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The neutral divacancy in silicon
Sofid State Communications, Vol. 43, No. 1, pp. 41--46, 1982. Printed in Great Britain.
0038-1098/82/250041-06503.00/0 Pergamon Press Ltd.
THE NEUTRAL DIVACANCY IN SILICON E.G. Sieverts Natuurkundig Laboratorium der Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands and J.W. Corbett Institute for the Study of Defects in Solids, State University of New York at Albany, Albany, NY 12222, U.S.A.
(Received 18 January 1982 by A.R. Miedema) Extended HiJckel Theory calculations have been carried out on a cluster of silicon atoms to examine the relative stability of two configurations of the divacancy: (1) two vacancies on adjacent sites, i.e. the "normal" divacancy configuration; and (2) two vacancies separated by two occupied lattice sites, i.e. a configuration similar to Hornstra's "sponge" defect with a double Si-Si bond. It was found that the two configurations have comparable total energy and that the sponge-like defect is metastabte against moving the vacancies to the normal divacancy configuration. It is argued that the sponge-like defect is a viable model for the defect giving rise to the N L l l (S = 1) EPR spectrum. It is also argued that the I1 (S = 1) EPR spectrum, which had been attributed to the neutral, normal divacancy configuration, is the same as spectrum A14 which had previously been identified with a (divacancy + oxygen) complex.
triplet state EPR spectrum [10]. As we will discuss in Section 2, we now question that assignment. In a previous publication it was suggested that the S = 1 spectrum labelled NL11 might be related to a neutral divacancy configuration [ 16]. This spectrum is of the main interest in the present paper. In Section 2 we will suggest that a "sponge" defect configuration is in accord with the available experimental information. The main subject of this paper is a calculation of the stability of the sponge defect, compared to the usual divacancy configuration, using extended HiJckel theory (EHT).
1. INTRODUCTION THE DIVACANCY is one of the most studied lattice defects in silicon. Divacancies are easily introduced in silicon crystals by irradiation with high-energy electrons or by 3' irradiation. Also part of the radiation damage from heavy particle impact consists of divacancies. A wide variety of experiments on divacancies has been performed. Magnetic resonance experiments especially have provided a wealth of information about the atomic and electronic structure of divacancies and about their kinetics [1-8]. The singly positive (V2*) and the singly negative (V2-) charge states are paramagnetic with a spin S = ½, and their electron paramagnetic resonances (EPR) spectra have been observed. From EPR [1,2, 7, 8], optical [9, 10], and DLTS experiments [8, 11-13] various energy levels in the bandgap, related to the divacancy, have been determined. Together with the observed presence or absence of the EPR spectra of V2*and V2- as a function of the position of the Fermi level, these experiments gave evidence for the existence of a neutral and a doubly negative charge state as well, which states need not have a paramagnetic ground state. Especially the neutral charge state V° is of interest as it occurs in (near-) intrinsic material. Moreover, from a theoretical point of view, it is the simplest state, as Coulombic effects are expected to be smallest. The neutral divacancy has been attributed to a
2. EPR EXPERIMENTS 2.1. Spectra A14 and 11 So far, in one paper the neutral divacancy has emphatically been claimed to be observed with EPR in its S = 1 state [14]. Recently we have reanalyzed the experimental data of the corresponding spectrum which had been labelled I1. Computer fits of the spin Hamiltonian parameters to the rotation patterns of this spectrum and of an earlier reported spectrum, labelled A14 [ 15 ], resulted within the experimental errors to the same values. This suggests that A14 and I1 are in fact the same spectrum, corresponding to the same defect. Additional arguments for this identity can be found in the fact that both spectra have been observed under the same experimental conditions, in silicon material of the same type 41
42
THE NEUTRAL DIVACANCY IN SILICON
and resistivity, both quartz crucible grown, after the same sort of electron irradiations (in the same accelerator). Spectrum A14 had been identified as an o x y g e n vacancy complex in which one oxygen atom occupies two empty silicon sites [15]. There is no reason to dispute the presence of oxygen, as the spectrum (whether A14 or I1) is found in oxygen containing QC material, while it has never been observed in floating zone material, even if the Fermi level had moved to the middle of the bandgap where I:2+nor V:- could be observed anymore. The misinterpretation as to regarding I 1 as a new spectrum may have resulted from an error in the parameters of A l 4 as published [15]. The published values result in a rotation pattern for magnetic field directions in the (011) crystal plane, which deviates appreciably from the one actually shown. The parameters of our dual fit to the date points of A I 4 and I 1 are: gl = 2.0020,
g2 = 2.0090,
g3 = 2.0093,
bonds of this defect should be separated by four lattice sites, i.e. as though they were the two dangling bonds in a {110} plane at the ends of a planar tetravacancy. The P3 spectrum (S = ½) [17] has been identified [18, 19] with a single electron shared between these two dangling bonds o f a planar tetravacancy. The P3 spectrum is observed following neutron irradiation, and not after a 1.5 MeV electron irradiation which produces the NLI 1 center. The NL11 center was observed in a concentration comparable to, but less than that of the V2-. We argue therefore that the NL11 spectrum is not due to a tetravacancy (or a more complex defect). Hornstra [20, 21 ] proposed what he called a "sponge" defect, the simplest form of which has two vacancies separated by two atoms which relax from their lattice positions in the diamond (silicon) lattice to form an ethylene-like double bond configuration. In the next section we present EHT calculations on the sponge defect and consider its suitability for the NL11 spectrum. 3. EHT CALCULATIONS
0g = 33.1 ° DI = T-185MHz, D 3 =
+
67 MHz,
Vol. 43, No. I
D2 = -+ l l 8 M H z , 0z~ = 2.3 °.
