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The Interstitial Carbon–Dioxygen Center in Irradiated Silicon

: We investigated, experimentally as well as theoretically, defect structures in electron irradiated Czochralski-grown silicon (Cz-Si) containing carbon. Infrared spectroscopy (IR) studies observed a band at 1020 cm − 1 arisen in the spectra around 300 ◦ C. Its growth occurs concomitantly with the decay out of the well-known vacancy-oxygen (VO) defect, with a Local Vibrational Mode (LVM) at 830 cm − 1 and carbon interstitial-oxygen interstitial (C i O i ) defect with a LVM at 862 cm − 1 , in silicon (Si). The main purpose of this work is to establish the origin of the 1020 cm − 1 band. One potential candidate is the carbon interstitial-dioxygen (C i O 2i ) defect since it is expected to form upon annealing out of the C i O i pair. To this end, systematic density functional theory (DFT) calculations were used to predict the lowest energy structure of the (C i O 2i ) defect in Si. Thereafter, we employed the dipole–dipole interaction method to calculate the vibrational frequencies of the structure. We found that C i O 2i defect has an LVM at ~1006 cm − 1 , a value very close to our experimental one. The analysis and study of the results lead us to tentatively correlate the 1020 cm − 1 band with the C i O 2i defect. the samples were subjected to isochronal anneals at selective temperatures up to ~600 ◦ C in open furnaces. Successive anneals with increased temperature in steps of ∆ T ~10 ◦ C and duration ∆ t = 20 min were conducted. After each annealing step, IR spectra were recorded at room temperature (RT) by means of a Fourier Transform Infrared (FTIR) spectrometer with a resolution of 1 cm − 1 . The two phonon background absorption was always subtracted from each spectrum by using a Float-zone sample of equal thickness with that of the Cz samples.


Introduction
The properties and behavior of semiconductors are affected by point defects and impurities introduced in the lattice during crystal growth and material processing. Si mainly contains carbon (C) and oxygen (O), which are unintentionally introduced impurities during crystal growth [1,2]. Upon irradiation, numerous reactions occur, leading to the formation of a variety of carbon-related and oxygen-related defects. Among these, the carbon interstitial (C i ), carbon interstitial-oxygen interstitial (C i O i, carbon interstitial-carbon substitutional (C i C s ), and the vacancy-oxygen (VO), which give rise to electrical and optical signals and have been studied both theoretically and experimentally using a range of techniques [1][2][3][4][5][6][7][8][9][10]. Notably, the C i O i, C i C s, and the VO are important recombination centers with adverse effects on the performance of Si-based devices [8][9][10]. Upon thermal annealing, these defects participate in many reactions leading to the production of various complexes. Therefore, it is necessary to know all the properties and behavior of these defects in order to improve the performance of the relative devices.
In the present study, we mainly investigate defects formed upon annealing out of the C i O i pair. The latter defect anneals out mainly by dissociation [1,11]. However, C i O i pairs participate in reactions with other defects where a small percentage of the C i O i migrate as an entity [1]. It has been suggested [12] that in the course of this migration, C i O i reacts with the VO. Both centers anneal out around 300 • C, and when they encounter, they lead to the formation of the carbon substitutionaldioxygen (C s O 2i ) defect, with a Local Vibrational Mode (LVM) frequency at 1048 cm −1 . Alternatively, C s O 2i could form according to the reaction [13], C i + VO 2 → C s O 2i . Reasonably, upon C i O i annealing, other carbon-related complexes could also form. Such complex is the carbon interstitial-dioxygen (C i O 2i ) defect [14,15]. In our studies, besides the 1048 cm −1 band, we have seen another one at 1020 cm −1 to arise in the spectra around 300 • C. This band is probably connected with the formation of new second-generation defects formed upon the disappearance of the C i O i pair. A potential candidate for the origin of the 1020 cm −1 band is the C i O 2i complex.
In a recent theoretical study [15], the relevant reactions and the migration paths of the interstitial carbon and interstitial oxygen impurities in Si were explored in detail. In particular, a model was presented regarding the formation and dissociation mechanisms of the C i O i and the C i O 2i complexes. The suggested [15] reaction paths for the formation of the latter defect involves (i) a further accumulation of oxygen in Formation mechanism (i) can occur via oxygen migration with an energy barrier of 2.53 eV, or C i O i migration, with a barrier of 2.45 eV. However, the dissociation of C i O i through reaction C i O i → C i +O i , has a barrier of 2.29 eV, providing the necessary conditions for formation reaction ii) to occur, ending up to a more stable C i O 2i complex, at a barrier of 2.33 eV. Early photoluminescence (PL) studies reported thermal treatments at 350-450 • C, have correlated the decay of the C-line (789.5 meV) of the C i O i defect with the growth of the P-line (767 meV) attributed to the C i O 2i defect [1,16]. Recent deep level transient spectroscopy (DLTS) studies have monitored the decay of the C i O i pair and the formation of the C i O 2i structure via the observation of the corresponding electronic levels at E V + 0.36 eV and E V + 0.39 eV [17] . These conclusions are in agreement with previous PL and DLTS measurements referring to the investigation of the C i O 2i defect [18,19]. It was suggested that the annealing of the C i O i occurs via dissociation into C i and O i , where a percentage of the released C i atoms are trapped by oxygen dimers to form the C i O 2i [17,18].
Defects that introduce electronic levels in the gap most possibly affect the functionality of devices by deteriorating in general their performance. It is, therefore, important to identify the origin of any defect signal appearing in the measurements. In this work, we have employed Infrared spectroscopy (IR) measurements coupled with density functional theory (DFT) and dipole-dipole interaction calculations to investigate the 1020 cm −1 band in irradiated Si. The whole analysis of the results has led us to correlate the 1020 cm −1 band with the C i O 2i defect.

