Vacancy In Diamond Research Articles

Simulations of large multi-atom vacancies in diamond

We generated and evaluated energetically a very large number of vacancy V n clusters representing nanosize voids or cavities in diamond for n up to 14 using a new generational algorithm. We evaluated the relaxed geometries and energies of these contiguous vacancy clusters using a tight binding density functional theory (TBDFT). For up to n = 7 we generated all possible structures and evaluated their relaxed geometries. For n = 8 through n = 14 we selectively generated a large number of vacancy clusters and obtained highly stable structures and their energies. By analyzing the energy levels and the corresponding orbitals, we identified the surface states of the voids and their symmetries. Significant differences with respect to vacancy clusters in silicon were found. The results were interpreted by finding that certain structures become relatively more stable due to a process we call local graphitization, which can be identified by a tetrahedron of graphitization (TOG), and it can be characterized by elongation of certain carbon–carbon contacts and by the concomitant appearance of new states in the gap. The beginning of graphitization, as indicated by geometrical and energetic descriptors in small stable vacancy clusters, may have a role in the formation mechanisms of various sp 2 hybridized structures in carbons.

Local modes of vibration at the vacancy and vacancy models of defects in diamond

Abstract The carbon vacancy in diamond and many similar defects have strong electron correlation giving rise to molecular multiplet structures. Sophisticated electron–phonon interaction subsequently occurs at these defects giving rise to optical and other effects associated with a dynamic Jahn Teller interaction. Using ab-initio calculations the full vibrational spectrum of both the neutral and negatively charged vacancy are obtained. Calculated local modes are consistent with earlier interpretations of vacancy properties as based upon Group Theory. Modification of the vibration spectra by a heavy metal – here nickel – is also examined and implications for defect vacancy models briefly discussed.

FullyAb InitioFinite-Size Corrections for Charged-Defect Supercell Calculations

In ab initio theory, defects are routinely modeled by supercells with periodic boundary conditions. Unfortunately, the supercell approximation introduces artificial interactions between charged defects. Despite numerous attempts, a general scheme to correct for these is not yet available. We propose a new and computationally efficient method that overcomes limitations of previous schemes and is based on a rigorous analysis of electrostatics in dielectric media. Its reliability and rapid convergence with respect to cell size is demonstrated for charged vacancies in diamond and GaAs.

Explanation of atomic displacement around lattice vacancies in diamond based on electron delocalization

The relationship between unpaired electron delocalization and nearest-neighbor atomic relaxations in the vacancies of diamond has been determined in order to understand the microscopic reason behind the neighboring atomic relaxation. The Density Functional Theory (DFT) cluster method is applied to calculate the single-electron wavefunction of the vacancy in different charge states. Depending on the charge and spin state of the vacancies, at outward relaxations, 84-90% of the unpaired electron densities are localized on the first neighboring atoms. The calculated spin localizations on the first neighboring atoms in the ground state of the negatively charged vacancy and in the spin quintet excited state of the neutral vacancy are in good agreement with Electron Paramagnetic Resonance (EPR) measurements. The calculated spin localization of the positively charged vacancy contrasts with the tentative assignment of the NIRIM-3 EPR signal to this center in (p-type) semiconductor diamond. The sign of the lattice relaxation in the diamond vacancy is explained based on the effect of electron delocalization on nearest-neighbor ion-ion screening, and also its effect on the bond length of neighboring atoms.

Theoretical study of migration processes in bulk diamond

A large number of complex defects are seen in natural and synthetic diamonds, but it is not known whether they form during growth or as a result of later processes. An understanding of diffusion profiles of the dopant impurities is crucial for design of electronic devices. We present here theoretical work on migration processes for several complexes including N, H and vacancies in diamond, to find out how they form. First-principles density functional calculations have been performed to study structural properties and the activation energies for migration of these defects. Migration paths were derived by constructing a set of several intermediate structures between two energy minima by linear interpolation. The effect of temperature on calculated barriers is described by including vibrational energy and entropy. It was found that the energy barrier for migration of interstitial hydrogen between two bond-centred positions is 2.8 eV. Also, hydrogen is readily trapped by both vacancies and by the N–V complex. Energies liberated in these reactions are 5.5 eV and 5.8 eV respectively.