(For the meaning of these spin Hamiltonian parameters, see [14, 15].) The aspect of the rotation pattern is especially sensitive to the errors of about 5 ° in the angles 0. In [14] it is argued that the temperature dependence of the zero-field splitting tensors D of A14 and I1 are different. The absence of a temperature dependence of the principal value/)3 in spectrum AI4, in contrast to I1, can be explained by assuming that one has looked at an incorrect magnetic field direction, 5 ° from the actual principal axis, consistent with the above errors. When putting equal the temperature effects of the principal value/92 for A14 and I1 at the standard temperature of 77 K, those effects are also equal for most of the temperature range. Finally it should be mentioned that a mutual conversion between spectrum I1 and the spectrum of V2under illumination, as was observed [14], is not at all conclusive for an identification with different charge states of the same defect, as such effects occur frequently between various EPR spectra in silicon. In view of the above arguments and observations, we conclude that A14 and I1 are the same spectrum. 2.2. Spectrum NL11 In a previous publication, the S = 1 spectrum NL11 has speculatively been suggested as a candidate for the neutral divacancy [16]. From the observed spin-spin interaction of NL11 one can argue that the two dangling
3.1. Extended Hiickel theory Extended Htickel theory (EHT) is a simple semiempirical one-electron L C A O - M O approach. Originally developed in the field of organic chemistry, it was introduced for calculations of defects in diamond and silicon by Messrner and Watkins and it has been widely used in treating defect configurations in semiconductors [22, 23]. EHT has been used in a number o f calculations of the properties of the divacancy in silicon, i.e. the two vacancies at the nearest neighbour distance [ 2 4 - 2 7 ] . Since we are considering a neutral intrinsic defect with no major charge transfer effects anticipated (or found) we use the common EHT approach rather than the iterative EHT used most recently in divacancy calculations [27]. EHT uses molecular orbitals ffi which are linear combinations of atomic orbitals ~j (for which generally Slater-type 3s and 3p orbitals are chosen): ~i = ZkCk,~. A solution of the secular equations Z,k(Hi~ -- eiSik)cki = 0 is obtained using the WolfsbergHelmholtz approximations Hjk = (q~ilHl~bk) = --½Kik(Ii +Ik)Sik and
(]--/=k)
H n = - - I j.
Here Sik = (¢jl~bk), li is the empirical ionization energy o f the orbital ], and Kjk is an empirically adjusted parameter. Depending on the kind of calculation to be performed, in the past, different sets of parameters have been used. With the Slater-orbital exponents ~', = 1.87, ~'p = 1.60 and the parameters K,, = Km, = 1.75,
Vol. 43, No. 1
THE NEUTRAL DIVACANCY IN SILICON
43
3
11 3 3 ' - 132
0 - ~
I~0el D1T],~[0~ 1] Fig. 1. Model of the cluster on which calculations have been performed. In a perfect cluster all 52 sites are occupied. In the defect clusters, two atoms replace the four dashed central ones all of which lie in the (011) plane. For reference some lattice sites have been labeled.
Ksp = 1.3125, the bandgap and bandstructure of silicon can satisfactorily be reproduced [25, 26, 28]. This choice however, gives very poor results for the elastic properties of the lattice. In calculations on clusters without any lattice defect, an instability of the central atoms upon lattice deformation was found. Therefore a different set has been used in the present calculations: ~'s = 1.634, ~'u = 1.426, Ks, = Kpp = Ksp = 1.75. Although this set gives much to wide a bandgap, it results in a stable lattice configuration, so that the total EHT energy EEHT = ~iniEi (with n i the occupation number of level Ei) can meaningfully be used for the determination of stable defect configurations. The present calculations have been performed on finite clusters of silicon atoms. The unpaired dangling bonds at the surface have been paired with an extra electron. Although this introduces a net negative charge, it does not influence the average numbers of electrons on the central atoms which are the ones we are primarily interested in. All of the energy levels which correspond with the surface electrons are found in the valence band. Details on the clusters and results will be presented in Section 3.2. 3.2.