Experimental
We used Czochralski (Cz-Si) p-type (boron-doped) samples with a resistivity of ρ~10 Ω cm. The initial oxygen and carbon concentrations were [O i ] = 1.1 × 10 18 and [C s ] = 1.6 × 10 17 cm −3 , respectively. The samples were irradiated with 2 MeV electrons with a fluence of 1 × 10 18 cm −2 at about 80 • C, using the Dynamitron accelerator at JAERI (Takasaki, Japan). After irradiation, the samples were subjected to isochronal anneals at selective temperatures up to~600 • C in open furnaces. Successive anneals with increased temperature in steps of ∆T~10 • C and duration ∆t = 20 min were conducted. After each annealing step, IR spectra were recorded at room temperature (RT) by means of a Fourier Transform Infrared (FTIR) spectrometer with a resolution of 1 cm −1 . The two phonon background absorption was always subtracted from each spectrum by using a Float-zone sample of equal thickness with that of the Cz samples.

Theoretical
Here, we employed spin-polarized DFT calculations using the Vienna Ab initio Simulation Package (VASP) code [20,21]. Plane wave basis sets and projected augmented wave (PAW) [22] potentials were applied to solve the standard Kohn-Sham (KS) equations. The supercell consisted of 250 Si atomic sites. The generalized gradient approximation (GGA) by Perdew, Burke, and Ernzerhof (PBE) [23] was employed for the exchange-correlation effects. The plane wave basis set extended to a cut-off of 500 eV. The 2 × 2 × 2 Monkhorst-Pack [24] k-point mesh yielded 8 irreducible k-points. Both positions of atoms and lattice parameters were relaxed simultaneously for the Geometry optimizations (constant pressure conditions) using a conjugate gradient algorithm [25]. Convergence criteria were: Force tolerance 0.001 eV/Å and stress tensor 0.002 GPa. The dispersion interactions were accounted for in the form introduced by Grimme et al. [26]. The present calculations were well converged, and the adequacy of the present methodology was discussed in previous work [27][28][29][30][31]. Figure 1 represents characteristic segments of the IR spectra of electron irradiated Si samples, recorded after irradiation, and at the temperature of 350 • C in the course of the isochronal anneals performed in this experiment. Well-known bands at 830 cm −1 (VO), at 862 cm −1 (C i O i ), and a pair at 936, 1020 cm −1 (C i O i (Si I )), were present in the samples immediately after irradiation [30]. After the 350 • C anneal, the first two bands of VO and C i O i diminished substantially, although the pair of bands of the C i O i (Si I ) defect disappeared as expected since they were stable up to~180 • C [32]. Additionally, a set of new bands emerged in the spectra, those at 888 cm −1 (VO 2 ), 1048 cm −1 (C s O 2i ) [12,13], and another band at 1020 cm −1 . The latter band grown in the spectra at~300 • C in the course of annealing was different from the 1020 cm −1 of the C i O i (Si I ) defect appearing in the spectra immediately after irradiation. Its study is the main focus of the present work.

