next up previous contents
Next: Interatomic interactions Up: No Title Previous: Hydrogen in diamond

The goal of the research

In the present research, the structure and the stability of native defects in diamond will be investigated under different conditions of temperature. These defects are formed by the simulation of a ``cold'' implantation, as usually done by the CIRA scheme. Since the computation time available enables only the simulation of physical phenomena that last few tens of picoseconds, the diffusion of defects in diamond (which is very slow) cannot be investigated for appreciable time. Thus, the fast crystal reconstruction or relaxation is the major topic of the thesis, as well as rapid vacancy-interstitial recombinations that take place in the early stages of the annealing.

In the MSc research of D. Saada [20], an ion-impact was simulated by giving a sudden momentum to a bulk atom in a random direction, at a temperature of 0K (section 6.4 in ref. [20] and ref. [57]). The energy of the atom was eight time (416 eV) larger than the displacement threshold energy to create a vacancy-interstitial pair, calculated to be 52 eV. Consequently, a significant damage volume was created along the irradiation track, with an average size of 1 nm, including sp3-like as well as sp2-like bonds. In that manner, a ``cold'' ion implantation was simulated, leading to a configuration whose annealing will be studied in the present research. One can change the density of defects created by modulating the number of carbon atoms knocked from their lattice site, their initial kinetic energy and the size of the sample. Thus, from samples generated with different densities of defects, the effects of the annealing process in the crystal structure can be investigated.

One has to keep in mind that ion implantation induces volume expansion [22], due to the addition of atoms, to the formation of vacancies and interstitials and to the graphitization of the irradiated volume, the density of diamond being greater than that of graphite (3.51 gr/cm3 and 2.26 gr/cm3 respectively). Thus particular care must be taken of the pressure applied to the sample. In the present research, the volume of the sample and the number of atoms are kept fixed. The defects created during the bombardment are therefore embedded in a diamond matrix that should apply a high pressure to the damaged region. This situation is similar to that occurring at the end of the ion track in experiment, where the kinetic energy of the atoms is down to about few hundreds of eV, and the damage is mainly due to nuclear stopping. This could also occur at Mev implantation energies, where the ion injected enters very deeply the diamond lattice, and creates deeply buried layers. The present simulation relates therefore to the ``end of track'' damage and its annealing. The annealing process is simulated by a molecular dynamic technique, and the interatomic interactions are described by the potential of Tersoff [21], which has been shown to properly describe both diamond and graphite bonding. To study the structure of a particular sample, the mean displacement of each atom is calculated at several intervals of time. To optimize the mean calculation and reduce the error, few samples are generated with the same parameters (temperature, pressure and defects density), and computation of the average of the mean displacement of the atoms are done for the same time intervals, leading to a configuration of mean displacement of the atoms. The potential energy of this configuration is then minimized to obtain the final configuration of the sample that is investigated. This computation procedure is applied to obtain results independent of the thermal fluctuations.

It is also of great importance to understand the mechanism of dopant compensation that was observed in experiment. To this purpose, electronic energy levels induced by specific defects (namely vacancy and <100> split interstitial) has been calculated in the present research, by using a tight binding model described below. With the same model, the behavior of hydrogen in diamond has been investigated. A detailed comprehension, at an atomistic level, of hydrogen in diamond is of basic importance for the reason explained above, and requires understanding the relative energetics of different possible sites for hydrogen. The electronic energy levels induced by hydrogen are also studied, and the motion of hydrogen is inquired as a function of the temperature.

Few models are available to describe the interatomic interactions and the dynamical motion of atoms. The most accurate is the ab initio model based on density functional theory [86]. In this model, the local density approximation (LDA) [87] is very often used for the exchange-correlation interaction, and can also be modified with a gradient correction (GGA) [88]. In a large majority of calculations found in literature, plane waves are used as a basis for the electronic wave functions, and pseudopotentials [89] describe the interaction between the valence electrons and the ionic core. The atoms are considered as classical, and the Newton's equations are solved to obtain the atomic positions and velocities as a function of the time.

The second model, which is widely used, is the tight binding model [90], explained below in more details. Here, only a reduced basis of four orbitals is used, and an empirical functional describes the repulsive part of the interatomic interaction. This model is less accurate than the precedent but much less computationally expensive. With these two models the energy levels induced by defects or impurities in diamond can be calculated. In the present research on hydrogen in diamond, relatively long computation times are needed to study the motion of hydrogen (see below), precluding, thus, the use of the ab initio model. The tight binding model is accurate enough and has been therefore chosen here over ab initio model for the calculations of hydrogen in diamond.

Finally the classical potential (see next section) is applied in the first part of the research concerning the simulation of damage in diamond. In these calculations, a sufficiently large defect volume must be created, embedded in a diamond matrix. This requires therefore very large samples containing 5120 carbon atom to minimize the size effects and to obtain reliable statistic. The ab initio and tight binding models cannot be implemented to this kind of problems due to their expensive resources required.

next up previous contents
Next: Interatomic interactions Up: No Title Previous: Hydrogen in diamond
David Saada