Solid State Communications, Vol. 68, No. 6, pp. 587-589, 1988. Printed in Great Britain.
0038-1098/88 $3.00 + .00 Pergamon Press plc
T H E E L E C T R I C F I E L D G R A D I E N T AT 19F IN D I A M O N D S. Connell, K. Bharuth-Ram j, H. Appel 2, J.P.F. Sellschop and M. Stemmet Schonland Research Centre for Nuclear Science, University of Witwatersrand, Johannesburg 2000, S.A. and J.E. Lowther 3 School of Physics, University of Bath, Bath BA2 7AY, UK
(Received 29 April 1988 by C.W. McCombie)
Time Differential Perturbed Angular Distribution (TDPAD) studies of fluorine isotopes implanted into diamond have revealed two distinct quadrupole interaction frequencies, 5 9 M H z and 23MHz. These signals are consistent with cluster model molecular orbital calculations representing fluorine on substitutional and interstitial sites. At the substitutional site the electric field gradient is large but the fluorine ion experiences only a small deviation from tetrahedral symmetry resulting in the small T D P A D resonance. Conversely, at the interstitial site, where the electric field gradient is smaller, the distortion from tetrahedral symmetry is large and this gives the higher T D P A D frequency. T I M E D I F F E R E N T I A L Perturbed Angular Distribution (TDPAD) has proved to be a valuable tool in the study of molecular species as well as covalent solids. The fluorine isotope 19F has a relatively long lived nuclear excited state, and so the quadrupole interaction or electric field gradient (EFG) at the site can be measured. Studies of a fluorine isotope in atomic form in a variety of well specified molecular and crystalline materials have been made [I-4], where relatively constant field gradients are often observed characteristic of some common bonding within each system. This follows because the EFG reflects the immediate nature of the surroundings of the fluorine probe. We have extended T D P A D studies [5, 6], to investigate fluorine in diamond. Fluorine was introduced into the diamond by evaporating 30pgcm 2 layer of CaF, onto the surface of diamond wafers, and the ~F nuclei were excited using the t~F(p, p')~gF reaction and recoil implanted into the crystal using a pulsed 4 M e V proton beam. Time differential perturbed angular distributions of the 197 keV "/-rays from the 19F 5+/2 ~ 1'/2 transition were observed, in these Physics Department, University of Durban-Westville, Durban 4000, S.A. 2 Universitat Karlsruhe, Postfach 3640, D 7500 Karlsruhe, R.G. ~On sabbatical leave from Department of Physics, University of Witwatersrand, Johannesburg, S.A.
experiments, two distinct characteristic T D P A D frequencies were always observed for all types of natural diamond. Table 1 summarizes the measured T D P A D parameters describing the EFG in the principal axes of the two sites. The quadrupole frequency vo is proportional to V..:, the largest principal component of the EFG, and to Q the nuclear moment (vQ = eQV:./h). Asymmetry of the EFG is measured by the parameter r/ = (V, - V,,)IV.:, and ~, represents a gaussian distribution of T D P A D frequencies. In common with some other molecular and crystalline materials, a characteristic T D P A D resonant frequency of about 5 9 M H z is observed similar to the F-C bond frequency observed in a variety of molecular solids [I-3]. In diamond the site at which ~F gives this frequency has a ( 1 1 1 ) symmetry although the precise location of the site in the lattice is not established in the experiment. T D P A D of fluorine in diamond also gives another distinctively characteristic signal. This site gives a broad resonance corresponding to a largc distribution of frequencies (about thirty percent) around the value of 23MHz. The site also has a (I 1 I) symmetry, although thc precise nature of the signal is controversial - its origin cannot be established experimentally. In an attempt to shed some light on the nature of the T D P A D frequencies, cluster model molecular orbital calculations have been undertaken to give some indication as to where the fluorine is located in the diamond lattice. Theoretical total energy calculations
E L E C T R I C F I E L D G R A D I E N T A T I'~F IN D I A M O N D
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Table 1. Experimental T D P A D parameters (?[ ~'~Fin Diamond Site
(1 1 I)
(1 I I )
vo is the T D P A D frequency. "~ is a measure of the distribution o f T D P A D frequencies. r/is the asymmetry parameter. were performed with the ~*'F a t o m moved along the (1 1 I ) d i a m o n d axes - as indicated from the principal axes of the T D P A D frequencies - and the energy minima interpreted as a possible residence site for the 19F.