IR Measurements
Crystals 2020, 10, x FOR PEER REVIEW 3 of 10

Theoretical
Here, we employed spin-polarized DFT calculations using the Vienna Ab initio Simulation Package (VASP) code [20,21]. Plane wave basis sets and projected augmented wave (PAW) [22] potentials were applied to solve the standard Kohn-Sham (KS) equations. The supercell consisted of 250 Si atomic sites. The generalized gradient approximation (GGA) by Perdew, Burke, and Ernzerhof (PBE) [23] was employed for the exchange-correlation effects. The plane wave basis set extended to a cut-off of 500 eV. The 2 × 2 × 2 Monkhorst-Pack [24] k-point mesh yielded 8 irreducible k-points. Both positions of atoms and lattice parameters were relaxed simultaneously for the Geometry optimizations (constant pressure conditions) using a conjugate gradient algorithm [25]. Convergence criteria were: Force tolerance 0.001 eV/Å and stress tensor 0.002 GPa. The dispersion interactions were accounted for in the form introduced by Grimme et al. [26]. The present calculations were well converged, and the adequacy of the present methodology was discussed in previous work [27][28][29][30][31]. Figure 1 represents characteristic segments of the IR spectra of electron irradiated Si samples, recorded after irradiation, and at the temperature of 350 °C in the course of the isochronal anneals performed in this experiment. Well-known bands at 830 cm −1 (VO), at 862 cm −1 (CiOi), and a pair at 936, 1020 cm −1 (CiOi(SiI)), were present in the samples immediately after irradiation [30]. After the 350 °C anneal, the first two bands of VO and CiOi diminished substantially, although the pair of bands of the CiOi(SiI) defect disappeared as expected since they were stable up to ~180 °C [32]. Additionally, a set of new bands emerged in the spectra, those at 888 cm −1 (VO2), 1048 cm −1 (CsO2i) [12,13], and another band at 1020 cm −1 . The latter band grown in the spectra at ~300 °C in the course of annealing was different from the 1020 cm −1 of the CiOi(SiI) defect appearing in the spectra immediately after irradiation. Its study is the main focus of the present work.   Figure 2 shows the thermal evolution of the VO, VO 2 as well as that of the C i O i and 1020 cm −1 bands. The latter band appeared in the spectra in the temperature range of 300 to 550 • C. Its evolution seemed to be connected with the decay of the C i O i defect and a potential candidate for its origin was the C i O 2i structure. We have performed DFT calculations in conjunction with dipole-dipole interaction calculations to investigate the possible connection of the 1020 cm −1 band with the C i O 2i structure.

IR Measurements
Crystals 2020, 10, x FOR PEER REVIEW 4 of 10 seemed to be connected with the decay of the CiOi defect and a potential candidate for its origin was the CiO2i structure. We have performed DFT calculations in conjunction with dipole-dipole interaction calculations to investigate the possible connection of the 1020 cm −1 band with the CiO2i structure.

