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Amorphous carbon

During the irradiation of diamond by atoms, many bonds are broken, leading to point defects and eventually to clusters of defects. At a high enough irradiation dose, amorphization of the crystal structure may occur and two specific amorphous forms of carbon may appear: the tetrahedrally bonded Diamond-like Amorphous Carbon which will be denoted by ta-C and the sp2 bonded Graphite-like Amorphous Carbon named a-C. These two structures can be distinguished clearly by their macroscopic and microscopic properties. The former material has higher density, is transparent, electrically insulating and much harder than the latter. From the microscopic point of view, the ratio of fourfold, diamond-like bonds to threefold, graphite-like bonds (sp3/sp2) determines the kind of structure obtained.

To study the properties of these amorphous solids, many samples were grown in the laboratory. For example, by evaporation in an electron beam or carbon arc, one can produce an a-C solid with a majority of sp2 bonds [35,36,37,38], while a mainly sp3 bonded ta-C solid can be prepared by ion beam deposition, with ion energies between several ten and several hundred eV [39,40,41,42].

During the slowing down process of energetic atoms in a solid, the kinetic energy of a moving ion is partially transferred to host atoms by elastic collisions. The recoiling atoms, in turn, transfer part of their energy to other atoms, etc. Hence a cascade evolves resulting in the formation of a highly disrupted, very hot, region inside the solid. This phenomenon, which is well known in the case of ion-implantation, is called a "thermal spike". It can be viewed as the short term local melting of the implantation affected region. This melting is followed by a rapid quenching of the liquid phase to form a damaged, amorphous, solid structure. This is the basis of the most widely used computational method to create amorphous materials, including carbon, which consists of rapidly quenching a liquid phase of carbon by ab initio [43,44] or tight-binding [45] molecular dynamics. By investigating the mean square displacement of the atoms during the cooling of the melt and the time required for it to relax, Marks et. al. [44,46] evaluated the life-time of the thermal spike in diamond to be less than 1 picosecond, for energetic impacts below 400 eV. The calculations of Refs. [44,46] have shown that a rapid quench of liquid carbon can produce a tetrahedrally bonded amorphous carbon, similar to the material produced experimentally [39,42] by the deposition of energetic (of the order of a few tens to hundreds of eV) carbon atoms (Ref. [40]).

The Monte Carlo method with empirical potential was used by J. Tersoff [47] and P. C. Kelires [48] to generate amorphous carbon lattices in three different ways. By simulation of homogeneous condensation of vapor [47] and by ultrafast quenching of liquid carbon [47,48], the resulting samples were rather graphitic a-C, with a bond angle distribution peaked around 120o, as expected. The third way was a simulation of molten carbon quenched under a pressure of 1 Mbar [47,48], producing a ta-C lattice, identical to that produced by D. R. McKenzie in the laboratory [39], though the Tersoff sample was poorer in fourfold sp3 bonds and the bond angle distribution showed two overlapping peaks centered at 110o and 120o. This procedure is not directly related to the kinetics of the actual growth process, but is based on the concept of applied pressure that attempts to reproduce the high compressive stress generated by energetic atoms during deposition [39].

The process of diamond-like film growth itself, by deposition of energetic carbon atoms, has been simulated by H. P. Kaukonen et alwith a molecular dynamics technique, applied to the Tersoff potential [16]. The sample created was very similar to that of McKenzie et al. With the same empirical potential, U. Stephan and M. Haase [49] generated amorphous carbon structures via molecular dynamics calculations, at three different densities fixed at the beginning. The mean bond angle and the mean coordination obtained were close to those of graphite.

Another computational technique used to ``create'' amorphous lattices was performed by G. Galli, R. Martin, R. Car and M. Parrinello [50]. They used an ab initio molecular dynamics where the motion of the atomic core is treated classically, while the electron wave functions are represented in terms of a large basis set of plane waves, keeping the energy of the whole system closed to a minimum with respect to the wave functions. In this two ``quantum'' method, the electron-electron interaction (Hartree) and the exchange-correlation term are evaluated by means of the local density approximation [51]. This technique is more accurate than the classical ones presented above, but numerically intensive and unable to describe the dynamic of thousands atoms in a reasonable simulation time. The 54 atoms a-C lattice, formed in ref. [50] by quenching from a liquid, consisted of 85% sp2 bonds at 300 K, with an average bond angle of 117o, starting from a density of 2 gr/cm3.

Finally, a tight binding molecular dynamics method was applied by C. Z. Wang et al [52,53] to generate amorphous carbon samples. Here, the electron wave functions are expanded in terms of a basis set of valence electrons wave functions, rather than plane waves, controlling the attractive part of the potential, while the repulsive one is treated empirically. The samples were obtained by quenching 216 atoms from the liquid phase, at four different densities (that were determined by varying the volume of the sample, the number of atoms being fixed), to investigate the effects of density on the macroscopic structures [52,53], leading to a-Cstructures for low densities and to ta-C structures for high densities.


next up previous contents
Next: Structure of amorphous carbon Up: Structural modifications induced by Previous: Structural modifications induced by
David Saada
2000-06-22