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We present our latest advancements of machine-learned potentials (MLPs) based on the neuroevolution potential (NEP) framework introduced in [Fan et al., Phys. Rev. B 104, 104309 (2021)] and their implementation in the open-source package GPUMD. We increase the accuracy of NEP models both by improving the radial functions in the atomic-environment descriptor using a linear combination of Chebyshev basis functions and by extending the angular descriptor with some four-body and five-body contributions as in the atomic cluster expansion approach. We also detail our efficient implementation of the NEP approach in graphics processing units as well as our workflow for the construction of NEP models, and we demonstrate their application in large-scale atomistic simulations. By comparing to state-of-the-art MLPs, we show that the NEP approach not only achieves above-average accuracy but also is far more computationally efficient. These results demonstrate that the GPUMD package is a promising tool for solving challenging problems requiring highly accurate, large-scale atomistic simulations. To enable the construction of MLPs using a minimal training set, we propose an active-learning scheme based on the latent space of a pre-trained NEP model. Finally, we introduce three separate Python packages, GPYUMD, CALORINE, and PYNEP, which enable the integration of GPUMD into Python workflows., Comment: 29 pages, 15 figures, code and data available

The thermal properties of two-dimensional (2D) materials, like MoS$_2$, are known to be affected by interactions with their environment, but this has primarily been studied only with SiO$_2$ substrates. Here, we compare the thermal conductivity (TC) and thermal boundary conductance (TBC) of monolayer MoS$_2$ on amorphous (a-) and crystalline (c-) SiO$_2$, AlN, Al$_2$O$_3$, and $\textit{h}$-BN monolayers using molecular dynamics. The room temperature TC of MoS$_2$ is ~38 Wm$^{-1}$K$^{-1}$ on amorphous substrates and up to ~68 Wm$^{-1}$K$^{-1}$ on crystalline substrates, with most of the difference due to substrate interactions with long-wavelength MoS$_2$ phonons (< 2 THz). An $\textit{h}$-BN monolayer used as a buffer between MoS$_2$ and the substrate causes the MoS$_2$ TC to increase by up to 50%. Length-dependent calculations reveal TC size effects below ~2 $\mu$m and show that the MoS$_2$ TC is size- but not substrate-limited below ~100 nm. We also find that the TBC of MoS$_2$ with c-Al$_2$O$_3$ is over twice that with c-AlN despite a similar MoS$_2$ TC on both, indicating that the TC and TBC could be tuned independently. Finally, we compare the thermal resistance of MoS$_2$ transistors on all substrates to show that MoS$_2$ TBC is the most important parameter for heat removal for long-channel (> 150 nm) devices, while TBC and TC are equally important for short channels. This work provides important insights for electro-thermal applications of 2D materials on various substrates., Comment: 16 Pages, 6 Figures, Supplementary Information

The design of new applications, especially those based on heterogeneous integration, must rely on detailed knowledge of material properties, such as thermal conductivity (TC). To this end, multiple methods have been developed to study TC as a function of vibrational frequency. Here, we compare three spectral TC methods based on velocity decomposition in homogenous molecular dynamics simulations: Green-Kubo modal analysis (GKMA), the spectral heat current (SHC) method, and a method we propose called homogeneous nonequilibrium modal analysis (HNEMA). First, we derive a convenient per-atom virial expression for systems described by general many-body potentials, enabling compact representations of the heat current, each velocity decomposition method, and other related quantities. Next, we evaluate each method by calculating the spectral TC for carbon nanotubes, graphene, and silicon. We show that each method qualitatively agrees except at optical phonon frequencies, where a combination of mismatched eigenvectors and a large density of states produces artificial TC peaks for modal analysis methods. Our calculations also show that the HNEMA and SHC methods converge much faster than the GKMA method, with the SHC method being the most computationally efficient. Finally, we demonstrate that our single-GPU modal analysis implementation in GPUMD (Graphics Processing Units Molecular Dynamics) is over 1000 times faster than the existing LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) implementation on one CPU., Comment: 19 Pages, 8 Figures

