S. A. Kajihara

Theory of native defects, doping and diffusion in diamond and silicon carbide

Abstract The properties of native defects and impurities in diamond and SiC are investigated via large-scale band structure and Car-Parrinello calculations. In diamond, the activation energy for self-diffusion is very high in the intrinsic material (9 eV) but decreases by up to 3 eV in either p- or n-type material. Phosphorus, lithium and sodium are shallow donors, but their solubilities are very low, which makes them unsuitable for incorporation into diamond via in-diffusion. Instead, kinetic trapping during growth or ion implantation must be used. Considering the stability at the dopant site, substitutional phosphorus is expected to diffuse by the vacancy mechanism and to have a high activation energy by analogy to self-diffusion. Both lithium and sodium diffuse through the interstitial channel. Lithium is a relatively fast diffuser while sodium should be stable up to moderately high temperatures. For nitrogen in diamond, the well known (111) distortion is found to be due to the interaction of the fully occupied nitrogen lone pair with the dangling bond of the C(111) atom. The single electron associated with the center resides in an antibonding orbital formed from the dangling hybrid and the nitrogen lone pair. This orbital has most of its amplitude on the carbon atom. In SiC, the lowest energy defect in n-type and intrinsic material is the electrically inactive silicon antisite, while the lowest energy defect in p-type SiC is the doubly positive carbon vacancy. The electrons released by the vacancies compensate acceptor dopants, leading to strong self-compensation effects when doping occurs during crystal growth. In carbon-rich SiC, the dominant defect for all Fermi level positions is the electrically inactive carbon antisite. In boron-doped SiC, B C is preferred for silicon-rich material while, in carbon-rich SiC, B C and B Si have similar formation energies.

Impurity incorporation and doping of diamond

Abstract Electronic applications require the ability to dope diamond p- and n-type. Boron is well known to dope both natural and synthetic diamond p-type. N-type doping, however, has proven exceedingly difficult. In this work, the suitability of several impurities for n-type doping is investigated theoretically. We also examine the well-known nitrogen deep impurity as well as the effect of simultaneous doping with N and B on the thermodynamic equilibrium between diamond and graphite. The calculations were carried out using local density theory, the pseudopotential formalism, and the Car- Parrinello method. The impurities were embedded in a large supercell and atomic relaxations were computed using ab initio forces. The impurities Li, Na and P are shown to be shallow donors, but they have very low solubilities. This makes their incorporation via in-diffusion difficult and leaves ion implantation and possibly incorporation during growth as the only alternatives. Once incorporated, Li is found to be a fast diffuser whereas Na will be stable up to moderate temperatures. The most suitable shallow donor is Na, which occupies an interstitial site. It is particularly appropriate for ion implantation, since no self-implantation step to create vacant sites is necessary.

N-Type Doping and Diffusion of Impurities in Diamond

First-principles calculations were used to study Li, Na, and P as prospective shallow donors in diamond. As expected, P prefers the substitutional site while Li and Na are interstitial donors. All three impurities were found to be shallow. However, their solubilities are very low, which makes them unsuitable for incorporation into diamond via in-diffusion. Instead, kinetic trapping during growth or ion implantation must be used. Interstitial impurities are particularly appropriate for ion implantation, since there is no need to replace host atoms. Considering the stability of the impurity at the dopant site, substitutional P is expected to diffuse by the vacancy mechanism and to have a high activation energy by analogy to self-diffusion. For Li and Na, the activation energies for interstitial channel diffusion are 0.85 and 1.6 eV, respectively. Li is thus a fast diffuser even at room temperature, while Na would remain stable up to moderate temperatures.

Quantum molecular dynamics simulations of fullerenes and graphitic microtubules

We describe the results of extensiveab initio molecular dynamics calculations of the properties of fullerenes and microtubules. Our finite temperature quantum MD simulations for solid C60 are in excellent agreement with NMR, photoemission and neutron scattering data. The C60 isomer containing two pairs of adjacent five-fold rings has a binding energy only 1.6 eV smaller than that of perfect C60, but the transformation between these two structures is hindered by a 5.4 eV barrier. It thus requires high temperatures and long annealing times. High temperatures are also needed for the transformation of the lowest energy C20 isomer, a dodecahedron, to a corannulene structure, which can be thought of as a fragment of C60. The corannulene structure is a natural precursor for the formation of C60. Simulations of reactions show that C2 can insert into C58, perfect C60, and defect C60 fullerenes without an activation barrier, while C3 attaches only to their surfaces. Evaporative fragmentation of carbon clusters during annealing is unlikely, but atom and fragment exchange during collision favor locally most stable structures, such as C60. These results may explain the large increase in the abundance of C60 and C70 when carbon clusters are annealed at high density. We have also carried out calculations for paradigmatic microtubules, both reflection-symmetric and chiral. We find that the optimized geometries of the tubules are close to the ideal ones. It is possible to fabricate tubules with direct band gaps away from the Γ point by exploiting the similarities between the projected band structure of graphite and that of the tubule. The semiconducting tubules can be doped n- and p-type by substitutional N and B, respectively.

QUANTUM MOLECULAR DYNAMICS OF CLUSTERS

Recent quantum molecular dynamics studies of Al and carbon clusters are described. For Al, we focused on the 13- and 55-atom clusters, which can assume perfect icosahedral and cubic structures. However, the distortions from these ideal structures are substantial. For the 55-atom cluster, several inequivalent but nearly energetically degenerate structures are found, due to the short range of the screened interatomic interactions. For solid C60, it is found that the soccerball structure is well-preserved in the solid. The intermolecular interactions are so weak that the individual C60 can rotate at relatively low temperatures. At high temperatures vibrations cause large distortions, but the cage structure is still preserved. The C60 isomer containing two pairs of adjacent five-fold rings has a binding energy only 1.6 eV smaller than that of perfect C60, but the transformation between these two structures is hindered by a 5.5 eV barrier. It thus requires high temperatures and long annealing times. High temperatures are also needed for the transformation of the lowest energy C20 isomer, a dodecahedron, to a corannulene structure, which can be thought of as a fragment of C60. The corannulene structure is a natural precursor for the formation of C60. These results are consistent with the experimental findings that high temperatures are necessary for the formation of substantial quantities of C60. A formulation and the first applications of a new, real space quantum molecular dynamics method, particularly suitable for cluster calculations, are also described.

STRUCTURE, DYNAMICS, AND FORMATION OF CARBON AND ALUMINUM CLUSTERS

The results of recent ab initio molecular dynamics studies of C and Al clusters are presented. The simulations have shown that C60 molecular structure is well preserved in the solid and that the individual C60 molecules start to rotate at relatively low temperatures. Our results are in very good agreement with NMR, photoemission, and neutron scattering data. At high temperatures C60 undergoes large amplitude soccerball-rugbyball oscillations, but the cage structure is still preserved. The C60 isomer containing two pairs of adjacent pentagons has a binding energy only 1.6 eV smaller than that of perfect C60, but high temperatures and long annealing times are required for the transformation between these two structures. Its activation energy is 5.4 eV. We have also studied the various isomers of C20, since it could form the smallest possible fullerene. At T=0, the lowest energy isomer is indeed a dodecohedral structure. However, high temperatures favor the corannulene structure, which is a perfect precursor...