastic nucleation model where the atoms are diffusing on a 2D grid, clusters are formed as two atoms meet each other on a node, and the unstable clusters may disaggregate with a prescribed rate.  A critical size of the stable nuclei is taken from the thermodynamic nucleation theory which strongly depends on the ratio of the instantaneous concentration of atoms on the substrate to the saturation concentration [1]. Our simulations show that the model developed is able to demonstrate long incubation time followed by a rapid nucleation of new nanowires.  

Support of the Russian Science Foundation under Grant N14-11-00083 is kindly acknowledged.
1. A. Baronov, K. Bufkin, D. W. Shaw, B.L. Johnson and D.L. Patrick, A simple model of burst          nucleation.  Phys. Chem. Chem. Phys., 17 (2015), 20846.
2. S. Fernández-Garrido, V. M. Kaganer, K. K. Sabelfeld,  T. Gotschke, J. Grandal,  E. Calleja, L.  Geelhaar,  and O. Brandt, Self-regulated radius of spontaneously formed GaN nanowires in molecular beam epitaxy.  Nano letters, 13(7) (2013), 3274-80.
3. Sabelfeld, K. K.,  Kablukova, E. G. Stochastic model and simulation of growth and coalescence of spontaneously formed GaN nanowires in molecular beam epitaxy. Computational Materials Science, 141 (2018), 341-352.


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