Quantifying thermal and nonthermal contributions to disorder in ultrashort laser irradiated germanium: Nonadiabatic quantum molecular dynamics study

We elucidate the origin of the ultrashort laser-driven lattice disorder in germanium through nonadiabatic quantum molecular dynamics simulations. The total disorder is dissected into disorder components arising from electron-phonon coupling, covalent bond softening, and ionic thermal activation caused by potential energy surface modification, using which thermal and nonthermal effects are quantified. We find that, although the bond softening effect initially dominates irrespective of the excitation density, the eventual ultrashort laser-driven phase transition involves both the thermal and nonthermal elements in it, with the level of their effects regulated by the electronic excitation density.

Figure 1

Schematic representation of fundamental mechanisms involved in ultrashort laser-driven phase transformation of covalently bonded materials. (a) The phase transformation resulting from ionic thermal activation caused by transfer of excited electronic energy to the lattice via electron-phonon coupling. This process is denoted as “th_ep.” (b) The phase transformation resulting from weakening of interatomic bonding caused by the PES shape modification. This process is denoted as "bs." (c) The phase transformation resulting from the effects of both the weakened interatomic bonding caused by PES shape modification (bs) and the PES minimum position shift that thermally activates the lattice (th_pes). This process includes overall effects caused by the PES change denoted as "pes." (d) The phase transformation occurring under repulsive PES in high excitation densities. This process includes pes, i.e., both bs and th_pes. The curved solid and dashed lines are the ground- and excited-state PESs, respectively. The gray solid and dashed arrows represent barrier crossing and ionic acceleration, respectively. The dotted arrow indicates the amount of the PES minimum position shift in the reaction coordinate.

Figure 2

Results of the excited-state NAQMD simulation in the microcanonical ensemble (NVE_NA). (a) The excitation density-dependent time evolution of the disorder parameter. The time evolution of (b) the MSD, (c) the ionic temperature, and (d) the band-gap energy. (e) The RDFs are denoted for the times the lattice disorder reaches 50% (top left panel), 70% (top right panel), and 100% (bottom left panel) of the maximum disorder and for the time long enough after the maximum disorder is achieved (bottom right panel), and (f) the corresponding lattice structures are shown for $n=8.1\%$. The atoms are colored according to the disorder parameter.

Figure 3

Comparison of the NVE_NA simulation and experimental results. (a) The fluence dependence of melting time of Ge, where the conversion of the excitation density to the absorbed fluence was made using the nonlinear model in Eq. (21). Our simulation results compare well with those of the time-resolved resonant x-ray scattering experiment [40] and Sokolowski et al. [23]. (b) Subpicosecond MSD data of Si reported by Zjilstra et al. [45]. (c) Subpicosecond MSD data of Ge obtained with NVE_NA simulations for comparison with (b).

Figure 4

Results of the various excited-state QMD simulations. A comparison of the disorder parameter time evolution among [(a)–(d)] NVE_NA, NVE_AD, and NVT_NA, and [(e)–(h)] the NVT_NA results. The excitation density-dependent time evolution of (e) MSD and (f) band-gap energy. (g) The lattice structures and (h) the RDFs are shown for the times during which the lattice disorder reaches 50% (top left panel), 70% (top right panel), and 100% (bottom left panel) of the maximum disorder achieved by NVT_NA and for the time long enough after the maximum disorder by NVT_NA was achieved (bottom right panel).

Figure 5

Time-dependent contribution of various disorder components to the total disorder. (a) Nonthermal disorder component originating from the covalent bond softening. Thermal disorder component associated with (b) the PES change and (c) electron-phonon coupling. (d) Time evolution of the nonthermal contribution to the total disorder. (e) Bar graph of the nonthermal contribution to the total disorder at the melting time, with the number on top of each bar indicating the melting time.