Electron paramagnetic resonance studies of the neutral nitrogen vacancy in diamond

Despite the numerous experimental and theoretical studies on the negatively charged nitrogen vacancy center $({\mathrm{NV}}^{\ensuremath{-}})$ in diamond and the predictions that the neutral nitrogen vacancy center $({\mathrm{NV}}^{0})$ should have an $S=\frac{1}{2}$ ground state, ${\mathrm{NV}}^{0}$ has not previously been detected by electron paramagnetic resonance (EPR). We report new EPR data on a trigonal nitrogen-containing defect in diamond with an $S=\frac{3}{2}$ excited state populated via optical excitation. Analysis of the spin Hamiltonian parameters and the wavelength dependence of the optical excitation leads to assignment of this $S=\frac{3}{2}$ state to the $^{4}A_{2}$ excited state of ${\mathrm{NV}}^{0}$. This identification, together with an examination of the electronic structure of the NV centers in diamond, provides a plausible explanation for the lack of observation (to date) of an EPR signal from the ${\mathrm{NV}}^{0}$ ground state.

Ab initiostudy of lithium and sodium in diamond

Interstitial lithium and sodium have been suggested as alternatives to phosphorus to achieve shallow $n$-type doping of diamond. Experimental results have, however, been contradictory. We report ab initio density functional theory modeling of lithium and sodium in diamond and show that although interstitial Li and Na are likely to behave as shallow donors, interstitial Li will readily diffuse with a low activation energy and that it is energetically favorable for both species to be trapped at existing vacancies in diamond. The resulting substitutional centers are themselves not only passivated but also induce deep levels in the band gap of diamond, compensating the remaining donors. This explains the high resistivity observed in lithium and sodium doped diamond. This demonstrates that samples should not be exposed to elevated temperatures in order to prevent Li diffusion, while concentrations of vacancies and other defects should be minimized to restrict the formation of compensating substitutional Li acceptors, if $n$-type doping of diamond is to be achieved with Li. For sodium, we show that it is energetically favorable for Na to be incorporated in diamond as a substitutional acceptor rather than as an interstitial donor. This is consistent with experimental observations of Na diffusing as a negative ion under electric bias in diamond. It is therefore unlikely that diamond will be successfully $n$-type doped with Na.

Li and Na in diamond: A comparison of DFT models

Interstitial Li and Na have been suggested as alternatives for achieving shallow n-type doping of diamond. Experimental results have however been contradictory. We report ab initio density functional theory modeling of Li and Na in diamond and compare results using periodic pseudopotential plane wave, and all-electron APW + lo methods together with finite clusters using Gaussian basis sets. We show that although interstitial Li and Na are likely to behave as shallow donors, interstitial Li readily diffuses and it is energetically favorable for interstitial Li and Na to be trapped at existing vacancies in diamond. The resulting substitutional centers are not only passivated but also compensate other interstitial Li and Na donors. Na is shown to be incorporated in diamond as a substitutional acceptor, consistent with experimental observations.

Generalized Hubbard model for many‐electron states of the diamond vacancies: A non‐CI approach

AbstractMany‐electron calculations based on a generalized Hubbard Hamiltonian for electronic states of the diamond vacancies are reported. The model does not use the configuration interaction (CI) method and proper tetrahedral symmetry and spin properties of the defect are included in the Hamiltonian. Atomic orbital bases are introduced for the Hamiltonian calculation. Excited states of both neutral and negatively charged vacancies in diamond are calculated. The calculated values for the experimentally observed first dipole transition energies of the vacancies in diamond, GR1 and ND1 bands, are in good agreement with experiment. To obtain these results, we used a semi‐empirical Hamiltonian parameter. The position of the low‐lying 3T 1 state was found to be 260 meV above the ground state, which is consistent with experimental expectations. In addition to the energy spectrum, the model gives all eigenfunctions of the vacancies, which have not been calculated before. This model has high potential for further applications in point defects of diamond and other semiconductors. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Simulations of Multi-atom Vacancies in Diamond

AbstractMulti-atom vacancies and pores in diamond-structured carbon phases play an important role in carbon sieves and carbon based storage. The size and shape of pores have a profound effect on the energetics of adsorptive storage. We are modeling large numbers of vacancy configurations with a combination of ab initio density functional theory (DFT), tight binding DFT and simpler methods based on Brenner-potentials and modified Brenner potentials. The more accurate calculations serve as the basis of the parametrization which is then used in lattice Monte Carlo simulations on more complex vacancies. The results will be put in the context of SiC-derived porous carbon materials with the purpose to explore basic questions of energetics in porous carbons.