Results
Calculations have been performed on clusters with or without vacancies. The perfect cluster consisted of 52 atoms and is shown in Fig. 1. The oblong shape has been chosen to permit a sponge-like divacancy to be accommodated. The central portion of the resulting energy levels of the perfect cluster is shown in Fig. 2(a). The levels leave a bandgap of about 5.5 eV. All electrons of the system can be accommodated in the levels below the gap, while none of these valence band levels is left unoccupied. If the central atoms, labelled d, were displaced from their regular lattice position, the total
-1-2-3--
-41 2 g - 1 2 7 - -
-5-
1 3 0 - 1 2 9 ~ 1 2 8 . ~
1 2 8 - -
127--6--
-
i
-7
m I
111. ,~
i,
--8 ""
a
b
c
d
Fig. 2. Energy levels from EHT calculations (a) for a perfect cluster of 52 atoms, (b) for a sponge divacancy with two central atoms in the plane with the sites labeled 1 in Fig. 1, (c) for a regular divacancy, and (d) for a relaxed sponge divacancy with two central atoms at regular lattice positions labeled d in Fig. 1. EHT energy increased, as it should do for a perfect cluster. The defect clusters started with 48 atoms at their regular lattice positions, indicated by the full circles in Fig. I, resulting in a planar tetravacancy. To arrive at a divacancy, two more atoms were added at varying positions in the center of the cluster. In order to conserve at least 2/m (C2h) defect symmetry, these positions are confined to the (071)plane of the four dashed, unoccupied lattice sites (labelled c and d in Fig. 1), while the two atoms are kept at symmetric positions with respect to the center of the cluster. The atoms adjacent to the vacancies were not relaxed. From the calculated EHT energies for different positions, an energy contour plot in the (071) plane could be derived (Fig. 3). The central part of this plot is left blank, as for such small interatomic distances the present calculations are not meaningful. This plot indicates that there are two defect configurations of (local) minimum energy. These minimum energy values are not significantly
44
THE NEUTRAL DIVACANCY IN SILICON
0
O
3tl l[o,] 80
85
75
85
0
®
O [~oo]
~
....
bo
0
O @
\TS 85
0
80
Q3
0
Fig. 3. Energy contours of EEHr for divacancy configurations with two central atoms at symmetric positions in the (011) plane. The energy values indicated along the contours at 5 eV intervals are to be reckoned negative with respect to an arbitrary reference value. Solid circles indicate atoms in the (011) plane, open circles are atoms in planes just above and be_low, and + signs indicate unoccupied sites in the (01 I) plane. The labels 1,2, 3, c, and d refer to Fig. 1. different. In both configurations the two variable atoms are very close to regular lattice positions. If the two atoms are close to the sites c, the structure is that of a normal divacancy, if close to d it is a (partially) dissociated divacancy, whose structure is relaxed from a sponge configuration, with the atoms at normal lattice sites. The results for three special configurations will be considered in more detail. If a sponge with an ethylene-like structure is assumed, the two central atoms should be on the dashed line in Fig. 3, forming a plane molecule together with the four atoms labelled 1. Energy levels for such a case are shown in Fig. 2(b). Some levels are found in the bandgap. Both the levels labelled 127 and 129 correspond to molecular orbitals which are mainly localized on the two dangling bond atoms 3. Thye are sp-hybrids of 94% p-character and lobes in the [I 11] bond directions towards the vacancies. In the valence band, levels
Vol. 43, No. 1
58 and 111 are MO's mainly localized on the two central atoms. They are a-bonding combinations o f p lobes close to the [311 ] direction connecting these two atoms. Level 51 mainly corresponds to p-orbitals in the [011] direction in the "molecular" plane and perpendicular to the interatomic direction, level 63 to p-orbitals close to the [233] direction perpendicular to the plane. Both form n bonds between the central atoms. The unoccupied levels 135,132,199, and 133 are the antibonding combinations, respectively. Due to the different environment and considerable admixture of other atomic orbitals, the ordering of the energy levels differs from that in ethylene. Nevertheless, the electronic structure resembles that of the carbon double bond. Figure 2(c) shows that in a normal divacancy configuration with atoms at the sites c, there are also levels in the bandgap. The levels 127 and 128 are mainly localized on the atoms c. Level 127 is an antibonding combination of sp-hybrids with 84% p-character and lobes in the [ 111 ] dangling bond directions. Level 128 arises from a 95% p-bonding combination with lobes close to [211 ], deviating nearly 20 ° from [ 111 ]. Bent bond orbitals between the four atoms 1, as often encountered in divacancy models, can also be recognized. The levels 129 and 130 are in part made up from antibonding combinations of such orbitals. The energy levels for the partially dissociated divacancy configuration with atoms at the sites d are shown in Fig. 2d. The levels 128 and 130 are found to be mainly 93% p - 7 % s hybrids on the far atoms 3, along the [111] dangling bond directions in odd and even combinations respectively, just as occurs in the tetravacancy. Several MO's have an important localization on the central atoms labelled d. Among these especially lr bond configurations with pure p orbitals in [011 ] directions are prominent. Between the two pairs of atoms 2, bent bonds can be recognized in bonding and antibonding combinations of lobes close to the [111] and [111] directions. In this the electronic structure resembles those given just from group theoretical arguments. 3.3. Discussion In the past many EHT calculations on silicon have been performed, often providing insight concerning defect configurations. In some cases comparison with experimental data could be made (e.g. [5, 25-27]). It is also clear that the simple, semiempirical, one-electron, EHT approach certainly has its limitations in predicting quantitative data for defects in silicon. Therefore we will restrict ourselves to qualitative conclusions and not go into a discussion of the exact order of the energy levels in the various cases in Section 3.2, the more so as always considerable fractions of many remote orbitals form part
