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First-principles study on the local vibrational modes of nitrogen–oxygen defects in silicon
ARTICLE IN PRESS
Physica B 401–402 (2007) 159–162 www.elsevier.com/locate/physb
First-principles study on the local vibrational modes of nitrogen–oxygen defects in silicon N. Fujitaa,, R. Jonesa, S. O¨bergb, P.R. Briddonc a
School of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, UK Department of Mathematics and HPC2N, Lulea˚ University of Technology, SE-97187 Lulea˚, Sweden c Physics Centre, School of Natural Science, University of Newcastle upon Tyne, Newcastle NE1 7RU, UK b
Abstract In this paper we investigate the interaction of nitrogen and oxygen by means of local density functional theory. While nitrogen-pairoxygen defects (N2 –Om ) have been studied in detail previously, the existence and role of nitrogen–oxygen defects containing only one nitrogen atom (N–On ) is still controversial. Motivated by recent infrared absorption measurements, where several new absorption lines were observed, we present first-principles studies on the ground state configuration, binding energy and local vibrational modes of NO and NO2 . We suggest that the NO2 defect gives rise to the experimentally observed lines at 1002, 973 and 855 cm1 . r 2007 Elsevier B.V. All rights reserved. Keywords: Modelling; Silicon; Nitrogen; Oxygen; Local vibrational modes
1. Introduction Today it is well known that nitrogen has significant effects on the materials properties of silicon. It strongly enhances oxygen precipitation which improves the gettering potential of Czochralski silicon (Cz-Si) [1,2]. In float-zone silicon (FZ-Si), it suppresses void formation [3], whereas in Cz-Si it leads to an increased density of smaller voids compared with nitrogen-free Cz-Si. Since voids can lead to device failure, there has been a concerted attempt [4] to understand the interactions between nitrogen, oxygen and vacancies at high temperature. Here we limit ourselves to the electrically active interstitial nitrogen–oxygen (NO) and the nitrogen–oxygenpair (NO2 ) defect. Previously, it has been suggested that neither NO nor NO2 plays an important role due to their negligible concentrations in the material [5]. However, this result was based on experimental data, where the nitrogen concentration of the sample was unusually high ð½N ¼ 1:84 1016 cm3 Þ [6]. Recently, it has been shown that both the NO and the NO2 defect can play a significant role at lower nitrogen concentrations [7,8]. Corresponding author. Tel.: +44 26 4137; fax: +44 26 4111.
E-mail address: [email protected] (N. Fujita). 0921-4526/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2007.08.136
While it is known that the NO2 defect is a member of the nitrogen related shallow thermal donor (STD) family, it was also proposed that the NO defect can act as a STD. The dominant form of nitrogen in both FZ-Si and Cz-Si introduced during growth is the nitrogen-pair defect, which was successfully identified in a combined study of channeling and infrared absorption measurements coupled with first-principles calculations [9]. The combination of such experimental and theoretical efforts also led to the identification of the dominating nitrogen–oxygen species in Cz-Si, where four strong bands at 1030, 999, 805 and 739 cm1 are observed in addition to the two lines at 963 and 766 cm1 attributed to the nitrogen-pair [10]. One hour isochronal annealing shows that the intensity of the two lines associated with the nitrogen dimer is decreasing between 400 and 600 1C while the three lines due to nitrogen–oxygen defect complexes become more prominent. Between 600 and 800 1C the intensity of the nitrogen pair related bands is highly increasing, reaching its maximum at about 800 1C [6]. Above 800 1C the intensity of these two lines drops until the bands are annealed out completely at 1100 1C. The intensity of the nitrogen–oxygen related bands decrease above 600 1C. This completely complementary annealing behaviour indicates that there
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160
