Vacancy In Diamond Research Articles

Molecular-Orbital Treatment for Deep Levels in Semiconductors: Substitutional Nitrogen and the Lattice Vacancy in Diamond

Molecular-Orbital Treatment for Deep Levels in Semiconductors: Substitutional Nitrogen and the Lattice Vacancy in Diamond

The theory of defects in irradiated semiconductors

Developments in the theory of defects in semiconductors rire reviewed, with emphasis on changes since the Santa Fe meeting and on the points which were controversial then. It has become clear that most of the desirable simplifications are invalid for vacancies in diamond and silicon, and probably also for similar systems. In particular one cannot use the one-electron approximation, the rigid lattice approximation, the Jahn-Teller instability with coupling within isolated levels alone, nor some of the conceptually acceptable treatments of the lattice distortion. The successes and weaknesses of the various approaches are reviewed, and some of the potential methods are described.

An LCAO-MO treatment of the vacancy in diamond

Abstract A simple molecular orbital treatment which has previously been applied successfully to the substitutional nitrogen donor and boron acceptor in diamond is here applied to the vacancy in diamond. Localized levels associated with the vacancy are found in the gap and an outward relaxation of the four neighbors surrounding the vacancy is predicted. Jahn-Teller effects are found to give stabilization energies of ∼0.5 eV. A critical comparison to the ‘defect molecule’ approach of Coulson and Kearsley and Yamaguchi is included.

Lattice distortion near vacancies in diamond and silicon. I

A dynamical relaxation procedure, coupled with a valence force potential, has been used to calculate the distortion around point defects in a diamond-type crystal. The method has been applied to the vacancy in diamond and silicon. The response of the lattice to symmetrized forces on the nearest neighbours to the vacancy was calculated. The results can be used in estimates of point defect properties which depend on lattice distortion, including the jahn-teller effect, and formation energies. The ratios of the atomic displacements under uniform external stresses for the perfect lattice and for the lattice with a vacancy are also determined.

Lattice distortion near vacancies in diamond and silicon. Ii

Lattice distortion near vacancies in diamond and silicon. Ii

Isolated single vacancy in diamond—I. Electronic structure

Some of the assumptions underlying the molecular approach to the determination of the electronic properties of the vacancy in diamond have been examined. The ordering of the lowest electronic levels of the neutral and single negatively charged states of the vacancy is sensitive to the choice of atomic functions to represent the 2 s and 2 p orbitals on the atoms nearest the defect as well as to the symmetric relaxation of these atoms. However, for limited delocalisation of electronic charge from the vacancy there is no change in the ordering of the lowest levels. The 3 T 1 electronic state is predicted as the ground state of the neutral vacancy if the atoms nearest the defect relax towards its centre as implied by the molecular model; however, for a symmetric relaxation of the nearest neigh-bours away from the centre of the vacancy the 1 E level is more likely to be the lowest level. Present experimental knowledge of the vacancy in diamond does not resolve this uncertainty.

Isolated single vacancy in diamond-II. Jahn-Teller effect

The Jahn-Teller splittings for the lowest degenerate electronic states of the single isolated vacancy in diamond in the single positive, neutral and negatively ionized charged states have been calculated to first order. The magnitude of the linear coupling force terms is largely independent of the choice of atomic functions to represent the orbitals on the carbon atoms in the two cases considered, but it is sensitive to the extent of configuration interaction between electronic states of the same symmetry. The results demonstrate that it is necessary to include terms involving the derivatives of the overlap integrals in any such calculations. In some cases the predicted splittings are very large. Reasons for including higher-order terms in a more detailed calculation are discussed.

Calculation of diamond GRI band lineshape

Vibronic spectra lineshape functions have been calculated for models of the diamond vacancy, divacancy, substitutional impurities and vacancy-nitrogen neighbor centers. The best fit to the GRI band is obtained from the vacancy center calculations.

Study of the neutral vacancy in semi-conductors

The neutral vacancy in semi-conductors is studied by using the Green's operator method combined with the tight-binding approximation. A simple model for the band structure with only one resonance integral between first neighbours is used. First a two-band linear semi-conductor, where analytical solutions are obtained, is studied and then the method is applied to diamond. In both cases bound states are obtained whose extension is discussed. Application is made to the calculation of the formation energy of the vacancy in diamond which is found to be about 9 eV without taking relaxation into account.

The Jahn-Teller instability with accidental degeneracy

The Jahn-Teller theorem predicts that orbitally degenerate complexes in solids can lower their energy by a distortion which lowers their symmetry. Exact degeneracy is not necessary for this instability; usually it suffices if the actual separation of the energy levels involved is less than the energy reduction which would result if they were exactly degenerate. We discuss various cases of accidental degeneracy in cubic and tetrahedral systems. With accidental degeneracy it is possible to get mixed distortions which involve both trigonal and tetragonal distortions. These have probably been observed for the negative vacancy in silicon, and possibly for the neutral vacancy in diamond. The theory is applied to both these cases, and it is compared with the earlier qualitative arguments of Watkins.

The optical absorption of the neutral vacancy in diamond

Optical absorption by the neutral vacancy in diamond has been predicted to occur between the ground 1E state and the 1T2 excited state. Both these states are orbitally degenerate and should show Jahn Teller distortions. We have calculated the Huang-Rhys Factor for the transition (the fraction of the intensity in the zero phonon line) and the first and second moments of the absorption band. Also we discuss the response of the zero phonon line to externally applied stresses. Our model assumes that the vacancy interacts with just six modes, corresponding to the normal modes of the neighbours of the vacancy. The coupling of the electronic and nuclear motion is estimated from an LCAO model.The results are compared with observations of the GR1 band, which has been attributed to the vacancy. The predicted Huang-Rhys factor S ~ 3.7 and the first and second moments of the band support this identification. Further our model predicts that luminescence from this band should be unpolarised, as observed. However the predicted stress splitting of the zero phonon line differs from that observed. Possible explanations of this are discussed.