Voi. 43, No. 1
45
THE NEUTRAL DIVACANCY IN SILICON
of the MO's. In the present case we can conclude from the calculated EHT energies that two configurations are candidates for the neutral combination of two vacancies. In both the normal and the partially dissociated divacancy the stable configuration has silicon atoms very close to normal lattice positions, hence we favor the term "relaxed sponge" for the partially dissociated divacancy. Experiment appears to indicate that the normal divacancy configuration is the favored one for V2* and V2- and presumably for V°. The present calculations support the view that a sponge-like defect is also energetically possible and hence a candidate for a model for the NL11 spectrum. The divacancy "sponge" model with a planar structure which resembles the double carbon bond in organic chemistry, is energetically much less favorable. We note, however, that the tendency to form double bonds is much less in silicon than in carbon, so that one may f'md the sponge (as opposed to our relaxed sponge) in diamond. Similarly one could imagine the NL11 spectrum in silicon arising from a [VCCV] complex, i.e. the vacancies at the sites c and two carbon impurity atoms at d (or double-bonded in the sponge configuration); the relatively large production rate of the NL11 spectrum argues against the [VCCV] complex in favor of an intrinsic defect. In both partially dissociated divacancy configurations two dangling bonds are left, separated by a string of four lattice sites. This is consistent with the observed spin-spin interaction of spectrum NL11. In a neutral charge state of the defect, 127 levels can be filled completely. In view of the present qualitative conclusions, the order of the energy levels and hence their filling deserve no detailed consideration. Moreover, EHT is a one-electron approach so that we cannot derive conclusions whether unpaired electrons will couple to an S = 1 triplet state. The calculated dangling bond levels are always close to the Fermi level, though. In experiments S = 1 states have been observed in EPR either in a pure neutral cluster of at least four vacancies, or in neutral, oxygen containing clusters with only two or more vacancies [11 ]. In these cases the S = 1 states were either the ground state or should be only slightly above the S = 0 state as they could easily be populated thermally. This shows the apparent trend that coupling of two dangling bond electrons to S = 1 can only easily occur if their orbitals have far enough spatial separation or are screened by other atoms without unpaired electrons. In a partially dissociated divacancy both conditions are satisfied. Therefore we conclude that the relaxed sponge configuration which was found as one of the favorable defect structures from EHT calculations, may reasonably give rise to S = 1 in
its ground state or in an excited state of only slightly higher energy.
Acknowledgements - The present work was supported in part by the office of Naval Research under contract No. N00014-75-C-0919. We would like to thank Dr C. Weigel for important discussions and Dr Vijay A. Singh, who made available the EHT programs and discussed the results. REFERENCES 1. 2. 3.
4. 5. 6. 7.
8. 9. i0. I 1. 12. 13.
14. 15. 16. 17. 18. 19. 20. 21. 22. 23.
G.D. Watkins & J.W. Corbett,Phys. Rev. 138, A543 (1965). C.A.J. Ammerlaan & G.D. Watkins, Phys. Rev. BS, 3988 (1972). J.G. de Wit, C.A.J. Ammerlaan & E.G. Sieverts, Lattice Defects in Semiconductors 1974 (Edited by F.A. Huntley), p. 178. The Institute of Physics, London (1975). J.G. de Wit, E.G. Sieverts & C.A.J. Ammerlaan, Phys. Rev. B14, 3494 (1976). E.G. Sieverts, S.H. Muller & C.A.J. Ammerlaan, Phys. Rev. B18, 6834 (1978). E.G. Sieverts,J. Phys. C14, 2217 (1981). R.H. van der Linde & C.A.J. Ammerlaan,Defects and Radiation Effects in Semiconductors 1978 (Edited by J.H. Albany), p. 242. The Institute of Physics, London (1979). Y.H. Lee, L.J. Cheng, P.M. Mooney & J.W. Corbett, Solar Cells High Efficiency and Radiation Damage, p. 179. NASA, Washington, DC (1977). A.H. Kalma & J.C. Corelli, Phys. Rev. 173,734 (1968). R.C. Young & J.C. Co relli, Phys. Rev. BS, 1455 (1972). A.O. Evwaraye & E. Sun,J. Appl. Phys. 47, 3776 (1976). P.M. Mooney, L.J. Cheng, M. Siili, J.D. Gerson & J.W. Corbett,Phys. Rev. B15, 3836 (1977). L.C. Kimerling, Radiation Effects in Semiconductors 1976, p. 221. (Edited by N.B. Urli and J.W. Corbett), The Institute of Physics, London (1979). P.R. Brosious, in Reference [7], p. 248. Y.H. Lee & J.W. Corbett,Phys. Rev. BI3, 2653 (1976). E.G. Sieverts, S.H. Muller & C.A.J. Ammerlaan, Solid State Commun. 28,221 (1978). W. Jung&G.S. Newell,Phys. Rev. 132,648 (1963). K.L. Brower,Rad. Eft. 8,213 (1971). Y.H. Lee & J.W. Corbett, Phys. Rev. B9,4351 (1974). J. Hornstra, Philips Research Laboratory Report Nr. 3497 (1959, unpublished). J.W. Corbett, Electron Radiation Damage in Semiconductors and Metals, p. 82. Academic Press, New York (1966). R.P. Messmer & G.D. Watkins, Phys. Rev. B7, 2568 (1973). C. Weigel, D. Peak, J.W. Corbett, G.D. Watkins & R.P. Messmer,Phys. Rev. B8, 2906 (1973).
46 24. 25. 26.
THE NEUTRAL DIVACANCY IN SILICON T.F. Lee & T.C. McGill,J. Phys. C6, 3438 (1973). C.A.J. Ammerlaan & C. Weigel, in Reference [13], p. 448. C.A.J. Ammerlaan & J.C. Wolfrat, Phys. Status Solidifb) 89, 85 (1978).
27.
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C. Weigel & C.A.J. Ammerlaan, Phys. Status Solidi
(b) 94, 505 (1979). 28.