Improved long-range reactive bond-order potential for carbon. I. Construction

We present LCBOPII, an improvement of the long-range carbon bond-order potential (LCBOP) by Los and Fasolino [Phys. Rev. B 68, 024107 (2003)]. LCBOPII contains a coordination dependent medium range term for bond distances between 1.7 and $4\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$, meant to reproduce the dissociation energy curves for single, double, and triple bonds and improve the reactive properties as well as the description of the liquid and of low coordinated phases. Other features of LCBOPII are a coordination dependent angular correlation, a correction for antibonding states, and a conjugation dependent torsional interaction based on ab initio calculations of the torsional barriers for a set of molecular configurations. We present results for the geometry and energetics of the graphite-to-diamond transformation and of the vacancy in diamond and graphite as well as the prediction of the energy barrier of the 5-77-5 defect in graphite and graphene for which ab initio results are available only for unsuitably small samples. In the accompanying paper (Ghiringhelli et al., Phys. Rev. B 72, 214103 (2005) we use LCBOPII to evaluate several properties, including the equation of state, of liquid carbon.

Density-functional calculations of defect formation energies using the supercell method: Brillouin-zone sampling

Using the DFT supercell method, the BZ sampling error in the formation energy and atomic structure are investigated for vacancy and interstitial defects in diamond and silicon. We find that the $\mathbf{k}$-point sampling errors in the total energy vary considerably depending on the charge state and defect type without systematic cancellation, even for the same size of supercell. The error in the total energy increases with decreasing electronic perturbation of the defect system relative to the perfect bulk; this effect originates in the localization of electronic states due to the symmetry reduction induced by the presence of a defect. The error in the total energy is directly transferred to the formation energy, and consequently changes the thermodynamic stability of charge states and shifts the ionization levels. In addition, in force calculations and atomic structure determinations, the $\mathbf{k}$-point sampling error is observed to increase as the charge becomes more negative. The $\ensuremath{\Gamma}$-point sampling results in erroneously large relaxation of the four atoms surrounding a vacancy in diamond. We suggest that stronger repulsions between electrons occupying degenerate defect levels at $\ensuremath{\Gamma}$-point compared to those occupying split energy levels at other $\mathbf{k}$ points induces larger atomic movements.

Lattice relaxation in many-electron states of the diamond vacancy

Symmetric lattice relaxation around a vacancy in diamond and its effect on many electron states of the defect have been investigated. A molecular approach is used to evaluate accurately electron-electron $(e\text{\ensuremath{-}}e)$ interaction via a semiempirical formalism which is based on a generalized Hubbard Hamiltonian. Coupling of the defect molecule to surrounding bulk is also considered using an improved Stillinger-Weber potential for diamond. Strong dependence of the electronic energy levels to the relaxation size of the nearest neighbor (NN) atoms indicates that in order to obtain quantitative results the effect of lattice relaxation should be considered. Except for the high spin state of the defect $^{5}A_{2}$, the order of other lowest levels, particularly the ground state of the vacancy $^{1}E$ does not change by the relaxation. At 12% outward relaxation, there is a level crossing between $^{5}A_{2}$ and the excited state of the well-known GR1 transition $^{1}T_{2}$. The reported level crossing confirms the predicted relative energies of these states in the band gap that was speculated by monitoring the temperature dependence of the electron paramagnetic resonance (EPR) signal. By considering the outward relaxation effect, we obtained midgap position for the $^{5}A_{2}$ state in agreement with the suggestion made by EPR. The position of the low lying $^{3}T_{1}$ level varies from $100\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}400\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ with increasing outward relaxation. When the ion-ion interaction of the NN atoms is included the outward relaxation lowers the energies of all electronic states. The relaxing force is different for investigated electronic states. By considering the interaction of the first and second shell neighbors of the vacancy, the calculated elastic barrier restricts outward relaxation of the vacancy to 12% for the ground and 18% for the $^{5}A_{2}$ excited state. The calculated equilibrium bond lengths are in very good agreement with ab initio density functional theory and EPR measurement data. Electronic configurations in the unrelaxed and relaxed eigenfunctions of the Hamiltonian are reported. Our results also suggest that there is an outward relaxation if Hund rule is applicable.

