Introduction

Quantum dots are nanometer-sized particles or islands of a semiconductor material embedded in another semiconductor material. They have electronic properties different from that of the bulk due to quantum confinement, and thus hold a promise for nanotechnology applications such as LED's, detectors, data memory devices, lasers, and single electron transistors. However, fabricating a regular, perfectly aligned dot structure is still a challenging issue. Rather than using an accurate positioning device, such as a focused ion beam, it is preferable to use the technique of self-organizing/assembling growth via a strain relaxation mechanism. This is done by depositing the vapor of a material onto a substrate made of a material with a different lattice parameter. It is found experimentally in many material systems that heteroepitaxial growth results in spontaneous self-organization and assembly of islands. [l1,2]

The driving force for the quantum dot formation is the reduction of the total energy with a contribution from the elastic strain energy. The elastic strain arises by the lattice misfit between the film and the substrate material. Initially, the combination of the surface/interfacial energies and the strain energy are such that the system favors wetting. Therefore, the film material forms a flat wetting layer over the substrate. As the film material is deposited, the thickness of the film increases and the strain relaxation mechanism will result in island formation, despite an increase in the surface energy. At the early stage of surface roughening, the material is more relaxed at the crest than at the valley. In other words, the area at the crest has a lower chemical potential. Consequently, the film material diffuses from the valley to the crest, which eventually leads to island formation.[3]

In this project, we examine the formation of quantum dots by employing the finite element method formulated by Ref. 4,5.

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[1] P. Liu, Y. W. Zhang, and C. Lu, Phys. Rev. B 68 (2003).

[2] Y. Ni, A. K. Soh, and L. H. He, Journal Of Crystal Growth 269 , 262 (2004).

[3] S. M. Wise, J. S. Lowengrub, J. S. Kim, and W. C. Johnson, Superlattices Microstructures 36 ,

293 (2004).

[4] B. Sun, Z. Suo, and W. Yang, Acta Materialia 45 , 1907 (1997).

[5] B. Sun and Z. Suo, Acta Materialia 45 , 4953 (1997).