Self-Learning Method for Construction of Analytical Interatomic Potentials to Describe Laser-Excited Materials

Large-scale simulations using interatomic potentials provide deep insight into the processes occurring in solids subject to external perturbations. The atomistic description of laser-induced ultrafast nonthermal phenomena, however, constitutes a particularly difficult case and has so far not been possible on experimentally accessible length scales and timescales because of two main reasons: (i) ab initio simulations are restricted to a very small number of atoms and ultrashort times and (ii) simulations relying on electronic temperature- ($T_e$) dependent interatomic potentials do not reach the necessary ab initio accuracy. Here we develop a self-learning method for constructing $T_e$-dependent interatomic potentials which permit ultralarge-scale atomistic simulations of systems suddenly brought to extreme nonthermal states with density-functional theory (DFT) accuracy. The method always finds the global minimum in the parameter space. We derive a highly accurate analytical $T_e$-dependent interatomic potential $\mathrm{\Phi }(T_e)$ for silicon that yields a remarkably good description of laser-excited and -unexcited Si bulk and Si films. Using $\mathrm{\Phi }(T_e)$ we simulate the laser excitation of Si nanoparticles and find strong damping of their breathing modes due to nonthermal melting.

Figure 1

Error $⟨W⟩$ averaged over $T_e=316\mathrm{K}$ and $T_e=18946\mathrm{K}$ as a function of $N_c$ for all polynomial-degree combinations up to the upper degree limits (see text). Each red dot represents an interatomic potential which is, for the corresponding polynomial-degree combination, a global minimum in parameter space. $⟨W⟩$ decreases insignificantly for large values of $N_c$, indicating that the chosen upper degree limits are high enough. The subset $S_{\text{best}}$ is highlighted in light blue (see text), the series ${\mathrm{\Phi }}^{(k)}$ is highlighted in black (see text), and the final choice, $\mathrm{\Phi }(T_e)$, is highlighted in green and marked by an arrow.

Figure 2

Specific heat of the electrons $C_e$ as a function of $T_e$ for diamondlike bulk Si. The upper inset indicates the phonon band structure of diamondlike bulk Si at $T_e=18315\mathrm{K}$. The lower inset shows the Helmholtz free cohesive energy $E$ of the diamondlike (red diamonds), fcc (magenta crosses), bcc (green circles), and Sc (blue squares) structures as a function of the lattice parameter at $T_e=18315\mathrm{K}$. Black dashed curves represent ab initio data obtained using the code chives and colored solid curves represent the values obtained from $\mathrm{\Phi }(T_e)$.

Figure 3

Atomic root-mean-square displacements (RMSDs) during nonthermal melting [17] for bulk Si at $T_e=22104\mathrm{K}$ from MD simulations with 288 atoms performed ab initio (black dashed curve) and using $\mathrm{\Phi }(T_e)$ (red solid line) averaged over 40 runs. The inset shows the RMSD during thermal phonon squeezing [9] at $T_e=15789\mathrm{K}$ averaged over 10 runs with 640 bulk Si atoms.