Embedded Files
In 2013 I earned a Ph.D. in Mechanical and Aerospace Engineering from the University of California Irvine under the supervision of Professor Gamero-Castaño. My doctoral dissertation focused on the atomistic modeling of hyervelocity impacts of electrosprayed nanodroplets on single-crystal silicon. I used classical molecular dynamics (MD) simulations to model the changes induced in the crystalline structure of silicon slabs that receive the impact of droplets with diameters of a few nanometers directed at several kilometers per second. If the projectile's velocity is higher than 3 km/s the simulations reproduce the amorphization of a thin layer and the sputtering of a number of atoms. Amorphization and sputtering have been previously observed in experiments where single-crystal silicon wafers were exposed to beamlets of electrosprayed nanodroplets [1] [2].
To model a nanodroplet impact I use the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), a classical molecular package written in C++. Molecular Dynamics is a technique where the equations of motion of atoms are integrated. The interaction forces between these particles are derived from a interatomic potential. Molecular Dynamics is ideal to predict the thermodynamic properties of gas, liquid, or solid systems. Temperature, pressure, and density are calculated as ensemble averages of the momenta, positions, and forces. In addition, the radial distribution function g(r) is calculated to obtain identify the range order. I perform the thermodynamic and structural analysis of data using algorithms written C/C++, Fortran, Matlab, and Python which are executed in serial or in parallel (MPI or OpenMP).
Amorphization of Silicon by Nanodroplet Impact
Amorphization of Silicon by Nanodroplet Impact
The mechanism
The first part of my PhD research has been conducted to identify the mechanism behind the amorphization of silicon by nanodroplet impacts. A single MD simulation has been modeled to reproduce the impact of a droplet of a diameter of 10 nm directed at 6.4 km/s against a crystalline silicon slab. The (100) Si target has a cross section of 48.88 x 48.88 nm2 across the x-z plane with a depth of 30.56 nm along y axis. The projectile is composed of 1224 spheres arranged in a hexagonal-closed package. Each sphere has a radius of 0.422 nm, a mass of 391.31 amu, and represents a molecule of the ionic liquid 1-ethyl-3-methylimidazolium bis (trifluoro-methylsulfonyl) imide [emim][Im], C8H11F6N3O4S2. The interactions between silicon atoms are described by the Stillinger-Weber [3] semiempirical potential. The interactions between droplet molecules and between droplet molecules and silicon atoms are described by the Ziegler-Biersack-Littmark potential [4]. A thermal bath at 293 K is applied to all lateral boundaries of the solid expect to the face (010). This thermostat avoids the reflection of the shock wave generated upon the initial contact between the droplet and the solid surface. The slab is relaxed for 20 ps before the velocity of 6.4 km/s is imposed on the droplet.
Our strategy consists on tracking the thermodynamic state of several crystalline samples that will be converted into amorphous. The sample analyzed here is a system of particles located at 1.5 nm below the crater surface and aligned along the y-axis at the end of the 70-ps simulation. This ensemble encloses around 280 atoms. The existence of local thermal equilibrium is confirmed since the vibrational kinetic energies inside this system follow a Maxwell-Boltzmann distribution. The figures attached show the evolution of the temperature T, melting temperature Tm(P) (which for silicon decreases with increasing hydrostatic pressure), hydrostatic pressure P, and average coordination number CN for the entire simulation. This control volume starts to notice the effects of the shock compression at 1.2 ps of simulation. After this point the pressure and temperature start to rise surpassing values of 15 GPa and 1900 K, respectively. At such conditions this control volume confines atoms in liquid state since the melting point has been reached. The average coordination number ranges between 5 and 6 which proves the formation of this metallic phase of silicon. At 10 ps the temperature of the molten layer starts to decay as its internal energy is being transferred to its neighboring cooler areas. The thermal bath is responsible for the dissipation of the vibrational kinetic energy in the entire slab. The thermal decay of the control volume is well fitted using an exponential function. At 30 ps this liquid phase is solidified at a temperature of around 900 K with a cooling rate of 0.9 x 1011 K/s which shows that recrystallization is avoided. As a consequence, the final amorphous state is yielded in the areas surrounding the crater surface with temperatures slightly above the thermal bath. The animation below shows the evolution of the temperature field in a crystalline silicon slab upon the impact of an emim-t2fN droplet. This animation shows the trajectories of particles between the planes z = -0.5 nm and z = 0.5 nm. Within the first 3 ps the projectile loads more than the 90 % of its kinetic energy (101.3 keV) on the solid. As a result, a thin layer of liquid Silicon is formed with a thickness of nearly half of the droplet's diameter. Green color in the legend indicates that the melting point (1685 K at Patm) is surpassed within the first 5 ps of simulation. After approximately 20 ps, this liquid layer is then rapidly quenched yielding the final amorphous structure.