must be some interaction between nitrogen and nitrogen– oxygen defects between 400 and 800 1C. In recent IR measurements by Inoue et al. [11], N-doped Cz-Si samples with various concentrations of nitrogen were used. The resulting absorbance spectra showed a similar temperature dependence of the various bands as observed by Qi et al. [6]. Furthermore several new peaks were found after 2 h of annealing below 900 1C. Two peaks at 1018 and 810 cm1 were tentatively assigned to the N2 O2 defect in a previous study [5]—however, the origin of several other peaks remained unclear. Motivated by these experimental results, we present the atomic structures, binding energies and local vibrational modes (LVMs) of the NO and the NO2 defect in the following. 2. Method Within this work we use the AIMPRO local density functional theory code [12,13] to find the minimum energy configuration of the two defect structures and to investigate their corresponding binding energies and LVMs. All calculations are performed in 216 atom cubic silicon supercells. The chosen size of the supercells ensures that the spacial separation of the defect and its periodically repeated images is adequate to simulate an isolated defect in the material. Core electrons on Si, N and O are eliminated by using the norm-conserving pseudopotentials by Hartwigsen, Goedecker and Hutter [14]. The wavefunction basis consists of independent s, p and d Gaussian orbitals. Eight special k-points generated by a 2 2 2 Monkhorst–Pack [15] grid are used to sample the Brillouin zone. All atoms in the cell are allowed to relax to find the stable structures. The binding energy of a defect formed by the reaction A þ B ! AB is given as E b ðABÞ ¼ E f ðAÞ þ E f ðBÞ E f ðABÞ,
potential [16], fitted from the double derivatives of bulk silicon obtained using AIMPRO, is used. Previously, it has been shown that the AIMPRO method leads to a binding energy of 3.67 eV for N2 and IR-active modes at 968 and 773 cm1 compared with experimental values of 962 and 765 cm1 [17]. Furthermore the effect of isotope substitution could be reproduced successfully. The method also yielded in a migration barrier of 2.7 eV for N2 [18] which is close to other calculations [19,20].
3. Results and discussion The NO defect which is shown in Fig. 1 is situated in one of the six identical planes of the diamond lattice. We find that in the neutral ground state configuration the oxygen atom is overcoordinated, forming a square together with the nitrogen atom and their two common silicon bonding neighbours. Previous density functional theory calculations where the NO defect was embedded in a small hydrogen terminated cluster ðSi79 H68 Þ suggested a slightly different structure, in which the oxygen atom is two-fold coordinated and located in a bond centered position [21]. Our present calculations show that this structure is slightly higher in energy by about 0.2 eV. Considering the formation of NO by the reaction N þ O ! NO we find a binding energy of 1.5 eV. The local vibration modes including different isotope substitutions of nitrogen and oxygen are presented in Table 1. We find three LVMs which are strongly localised on the defect atoms. In the case of 14N16O the upper two modes at 1001 and 801 cm1 are related to the nitrogen atom, whereas the oxygen gives rise to another mode at 722 cm1 .
(1)
x
where E tot ðAÞ P is the total energy of the supercell containing the defect, x nx mx is the sum over all atoms with mx being the chemical potential of n atoms of the respective species x contained in the investigated system. The entropy term TS is normally neglected. To determine the LVMs of a relaxed structure we need to calculate the second derivatives of the total energy with respect to the positions of the atoms which are forming the defect and their neighbours. In practice only the entries of the dynamic matrix, which are related to the defect atoms and their neighbours are calculated explicitly. For bulk-like atoms away from the defect a Musgrave–Pople interatomic
140°
1.84
where E f ðAÞ, E f ðBÞ and E f ðABÞ are the formation energies of the defect structures A, B and AB, respectively. Thus a bound system is represented by a positive binding energy at absolute zero and neglecting zero-point energies. The formation energy E f of a defect A is given as X nx mx þ TS, (2) E f ðAÞ ¼ E tot ðAÞ
1.72 126°
97° 92°
1.74 N 1.75
O 1.76
1.78 2.38
Fig. 1. (Color online) Ground state configuration of the neutral NO defect in silicon.
Table 1 Local vibrational modes of the nitrogen–oxygen (NO) defect in silicon, including isotope substitutions of the involved defect atoms 14
N16O
15
14
1001 801 722
974 783 721
999 800 690
All modes are given in cm1 .