DFT Results
Before proceeding, in order to be an agreement between the notation of DFT outcomes and that used in the dipole-dipole analysis, we will make a few remarks. When used, C refers to the Ci defect, O(1) refers to the Oi atom in the CiOi defect, and O(2) refers to the second Oi atom in the CiO2i defect. Thus, at some points, the CiOi defect is noted C-O(1).
The application of DFT calculations in the semiconductor materials is well established, and they can be used to provide information on the electronic properties and structure of point defects [33]. Considering defect clusters, their exact structure and geometry cannot be easily determined using experiments. This is an area where computational simulation can offer complementary information. To predict the prevalent structure, we considered all possible configurations (nearest neighbor, next nearest neighbor, and further apart) first for the CiOi and thereafter the CiO2i defect. The lowest energy CiOi defect is in excellent agreement with the structure previously reported [34][35][36]37] and references therein. Adding a further Oi leads to the formation of the CiO2i defect (refer to Figure 3). It should be stressed that the reported structure is the lowest energy one after systematically examining all possible configurations of the CiO2i defect in the Si lattice. This structure was thereafter adopted as the most possible one for our calculations.

DFT Results
Before proceeding, in order to be an agreement between the notation of DFT outcomes and that used in the dipole-dipole analysis, we will make a few remarks. When used, C refers to the C i defect, O(1) refers to the O i atom in the C i O i defect, and O(2) refers to the second O i atom in the C i O 2i defect. Thus, at some points, the C i O i defect is noted C-O(1).
The application of DFT calculations in the semiconductor materials is well established, and they can be used to provide information on the electronic properties and structure of point defects [33]. Considering defect clusters, their exact structure and geometry cannot be easily determined using experiments. This is an area where computational simulation can offer complementary information. To predict the prevalent structure, we considered all possible configurations (nearest neighbor, next nearest neighbor, and further apart) first for the C i O i and thereafter the C i O 2i defect. The lowest energy C i O i defect is in excellent agreement with the structure previously reported [34][35][36][37] and references therein. Adding a further O i leads to the formation of the C i O 2i defect (refer to Figure 3). It should be stressed that the reported structure is the lowest energy one after systematically examining all possible configurations of the C i O 2i defect in the Si lattice. This structure was thereafter adopted as the most possible one for our calculations.
For completeness, we also considered the density of states (DOS) plots and charge density plots (refer to Figure 4). There is a small gap state noted just below the Fermi level (refer to Figure 4a). This state belongs to the carbon interstitial, as confirmed by the atomic DOS of carbon (refer to Figure 4b). States belonging to the oxygen interstitial are mainly located in the deeper level (between 0 eV and 1 eV) (refer to Figure 4c,d). Charge density plots of oxygen di-interstitials are shown in Figure 4g,h. Decomposed charge density plot associated with carbon interstitial is delocalized over Si atoms it bonded to. Decomposed charge density plots of oxygen interstitials delocalized over the square planar ring. For completeness, we also considered the density of states (DOS) plots and charge density plots (refer to Figure 4). There is a small gap state noted just below the Fermi level (refer to Figure 4a). This state belongs to the carbon interstitial, as confirmed by the atomic DOS of carbon (refer to Figure 4b).
States belonging to the oxygen interstitial are mainly located in the deeper level (between 0 eV and 1 eV) (refer to Figure 4c,d). Charge density plots of oxygen di-interstitials are shown in Figure 4g,h. Decomposed charge density plot associated with carbon interstitial is delocalized over Si atoms it bonded to. Decomposed charge density plots of oxygen interstitials delocalized over the square planar ring.   For completeness, we also considered the density of states (DOS) plots and charge density plots (refer to Figure 4). There is a small gap state noted just below the Fermi level (refer to Figure 4a). This state belongs to the carbon interstitial, as confirmed by the atomic DOS of carbon (refer to Figure 4b).
States belonging to the oxygen interstitial are mainly located in the deeper level (between 0 eV and 1 eV) (refer to Figure 4c,d). Charge density plots of oxygen di-interstitials are shown in Figure 4g,h. Decomposed charge density plot associated with carbon interstitial is delocalized over Si atoms it bonded to. Decomposed charge density plots of oxygen interstitials delocalized over the square planar ring.  Black circle refers to a carbon atom, and red circles refer to oxygen atoms.  Figure 5 is a simplified structure model configuration of the CiO2i defect derived by DFT calculations. In essence, Figure 5 displays part of the lattice of Figure 3 containing the C and O(1) atoms settled in the (110) plane and the second oxygen interstitial atom, O(2). The C-O(1) direction forms an approximately 20° deeping angle with the 1 10 direction (the Si4-Si5 direction). Both C-O(1) and O(2) are IR active with reported [5] apparent charges and can be considered as two oscillating interacting dipoles. To estimate the LVM frequencies of the CiO2i defect, we applied a previously used procedure [38,39]   Regarding the C-O(1) dipole, C and O(1) atoms are taken as one particle with mass corresponding to the reduced mass of oxygen and carbon atom µ, located at the center of mass, at distance d from O(1) atom. The reduced mass µ is derived from the relation