Details of a theoretical model for electronic structure of the diamond vacancies

A new model to calculate electronic states of the diamond vacancies has been developed using many body techniques. This model is based on physical assumptions of previous molecular models but does not use configuration interaction. Present model allows an accurate and unified treatment of electronic levels and related eigen functions for diamond vacancies, in addition to transition energies of the first dipole-allowed transitions in the neutral ( V 0) and negatively charged ( V −) vacancies, GR1 and ND1 band. For the first time, we calculated their optical transition intensities. For obtaining these results, we solved a generalized form of the Hubbard Hamiltonian, which consists of all electron–electron interaction terms on atomic orbital basis. Spatial symmetry of the defect, T d symmetry, is included in the form of the Hamiltonian, and the eigen states have automatically the correct spin and symmetry properties. We discuss the possibility of the reduction of the wide gap between theoretical and semiempirical wisdom by including deformation of the dangling orbital or delocalization of the vacancy electrons to the next nearest neighbor (NNN) atoms of the vacancies. Our prediction for low lying the 3T 1 level of the neutral vacancy in diamond is consistent with experimental expectations. We report the variation of the ground and excited states of the GR1 and ND1 lines with hopping parameter t and also the electronic configurations of these states.

Entropy of point defects calculated within periodic boundary conditions

A possibility to calculate both the entropies of formation and migration of point defects in semiconductors is presented. Knowledge of the entropic contributions is especially important for the correct description of high-temperature processes like growth or annealing. Using the self-consistent charge density-functional based tight-binding method (SCC-DFTB) we have calculated the predominant part of the entropy, resulting from lattice vibrations. Strong finite-size effects have been observed while investigating the formation entropies of isolated vacancies in diamond and silicon. We demonstrate how these problems can be overcome with the help of linear elasticity theory.

Quantum Monte Carlo study of the optical and diffusive properties of the vacancy defect in diamond.

Fixed-node diffusion quantum Monte Carlo (DMC) calculations of the ground and excited state energetics of the neutral vacancy defect in diamond are reported. The multiplet structure of the defect is modeled using guiding wave functions of the Slater-Jastrow type with symmetrized multideterminant Slater parts. For the ground state we obtain the 1E state in agreement with experiment. The calculated energy of the lowest dipole allowed transition is consistent with the experimentally observed GR1 band, which has long been identified with the neutral vacancy in diamond, although no previous first-principles ab initio calculation of this transition exists. The calculated multiplet splitting of over 2 eV indicates the importance of a proper treatment of electron exchange and correlation in this system. DMC calculations of the formation and migration energy of the vacancy defect are presented.

Microstructure of high-pressure-synthesized diamonds under rapid quenching and electron irradiation

A type of synthetic diamond single crystal about 0.4–0.5 mm in dimension prepared under high pressure–high temperature (HPHT) in the presence of a FeNi molten catalyst was quenched from HPHT and irradiated with 300 keV electrons at room temperature. Transmission electron microscopy was employed to examine the microstructure of the diamond single crystal before and after electron irradiation. It was found that there exists a large amount of cellular interfaces in the quenched diamond sample, which indicates the growth condition of the diamond under HPHT. Hexagonal dislocation loops about several tens of nanometers in dimension were observed in the high-pressure-synthesized diamond single crystal before electron irradiation, which strongly suggests that a number of vacancies were quenched-in due to rapid quenching from high temperature at the end of diamond synthesis, and were aggregated in the synthetic diamond to form vacancy disks on the (111) plane, the collapse of such vacancy disks forming vacancy-type dislocation loops. After electron irradiation, it was found that defect clusters present as interstitial-character dislocation loops were formed in the electron-irradiated region of the diamond. The interstitial dislocation loops grow with increase of the irradiation time. The present study, in comparison to previous work on ion implantation on diamond, indicates that electron irradiation does not induce a phase transformation but produces interstitial dislocation loops due to the migration of interstitial atoms and vacancies. The result of the study directly indicates that interstitials and vacancies in diamond are mobile at room temperature under electron irradiation. Nitrogen, as the most important kind of impurity contained in the HPHT as-grown diamond, probably acts as nucleation of the interstitial loops.