N16O
N18O
ARTICLE IN PRESS N. Fujita et al. / Physica B 401–402 (2007) 159–162
The observed downward shifts after isotope substitution clearly confirm these assignments. The minimum energy structure of the NO2 defect is shown in Fig. 2. Considering a planar defect within one of the h1 1 0i planes, there are two possible nearest neighbour sites for the second oxygen atom. We find that the oxygen atom favours a bond centred position, where it bridges the Si–Si bond next to the oxygen atom of the NO square. The binding energy of the second atom to NO, i.e. considering the reaction NO þ O ! NO2 is 1.1 eV. Our calculations show that the previously suggested C 2v symmetry configuration (O–N–O) where the two oxygen atoms are situated on either side of the nitrogen atom is higher in energy by about 0.2 eV [21]. If the symmetry is intentionally broken both oxygen atoms remain two-fold coordinated, however the relaxed structure is then only 0.1 eV higher in energy than the N–O–O structure depicted in Fig. 2. Since the NO2 defect possesses two spatial configurations which are almost equal in energy, the LVMs of both NO2 structures are given in Table 2. Both NO2 defects give rise to five different vibrational modes. For the N–O–O structure the highest mode at 1022 cm1 is strongly localised on the nitrogen atom. Substituting 14N with 15N results in a downward shift of this mode by 26 cm1 . The second highest mode at 977 cm1 is related to the two-fold
1.79 1.72 124°
94° 97°
1.74 N 1.75
141° 1.72 1.63 O1 132° 1.78 O2 1.68
Table 2 Local vibrational modes of the two lowest energy configurations of the nitrogen–oxygen-pair (NO2 ) defect, including isotope substitutions of the involved defect atoms
O–N–O
14
N16O16O
14
14
1022 (N) 977 (O2) 812 (N,O1) 794 (N,O1) 670 (O2)
1022 (N) 934 (O2) 812 (N,O1) 793 (O1,N) 661 (O2)
16
1084 (N) 970 (O2) 856 (N) 751 (O1) 658 (O2)
O14N16O
N16O18O
14
15
1018 (N) 976 (O2) 805 (N) 766 (O1) 667 (O2)
1018 (N) 933 (O2) 805 (N) 765 (O1) 657 (O2)
996 976 805 781 670
16
18
18
16
1083 (N) 929 (O2) 855 (N) 751 (O1) 649 (O2)
1082 (N) 970 (O2) 856 (N) 716 (O1) 658 (O2)
1081 (N) 928 (O2) 855 (N) 716 (O1) 649 (O2)
1054 (N) 969 (O2) 836 (N) 750 (O1) 658 (O2)
O14N18O
N18O16O
O14N16O
N18O18O
O14N18O
coordinated oxygen atom (O2). The modes at 812 and 794 cm1 are localised on the first oxygen atom (O1) and the nitrogen atom. The lowest mode at 670 cm1 refers to O2, but is not as strongly localised on O2 as the mode at 976 cm1 . Comparing the experimentally observed lines at 1002, 973 and 855 cm1 suggests that these modes are related to the NO2 defect. Considering the energetically slightly less favourable O–N–O structure, the nitrogen related modes are found at 1084 and 856 cm1 . The upper mode is about 60 cm1 higher than the highest calculated mode of the N–O–O structure. The two oxygen atoms give rise to three modes at 970, 751 and 658 cm1 . One should notice the similarity of the two modes at 970 and 658 cm1 compared to the modes at 976 and 670 cm1 of the N–O–O structure. Isotope substitutions do not alter the localisation of the respective defect atoms. 4. Summary In summary, we presented the neutral ground state configurations and local vibrational modes of the NO and NO2 defect in silicon. The upper three calculated modes of the NO2 defect are reasonably close to the experimental modes at 1002, 973 and 855 cm1 and hence we suggest that these modes are due to NO2 . However a definite assignment can only be made, if the isotopic shifts we presented here in this paper can be reproduced by experimental measurements. Experimental modes which could correspond to our calculated modes for the NO defect have not been observed yet. Acknowledgements
Fig. 2. (Color online) Ground state configuration of the neutral NO2 defect in silicon.