LVM Estimations via the Dipole-Dipole Interaction Method
while the distance d from the relation To estimate the LVM frequencies of the C i O 2i defect, we applied a previously used procedure [38,39] based on the interaction of the C-O(1) and O(2) dipoles. The force constant of the perturbed oscillating C-O(1) entity is K C−O(1) and is given by the relation where ω C−O(1) are the LVM frequencies of the C-O(1) defect. Similarly, the force constant of the oscillating O(2) atom, K O(2) , is given by the relation (4) and corresponds to the ω O(2) =1107 cm −1 LVM frequency of the oxygen interstitial atom [2]. In this analysis, we use the values of K C−O(1) corresponding to the strongest experimentally detected LVM line at 862 cm −1 and the reported line [1,40] at 1116 cm −1 , both attributed to carbon-related modes. We whereq 1 ,q 2 are the unit vectors along the C-O(1) and [1 1 1] directions, respectively. The potential energy of the interacting dipole moments is given by [42] wheren is the unit vector along the direction that connects the two dipoles and d µ−O(2) = 3.36 Å is the distance between them. The motion of the two dipoles is described by the effective Hamiltonian By comparing Equations (6) and (7), we obtain the q-independent part λ, to be equal to λ = 138 J/m 2 . The Hamiltonian of Equation (7) has two normal modes with frequencies where "+" preceding the inner square root corresponds to the antisymmentric normal mode and "−" to the symmetric one. For ω C−O(1) = 862 cm −1 and ω O(2) = 1107 cm −1 we find ω =1006 cm −1 . Among them, we consider the band at 1006 cm −1 as the most possible candidate to be related to our experimental findings, as discussed below.