R.P. Messmer, in Reference [3], p. 44.
0038-1098/82/250041-06503.00/0 Pergamon Press Ltd.
THE NEUTRAL DIVACANCY IN SILICON E.G. Sieverts Natuurkundig Laboratorium der Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands and J.W. Corbett Institute for the Study of Defects in Solids, State University of New York at Albany, Albany, NY 12222, U.S.A.
(Received 18 January 1982 by A.R. Miedema) Extended HiJckel Theory calculations have been carried out on a cluster of silicon atoms to examine the relative stability of two configurations of the divacancy: (1) two vacancies on adjacent sites, i.e. the "normal" divacancy configuration; and (2) two vacancies separated by two occupied lattice sites, i.e. a configuration similar to Hornstra's "sponge" defect with a double Si-Si bond. It was found that the two configurations have comparable total energy and that the sponge-like defect is metastabte against moving the vacancies to the normal divacancy configuration. It is argued that the sponge-like defect is a viable model for the defect giving rise to the N L l l (S = 1) EPR spectrum. It is also argued that the I1 (S = 1) EPR spectrum, which had been attributed to the neutral, normal divacancy configuration, is the same as spectrum A14 which had previously been identified with a (divacancy + oxygen) complex.
triplet state EPR spectrum [10]. As we will discuss in Section 2, we now question that assignment. In a previous publication it was suggested that the S = 1 spectrum labelled NL11 might be related to a neutral divacancy configuration [ 16]. This spectrum is of the main interest in the present paper. In Section 2 we will suggest that a "sponge" defect configuration is in accord with the available experimental information. The main subject of this paper is a calculation of the stability of the sponge defect, compared to the usual divacancy configuration, using extended HiJckel theory (EHT).
1. INTRODUCTION THE DIVACANCY is one of the most studied lattice defects in silicon. Divacancies are easily introduced in silicon crystals by irradiation with high-energy electrons or by 3' irradiation. Also part of the radiation damage from heavy particle impact consists of divacancies. A wide variety of experiments on divacancies has been performed. Magnetic resonance experiments especially have provided a wealth of information about the atomic and electronic structure of divacancies and about their kinetics [1-8]. The singly positive (V2*) and the singly negative (V2-) charge states are paramagnetic with a spin S = ½, and their electron paramagnetic resonances (EPR) spectra have been observed. From EPR [1,2, 7, 8], optical [9, 10], and DLTS experiments [8, 11-13] various energy levels in the bandgap, related to the divacancy, have been determined. Together with the observed presence or absence of the EPR spectra of V2*and V2- as a function of the position of the Fermi level, these experiments gave evidence for the existence of a neutral and a doubly negative charge state as well, which states need not have a paramagnetic ground state. Especially the neutral charge state V° is of interest as it occurs in (near-) intrinsic material. Moreover, from a theoretical point of view, it is the simplest state, as Coulombic effects are expected to be smallest. The neutral divacancy has been attributed to a
2. EPR EXPERIMENTS 2.1. Spectra A14 and 11 So far, in one paper the neutral divacancy has emphatically been claimed to be observed with EPR in its S = 1 state [14]. Recently we have reanalyzed the experimental data of the corresponding spectrum which had been labelled I1. Computer fits of the spin Hamiltonian parameters to the rotation patterns of this spectrum and of an earlier reported spectrum, labelled A14 [ 15 ], resulted within the experimental errors to the same values. This suggests that A14 and I1 are in fact the same spectrum, corresponding to the same defect. Additional arguments for this identity can be found in the fact that both spectra have been observed under the same experimental conditions, in silicon material of the same type 41
42
THE NEUTRAL DIVACANCY IN SILICON
and resistivity, both quartz crucible grown, after the same sort of electron irradiations (in the same accelerator). Spectrum A14 had been identified as an o x y g e n vacancy complex in which one oxygen atom occupies two empty silicon sites [15]. There is no reason to dispute the presence of oxygen, as the spectrum (whether A14 or I1) is found in oxygen containing QC material, while it has never been observed in floating zone material, even if the Fermi level had moved to the middle of the bandgap where I:2+nor V:- could be observed anymore. The misinterpretation as to regarding I 1 as a new spectrum may have resulted from an error in the parameters of A l 4 as published [15]. The published values result in a rotation pattern for magnetic field directions in the (011) crystal plane, which deviates appreciably from the one actually shown. The parameters of our dual fit to the date points of A I 4 and I 1 are: gl = 2.0020,
g2 = 2.0090,
g3 = 2.0093,
bonds of this defect should be separated by four lattice sites, i.e. as though they were the two dangling bonds in a {110} plane at the ends of a planar tetravacancy. The P3 spectrum (S = ½) [17] has been identified [18, 19] with a single electron shared between these two dangling bonds o f a planar tetravacancy. The P3 spectrum is observed following neutron irradiation, and not after a 1.5 MeV electron irradiation which produces the NLI 1 center. The NL11 center was observed in a concentration comparable to, but less than that of the V2-. We argue therefore that the NL11 spectrum is not due to a tetravacancy (or a more complex defect). Hornstra [20, 21 ] proposed what he called a "sponge" defect, the simplest form of which has two vacancies separated by two atoms which relax from their lattice positions in the diamond (silicon) lattice to form an ethylene-like double bond configuration. In the next section we present EHT calculations on the sponge defect and consider its suitability for the NL11 spectrum. 3. EHT CALCULATIONS
0g = 33.1 ° DI = T-185MHz, D 3 =
+
67 MHz,
Vol. 43, No. I
D2 = -+ l l 8 M H z , 0z~ = 2.3 °.
