ABSTRACT
Site-controlled Ga droplets on AlGaAs substrates are fabricated using area-selective deposition of Ga through apertures in a mask during molecular beam epitaxy (MBE). The Ga droplets can be crystallized into GaAs quantum dots using a crystallization step under As flux. In order to model the complex process, including the masked deposition of the droplets and a reduction of their number during a thermal annealing step, a multiscale kinetic Monte Carlo (mkMC) simulation of self-assembled Ga droplet formation on AlGaAs is expanded for area-selective deposition. The simulation has only two free model parameters: the activation energy for surface diffusion and the activation energy for thermal escape of adatoms from a droplet. Simulated droplet numbers within the opening of the aperture agree quantitatively with the experimental results down to the perfect site-control, with one droplet per aperture. However, the model parameters are different compared to those of the self-assembled droplet growth. We attribute this to the presence of the mask in close proximity to the surface, which modifies the local process temperature and the As background. This approach also explains the dependence of the model parameters on the size of the aperture.
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 × 106 cm-2 is highly demanding in particular for the KMC simulation. Both models consider two material related model parameters, the energy barrier ES for surface diffusion of free adatoms and the energy barrier EE for escape of atoms from droplets. The rate model quantitatively reproduces the droplet densities with ES = 0.19 eV, EE = 1.71 eV for Al droplets and ES = 0.115 eV for Ga droplets. For Ga, the values of EE 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 ES = 0.19 eV, EE = 1.44 eV for Al, and ES = 0.115 eV, EE = 1.24 eV (T≤ 300 °C) or EE = 1.24 + 0.06 (T[°C] - 300)/100 eV (T>300 °C) for Ga. The deviating EE is attributed to a re-nucleation effect that is not considered in the mean-field assumption of the rate model.