In terms o f the cluster model a p p r o a c h [8, 9] thc quadrupole tensor has the following components: q,
(4(r 3 ) / 5 . 3 . p , ,
- p , , - - Pkk)
where p , are c o m p o n e n t s o f the bond order matrix, as obtained from the cluster model calculation. In the present case we have evaluated these c o m p o n e n t s using the C N D O / 2 molecular orbital approach, with carbon parameters taken from solid state properties . This is a semi empirical self-consistent method, with parameters (in eV) for c a r b o n being E, = 7.0, E e = 5.5, /3 = - 1 0 . 2 and /~ = 1.765a.u. F o r the fluorine defect, the parameters were E, = 16.07. Ep = 10.09, [~ = - 18.95 and F~ = 2.82a.u. The d i a m o n d
lattice was simulated by clusters of 41 atoms for the substitutional site and 47 atoms in the case of the interstitial site, with hydrogenic atoms placed on the cluster surfaces. This gave the element o f the bond order matrix, which was then diagonalised at the ~F site to give the principal components of the quadrupole tensor, V,i, and hence the T D P A D frequencies. In calculating the T D P A D frequencies, we also used the Hartree Fock value o f (r ~) = 7.45a.u. and Q = 0.072barns as given in . Total energy results together with the computed T D P A D frequencies were evaluated and are shown in Figs. I and 2 as " F is displaced within the cluster along the ( 1 I I ) axis. A schematic representation for the one electron picture o f the electronic energy [evcls is shown in Fig. 3. The results for both the substitutional and tetrahedral - interstitial sites suggest that F could be a c c o m m o d a t e d at both sites. Calculated T D P A D frequencies at the cluster energy minima are about 23 and 55 M H z for the substitutional and interstitial sites respectively, with the electron configuration always being a r o u n d s~'~p5~', as c o m p u t e d from a
E Z Ihl
0-3 0n(A) Fig. I. Total energy (eV) for clusters representing ~"F on substitutional and interstitial sites as the 'gF atom is moved along the ( I 1 1) direction toward a C atom. The zero of energy in both cases is referred to the energy for ~gF positioned at the centrc o f the cluster. Dashed lines are for the interstitial site, and continuous for the substitutional site.
Fig. 2. T D P A D frequencies obtained from substitutional and interstitial clusters for the ~'~F movement indicated in l:ig. I. Arrows approximately indicate positions o f energy minima.
E L E C T R I C F I E L D G R A D I E N T AT 19F IN D I A M O N D
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. . - - e a
I F IP
a .,,Nct RID
. -----~ a
Fig. 3. Schematic representation for the one electron energy scheme of 19F as computed from the appropriate cluster. conventional Mullikan population analysis. In both cases the fluorine ion probably acts as a donor in diamond - similar to the nitrogen impurity. The broad nature of the T D P A D signal about 2 3 M H z can perhaps be explained in terms of the results shown in Figs. i and 2. On the substitutional site, the '~F ion is in a rather broad potential well, stable only very slightly off centre along any of the four (1 I 1) bonding directions. The nature and overall magnitude of this off centre distortion could be influenced by distant defects (vacancies) or other lattice perturbations such as Jahn-Teller distortions - as for nitrogen in diamond. Thus the broad resonance appears to reflect the distribution of different perturbed substitutional sites in the material. Another and perhaps more illuminating - way of looking at the situation is by reference to the one electron gap states in Fig. 3, where it is seen that substitutional 19F gives rise to deep levels in the gap. Electron states associated with these deep levels are well localised at ~F, so the broad nature of thc 23 MHz signal es~ntially rcflects a splitting of the tctrahedral symmetry levels. Contrary to the substitutional site, off-centre movement o f " F at the tetrahedral interstitial position is fairly large - the ~gF is displaced toward a C atom such that the internuclear separation is then roughly about the sum of the ionic radii (0.14 nm), The potential that the tqF finds itself in is sharp, and any deviation from the ionic radii F-C bond length difficult, as charge is mainly located on the F - C bond. We can also present an explanation of the relative firm identity of the interstitial T D P A D signal in terms of the elec-
tronic levels associated with ~"F. As shown in Fig. 3, a shallow occupied gap level near the valence band is associated with this interstitial centre having a wavefunction not as localised as was the substitutional case and thus not as affected by any distortion in the immediate vicinity of the ~F ion. In summary we have measured the T D P A D frequencies of ~ F implanted into natural diamond. Two distinct signals have always been observed each with a (1 1 ! ) lattice symmetry. To attempt to understand the possible locations of t9F and the origin of these signals, cluster model molecular orbital calculations were performed which suggested that the T D P A D signals originate from tgF on substitutional and off centre interstitial positions in the lattice.
Acknowledgements - Support from the Foundation for Research Development and Messrs de Beers Industrial Diamonds (Pty) Ltd (to Schonland Research Centre), is gratefully acknowledged. One of us (JEL) also expresses thanks to the SERC. REFERENCES I. 2. 3. 4. 5. 6. 7. 8. 9. 10. I I.
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