(For the meaning of these spin Hamiltonian parameters, see [14, 15].) The aspect of the rotation pattern is especially sensitive to the errors of about 5 ° in the angles 0. In [14] it is argued that the temperature dependence of the zero-field splitting tensors D of A14 and I1 are different. The absence of a temperature dependence of the principal value/)3 in spectrum AI4, in contrast to I1, can be explained by assuming that one has looked at an incorrect magnetic field direction, 5 ° from the actual principal axis, consistent with the above errors. When putting equal the temperature effects of the principal value/92 for A14 and I1 at the standard temperature of 77 K, those effects are also equal for most of the temperature range. Finally it should be mentioned that a mutual conversion between spectrum I1 and the spectrum of V2under illumination, as was observed [14], is not at all conclusive for an identification with different charge states of the same defect, as such effects occur frequently between various EPR spectra in silicon. In view of the above arguments and observations, we conclude that A14 and I1 are the same spectrum. 2.2. Spectrum NL11 In a previous publication, the S = 1 spectrum NL11 has speculatively been suggested as a candidate for the neutral divacancy [16]. From the observed spin-spin interaction of NL11 one can argue that the two dangling
3.1. Extended Hiickel theory Extended Htickel theory (EHT) is a simple semiempirical one-electron L C A O - M O approach. Originally developed in the field of organic chemistry, it was introduced for calculations of defects in diamond and silicon by Messrner and Watkins and it has been widely used in treating defect configurations in semiconductors [22, 23]. EHT has been used in a number o f calculations of the properties of the divacancy in silicon, i.e. the two vacancies at the nearest neighbour distance [ 2 4 - 2 7 ] . Since we are considering a neutral intrinsic defect with no major charge transfer effects anticipated (or found) we use the common EHT approach rather than the iterative EHT used most recently in divacancy calculations [27]. EHT uses molecular orbitals ffi which are linear combinations of atomic orbitals ~j (for which generally Slater-type 3s and 3p orbitals are chosen): ~i = ZkCk,~. A solution of the secular equations Z,k(Hi~ -- eiSik)cki = 0 is obtained using the WolfsbergHelmholtz approximations Hjk = (q~ilHl~bk) = --½Kik(Ii +Ik)Sik and
(]--/=k)
H n = - - I j.
Here Sik = (¢jl~bk), li is the empirical ionization energy o f the orbital ], and Kjk is an empirically adjusted parameter. Depending on the kind of calculation to be performed, in the past, different sets of parameters have been used. With the Slater-orbital exponents ~', = 1.87, ~'p = 1.60 and the parameters K,, = Km, = 1.75,
Vol. 43, No. 1
THE NEUTRAL DIVACANCY IN SILICON
43
3
11 3 3 ' - 132
0 - ~
I~0el D1T],~[0~ 1] Fig. 1. Model of the cluster on which calculations have been performed. In a perfect cluster all 52 sites are occupied. In the defect clusters, two atoms replace the four dashed central ones all of which lie in the (011) plane. For reference some lattice sites have been labeled.
Ksp = 1.3125, the bandgap and bandstructure of silicon can satisfactorily be reproduced [25, 26, 28]. This choice however, gives very poor results for the elastic properties of the lattice. In calculations on clusters without any lattice defect, an instability of the central atoms upon lattice deformation was found. Therefore a different set has been used in the present calculations: ~'s = 1.634, ~'u = 1.426, Ks, = Kpp = Ksp = 1.75. Although this set gives much to wide a bandgap, it results in a stable lattice configuration, so that the total EHT energy EEHT = ~iniEi (with n i the occupation number of level Ei) can meaningfully be used for the determination of stable defect configurations. The present calculations have been performed on finite clusters of silicon atoms. The unpaired dangling bonds at the surface have been paired with an extra electron. Although this introduces a net negative charge, it does not influence the average numbers of electrons on the central atoms which are the ones we are primarily interested in. All of the energy levels which correspond with the surface electrons are found in the valence band. Details on the clusters and results will be presented in Section 3.2. 3.2.
Results
Calculations have been performed on clusters with or without vacancies. The perfect cluster consisted of 52 atoms and is shown in Fig. 1. The oblong shape has been chosen to permit a sponge-like divacancy to be accommodated. The central portion of the resulting energy levels of the perfect cluster is shown in Fig. 2(a). The levels leave a bandgap of about 5.5 eV. All electrons of the system can be accommodated in the levels below the gap, while none of these valence band levels is left unoccupied. If the central atoms, labelled d, were displaced from their regular lattice position, the total
-1-2-3--
-41 2 g - 1 2 7 - -
-5-
1 3 0 - 1 2 9 ~ 1 2 8 . ~
1 2 8 - -
127--6--
-
i
-7
m I
111. ,~
i,
--8 ""
a
b
c
d
Fig. 2. Energy levels from EHT calculations (a) for a perfect cluster of 52 atoms, (b) for a sponge divacancy with two central atoms in the plane with the sites labeled 1 in Fig. 1, (c) for a regular divacancy, and (d) for a relaxed sponge divacancy with two central atoms at regular lattice positions labeled d in Fig. 1. EHT energy increased, as it should do for a perfect cluster. The defect clusters started with 48 atoms at their regular lattice positions, indicated by the full circles in Fig. I, resulting in a planar tetravacancy. To arrive at a divacancy, two more atoms were added at varying positions in the center of the cluster. In order to conserve at least 2/m (C2h) defect symmetry, these positions are confined to the (071)plane of the four dashed, unoccupied lattice sites (labelled c and d in Fig. 1), while the two atoms are kept at symmetric positions with respect to the center of the cluster. The atoms adjacent to the vacancies were not relaxed. From the calculated EHT energies for different positions, an energy contour plot in the (071) plane could be derived (Fig. 3). The central part of this plot is left blank, as for such small interatomic distances the present calculations are not meaningful. This plot indicates that there are two defect configurations of (local) minimum energy. These minimum energy values are not significantly
44
THE NEUTRAL DIVACANCY IN SILICON
0
O
3tl l[o,] 80
85
75
85
0
®
O [~oo]
~
....