Electrical and thermal properties of atomically thin two-dimensional (2D) materials are affected by their environment, e.g. through remote phonon scattering or dielectric screening. However, while it is known that mobility and thermal conductivity (TC) of graphene are reduced on a substrate, these effects are much less explored in 2D semiconductors such as MoS$_2$. Here, we use molecular dynamics to understand TC changes in monolayer (1L) and bilayer (2L) MoS$_2$ by comparing suspended, supported, and encased structures. The TC of monolayer MoS$_2$ is reduced from ~117 Wm$^{-1}$K$^{-1}$ when suspended, to ~31 Wm$^{-1}$K$^{-1}$ when supported by SiO$_2$, at 300 K. Encasing 1L MoS$_2$ in SiO$_2$ further reduces its TC down to ~22 Wm$^{-1}$K$^{-1}$. In contrast, the TC of 2L MoS$_2$ is not as drastically reduced, being >50% higher than 1L both when supported and encased. These effects are due to phonon scattering with remote vibrational modes of the substrate, which are partly screened in 2L MoS$_2$. We also examine the TC of 1L MoS$_2$ across a wide range of temperatures (300 to 700 K) and defect densities (up to 5$\times$10$^{13}$ cm$^{-2}$), finding that the substrate reduces the dependence of TC on these factors. Taken together, these are important findings for all applications which will use 2D semiconductors supported or encased by insulators, instead of freely suspended., Comment: 19 Pages, 7 Figures, Supplementary Information

Understanding the thermal properties of two-dimensional (2D) materials and devices is essential for thermal management of 2D applications. Here we perform molecular dynamics simulations to evaluate both the specific heat of $MoS_{2}$ as well as the thermal boundary conductance (TBC) between one to five layers of $MoS_{2}$ with amorphous $SiO_{2}$ and between single-layer $MoS_{2}$ and crystalline $AlN$. The results of all calculations are compared to existing experimental data. In general, the TBC of such 2D interfaces is low, below ~20 $MWm^{-2}K^{-1}$, due to the weak van der Waals (vdW) coupling and mismatch of phonon density of states (PDOS) between materials. However, the TBC increases with vdW coupling strength, with temperature, and with the number of $MoS_{2}$ layers (which introduce additional phonon modes). These findings suggest that the TBC of 2D materials is tunable by modulating their interface interaction, the number of layers, and finding a PDOS-matched substrate, with important implications for future energy-efficient 2D electronics, photonics, and thermoelectrics., Comment: 16 Pages, 4 figures, Supplemental info

Thermal properties of molybdenum disulfide (MoS$_2$) have recently attracted attention related to fundamentals of heat propagation in strongly anisotropic materials, and in the context of potential applications to optoelectronics and thermoelectrics. Multiple empirical potentials have been developed for classical molecular dynamics (MD) simulations of this material, but it has been unclear which provides the most realistic results. Here, we calculate lattice thermal conductivity of single- and multi-layer pristine MoS$_2$ by employing three different thermal transport MD methods: equilibrium, nonequilibrium, and homogeneous nonequilibrium ones. These methods allow us to verify the consistency of our results and also facilitate comparisons with previous works, where different schemes have been adopted. Our results using variants of the Stillinger-Weber potential are at odds with some previous ones and we analyze the possible origins of the discrepancies in detail. We show that, among the potentials considered here, the reactive empirical bond order (REBO) potential gives the most reasonable predictions of thermal transport properties as compared to experimental data. With the REBO potential, we further find that isotope scattering has only a small effect on thermal conduction in MoS$_2$ and the in-plane thermal conductivity decreases with increasing layer number and saturates beyond about three layers. We identify the REBO potential as a transferable empirical potential for MD simulations of MoS$_2$ which can be used to study thermal transport properties in more complicated situations such as in systems containing defects or engineered nanoscale features. This work establishes a firm foundation for understanding heat transport properties of MoS$_2$ using MD simulations., Comment: 14 pages, 6 figures