Modeling Mechanical and Structural Properties of Amorphous Silicon Carbide (aSiC) using MAPS and LAMMPS Plugin

Keywords

Molecular dynamic simulation / Reactive force field / amorphous Silicon carbide / Mechanical properties / Structural properties

Silicon carbide (SiC) is a very promising semiconductor material for high-temperature, high-frequency and high-power optoelectronic devices. Among SiC polytypes, its amorphous form (aSiC) appears to be of special interest as it enables more flexibility. By changing the degree of amorphization it is possible to adapt its structural and mechanical properties to match the technological needs. The development of computational experiments to accurately model and understand atomistic structure of aSiC has an important impact as it will allow scientists to predict materials properties and therefore design materials for specific applications.

In this case study a Tersoff [1] reactive potential within MAPS and the LAMMPS [2,3] plugin was used to generate aSiC material from 3C-SiC crystal structure. Next, aSiC mechanical properties were evaluated and compared with those of Si and C diamond crystals. Several analysis tools within MAPS platform were also leveraged to characterize the aSiC structural properties.

Build

3C-SiC poly-type was build entering the following experimental structural parameters within MAPS Crystal Builder:

  • Space group = F-43m (Space group number = 216)
  • Lattice parameter a = 4.3685 Å
  • Si (0.0; 0.0; 0.0)
  • C (0.25; 0.25; 0.25)

A 5x5x5 supercell was then created in order to obtain a cubic box with a lattice parameter of 21.84 Å.

For mechanical properties calculations, a 2x2x2 supercell of aSiC was created to form a 49x49x49 cubic cell. The carbon diamond and silicon crystal structures primitive cells were loaded from MAPS crystal structure library. Supercells of these elements were created in order to obtain systems of similar size as aSiC. The final Si and C diamond crystal systems formed two 50x50x50 cubic cells.

Simulate

Generation of aSiC

Tersoff potential from Erhart and Albe [4] containing parameters for silicon and carbon was used all along the study. MAPS and LAMMPS plugin was used for all the simulations.

The simulation protocol to create aSiC was similar to that exposed by Xue et al [5]. The 3C-SiC crystal structure was initially simulated at very high temperature (6000 K) for 200 ps. This initial step was used to randomize the initial conformation of the silicon carbide. The system was then gradually quenched to 300 K during 6 ns which corresponds to a cooling rate of 5.0 1012 K.s-1. Finally the aSiC material was equilibrated at 300 K for 500 ps. The 2x2x2 supercell of the final conformation of the material which is represented in Figure 1-a.

Similarly Si and C diamond crystalline systems were rapidly equilibrated at 300 K over 200 ps. The final equilibrated structures were used as a starting point for the mechanical properties calculations.

aSiC Mechanical Properties Simulation

The initial system compressed along the z axis. During the simulation, the c lattice parameter decreased up to 75% of its initial value (from 49.0 Å to 36.7 Å) while the two other were left free to equilibrate. The simulation was run for 5 ns. The initial and final structures of this simulation are represented in Figure 1-a and b. A similar simulation protocol was used to compute mechanical properties of Si and C diamond crystalline systems. For aSiC system, in order to obtain a higher accuracy another simulation was performed where the c lattice parameter was decreased up to 95% of its initial over a 10 ns simulation. The Young’s moduli were computed on the initial linear part of the stress/strain curve using MAPS mechanical properties analysis.

Analyse

Structural Properties

The chemical disorder parameter (X) was computed for the final conformation of the equilibration run of aSiC at 300 K. The chemical disorder parameter Xc (resp XSi) is defined for C (resp Si) atoms as NC-C/NC-Si (resp NSi-Si/NC-Si) where NC-C is the number of C-C bonds (resp NSi-Si the number of Si-Si bonds) and NC-Si the number of C-Si bonds. This parameter is a marker of the system disorder as it is ranging from 0 for a completely ordered up to 1 for a completely disordered system. The two disorder parameters were found to be similar around XC = XSi = 0.48 which is very good agreement with previous results from Xue et al [5].

Figure 1: Initial (top) and final (down) conformation of aSiC after subjecting it to a mechanical compression.

In order to further characterize aSiC material, pair distribution functions were computed for C-C, Si-Si and C-Si atom pairs. They are represented in Figure 2.

Figure 2: Pair distribution function for C-C, C-Si and Si-Si atom pairs.

The pair distribution function show a maximum around 1.47 Å for C-C pair, 1.85 Å for C-Si pair and 2.35 Å for Si-Si pair. These data are in the same range of order (less than 0.1 Å difference) as those obtained in previous study [5].

Mechanical Properties

The mechanical properties of the different systems was computed using MAPS-mechanical analysis tool. The Young’s moduli of Si, C diamond and aSiC are listed in the table below.

Materials Young’s Modulus (GPa)
Computed Experimental
Si 125 130 – 185
C diamond 1072 1050 – 1210
aSiC 325 XX

Table 1: Silicon, Carbon diamond and amorphous silicon carbide computed and experimental Young’s moduli.

The molecular dynamic simulations using Tersoff potentials allowed to reproduce accurately experimental values of the Young’s moduli of silicon and carbon diamond crystals. The Young’s modulus of aSiC materials was found to be lower than that of 3C-SiC system and in very good agreement with previous results [6-8].

Conclusion

MAPS Platform was used to study structural and mechanical properties of amorphous silicon carbide materials. MAPS building capabilities were used to generate the initial crystalline structure of the silicon carbide. MAPS-LAMMPS plugin was then used to simulate the annealing of 3C-SiC and the formation of the amorphous silicon carbide. This plugin was also leveraged to simulate the mechanical properties of aSiC and of crystalline Si and C diamond. The structural and mechanical properties of the obtained systems were analyzed within MAPS Platform and were found to be in good agreement with previous experimental or theoretical data.

References

  1. Tersoff, Phys. Rev. B, 1988, 37, 6991.
  2. Plimpton S., J. Comp. Phys., 1995, 117, 1-19.
  3. www.scienomics.com/classical_mesoscale/
  4. Erhart, Albe, Phys. Rev. B, 2005, 71, 035211.
  5. Xue K., Niu L.-S., Shi H.-J., J. App. Phys., 2008, 104, 053518.
  6. Ivashchenko V.I., Turchi P.E.A., Shevchenko V.I., Phys. Rev. B, 2007, 75 (8) 085209.
  7. Rino J.P. et al Phys. Rev. B, 2004, 70 (4), 045207.
  8. Xue K., Niu L.-S., J. App. Phys., 2009, 106 (6), 083505.