Recently, fabrication of advanced quantum-dot (QD) architectures gains a lot of interests due to its potential to realize novel nano-electronic and nano-photonic devices [1]. Self-assembled growth is a bottom-up process to create complex nanostructures without using cumbersome fabrication steps. Growths of self-assembled III-V QDs has continuously been investigated and applied with other techniques. In this work, we theoretically investigate the formation of QD ring in strained droplet epitaxy. A generic growth model is proposed to explain the experimentally observed results. 

Conventional droplet epitaxy can divided into 2 steps, i.e., (i) deposition of group-III metallic nano-droplet and (ii) crystallization by group-V material. For strained droplet epitaxy, the strain will accumulated in the nanostructures and thus the self-assembly process will occurred as the latest step (Fig. 1). Models for growth of unstrained nanostructures have existed [2]. Here, we extend these models to account for the intrinsic strain accumulated in nanostructures. By using numerical finite element method, the strain distribution and total strain energy are analyzed. We perform energetic comparisons of total energy (strain energy and surface energy) between homogeneous ring and QD ring structure. According to our calculation (Fig. 2(a)), the critical size/volume for triggering the self-assembly process can be estimated. It agrees well with the experimental results (Fig. 2(b)) [3-4]. 

In conclusion, we have extend the growth scenario of conventional unstrained droplet epitaxy to the strained systems. This work will improve the understanding of nanostructure fabrication processes and thus open the door to realize more complex and controllable nanostructures.

Fig. 1 Growth scenario for QD ring formation by strained droplet epitaxy

Fig. 2 (a) Variation of total energy showing critical size for nanostructure shape transition. Beyond the ring height of ~2.2 nm, QD is energetic preferential shape. (b) Atomic force microscopy images of single InP ring and QD ring obtained at different amount of indium deposition.

 References

[1] S. Kiravittaya, A. Rastelli, and O. G. Schmidt, “Advanced quantum dot configurations,” Rep. Prog. Phys. 72, 046502, (2009).

[2] X. L. Li and G. W. Yang, “On the physical understanding of quantum rings self-assembly upon droplet epitaxy,” J. Appl. Phys. 105, 103507, (2009).

[3] P. Boonpeng, W. Jevasuwan, S. Suraprapapich, S. Ratanathammaphan, and S. Panyakeow, “Quadra-quantum dots grown on quantum rings having square-shaped holes: Basic nanostructure for quantum dot cellular automata application,” Microelectron. Eng. 86, 853, (2009).

[4] W. Jevasuwan, P. Boonpeng, S. Thainoi, S. Panyakeow, and S. Ratanathammaphan, “InP ring-shaped quantum-dot molecules grown by droplet molecular beam epitaxy,” J. Cryst. Growth 323, 275, (2011).

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