Abstract
The temperature dependent density of Al and Ga droplets deposited on AlGaAs with molecular beam epitaxy is studied theoretically. Such droplets are important for applications in quantum information technology and can be functionalized e.g., by droplet epitaxy or droplet etching for the self-assembled generation of quantum emitters. After an estimation based on a scaling analysis, the droplet densities are simulated using first a mean-field rate model and second a kinetic Monte Carlo (KMC) simulation basing on an atomistic representation of the mobile adatoms. The modeling of droplet nucleation with a very high surface activity of the adatoms and ultra-low droplet densities down to 5 × 10 cm is highly demanding in particular for the KMC simulation. Both models consider two material related model parameters, the energy barrier for surface diffusion of free adatoms and the energy barrier for escape of atoms from droplets. The rate model quantitatively reproduces the droplet densities with = 0.19 eV, = 1.71 eV for Al droplets and = 0.115 eV for Ga droplets. For Ga, the values of are temperature dependent indicating the relevance of additional processes. Interestingly, the critical nucleus size depends on deposition time, which conflicts with the assumptions of the scaling model. Using a multiscale KMC algorithm to substantially shorten the computation times, Al droplets up to 460 °C on a 7500 × 7500 simulation field and Ga droplets up to 550 °C are simulated. The results show a very good agreement with the experiments using = 0.19 eV, = 1.44 eV for Al, and = 0.115 eV, = 1.24 eV ( 300 °C) or = 1.24 + 0.06 (T[°C] − 300)/100 eV ( °C) for Ga. The deviating is attributed to a re-nucleation effect that is not considered in the mean-field assumption of the rate model.
Highlights
Semiconductor quantum dots (QDs) are established as quantum emitters and represent essential building blocks for quantum information technology [1,2,3]
We start the analysis of the experimental droplet density using classical nucleation theory [27,28,29], which predicts the density of stable three-dimensional clusters by a scaling law ND ∝ F p exp[ E/(k B T )]
The deposition temperature controls the density of Ga and Al droplets during droplet epitaxy and etching over several orders of magnitude
Summary
Semiconductor quantum dots (QDs) are established as quantum emitters and represent essential building blocks for quantum information technology [1,2,3] For their fabrication, the use of self-assembly techniques is a powerful approach providing versatile semiconductor nanostructures by molecular beam epitaxy (MBE) [4]. The computation time of a KMC simulation substantially increases for large simulation fields (required for the present low droplet densities) and for a high rate of monomer diffusion processes. This limits the maximal process temperature accessible by this method. By using a multiscale KMC algorithm [32], we have reduced the computation time by a factor of 30,000 in comparison to a conventional KMC approach and achieved very good agreement with experimental Al droplet densities up to a temperature of 460 °C on a 7500 × 7500 simulation field and with Ga droplets up to 550 °C
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