Local Strain-Mediated Chemical Potential Control of Quantum Dot Self-Organization in Heteroepitaxy

From observations of self-assembly of Ge quantum dots directed by substrate morphology, we propose the concept of control of ordering in heteroepitaxy by a local strain-mediated surface chemical potential. Using quite simple lithography, we demonstrate directed quantum dot ordering. The strain part of the chemical potential is caused by the spatially nonuniform relaxation of the strained layer, which in our study is the Ge wetting layer, but, more generally, can be a deposited strained buffer layer. This model provides a consistent picture of prior literature.

Figure 1

Simulated morphology evolution of (a) a stripe with $2\mu \mathrm{m}$ top width and (b) a square mesa (cross section) with $6\mu \mathrm{m}$ top width, under annealing at 1200 °C. $t/t_1$ is the normalized evolution time.

Figure 2

AFM images of Ge 3D island ordering on patterned Si(001) structures: (a) a stripe ridge; (b) a diamond-shaped stripe cross. (c) and (d) are the cross sections through (a) and (b), respectively, with $A{A}^{\prime }$ and $B{B}^{\prime }$ between dots and over dots, respectively. The $z$-scale difference in (c) and (d) is due to different plane-flatten processing. The nominal coverage is 60 ML.

Figure 3

Scanning electron microscope image of Ge 3D island ordering on patterned stripes on Si(001). ${\theta }_{\mathrm{G}\mathrm{e}}=60\mathrm{M}\mathrm{L}$. The stripes are oriented in $⟨110⟩$ directions, but ordering of Ge QDs is independent of direction. Other features (large islands at about half of the height in the upper corners, small islands at the bottom corners, etc.) can also be explained with the model [22].

Figure 4

Variation of the local surface chemical potential of stripe structures with position $X$ (solid line). The fitting parameter $(z_s-z_0)$ is 40 Å. The dashed line is the surface profile measured by AFM. The AFM scan underestimates the curvature because of tip convolution effects.