next up previous
Next: Structural Details Up: Amorphous Carbon and Silicon Previous: Introduction

Modelling Amorphous Materials

A major difficulty which is not easily overcome by the ab initio and empirical methods used previously is the non-periodicity displayed in amorphous materials. For this reason it is necessary to use the supercell method again. Also, in order to get a reasonable range of bonding configurations a large number of atoms per supercell are required. Due to the compute intensive nature of ab initio methods coupled with the high energy plane wave cut off required for the carbon pseudopotential, a 64 atom supercell was the largest that could be reasonably dealt with.

The initial starting configuration of atoms in the supercell was that of randomly packed particles constrained by a minimum separation. This is equivalent to a random packing of hard spheres. Both the carbon and silicon simulations were started with the identical random configuration. In order to make a comparison to the complex structures studied in chapters 3 and 4, the density of the amorphous carbon was set to 3.4g/cm tex2html_wrap_inline5362 which, experimentally, is found to form a distorted diamond-like structure. The density chosen for amorphous silicon was 2.6g/cm tex2html_wrap_inline5362 and also the slightly lower density of 2.3g/cm tex2html_wrap_inline5362 which is about the same density as the amorphous silicon made from evaporated silicon samples which, again, is thought to predominantly formed from distorted tetrahedral units. In the ab initio calculations in Chapter 3, it was found that LDA tended to underestimate the lattice parameter of structures by about 2%. The density of the structures are therefore overestimated. For this reason the density chosen above are higher than experiment by this amount.

Earlier calculations performed by modelling the atomic interactions by the empirical Tersoff potential[118, 134] or a tight-binding approach[121, 122] were computationally fast enough to allow quenching from the melt to be performed in order to construct the model amorphous materials. A similar approach has been tried with a full ab initio calculation[117] with a smaller supercell of 54 atoms (at the graphitic-like density of 2g/cm tex2html_wrap_inline5362 ), but this required the rather unrealistic cooling rate of the bulk material of tex2html_wrap_inline7274 K/s.

In the calculations given here, the atoms are simply allowed to relax by a conjugate gradients algorithm under the influence of the Hellmann-Feynman forces - there is no finite temperature molecular dynamics performed for annealing due to the long simulation times required. This will only create a single structure in the large phase space of possible configurations at the respective densities, but it will give a reasonable range of bonding topologies and will highlight the differences in the nature of amorphous silicon and diamond-like amorphous carbon. Since the calculations are fully ab initio there are no a priori bonding characteristics required unlike other large empirical calculations that have been performed (where normally either tex2html_wrap_inline7254 or tex2html_wrap_inline5368 bonding is assumed depending only on the coordination number of the respective atom, and therefore ignores the more unusual bonding topologies such as two-fold sp bonds or three-centre orbitals). This will allow any unusual types of bonding to be found such as the two or five fold coordination[125].

A tex2html_wrap_inline7282 FFT grid was required for the silicon using a plane wave cutoff of 250eV. The calculation for carbon required a tex2html_wrap_inline7284 using a cutoff of 408eV.


next up previous
Next: Structural Details Up: Amorphous Carbon and Silicon Previous: Introduction

Stewart Clark
Thu Oct 31 19:32:00 GMT 1996