N–O–O
161
N16O16O (N) (O2) (O1,N) (N) (O2)
O15N16O
The atoms denoted in brackets refer to the localisation of the modes on these atoms (for N–O–O see Fig. 2). All modes are given in cm1 .
S.O¨. would like to thank the Swedish National Infrastructure for Computing (SNIC) and The Swedish Research Council for financial support. N.F. is grateful to EPSRC for funding. References [1] Q. Sun, K.H. Yao, H.C. Gatos, J. Appl. Phys. 71 (1992) 3760. [2] G. Kissinger, A. Huber, K. Nakai, O. Lysytskij, T. Mu¨ller, H. Richter, W. von Ammon, Appl. Phys. Lett. 87 (2005) 101904. [3] V.V. Voronkov, R. Falster, Mater. Sci. Eng. B 114–115 (2004) 130. [4] A. Taguchi, H. Kageshima, K. Wada, J. Appl. Phys. 97 (2005) 053514. [5] N. Fujita, R. Jones, S. O¨berg, P.R. Briddon, J. Mater. Sci. Mater. Electron. 18 (2007) 683. [6] M.W. Qi, S.S. Tan, B. Zhu, P.X. Cai, W.F. Gu, X.M. Xu, T.S. Shi, J. Appl. Phys. 69 (1990) 3775. [7] N. Fujita, R. Jones, S. O¨berg, P.R. Briddon, Appl. Phys. Lett. 91 (2007) 051914. [8] H. Ono, M. Horikawa, Japan J. Appl. Phys. 42 (2003) L261. [9] R. Jones, S. O¨berg, F. Berg Rasmussen, B. Bech Nielsen, Phys. Rev. Lett. 72 (1994) 1882. [10] R. Jones, C. Ewels, J. Goss, J. Miro, P. Dea´k, S. O¨berg, F. Berg Rasmussen, Semicond. Sci. Technol. 9 (1994) 2145. [11] N. Inoue, M. Nakatsu, K. Tanahashi, H. Yamada-Kaneta, H. Ono, V.D. Akhmetov, O. Lysytskiy, H. Richter, Solid State Phenom. 108–109 (2005) 609.
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[12] P. Briddon, R. Jones, Phys. Status Solidi B 217 (2000) 131. [13] J.P. Goss, M.J. Shaw, P.R. Briddon, Top. Appl. Phys. 104 (2007) 69. [14] C. Hartwigsen, S. Goedecker, J. Hutter, Phys. Rev. B 58 (7) (1998) 3641. [15] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (12) (1976) 5188. [16] M.J.P. Musgrave, J.A. Pople, Proc. R. Soc. 268 (1962) 474. [17] J.P. Goss, I. Hahn, R. Jones, P.R. Briddon, S. O¨berg, Phys. Rev. B 67 (2003) 045206.
[18] N. Fujita, R. Jones, J.P. Goss, P.R. Briddon, S. O¨berg, Appl. Phys. Lett. 87 (2005) 021902. [19] N. Stoddard, P. Pichler, G. Duscher, W. Windl, Phys. Rev. Lett. 95 (2005) 025901. [20] H. Sawada, K. Kawakami, A. Ikari, W. Ohashi, Phys. Rev. B 65 (2002) 075201. [21] C.P. Ewels, R. Jones, S. O¨berg, J. Miro, P. Dea´k, Phys. Rev. Lett. 77 (1996) 865.