bo
0
O @
\TS 85
0
80
Q3
0
Fig. 3. Energy contours of EEHr for divacancy configurations with two central atoms at symmetric positions in the (011) plane. The energy values indicated along the contours at 5 eV intervals are to be reckoned negative with respect to an arbitrary reference value. Solid circles indicate atoms in the (011) plane, open circles are atoms in planes just above and be_low, and + signs indicate unoccupied sites in the (01 I) plane. The labels 1,2, 3, c, and d refer to Fig. 1. different. In both configurations the two variable atoms are very close to regular lattice positions. If the two atoms are close to the sites c, the structure is that of a normal divacancy, if close to d it is a (partially) dissociated divacancy, whose structure is relaxed from a sponge configuration, with the atoms at normal lattice sites. The results for three special configurations will be considered in more detail. If a sponge with an ethylene-like structure is assumed, the two central atoms should be on the dashed line in Fig. 3, forming a plane molecule together with the four atoms labelled 1. Energy levels for such a case are shown in Fig. 2(b). Some levels are found in the bandgap. Both the levels labelled 127 and 129 correspond to molecular orbitals which are mainly localized on the two dangling bond atoms 3. Thye are sp-hybrids of 94% p-character and lobes in the [I 11] bond directions towards the vacancies. In the valence band, levels
Vol. 43, No. 1
58 and 111 are MO's mainly localized on the two central atoms. They are a-bonding combinations o f p lobes close to the [311 ] direction connecting these two atoms. Level 51 mainly corresponds to p-orbitals in the [011] direction in the "molecular" plane and perpendicular to the interatomic direction, level 63 to p-orbitals close to the [233] direction perpendicular to the plane. Both form n bonds between the central atoms. The unoccupied levels 135,132,199, and 133 are the antibonding combinations, respectively. Due to the different environment and considerable admixture of other atomic orbitals, the ordering of the energy levels differs from that in ethylene. Nevertheless, the electronic structure resembles that of the carbon double bond. Figure 2(c) shows that in a normal divacancy configuration with atoms at the sites c, there are also levels in the bandgap. The levels 127 and 128 are mainly localized on the atoms c. Level 127 is an antibonding combination of sp-hybrids with 84% p-character and lobes in the [ 111 ] dangling bond directions. Level 128 arises from a 95% p-bonding combination with lobes close to [211 ], deviating nearly 20 ° from [ 111 ]. Bent bond orbitals between the four atoms 1, as often encountered in divacancy models, can also be recognized. The levels 129 and 130 are in part made up from antibonding combinations of such orbitals. The energy levels for the partially dissociated divacancy configuration with atoms at the sites d are shown in Fig. 2d. The levels 128 and 130 are found to be mainly 93% p - 7 % s hybrids on the far atoms 3, along the [111] dangling bond directions in odd and even combinations respectively, just as occurs in the tetravacancy. Several MO's have an important localization on the central atoms labelled d. Among these especially lr bond configurations with pure p orbitals in [011 ] directions are prominent. Between the two pairs of atoms 2, bent bonds can be recognized in bonding and antibonding combinations of lobes close to the [111] and [111] directions. In this the electronic structure resembles those given just from group theoretical arguments. 3.3. Discussion In the past many EHT calculations on silicon have been performed, often providing insight concerning defect configurations. In some cases comparison with experimental data could be made (e.g. [5, 25-27]). It is also clear that the simple, semiempirical, one-electron, EHT approach certainly has its limitations in predicting quantitative data for defects in silicon. Therefore we will restrict ourselves to qualitative conclusions and not go into a discussion of the exact order of the energy levels in the various cases in Section 3.2, the more so as always considerable fractions of many remote orbitals form part
Voi. 43, No. 1
45
THE NEUTRAL DIVACANCY IN SILICON
