Theory of a carbon-oxygen-hydrogen recombination center in n-type Si

We have recently found that in-diffusion of hydrogen into n-type Si crystals containing oxygen and carbon impurities can result in the formation of powerful recombination centers (M. Vaqueiro-Contreras et al., to appear in PSS RRL). Here, we describe a combination of ﬁ rst-principles calculations and electrical measurements to investigate the composition, structure, electrical activity and recombination mechanism of a carbon-oxygen-hydrogen complex (COH) in Si. We found a defect comprising a carbon-oxygen complex connected to an H atom whose location depends on the charge state of the complex, and showing a calculated acceptor level at E v þ 0.3 eV, a few meV away from the observations. Bistable carbon – oxygen – hydrogen complex in silicon. Carbon, oxygen, hydrogen, and silicon atoms are shown in gray, red, black, and white, respectively.

1 Introduction Hydrogen, oxygen and carbon species are common contaminants in several kinds of silicon materials. Their origin is broad-based, ranging from the graphite components in the Czochralski (Cz) furnace (carbon), to the intrinsic composition of the SiO 2 crucible (oxygen), or simply, they may be unavoidable (such as hydrogen) [1][2][3]. Their presence is not always unintentional though. For instance, during solar cell fabrication, specific impurities are deliberately introduced, one prominent example being the deposition of a front-facing silicon nitride anti-reflection layer, which introduces large quantities of fast-diffusing atomic hydrogen into the Si [4]. This process brings important benefits, such as the reduction of surface recombination, although the underlying mechanism and possible side-effects of H injection are far from clear.
Isolated carbon and oxygen impurities in Si are electrically inert and have been subjected to extensive experimental and theoretical studies. In as-grown Cz-Si, they occur in large concentrations (usually in magnitudes of ppm atoms), normally occupying substitutional (C s ) and bond-centered interstitial (O i ) sites of the Si lattice, respectively. More than four decades ago, Newman, Willis and Bean assigned an infrared absorption band at 1104 cm À1 to a vibrational mode localized on a substitutional-carboninterstitial-oxygen (CO) complex in Si [5,6]. Combined annealing and isotope frequency shift data led the authors to the interpretation that the band resulted from the capture of a diffusing O i impurity, which becomes mobile above $450 8C, by a substitutional carbon atom. These results were later supported and translated into an atomistic model by Kaneta and co-workers [7], where the O atom was not directly connected to C. Instead, C and O atoms were separated by an intermediate Si atom forming a C s -Si-O i unit, avoiding the formation of a C-O bond, in favor of stronger Si-O and C-Si bonds. The electronic activity of this center was not addressed at the time, but considering the coordination of the C, O, and Si-ligand atoms, the complex is expected to be electrically inactive.
Atomic hydrogen is an amphoteric impurity with negative-U ordered donor and acceptor occupancy levels at E c À 0.18 eV and $E c À 0.5 eV [8][9][10][11], respectively. It is a bistable impurity À in the positive charge state it is most stable on the site of highest electron density, that is at the bond-center site (H þ BC ), while in the negative charge state it avoids high electron density regions due to Coulomb repulsion, preferring to be located at the tetrahedral interstitial site (H À T ) [3]. The neutral defect is more stable at the BC site, meaning that the donor level involves essentially a direct transition between bond-centered H 0 BC and H þ BC þ e À states, hereafter referred to as a H BC (0/þ) transition, where the final state includes a free electron in the conduction band. On the other hand, the acceptor is the energy difference between H À T and H 0 BC þ e À , therefore involving a considerable lattice relaxation energy. This indirect transition is referred to as H T/BC (À/0).
Atomic H is known to interact effectively with both carbon and oxygen impurities in Si. For the case of carbon, theory and (Laplace) deep-level transient spectroscopy (DLTS) studies agree that the most stable form of a CH complex is the one in which the H sits between the C atom and its Si first neighbor [12]. Unlike isolated bond-centered H, it was reported that the C-H-Si defect (labeled CH II ) shows a positive-U ordering of its donor and acceptor states at E v þ 0.33 eV and E c À 0.16 eV, respectively [12]. An additional donor level at E c À 0.22 eV (labeled CH I ) was connected to a metastable precursor of CH II , and was suggested to consist on a Si-H-Si unit neighboring the C s atom [12]. In a recent report by St€ ubner and co-workers [13], from the analysis of DLTS, field-induced change of emission rates, annealing and depth-profile data, it was confirmed that the E c À 0.16 eV level (CH II in Ref. [12], but now referred to as CH A ) is an acceptor. However, they could not find any sign of CH I . Instead, a shallower donor transition at E c À 0.14 eV (labeled CH B ) was assigned to a CH n complex involving n > 1 hydrogen atoms [13].
With regards to the interaction of atomic H with O i , we know from DLTS that the electrical levels of OH are close to those of isolated H. Accordingly, donor and acceptor occupancy transitions at E c À 0.17 eV and E c À 0.68 eV were assigned to OH in Si [10,11]. Although first-principles modeling predict that hydrogen enhances oxygen diffusivity and that it does not bind directly to O [14][15][16], calculations of the electronic structure and electronic levels of OH in Si have not been reported so far.
We have recently reported the formation of powerful recombination centers in n-type silicon as a result of the reaction between hydrogen, carbon and oxygen species [17]. Accordingly, hole traps H 1 and H 2 at 0.38 and 0.36 eV above E v , respectively, were detected in Cz-Si subject to wet etching, remote plasma exposure and silicon nitride deposition, and they were assigned to COH complexes. We also demonstrated that the concentration of these COH defects is high enough to have a substantial impact on the minority carrier lifetime of Si-based solar cells.
Below we report on our latest results on the search for the atomistic and electronic details of the COH-related recombination center in Si by combining first-principles calculations with DLTS and LVM infrared absorption measurements. The next section starts with a description of the methods employed, which is followed by a summary of the key observations related to the complex. We then report on the interaction of atomic H with C and O. These results are particularly instructive. They provide us with the fundamental physical-chemical guidelines behind the model that explains the formation and properties of COH. Among the calculated observables we report binding energies, vibrational mode frequencies and electronic transitions. Schottky diodes and Ohmic contacts were fabricated on the samples prior to capacitance-voltage and DLTS measurements. Minority carrier transient spectroscopy (MCTS) [18] using a 940 nm light emitting diode for optical excitation from the back of the slice was used to determine the electronic properties of hole traps including directly measured capture cross sections used to calculate the contribution of carrier recombination at the traps to the minority carrier lifetime.
Local mode optical absorption measurements were undertaken at 30 K in the wavenumber range 500-1500 cm À1 in order to observe the vibrational modes of CO n complexes in the samples.
Minority carrier lifetime measurements were made using a Semilab WT-2000 PVN m-PCD machine and iodine/ ethanol surface passivation of the wafers.