Physica B 401–402 (2007) 159–162 www.elsevier.com/locate/physb
First-principles study on the local vibrational modes of nitrogen–oxygen defects in silicon N. Fujitaa,, R. Jonesa, S. O¨bergb, P.R. Briddonc a
School of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, UK Department of Mathematics and HPC2N, Lulea˚ University of Technology, SE-97187 Lulea˚, Sweden c Physics Centre, School of Natural Science, University of Newcastle upon Tyne, Newcastle NE1 7RU, UK b
Abstract In this paper we investigate the interaction of nitrogen and oxygen by means of local density functional theory. While nitrogen-pairoxygen defects (N2 –Om ) have been studied in detail previously, the existence and role of nitrogen–oxygen defects containing only one nitrogen atom (N–On ) is still controversial. Motivated by recent infrared absorption measurements, where several new absorption lines were observed, we present first-principles studies on the ground state configuration, binding energy and local vibrational modes of NO and NO2 . We suggest that the NO2 defect gives rise to the experimentally observed lines at 1002, 973 and 855 cm1 . r 2007 Elsevier B.V. All rights reserved. Keywords: Modelling; Silicon; Nitrogen; Oxygen; Local vibrational modes
1. Introduction Today it is well known that nitrogen has significant effects on the materials properties of silicon. It strongly enhances oxygen precipitation which improves the gettering potential of Czochralski silicon (Cz-Si) [1,2]. In float-zone silicon (FZ-Si), it suppresses void formation [3], whereas in Cz-Si it leads to an increased density of smaller voids compared with nitrogen-free Cz-Si. Since voids can lead to device failure, there has been a concerted attempt [4] to understand the interactions between nitrogen, oxygen and vacancies at high temperature. Here we limit ourselves to the electrically active interstitial nitrogen–oxygen (NO) and the nitrogen–oxygenpair (NO2 ) defect. Previously, it has been suggested that neither NO nor NO2 plays an important role due to their negligible concentrations in the material [5]. However, this result was based on experimental data, where the nitrogen concentration of the sample was unusually high ð½N ¼ 1:84 1016 cm3 Þ [6]. Recently, it has been shown that both the NO and the NO2 defect can play a significant role at lower nitrogen concentrations [7,8]. Corresponding author. Tel.: +44 26 4137; fax: +44 26 4111.
E-mail address: [email protected] (N. Fujita). 0921-4526/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2007.08.136
While it is known that the NO2 defect is a member of the nitrogen related shallow thermal donor (STD) family, it was also proposed that the NO defect can act as a STD. The dominant form of nitrogen in both FZ-Si and Cz-Si introduced during growth is the nitrogen-pair defect, which was successfully identified in a combined study of channeling and infrared absorption measurements coupled with first-principles calculations [9]. The combination of such experimental and theoretical efforts also led to the identification of the dominating nitrogen–oxygen species in Cz-Si, where four strong bands at 1030, 999, 805 and 739 cm1 are observed in addition to the two lines at 963 and 766 cm1 attributed to the nitrogen-pair [10]. One hour isochronal annealing shows that the intensity of the two lines associated with the nitrogen dimer is decreasing between 400 and 600 1C while the three lines due to nitrogen–oxygen defect complexes become more prominent. Between 600 and 800 1C the intensity of the nitrogen pair related bands is highly increasing, reaching its maximum at about 800 1C [6]. Above 800 1C the intensity of these two lines drops until the bands are annealed out completely at 1100 1C. The intensity of the nitrogen–oxygen related bands decrease above 600 1C. This completely complementary annealing behaviour indicates that there
ARTICLE IN PRESS N. Fujita et al. / Physica B 401–402 (2007) 159–162
160
