Research efforts toward the development of direct-write subwavelength structuring technologies using ultrashort laser pulses are rapidly progressing at present.  With structure sizes in the range of 0.1 - 1 mm, femtosecond laser processing forfeits its universal character. In this case, single laser pulses can produce unexpected structures the physics of formation of which is still not fully understood.

Our current study is aimed on theoretical investigations of the physical mechanisms responsible for the formation of microshell and nanojet structures on the surface of metals [[i],[ii]], shown in Figure1. These structures are generated by a single laser pulses and are very reproducible. The geometrical size of these structures depends on the thickness of metal layer, but they are still observed with a thick metal targets as can be seen in the middle image.

Figure 1: SEM images [1 ,2 ] of an array of microshells and nanojets fabricated in a 60 nm thick gold film with femtosecond laser pulses (left); a nanojet produced in a 2500 nm thick gold layer (middle); and a double-shell structures produced in a 50 nm thick gold layer (right).

In this study, the theoretical investigation of microshell and nanojet generation is performed computationally with a combined two-temperature model – molecular dynamics technique [[iii]]. On atomic level, the model includes a description of the kinetics of nonequilibrium melting and resolidification [[iv],[v]] with Molecular Dynamics (MD) technique. In the meantime, on continuum level, this model ensures for an adequate description of the laser light absorption by the conduction band electrons, fast electron heat conduction, and electron-phonon equilibration with Two Temperature Model (TTM) technique.

The computational setup is shown in Figure 2. MD system represents the sample of Ni film on a silica substrate as a circular slab of 65 nm in diameter and 20 nm in thickness, consisting of 5,997,600 atoms. The description of electronic system, on the other hand, is represented on much greater, up to 1 µm, scale and the lateral wall of the circular slab is freely permeable for heat. Non-reflective boundary conditions are also applied on the lateral side of MD system to absorb the laser-induced pressure recoil.

The preliminary results of calculations reveal a complex mechanism of a nanobump formation. Based on the performed calculations, it can be suggested that this mechanism is mainly due to the interplay of two laser-induced processes. On one hand, we have the establishment of a strong temperature gradient in the vicinity of the laser spot and, as a result, the recoil of compressive/tensile pressure waves in both radial and vertical directions. The nanobump solidification, on the other hand, is mostly due to fast electron heat conduction in the multidimensional space that in turn results in an extremely fast cooling of the melted region.

Currently, we are bearing further calculations at New National Facility at Irish Centre of High-End Computing National, and more detailed discussions on this study are being prepared for the report in [[vi]].

Figure 2. Computational cell set-up used in MD calculations is represented by a snapshot taken at t = 60 ps from the simulation of 1 ps laser pulse interaction with 20 nm Ni film on a silica substrate at the absorbed fluence of 1.53 J/cm². The pulse diameter is 10 nm. Different types of boundaries are indicated schematically. The atoms are colored according to their local order parameter [Error! Bookmark not defined.]. Blue particles belong to the liquid and red particles have a crystalline surrounding. “Liquid strips” reveal the leftover of stacking faults that are left behind by partial dislocations and, having a higher energy, provide preferable sites for the beginning of melting.

Although the problem on ablation of silicon has been intensively studied for the last several decades, due to its vast application in industry and increasingly growing requirements on controllability of the ablative experiments, there are still many unsolved questions. The answers to these questions can not only reinforce the industrial applications, but also advance the understanding of fundamental physics of laser ablation of silicon.

The origin of the current study arises from a industrially focussed project where machining of silicon with nanosecond pulses was used for production of a sequence of slots and trenches in silicon wafer substrates[[i]]. Typically, the ejected matter from laser ablation forms a highly ionized plasma, which expands rapidly away from the surface and leads to the generation of a compression or shock wave.  As this shock wave propagates, at supersonic speeds, the pressure and temperature behind the wave decreases [[ii]].  The interaction of this rapidly changing thermodynamic state of the ambient, with the suspended ablated matter, can lead to the formation of vaporized matter droplets.  In features with a high aspect ratio, where the ratio of the depth of the feature to its width is greater than 1, re-deposition of laser generated debris on the side-walls of the laser drilled holes, reduces the machining rate where multiple passes of the laser is used.  By changing the laser process and environment in which the ablated material is transported can lead to reduced re-deposition  and this has been identified by NCLA as being of critical importance in increasing the throughput of laser ablative processes.

While experimental research is being developed further, the theoretical investigation, on the other hand, is mainly focused on computational study. Since the experiments on laser ablation of silicon encompass relatively large spatial and temporal scale, to describe this problem computationally it was decided use a composite approach. The main idea of this approach is to treat laser-silicon interaction on atomic level with Molecular Dynamics (MD) method for the first hundreds of picoseconds up to the formation of the ejected matter plume. Then, further expansion of this plume is currently thought to be described with Hydrodynamics Model (HD). Note that the output from MD calculations, such as cluster size and their velocity distribution will be used as an input into HD description.

The first step of the computational description of laser ablation of silicon is the creation of an appropriate atomistic model. Certainly, the classical MD approach under conditions realized during short (several picoseconds) pulse laser-silicon interaction fails to describe the laser energy absorption resulting in electron-hole free carriers generation, fast electron-hole conduction mechanism, and phonon emmitance due to relaxation of the electron-hole pairs. Therefore, an atomistic-continuum description, similar to the one for metals reported in [[iii]] is needed. In this model, the laser energy absorption, the fast electron-hole thermal conduction, and the electron-hole relaxation process will be described on continuum level based on the theory presented in [[iv],[v]]. The process of non equilibrium phase transformation, the evolution of laser-induced processes, and finally the formation of ablative plume, on the other hand, will be treated on atomic level with parameterization of the interatomic potential given by Stillinger and Webber in [[vi]]. However, if change of the potential versus electron-hole pair excitation is accounted for in a rather simplified manner in [[vii]] in the present model the change of bonding will be fitted according to the first principals calculation. Such fitting method was successfully applied in [[viii]] while creating a highly optimized potential for Si.

Furthermore, the expansion of the laser-plasma plume will be described on continuum level. However, on ordinary finite differences scheme might not work here properly as the plasma plume expansion as assisted with strong shocks registered in the experiments [2 ] and Essentially Non Oscillating (ENO) schemes [[ix]] should be used to avoid instabilities during calculations. Finally, it has been claimed repeatedly that gas dynamics equations are not suitable to describe laser plasma expansion. Therefore, the results of our calculations performed on continuum level will be compared with those obtained in more sophisticated models [[x]].

Currently, the atomistic part of the model is being implemented. The fitting of the interatomic potential has been planned to obtain in collaboration with Computational Group at Lawrence Livermore National Laboratory. The description of laser plasma plume expansion is currently thought to give in 1D case but with ENO scheme implemented.