Towards "on-demand" van der Waals epitaxy with an adaptive resource-driven online ensemble sampling simulation framework

Abstract

Traditional approaches to achieve targeted epitaxial growth involves exploring a vast parameter space of thermodynamical and kinetic drivers (e.g., temperature, pressure, chemical potential etc). This tedious and time-consuming approach becomes particularly cumbersome to accelerate synthesis and characterization of novel materials with complex dependencies on local chemical environment, temperature and lattice-strains, specifically nanoscale heterostructures of layered 2D materials. We combine the strength of next generation supercomputers at the extreme scale, machine learning and classical molecular dynamics simulations within an adaptive real time closed-loop virtual environment steered by Bayesian optimization to enable asynchronous ensemble sampling of the synthesis space, and apply it to the recrystallization phenomena of amorphous transition-metal dichalcogenide (TMDC) bilayer to form stack moiré heterostructures under various growth parameters. We show that such asynchronous ensemble sampling frameworks for materials simulations can be promising towards achieving on-demand epitaxy of van der Waals stacked moiré devices, paving the way towards a robust autonomous materials synthesis pipeline to enable unprecedented discovery of new functionalities.

Figures (10)

• Figure 1: Asynchronous active batch sampling strategy for optimal driving parameters for target twist angles. Goal is to transform a given initial structure with amorphous MoS$_2$ layer on top of a crystalline layer (amorph+Xtal), into crystallized twisted bi-layer with a predefined target (a). Asynchronous ensemble optimization (b) strategies using Bayesian acquisition of candidate recrystallization parameters (c). On the fly concurrent evaluations of atomistic simulation via a resource-adaptive dynamic orchestration under a parameter space consisting of annealing temperature, lattice and shear strains. Additionally, this space can easily be expanded (as indicated in smaller fonts) to consider other synthesis relevant parameters like chemical potential, pressure, ion/species flux etc. can naturally be (d) to identify the driving parameters ($\{p_i\}$) to achieve recrystallization with the target twist angle (e).
• Figure 1: Exploratory landscape of twist angles observed as a function of temperature and lattice strain extracted for various shear (in-plane tilt ratios) as depicted in the figures. The roughness of the landscape is indicative of the fact that traditional local as well as sequential Bayesian sampling approaches might perform poorly, showcasing the need for more global and stochastic asynchronous sampling strategies as explored in this work.
• Figure 2: Recrystallization under temperature and strain effects As temperature is quenched near 0 K (a, b), overall order starts to emerge in the top layer as shown in the bottom panel (c,d) for different snapshot in the MD trajectory. While only temperature driven (i.e., heating at 2500 K) trajectories lead to almost no significant interlayer twist---AB stacked 2H phase (c-iii), applying a lattice strain ($\epsilon_{lat}$) with a supercell shear of ($\epsilon_{sh}$) 1.5 % each, can induce a recrystallized bilayer with a twist angle ($\theta$) of around $8.7^\circ$ (d-iii).
• Figure 2: Diversity of growth parameters in each batch over the BO iterations The violin plots show the ability to navigate through a diverse set of growth paramters across individual batches through Thompson Sampling with "on demand" target twists
• Figure 3: Sampling a target twist with batch acquisition based on q-Expected Improvement Regret (absolute error) between sampled twist angle and the predefined target for q-EI based acquisitions with different batch sizes ($n_{batch}$) in (a). Solid lines correspond to the cumulative minimum of regret over the iterations. Mean regret evolution in (b) for the best sample in each batch over BO cycle iterations for varying batch sizes. The confidence interval shows standard deviation over 3 repetitions