Theoretical details
First-principles density functional calculations were carried out using the VASP package [19], which uses the projector-augment wave (PAW) method [20] to deal with core-electrons and planewaves with a maximum kinetic energy E cut ¼ 370 eV for the valence. Exchange-correlation interactions were Phys. Status Solidi A 214, No. 7 (2017) (2 of 6) 1700309 www.pss-a.com

Original
Paper dealt within the generalized gradient approximation [21], and the electron density (potential) was assumed to be converged when the energy change between two consecutive self-consistent steps was less than 1 meV. Substitutional C, interstitial O, and interstitial H impurities were inserted into pristine 216-Si-atom supercells with cubic shape, optimized lattice constant a ¼ 5.4687 Å, and respective Brillouin zones sampled over a 2 Â 2 Â 2 grid of special k-points. All defect structures were optimized using a quasi-Newton algorithm, until the forces acting on the atoms were converged within 0.01 eV ÅÀ 1 .
Electronic transitions were evaluated using the marker method [22]. Experimental levels from isolated interstitial H and from the vacancy-oxygen-hydrogen complex (VOH), were used as markers. When compared to bulk markers, these choices increase the accuracy of the calculated levels (often by about 0.1 eV) of complexes that incorporate bondcentered/tetrahedral H or a Si broken bond, respectively. The levels considered were H BC (0 [8][9][10][11]23].
LVM frequencies were obtained through diagonalization of a dynamical matrix composed of Hessian submatrices with respect to the displacement of impurity atoms plus their Si ligands. Hessian matrix elements were obtained numerically with explicit atomic displacements of 0.015 Aå long all symmetry-independent directions.
3 Experimental results In MCTS and DLTS spectra of the hydrogenated oxygen and carbon rich Si samples, four electron and four hole emission peaks were detected. In the DLTS spectrum shown in Fig. 1, the peak labeled as E 4 is associated with the so-called thermal double donors originating from oxygen complexes [24], whereas the peaks E 1 -E 3 are related to hydrogen complexes [25,26].
The E 1 -E 4 traps are not significant in terms of lifetime degradation and will not be further considered in this work. The MCTS spectrum and the L-MCTS spectrum, presented as an inset in the same figure, show hole emission related signals H 1 to H 4 . We have found that the dominant H 1 /H 2 signals are dependent of carbon, oxygen and hydrogen content.
Firstly, we have compared the DLTS and MCTS spectra of a FZ sample with almost negligible [O i ] and [C s ] with the spectra for Cz and CCz samples after hydrogenation. In the FZ hydrogenated samples the H 1 and H 2 signals were not detected [27], while for the Cz and CCz samples the signals showed a proportional increase with O i and C s content in the crystals. Secondly, the concentration depth profiles of the H 1 and H 2 traps are found to be similar to that for the phosphorus-hydrogen complex formed in the hydrogenated samples. This provides an evidence of the involvement of a single hydrogen atom into the defects, which give rise to the H 1 and H 2 traps. Finally, a good correlation has been found between the intensity of the LVM band with its maximum at 1104 cm À1 observed in the infrared absorption spectra of carbon and oxygen rich samples subjected to different heattreatments in the temperature range 550-700 8C and magnitudes of the MCTS signals due to the H 1 /H 2 traps in similarly heat-treated neighboring samples, which were hydrogenated and prepared for MCTS measurements [17]. The band at 1104 cm À1 is related to an LVM of the CO complex [5,6]. The results mentioned above give solid evidence of the carbon-oxygen-hydrogen composition of the complexes responsible for the H 1 /H 2 traps.