Discussion
The calculated frequency at 1006 cm −1 standing for the symmetric mode of the C i O 2i related to the 1116 cm −1 carbon-related mode of the C-O(1) defect lies very close to the experimental line at 1020 cm −1 , supporting the attribution of this line to the C i O 2i defect. Since the calculated dot product of the dipole moment vectors is positive, one would expect the symmetric modes at 872 and 1006 cm −1 to give stronger IR signals than the antisymmetric ones, at 1098 and 1205 cm −1 . In our spectra, only he symmetric mode at 1006 cm −1 is detectable. The other band at 872 cm −1 is not detected in our experiment. This is possibly because its weak signal is masked by the stronger signal of the VO 2 defect (Figure 1) in the same region. It is worth noting that if both dipoles oscillated along the direction connecting them, the theoretical outcome through the dipole-dipole interaction process would have provided a better fit (1021 cm −1 ) to the experimental value at 1020 cm −1 .
The present calculations provide support for the notion that the 1020 cm −1 line can originate from the C i O 2i defect. Regarding this correlation, it deserves noting that early IR studies of the evolution of carbon and its loss from solution, upon thermal treatments of Cz-Si at 450 • C, have revealed the formation of a band at 1026 cm −1 attributed to a carbon-oxygen dimer complex [43][44][45].
An important point: In our studies of electron irradiated silicon, the 1020 cm −1 band is formed around 300 • C upon the decay of the 862 cm −1 band of the C i O i pair. However, in proton-irradiated thermally treated Si, the formation of the C i O 2i occurs at temperatures above 400 • C according to the reaction C i +O 2i → C i O 2i [17][18][19]. The suggested mechanism in the latter reports involves the dissociation of the C i O i and the capture of the liberated carbon interstitials by oxygen dimers. Profoundly, at these temperatures the availability of oxygen dimers plays an important role in the validity of the above reaction. In our case of electron irradiated silicon, C i O 2i emerges in the spectra around 300 • C. However, the concentration of dimers at~300 • C is practically negligible [2], and the reaction C i +O 2i → C i O 2i could not account for the formation of the C i O 2i . Other reaction channels should govern the formation of the C i O 2i in our case. One suggested reaction is the following: It is known that C i O i anneals out mainly by dissociation (C i O i → C i + O i ), but a small percentage of them could migrate in the lattice as an entity [1,15], being trapped by O i atoms. This process leads to the formation of C i O 2i structure (O i + C i O i → C i O 2i ). Additionally, another reaction mechanism could be envisaged. It is known that among the reactions that VO pair participates upon annealing, the main two are the following [7]: VO + O i → VO 2 and VO + Si I → O i . In the latter reaction, sources of the participating self-interstitials are self-interstitial clusters formed in the course of the heavy irradiation of the Cz-Si [2]. In addition, O i could be additionally provided [7] by the dissociation of VO. Since VO anneals out in parallel with C i O i, the following scheme is suggested. The liberated O i atoms, in the course of VO dissociation or/and its destruction by self-interstitials, trap C i O i pairs leading to C i O 2i . Apparently, the above two suggested reaction channels for the formation of the C i O 2i defect may occur in parallel. Such reactions could account for the formation of the C i O 2i in irradiated Si and explain its appearance at lower temperatures than those in thermally treated Si.
Regarding the differences in the formation temperature of the C i O 2i defect between our electron irradiated samples and proton irradiated samples [17][18][19], the following should be noted: Proton irradiation generates higher order of damage than electron irradiation. This might result in more stable defects, which may need a higher temperature to anneal out. Additionally, the detected signal in our IR studies could refer to different states of the same defect reported in previous photoluminescence (PL) and DLTS measurements [17][18][19]. Further clarification of this issue requires future work.
Radiation defects in semiconductors attract a lot of interest, especially for technological purposes. Their presence in the Si lattice, in the course of material processing for special applications as for instance, radiation detectors, affect the device operation. Apparently, any information for such defects may improve the device functionality since it provides opportunities for their control. The present study is an attempt to determine the origin of an IR signal at 1020 cm −1 . We have connected it with a second-order generation carbon-oxygen related defect, that is the C i O 2i complex. In future work we shall use higher irradiation fluencies to study the annealing of the C i O 2i defect and the formation of larger complexes in this family of defects as the C i O 3i structure, recently predicted theoretically [15].

Conclusions
The annealing of defects in irradiated Cz-Si revealed a new IR band at 1020 cm −1 emerging in the spectra around 300 • C upon the decay of the 862 cm −1 band of the C i O i defect. PL and DLTS data have previously correlated certain signals with the formation of a C i O 2i defect grown in the spectra upon the decay of the C i O i defect. In the present study, we employed systematic DFT calculations to gain an understanding of the lowest energy structure of the C i O 2i defect. Thereafter, the dipole-dipole interaction calculations have estimated an LVM frequency at 1006 cm −1 related to this center. This value lies very close to the experimental one at 1020 cm −1 . We have assigned the latter band to the C i O 2i defect.