Size distribution control of metal nanoparticles using femtosecond laser pulse train: a molecular dynamics simulation

Abstract

Microscopic mechanisms and optimization of metal nanoparticle size distribution control using femtosecond laser pulse trains are studied by molecular dynamics simulations combined with the two-temperature model. Various pulse train designs, including subpulse numbers, separations, and energy distributions are compared, which demonstrate that the minimal mean nanoparticle sizes are achieved at the maximal subpulse numbers with uniform energy distributions. Femtosecond laser pulse trains significantly alter the film thermodynamical properties, adjust the film phase change mechanisms, and hence control the nanoparticle size distributions. As subpulse numbers and separations increase, alternation of film thermodynamical properties suppresses phase explosion, favors critical point phase separation, and significantly reduces mean nanoparticle size distributions. Correspondingly, the relative ratio of two phase change mechanisms causes two distinct nanoparticle size control regimes, where phase explosion leads to strong nanoparticle size control, and increasing ratio of critical point phase separation leads to gentle nanoparticles size control.

Appendix: Scaling factor

Initially, the electron and lattice temperatures are both 300 K. The electron temperature of the next time step can be obtained by Eq. (1), which considers electron heating by ultrashort laser. The energy exchange between the electrons and lattices within the time step and finite difference layer is estimated by

$$ \varDelta E_{\mathrm{exchange}} = \varDelta t G (T_{e}- T_{l}) V $$

(6)

where Δt is the time step, and V is the volume of a sample layer. The energy exchange leads to increase of the kinetic energy of the layer. The kinetic energy of the layer is

(7)

where v _xi,t ,v _yi,t , and v _zi,t are the velocities of atom i in the directions x,y, and z, respectively, and $\overline{v_{x,t}},\overline{v_{y,t}}$, and $\overline{v_{z,t}}$ are the average velocities of atom i in the directions x,y, and z, respectively.

The lattice temperature T _l is related to the kinetic energy of the layer by

(8)

where N is the number of atoms within the layer, and k _B is the Boltzmann constant. Hence,

$$ \frac{T_{{l} , t + \varDelta t} - T_{ l , t}}{T_{l, t}}= \frac{E_{k, t + \varDelta t} - E_{k, t}}{E_{k, t}}=\frac{\varDelta E_{\mathrm{exchange}}}{E_{k, t}} $$

(9)

where t is the time. Therefore,

(10)

According to Eq. (8) (the relation between the lattice temperature T _l and velocities of atoms) and Eq. (10), the energy exchange ΔtG(T _e −T _l )V is transferred to lattices by scaling the atom velocities with a factor β (Eq. (11)), which is equivalent to lattice energy increase by Eq. (2).

(11)