Jahn-Teller Effect for a Single Vacancy in Diamondlike Covalent Solids

The static Jahn-Teller effect is studied for a monovacancy ${\mathrm{V}}^{+}$, ${\mathrm{V}}^{0}$, and ${\mathrm{V}}^{\ensuremath{-}}$ in diamondlike covalent solids by a new method which applies to the case of linear combinations of atomic orbitals (LCAO) as wave functions. In this rigid LCAO model the orbitals are assumed to follow the nuclei rigidly in the deformation. The formal calculation is almost identical to that of the usual treatment of the Jahn-Teller effect by the perturbation method. For the vacancy in diamond we use the electronic structure determined by Coulson and Kearsley in a molecular model. We obtain energy lowerings of the order of 0.1 eV and distortion amplitudes of about 0.05 \AA{}. Finally we compare our results with the experimental data.

A variational approach to the study of strongly bound impurity states in crystals

Working within the Wannier function representation Koster and Slater have shown how to solve the problem of a localized perturbation in a simple cubic lattice having a single electronic energy band which is describable in terms of a Wannier function with only nearest-neighbour interactions. Here it is shown how to set up a simple variational method which leads to results in fair agreement with those of Koster and Slater for bound impurity states and at the same time is readily extended to single-band models of other crystal structures described by Wannier functions which may have other than nearest-neighbour interactions. Some results are given for the body-centred cubic lattice with a single band and only nearest-neighbour interactions. On making the assumption that it is reasonable to separate the band index and lattice site dependence of the expansion coefficients the method is extended to multi-band models of crystals. In particular, it is shown how to locate the energy of a localized impurity state produced by a strongly repulsive perturbation in a diamond-like crystal having eight bands for which the corresponding Wannier functions have only nearest-neighbour interactions. It is indicated that the results may have relevance to the discussion of bound states around a vacancy in diamond. Finally, it is expected that the method will be useful in the study of localized vibrational and spin states in perturbed crystals.

The electronic structure of the tetrachedral N2centre and of the neutral vacancy in diamond

The N2 centre, a tetrachedral array of four F centres, and the neutral vacancy in diamond present similar theoretical problems. Their electronic structure has been calculated by a molecular orbital approach using one-electron wave functions centred on the geometric centre of the defect. The results are compared with those based on functions which are linear combinations of atomic orbitals (LCAO). We conclude that in LiF and KC1 the ground state of the N2 centre is 5A2 and the centre is not responsible for the N2 band, although it should give rise to spin resonance. For the diamond vacancy the ground state is 3T1 or possibly 1E. Previous calculations using LCAO wave functions give a 1E ground state for diamond. Possible ways of observing these centres are discussed.

Direct calculation of modes modified by a point imperfection

Abstract Lattice vibrations modified by a point imperfection can be usefully investigated using a model in which all crystal atoms except those in N shells round the imperfection are either held fixed or (for low frequency modes) forced to move according to an elastic continuum solution. By making full use of symmetry and using an electronic computer to calculate the relevant matrices as well as to diagonalize them, one can make N large enough to get sufficient information about modified lattice modes to treat most problems concerning their interaction with the centre. For an imperfection in an alkali halide we have considered the “spherical” vibrations of an 11-shell model and all the modes of vibration of a 4-shell model. The results have been applied to a discussion of the temperature dependence of the breadth of the F-band, and applications to calculations of entropies of formation and of localized modes are outlined. The spherical modes round a vacancy in diamond are determined for a 60-shell model. Work now completed on applying these results to explaining the Mossbauer-like structure of some optical absorption bands in diamond is mentioned. Possible applications to thermal conductivity and relaxation time calculations are indicated.

Electron Paramagnetic Resonance Investigation of the Vacancy in Diamond

Electron Paramagnetic Resonance Investigation of the Vacancy in Diamond

Electronic States of Single Vacancies in Diamond

Electronic states shown in the title are investigated by using molecular orbital technique and an interpretation is made of the observations on EPR, optical absorption etc. in irradiated diamond. Values of interatomic integrals, which appear in the expression of cohesive energy of a perfect crystal, are firstly modified in such ways that a calculated value of the cohesive energy agrees with the observed one, while values of intra-atomic integrals are set equal to those estimated from the observed values of spectral terms in a free carbon atom. On the basis of these modifications, values of the integrals are then obtained, which are related to electronic states of the vacancies. Energy levels are thus evaluated for V 0 , V + , V - etc., which mean each a neutral, a positively ionized and a negatively ionized vacancy etc.. By comparing these energy levels with each other, it may be assumed that after irradiation with particles of high energy, a much greater of V - appear in the natural crystal than any othe...

Theory of Localized Electronic States at Point Imperfections

A review is given of the present status of the theory of s and p electrons in deep traps. The theory of the F center in LiF is reviewed in detail including recent work on ionic displacements in the vicinity of the center. This is followed by a discussion of the work of Cohen and Heine and the general justification of the point ion approximation for the interaction of a trapped electron with a matrix composed of closed-shell ions. Vacancies in diamond are discussed, and new results are reported for the three-electron configuration of a vacancy in silicon. Trapped-hole centers in the alkali halides are mentioned briefly.