Direct link:
http://www.youtube.com/watch?v=upP2m4noIoM
More animations of hypervelocity impacts of electrosprayed nanodroplets can be visualized here
This work has been published in the Journal of Applied Physics [5].
The influence of the droplet's velocity and diameter
The second part of this section concentrates on the measurement of the thickness and volume of the amorphous silicon layer as a function of the projectile's diameter and velocity. MD simulations are conducted using droplets with diameters of 5, 10, 20, and 30 nm and the velocities from 1 to 6 km/s. Experimental data is also obtained to support are MD predictions.
To create a phase field a fine square grid with a resolution of 0.86 nm is defined in the silicon substrate, each cubical element typically enclosing 32 atoms. The radial distribution of the element is defined as the average of the radial distributions centered in each atom inside the cubical element. The total volume of the amorphous phase is obtained by adding the volumes of amorphous elements, and the thickness of the amorphous layer surrounding the crater is calculated by averaging the local thickness of the amorphous phase left by the impact.
The figure on the right-hand side shows the dependence of the thickness and volume of the amorphous layer on the projectile’s velocity and diameter. Thickness and volume are normalized with the diameter of the projectile and its volume, while a second horizontal axis displays the projectile’s molecular kinetic energy, Em = 0.5mm(vp)2 (mm is the molecular mass of Emi-Im). The thickness of the amorphous layer is a small fraction of the projectile’s diameter for velocities under 3 km/s, it increases to a fraction between 0.29 and 0.34 at 4 km/s, and remains approximately constant at higher velocities. The normalized volume of the amorphous phase is also negligible for impact velocities below 3 km/s, and increases almost linearly with the molecular energy at velocities higher than 3 km/s. The simulations thus indicate that although low velocity impacts randomize the atomic positions in the initial atomic layers of the target, a threshold velocity of approximately 3 km/s is needed to extend the amorphization to atoms that are not in direct contact with the projectile. Furthermore, when the amorphization is significant, the thickness and volume of the amorphous phase scale linearly with the diameter and volume of the projectile. In addition to the simulation results, the panel (a) also displays the thickness of the amorphous layers produced by the beamlet of electrosprayed nanodroplets (average diameter of 26 nm). The experimental curve matches well the MD simulations: it exhibits a threshold velocity between 3 km/s and 3.45 km/s for triggering the appearance of significant amorphization; and shows how the thickness of the amorphous layer increases with impact velocity before settling to a constant value. This constant value is twice as large as what is reproduced by the simulations, a disparity that may be related to the different impact conditions in the experiments: there is a natural variability in the diameter of the electrosprayed droplets; and the surface of the target in the experiments is modified by multiple impacts, with some four droplets typically hitting an area equal to the droplet’s cross section.
This work has been published in the Journal of Applied Physics [6].
References
[1] M. Gamero-Castaño, A. Torrents, L. Valdevit, and J.-G. Zheng, Phys. Rev. Lett. 105, 145701 (2010).
[2] M. Gamero-Castaño and M. Mahadevan, J. Appl. Phys. 106, 054305 (2009).
[3] F. H. Stillinger and T. A. Weber, Phys. Rev. B 31, 5262 (1985).
[4] J. F. Ziegler, J. P. Biersack, and U. Littmark, The Stopping and Range of Ions in Solids (Pergamon, New York, 1985).
[5] F. Saiz and M. Gamero-Castaño. Amorphization of silicon induced by nanodroplet impact: A molecular dynamics study. J. Appl. Phys. 112, 054302 (2012)
[6] F. Saiz, R. Borrajo-Pelaez, and M. Gamero-Castaño, The influence of the projectile's velocity and diameter on the amorphization of silicon by electrosprayed nanodroplets, J. Apply. Phys., 114, 034304 (2013).
Google Sites
Report abuse