must be some interaction between nitrogen and nitrogen– oxygen defects between 400 and 800 1C. In recent IR measurements by Inoue et al. [11], N-doped Cz-Si samples with various concentrations of nitrogen were used. The resulting absorbance spectra showed a similar temperature dependence of the various bands as observed by Qi et al. [6]. Furthermore several new peaks were found after 2 h of annealing below 900 1C. Two peaks at 1018 and 810 cm1 were tentatively assigned to the N2 O2 defect in a previous study [5]—however, the origin of several other peaks remained unclear. Motivated by these experimental results, we present the atomic structures, binding energies and local vibrational modes (LVMs) of the NO and the NO2 defect in the following. 2. Method Within this work we use the AIMPRO local density functional theory code [12,13] to find the minimum energy configuration of the two defect structures and to investigate their corresponding binding energies and LVMs. All calculations are performed in 216 atom cubic silicon supercells. The chosen size of the supercells ensures that the spacial separation of the defect and its periodically repeated images is adequate to simulate an isolated defect in the material. Core electrons on Si, N and O are eliminated by using the norm-conserving pseudopotentials by Hartwigsen, Goedecker and Hutter [14]. The wavefunction basis consists of independent s, p and d Gaussian orbitals. Eight special k-points generated by a 2 2 2 Monkhorst–Pack [15] grid are used to sample the Brillouin zone. All atoms in the cell are allowed to relax to find the stable structures. The binding energy of a defect formed by the reaction A þ B ! AB is given as E b ðABÞ ¼ E f ðAÞ þ E f ðBÞ E f ðABÞ,
potential [16], fitted from the double derivatives of bulk silicon obtained using AIMPRO, is used. Previously, it has been shown that the AIMPRO method leads to a binding energy of 3.67 eV for N2 and IR-active modes at 968 and 773 cm1 compared with experimental values of 962 and 765 cm1 [17]. Furthermore the effect of isotope substitution could be reproduced successfully. The method also yielded in a migration barrier of 2.7 eV for N2 [18] which is close to other calculations [19,20].
3. Results and discussion The NO defect which is shown in Fig. 1 is situated in one of the six identical planes of the diamond lattice. We find that in the neutral ground state configuration the oxygen atom is overcoordinated, forming a square together with the nitrogen atom and their two common silicon bonding neighbours. Previous density functional theory calculations where the NO defect was embedded in a small hydrogen terminated cluster ðSi79 H68 Þ suggested a slightly different structure, in which the oxygen atom is two-fold coordinated and located in a bond centered position [21]. Our present calculations show that this structure is slightly higher in energy by about 0.2 eV. Considering the formation of NO by the reaction N þ O ! NO we find a binding energy of 1.5 eV. The local vibration modes including different isotope substitutions of nitrogen and oxygen are presented in Table 1. We find three LVMs which are strongly localised on the defect atoms. In the case of 14N16O the upper two modes at 1001 and 801 cm1 are related to the nitrogen atom, whereas the oxygen gives rise to another mode at 722 cm1 .
(1)
x
where E tot ðAÞ P is the total energy of the supercell containing the defect, x nx mx is the sum over all atoms with mx being the chemical potential of n atoms of the respective species x contained in the investigated system. The entropy term TS is normally neglected. To determine the LVMs of a relaxed structure we need to calculate the second derivatives of the total energy with respect to the positions of the atoms which are forming the defect and their neighbours. In practice only the entries of the dynamic matrix, which are related to the defect atoms and their neighbours are calculated explicitly. For bulk-like atoms away from the defect a Musgrave–Pople interatomic
140°
1.84
where E f ðAÞ, E f ðBÞ and E f ðABÞ are the formation energies of the defect structures A, B and AB, respectively. Thus a bound system is represented by a positive binding energy at absolute zero and neglecting zero-point energies. The formation energy E f of a defect A is given as X nx mx þ TS, (2) E f ðAÞ ¼ E tot ðAÞ
1.72 126°
97° 92°
1.74 N 1.75
O 1.76
1.78 2.38
Fig. 1. (Color online) Ground state configuration of the neutral NO defect in silicon.
Table 1 Local vibrational modes of the nitrogen–oxygen (NO) defect in silicon, including isotope substitutions of the involved defect atoms 14
N16O
15
14
1001 801 722
974 783 721
999 800 690
All modes are given in cm1 .
