Unified model of droplet epitaxy for compound semiconductor nanostructures: Experiments and theory

We present a unified model of compound semiconductor growth based on kinetic Monte Carlo simulations in tandem with experimental results that can describe and predict the mechanisms for the formation of various types of nanostructures observed during droplet epitaxy. The crucial features of the model include the explicit and independent representation of atoms with different species and the ability to treat solid and liquid phases independently. Using this model, we examine nanostructural evolution in droplet epitaxy. The model faithfully captures several of the experimentally observed structures, including compact islands and nanorings. Moreover, simulations show the presence of Ga/GaAs core-shell structures that we validate experimentally. A fully analytical model of droplet epitaxy that explains the relationship between growth conditions and the resulting nanostructures is presented, yielding key insight into the mechanisms of droplet epitaxy.

Figure 1

KMC events. Simulations are run on a $1+1$ analog of GaAs zinc-blende structure. Ga atoms are colored red, As atoms are green. The model allows for atom desorption (A), surface diffusion (B), atom-atom exchanges (C), and atom deposition (D). The simulations are explicitly multispecies and atomistic, and evolve via events on individual Ga or As atoms.

Figure 2

Attachment and detachment events at the liquid-solid interface. This figure illustrates the attachment and detachment of an As atom in liquid Ga onto and from a perfectly flat liquid-solid interface, along with the intermediate state for the transitions. The intermediate species $\text{H}$ is colored blue. The black lines indicate the relevant bonds that contribute to the change in energy between the initial and intermediate states.

Figure 3

Substrate termination phase diagram as a function of deposition ratio and temperature, obtained from simulations and experiments. Those growth conditions resulting in a mostly Ga-terminated substrate are indicated by red squares, while green circles label As-terminated ones. The blue points above indicate the conditions where the transition from Ga to As termination occurred experimentally. The blue curve indicates the boundary between Ga and As-terminated given by Eq. (2).

Figure 4

Droplet epitaxy experimental results showing typical nanostructures observed over a range of substrate temperatures and As${}_4$ BEP.

Figure 5

Liquid droplets grown at $T=200$${}^{\circ }$C, 300${}^{\circ }$C, 350${}^{\circ }$C and $F_{\text{Ga}}=0.1$ ML/s. Here and throughout the paper, Ga and As atoms initially belonging to the substrate are colored red and green, respectively. Ga and As atoms deposited throughout the simulation are colored purple and blue, respectively.

Figure 6

Left panel: model snapshots of liquid droplet crystallization at various times for $T=275{}^{\circ }\mathrm{C}$ and $F_{\text{As}}=0.06$ ML/s resulting in a compact quantum dot. Ga and As atoms from the original substrate are colored red and green, respectively. Ga atoms deposited to form liquid droplets are colored purple, while As atoms deposited during crystallization are blue. Right panel: AFM images of the GaAs growth fronts in partially crystallized droplets after 10 s (top), 40 s (middle), and 90 s (bottom). Crystallization was obtained at $T=150{}^{\circ }\mathrm{C}$ and $5\times {10}^{-7}$ Torr As pressure.

Figure 7

Nanorings formed at $T=375{}^{\circ }\mathrm{C}$ and $F_{\text{As}}=0.10,0.20$, and $0.40$ ML/s.

Figure 8

Simulation snapshots at times $t=0,1.8,2.4$ s after crystallization, $T=150$ ${}^{\circ }\mathrm{C}$, and $F_{\text{As}}=0.8$ ML/s.

Figure 9

Simulation snapshots of a quantum dot annealed at high temperature at time $t$ after temperature was increased. (a) The dot after exposure to As deposition at $F_{\text{As}}=0.80$ ML/s and temperature $T=150$ ${}^{\circ }\mathrm{C}$. This results in a polycrystalline GaAs shell trapping a liquid Ga core. (b)–(d) Temperature is increased to $T=350$ ${}^{\circ }\mathrm{C}$ and the atoms rearrange in order to fully crystallize the liquid core.

Figure 10

Snapshots of liquid core formation at times $t=1.4,1.8$, and $2.0$ s after crystallization at temperature $T=350{}^{\circ }\mathrm{C}$ and deposition rate $F_{\text{As}}=1.0$ ML/s.

Figure 11

Sample A. (a) Planar view TEM micrograph of two (70 nm diameter) GaAs microislands. (b), (c) EDS maps of Ga and As, respectively, of the islands in (a).

Figure 12

Sample B. (a) SEM image of a GaAs microisland (250 nm diameter). (b) Planar view TEM micrograph of a GaAs microisland. (c), (d) EDS maps of Ga and As, respectively, of the island in (b). (e), (f) EF-TEM image for Ga and As, respectively, of another GaAs microisland (TEM image not shown).

Figure 13

Morphological dependence on growth conditions. This nanostructural phase map summarizes simulation results of droplet epitaxy and crystallization at various As deposition rates and temperatures. The three boundary curves indicate theoretically derived critical conditions delineating the simulation results and obtained in this section. The leftmost, black line is given by Eq. (9). The middle, red curve corresponds to Eq. (13). The rightmost, blue curve is given by Eq. (12).

Figure 14

Schematic of kinetic processes that determine nanostructural development.