Modeling amorphous thin films: Kinetically limited minimization

Atomic-scale models of amorphous structures are typically generated using a simulated annealing (SA) quench from a melt simulation protocol. This approach resembles the preparation of bulk glasses, but it may not be suitable for modeling amorphous materials produced using low-energy and low-temperature physical vapor deposition, where a deposited atom induces only local relaxations and no equilibrated melt is formed. To account for such growth conditions, we developed the kinetically limited minimization (KLM) technique, in which an amorphous structure is constructed from a randomly initialized structure in a number of local perturbation-relaxation steps. We compare formation energies as well as short- and medium-range order of KLM- and SA-generated structures of a-${\mathrm{In}}_2{\mathrm{O}}_3$, a-ZnO, and a-Si.

Figure 1

Atomic displacements induced by 1-, 5-, and 30-eV accelerated In and O atoms in c-${\mathrm{In}}_2{\mathrm{O}}_3$ as a function of time. Each plot shows the results of six simulations (three for In and three for O atoms). Full lines: the accelerated atoms; dashed lines: the remaining atoms; blue: In; red: O.

Figure 2

The change in energy of accepted moves during kinetically limited minimization as a function of a step number. Red: a-${\mathrm{In}}_2{\mathrm{O}}_3$; blue: a-ZnO; and green: a-Si (five runs for each material).

Figure 3

Formation energies of amorphous structures relative to formation energy of the respective ground-state crystal structure for a-Si (green), a-ZnO (blue), and a-${\mathrm{In}}_2{\mathrm{O}}_3$ (red), as a function of the (a) step number of KLM and (b) quench rate of SA. The green, blue, and red bands in (b) denote two standard deviations calculated from four different initial random structures.

Figure 4

Distribution of coordination numbers in crystal (solid black line), liquid (dashed black line), and amorphous ${\mathrm{In}}_2{\mathrm{O}}_3$, ZnO, and Si. (Solid lines: blue and cyan for SA with quench rates of 64 and 2500 K/ps, respectively, and red for KLM.)

Figure 5

Partial pair distribution functions in crystal (solid black line), liquid (dashed black line), and amorphous ${\mathrm{In}}_2{\mathrm{O}}_3$, ZnO, and Si (solid lines: blue and cyan for SA with quench rates of 64 and 2500 K/ps, respectively, and red for KLM).