Photoluminescence studies of type IIa and nitrogen doped CVD diamond

Photoluminescence (PL) studies were carried out on CVD, type IIa and high purity HPHT diamond samples irradiated with electrons of energies between 150 and 300 KeV; near threshold energies for carbon displacement. The majority of PL spectra are obtained using a 488-nm lasing line, with samples cooled to approximately 7 K. Of particular interest is the behaviour of the self-interstitial related centre, 3H, at 503.5 nm. The centre is particularly sensitive; its formation varies significantly with dose and dose rate and is severely quenched with incident laser power in excess of 10 mW. 3H is the dominant centre in highly doped (50–100 ppm) nitrogen samples, for doses between (1019–1020) el/cm2, but reduces with higher doses. In lower nitrogen (few ppm) samples, the centre is considerably weaker after equivalent doses, comparable to the Raman line. In type IIa crystals, creation of 3H varies considerably from sample to sample. Upon annealing, 3H is at an optimum between 310 and 330 °C for type IIa diamonds and vanishes by 400 °C. Indications show these temperatures increase slightly as nitrogen content is increased. Migration of the centre well outside the irradiated area is frequent, tens of microns after irradiation and hundreds of microns post annealing. Other centres of interest include GR1, the neutral diamond vacancy, which is found to be created linearly with dose and be rate independent. Using 325 and 457.9 nm lines the TR12 centre was studied. It has a strong dose rate dependence, growing as dose rate raised to a power of approximately 2 and is unaffected by annealing up to 700 °C. A 244-nm line was used to study the 5RL centre and contrary to some reports was observed in samples containing approximately 0.1 ppm of nitrogen. PL provides an extremely sensitive way of measuring the nitrogen concentration in diamond, to levels of less than 0.1 ppm. The problem remains how to obtain an accurate measurement.

The new assignment of hyperfine parameters for deep defects in diamond

Hyperfine (hf) parameters calculated for the vacancy in diamond show deviations from the experimental data, that have been ascribed to the neglect of lattice relaxations. Extending the formalism to include lattice relaxations we have removed the discrepancies for the interactions with the nearest neighbor ligand nuclei. However, the disagreement for the interactions with the next neighbor shell apparently increased thereby. Extending our calculations to include all ligands up to the fifth shell we show that the hf interaction assigned to the next nearest neighbor shell at (2 2 0) must be reassigned to the (3 3 1) ligand shell instead. The same reassignment holds for substitutional Ni defects in diamond and for several deep donors in silicon, but apparently not for the silicon vacancy in SiC.

Taming the excited state

The major ideas of chemistry, electrochemistry, and even microelectronics are associated with electronic ground states, or with states thermally accessible at modest temperatures. Photonics, and many realisations of quantum devices, require excited states. The energetic basis of life, photosynthesis, is possible only through excited state processes. Excited states are the basis of new processing methods for organic and inorganic systems. In wide gap materials, excited states and the processes they show are extraordinarily varied. Can they be controlled or exploited, rather than merely accessed in spectroscopy? When electronic excitation is used in materials modification, the ideas of charge localisation and energy localisation are central [1]. The basic processes are Energy transfer; Energy conversion; Energy control: Control of phase, which is more sutble (keeping a system on a specific energy surface is already challenging; keeping a system coherent in a way which can be exploited in quantum computing is far more difficult); and Dissipation, the antithesis of phase control. Length scales can span extreme miniaturisation in lithography or quantum dots, mesoscopic scales similar to optical wavelengths, and human scales. Timescales range even more widely, from femtosecond plasmon responses, through picoseconds for self-trapping or preplume ablation, to many years. These ranges identify different features in the “taming” of excited states. Some of these features are shown by simpler systems: F centres; the diamond vacancy; colossal magnetoresistance oxides, organics; and self-trapped excitons.