Self-Organized Quantum-Wire Lattice via Step Flow Growth of a Short-Period Superlattice

We develop a theoretical model for step flow growth of multilayer films, taking into account the interlayer step-step interaction induced by misfit strain. We apply the model to simulate the growth of strain-compensated short-period superlattices. Step-bunch ordering improves in successive layers, leading to self-organized growth of a lattice of quantum wires. This quantum-wire array has some similarities to the “lateral composition modulation” observed experimentally in short-period superlattices.

Figure 1

Cross section of the final structure in our simulation, consisting of 12 bilayers of alternating layers of equal tension and compression, with each layer 4 ML thick. Vertical scale is expanded by $\sim 10$ times for clarity. (a) Entire system. (b) Expanded view of a particularly well-ordered region of (a), showing more clearly the individual steps. Note the excellent uniformity of bunch size and spacing.

Figure 2

The pair correlation function of the steps at the surface of $A$ layers in $A\mathrm{\text{−}}B$ superlattice, for the $A1$, $A3$, $A5$, $A7$, $A9$, and $A11$ layers of the 12-bilayer film of Fig. 1. The results are each averaged over ten configurations well separated in time. Note the progressive improvement of ordering during growth of successive layers.

Figure 3

2D correlation function of steps from the 7th to the 11th layer, illustrating the formation of a 2D array of step bunches. (a) Between the same type of steps $(A\mathrm{\text{−}}A)+(B\mathrm{\text{−}}B)$. (b) Between the different type of steps $(A\mathrm{\text{−}}B)+(B\mathrm{\text{−}}A)$.

Figure 4

Structure factor of steps from the 7th to the 11th layer, showing the high degree of symmetry and order of the 2D array of step bunches.