of the MO's. In the present case we can conclude from the calculated EHT energies that two configurations are candidates for the neutral combination of two vacancies. In both the normal and the partially dissociated divacancy the stable configuration has silicon atoms very close to normal lattice positions, hence we favor the term "relaxed sponge" for the partially dissociated divacancy. Experiment appears to indicate that the normal divacancy configuration is the favored one for V2* and V2- and presumably for V°. The present calculations support the view that a sponge-like defect is also energetically possible and hence a candidate for a model for the NL11 spectrum. The divacancy "sponge" model with a planar structure which resembles the double carbon bond in organic chemistry, is energetically much less favorable. We note, however, that the tendency to form double bonds is much less in silicon than in carbon, so that one may f'md the sponge (as opposed to our relaxed sponge) in diamond. Similarly one could imagine the NL11 spectrum in silicon arising from a [VCCV] complex, i.e. the vacancies at the sites c and two carbon impurity atoms at d (or double-bonded in the sponge configuration); the relatively large production rate of the NL11 spectrum argues against the [VCCV] complex in favor of an intrinsic defect. In both partially dissociated divacancy configurations two dangling bonds are left, separated by a string of four lattice sites. This is consistent with the observed spin-spin interaction of spectrum NL11. In a neutral charge state of the defect, 127 levels can be filled completely. In view of the present qualitative conclusions, the order of the energy levels and hence their filling deserve no detailed consideration. Moreover, EHT is a one-electron approach so that we cannot derive conclusions whether unpaired electrons will couple to an S = 1 triplet state. The calculated dangling bond levels are always close to the Fermi level, though. In experiments S = 1 states have been observed in EPR either in a pure neutral cluster of at least four vacancies, or in neutral, oxygen containing clusters with only two or more vacancies [11 ]. In these cases the S = 1 states were either the ground state or should be only slightly above the S = 0 state as they could easily be populated thermally. This shows the apparent trend that coupling of two dangling bond electrons to S = 1 can only easily occur if their orbitals have far enough spatial separation or are screened by other atoms without unpaired electrons. In a partially dissociated divacancy both conditions are satisfied. Therefore we conclude that the relaxed sponge configuration which was found as one of the favorable defect structures from EHT calculations, may reasonably give rise to S = 1 in
its ground state or in an excited state of only slightly higher energy.
Acknowledgements - The present work was supported in part by the office of Naval Research under contract No. N00014-75-C-0919. We would like to thank Dr C. Weigel for important discussions and Dr Vijay A. Singh, who made available the EHT programs and discussed the results. REFERENCES 1. 2. 3.
4. 5. 6. 7.
8. 9. i0. I 1. 12. 13.
14. 15. 16. 17. 18. 19. 20. 21. 22. 23.
G.D. Watkins & J.W. Corbett,Phys. Rev. 138, A543 (1965). C.A.J. Ammerlaan & G.D. Watkins, Phys. Rev. BS, 3988 (1972). J.G. de Wit, C.A.J. Ammerlaan & E.G. Sieverts, Lattice Defects in Semiconductors 1974 (Edited by F.A. Huntley), p. 178. The Institute of Physics, London (1975). J.G. de Wit, E.G. Sieverts & C.A.J. Ammerlaan, Phys. Rev. B14, 3494 (1976). E.G. Sieverts, S.H. Muller & C.A.J. Ammerlaan, Phys. Rev. B18, 6834 (1978). E.G. Sieverts,J. Phys. C14, 2217 (1981). R.H. van der Linde & C.A.J. Ammerlaan,Defects and Radiation Effects in Semiconductors 1978 (Edited by J.H. Albany), p. 242. The Institute of Physics, London (1979). Y.H. Lee, L.J. Cheng, P.M. Mooney & J.W. Corbett, Solar Cells High Efficiency and Radiation Damage, p. 179. NASA, Washington, DC (1977). A.H. Kalma & J.C. Corelli, Phys. Rev. 173,734 (1968). R.C. Young & J.C. Co relli, Phys. Rev. BS, 1455 (1972). A.O. Evwaraye & E. Sun,J. Appl. Phys. 47, 3776 (1976). P.M. Mooney, L.J. Cheng, M. Siili, J.D. Gerson & J.W. Corbett,Phys. Rev. B15, 3836 (1977). L.C. Kimerling, Radiation Effects in Semiconductors 1976, p. 221. (Edited by N.B. Urli and J.W. Corbett), The Institute of Physics, London (1979). P.R. Brosious, in Reference [7], p. 248. Y.H. Lee & J.W. Corbett,Phys. Rev. BI3, 2653 (1976). E.G. Sieverts, S.H. Muller & C.A.J. Ammerlaan, Solid State Commun. 28,221 (1978). W. Jung&G.S. Newell,Phys. Rev. 132,648 (1963). K.L. Brower,Rad. Eft. 8,213 (1971). Y.H. Lee & J.W. Corbett, Phys. Rev. B9,4351 (1974). J. Hornstra, Philips Research Laboratory Report Nr. 3497 (1959, unpublished). J.W. Corbett, Electron Radiation Damage in Semiconductors and Metals, p. 82. Academic Press, New York (1966). R.P. Messmer & G.D. Watkins, Phys. Rev. B7, 2568 (1973). C. Weigel, D. Peak, J.W. Corbett, G.D. Watkins & R.P. Messmer,Phys. Rev. B8, 2906 (1973).
46 24. 25. 26.
THE NEUTRAL DIVACANCY IN SILICON T.F. Lee & T.C. McGill,J. Phys. C6, 3438 (1973). C.A.J. Ammerlaan & C. Weigel, in Reference [13], p. 448. C.A.J. Ammerlaan & J.C. Wolfrat, Phys. Status Solidifb) 89, 85 (1978).
27.
Vol. 43, No. 1
C. Weigel & C.A.J. Ammerlaan, Phys. Status Solidi
(b) 94, 505 (1979). 28.
R.P. Messmer, in Reference [3], p. 44.