N16O
N18O
ARTICLE IN PRESS N. Fujita et al. / Physica B 401–402 (2007) 159–162
The observed downward shifts after isotope substitution clearly confirm these assignments. The minimum energy structure of the NO2 defect is shown in Fig. 2. Considering a planar defect within one of the h1 1 0i planes, there are two possible nearest neighbour sites for the second oxygen atom. We find that the oxygen atom favours a bond centred position, where it bridges the Si–Si bond next to the oxygen atom of the NO square. The binding energy of the second atom to NO, i.e. considering the reaction NO þ O ! NO2 is 1.1 eV. Our calculations show that the previously suggested C 2v symmetry configuration (O–N–O) where the two oxygen atoms are situated on either side of the nitrogen atom is higher in energy by about 0.2 eV [21]. If the symmetry is intentionally broken both oxygen atoms remain two-fold coordinated, however the relaxed structure is then only 0.1 eV higher in energy than the N–O–O structure depicted in Fig. 2. Since the NO2 defect possesses two spatial configurations which are almost equal in energy, the LVMs of both NO2 structures are given in Table 2. Both NO2 defects give rise to five different vibrational modes. For the N–O–O structure the highest mode at 1022 cm1 is strongly localised on the nitrogen atom. Substituting 14N with 15N results in a downward shift of this mode by 26 cm1 . The second highest mode at 977 cm1 is related to the two-fold
1.79 1.72 124°
94° 97°
1.74 N 1.75
141° 1.72 1.63 O1 132° 1.78 O2 1.68
Table 2 Local vibrational modes of the two lowest energy configurations of the nitrogen–oxygen-pair (NO2 ) defect, including isotope substitutions of the involved defect atoms
O–N–O
14
N16O16O
14
14
1022 (N) 977 (O2) 812 (N,O1) 794 (N,O1) 670 (O2)
1022 (N) 934 (O2) 812 (N,O1) 793 (O1,N) 661 (O2)
16
1084 (N) 970 (O2) 856 (N) 751 (O1) 658 (O2)
O14N16O
N16O18O
14
15
1018 (N) 976 (O2) 805 (N) 766 (O1) 667 (O2)
1018 (N) 933 (O2) 805 (N) 765 (O1) 657 (O2)
996 976 805 781 670
16
18
18
16
1083 (N) 929 (O2) 855 (N) 751 (O1) 649 (O2)
1082 (N) 970 (O2) 856 (N) 716 (O1) 658 (O2)
1081 (N) 928 (O2) 855 (N) 716 (O1) 649 (O2)
1054 (N) 969 (O2) 836 (N) 750 (O1) 658 (O2)
O14N18O
N18O16O
O14N16O
N18O18O
O14N18O
coordinated oxygen atom (O2). The modes at 812 and 794 cm1 are localised on the first oxygen atom (O1) and the nitrogen atom. The lowest mode at 670 cm1 refers to O2, but is not as strongly localised on O2 as the mode at 976 cm1 . Comparing the experimentally observed lines at 1002, 973 and 855 cm1 suggests that these modes are related to the NO2 defect. Considering the energetically slightly less favourable O–N–O structure, the nitrogen related modes are found at 1084 and 856 cm1 . The upper mode is about 60 cm1 higher than the highest calculated mode of the N–O–O structure. The two oxygen atoms give rise to three modes at 970, 751 and 658 cm1 . One should notice the similarity of the two modes at 970 and 658 cm1 compared to the modes at 976 and 670 cm1 of the N–O–O structure. Isotope substitutions do not alter the localisation of the respective defect atoms. 4. Summary In summary, we presented the neutral ground state configurations and local vibrational modes of the NO and NO2 defect in silicon. The upper three calculated modes of the NO2 defect are reasonably close to the experimental modes at 1002, 973 and 855 cm1 and hence we suggest that these modes are due to NO2 . However a definite assignment can only be made, if the isotopic shifts we presented here in this paper can be reproduced by experimental measurements. Experimental modes which could correspond to our calculated modes for the NO defect have not been observed yet. Acknowledgements
Fig. 2. (Color online) Ground state configuration of the neutral NO2 defect in silicon.
N–O–O
161
N16O16O (N) (O2) (O1,N) (N) (O2)
O15N16O
The atoms denoted in brackets refer to the localisation of the modes on these atoms (for N–O–O see Fig. 2). All modes are given in cm1 .
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