Zeldovich Nucleation Rate, Self-Consistency Renormalization, and Crystal Phase of Au-Catalyzed GaAs Nanowires

Abstract

We present a self-consistent model for the Zeldovich nucleation rate that determines the nucleation probabilities, growth rates and even the preferred crystal structure of Au-catalyzed III-V nanowires fabricated by the vapor-liquid-solid growth method. The obtained expression accounts for the nucleation kinetics in ternary Au-III-V alloys and shows that the nucleation rate in vapor-liquid-solid nanowires is proportional to the As concentration, As diffusion coefficient in the droplet and the activity of solid GaAs. The leading exponential term of the nucleation rate is modified due to the self-consistency renormalization. As a result, the behavior of the effective nucleation barrier versus Ga concentration is changed significantly with respect to the commonly used expression. This strongly affects the values of Ga concentrations during growth which are obtained within the self-consistent approach with the known nanowire elongation rates. In turn, the renormalized nucleation rates change the predictions regarding the zincblende-wurtzite phase transitions in III-V nanowires. In particular, our calculations show why the Aucatalyzed GaAs nanowires grown by molecular beam epitaxy at 550 o C are predominantly wurtzite, while the high temperature hydride vapor phase epitaxy at 715 o C yields pure zincblende crystal structure. We also obtain useful estimates for the As diffusion coefficients in ternary Au-Ga-As liquids at different conditions.

Regimes of radial growth for Ga-catalyzed GaAs nanowires

“…The solutions to Eqs. (18) and (19) critically depend on the values of the two control parameters F 53 and F d , as discussed in the next section.…”

“…As in Refs. [17][18][19], we now assume that a very low concentration of arsenic atoms leads to only minor correction for the liquid chemical potential of gallium atoms that interact mainly between themselves. In this case, the chemical potential difference per a Ga-As pair in the liquid and solid states (all chemical potentials are measured in thermal units) can be put as…”

“…However, this is what is typically assumed in the self-consistent growth theories such as described in Refs. [12,[17][18][19] and means simply that the arsenic adsorption on the droplet surface is equalized by its desorption and the solid growth. Only in such case, the NW axial growth rate is given by the kinetic of the arsenic growth species, as observed experimentally [4,[10][11][12]15], while the kinetics of the droplet volume depends on the balance between the incoming and outgoing gallium atoms.…”

“…In the next step of our procedure, we note that the Zeldovich nucleation rate in Ga-catalyzed VLS growth is given by [12,18,22] …”

XXI Международный симпозиум Нанофизика и наноэлектроника", Нижний Новгород, 13-16 марта 2017 г. Нитевидные нанокристаллы GaP/Si (111), синтезированные методом молекулярно-пучковой эпитаксии с переключением гексагональной и кубической фазy -=SUP=-*-=/SUP=-

“…Верхняя граница для химических потенциалов является доста-точно резкой, т. е. вблизи µ max ННК растут либо в одной, либо в другой фазе [8][9][10][11][12][13]. Рост ННК вблизи нижней границы может происходить с образованием политипов [10,[13][14][15][16].…”