With L-MCTS we have carried out direct measurements of electron and hole capture cross-sections and hole emission rates of the H 1 and H 2 traps. The details of the measurement technique can be found in Ref. [27]. Capture cross-section measurements of minority and majority carriers resulted respectively in values of 9.8 Â 10 À16 and 2.0 Â 10 À17 cm 2 for H 1 , and of 7.9 Â 10 À16 and 1.95 Â 10 À17 cm 2 for H 2 . The defect levels obtained from the Arrhenius plots of T 2corrected hole emission rates correspond to 0.38 AE 0.01 eV and 0.36 AE 0.01 eV from the valence band for the H 1 and H 2 centers, respectively. These characteristics indicate that the defects have an acceptor-like behavior and likely to be powerful recombination centers in n-type material. Furthermore, it has been found that the H 1 /H 2 traps anneal out in the temperature range from 150 to 200 8C and their elimination resulted in significant improvement of lifetime in silicon wafers (see Refs. [17] and [27]). Figure 2(a) shows a substitutional carbon atom in Si with several Si ligands. It also shows some sites (black dots) among many at which we placed a hydrogen atom to investigate the relative stability of CH complexes. In agreement with Andersen et al. [12], we found that for all charge states investigated (À, 0, and þ), H prefers to connect directly to the carbon atom, close to site BC1. Other low-energy structures are The formation of a short C-H bond is an important stabilization factor for CH BC1 , in spite of the fact that it also leaves an unsaturated radical on the nearest Si atom. This dangling bond creates a semi-occupied one-electron state deep in the gap, making VOH an excellent marker to calculate its electronic levels. Comparing ionization energies and electron affinities of CH BC1 with the same quantities from VOH we obtain donor and acceptor levels for CH BC1 at E v þ 0.28 eV and E c À 0.17 eV, respectively, at most $0.05 eV away from the transitions observed at E v þ 0.33 eV and E c À 0.16 eV (labeled CH II ) [12,13].

Theoretical results 4.1 Carbon-hydrogen interactions
Also in line with Ref. [12], we found that in the positive and negative charge states the BC2 and AB(C) structures are metastable by only 0.30 and 0.23 eV, respectively. The former configuration comprises a Si-H þ BC -Si unit next to C s , and therefore it is expected to show donor activity in close resemblance to that of isolated H in Si. Here, isolated H BC should be a good marker. Accordingly, we obtain a CH BC2 (0/þ) transition at E c À 0.24 eV, about 0.02 eV deeper than the measured additional CH-related donor reported in Ref. [12] and labeled CH I . It is relevant to note that the calculated H BC2 (0/þ) location is deeper than CH BC1 (À/0) and also deeper than isolated H BC (0/þ). This is in excellent agreement with the relative locations of the CH I , CH II and E 3 0 DLTS signals [9,11,12]. We also found that CH BC4 (0/þ) (where H sits at the fourth neighboring BC-site to the C atom) has a donor level at 0.22 eV below E c , that is closer but still deeper than H BC (0/þ) and also still below H BC1 (À/0).
Following the suggestion of Ref. [13], that a CH n complex (with n > 1) could be responsible for a donor level at E c À 0.14 eV (labeled CH B ), we actually investigated that possibility for n ¼ 2. We found that CH 2 can adopt two nearly degenerate configurations (within 30 meV) similar to that of H Ã 2 in Si, forming C-H BC1 Á Á Á Si-H ABðSiÞ and H ABðCÞ -C Á Á Á H BC1 -Si trigonal structures. The configuration with both H atoms bound to the C atom is metastable by 0.6-1 eV (depending on the charge state). We also found that the two lowest-energy structures are electrically inert, and therefore, should the E c À 0.14 eV level belong to a CH n complex, our results indicate that n > 2, most likely with one H atom located on a Si-Si bond.

Oxygen-hydrogen interactions
Among the oxygen-hydrogen complexes investigated, those obtained after placing H next to interstitial O, as depicted in Fig. 2(b), had the lowest energy. While OH BC is the ground state in the positive charge state, OH AB was the most stable configuration in the negative charge state. The neutral defect is more stable with H at the BC-site (with OH 0 AB being metastable by 0.23 eV only). We note that the H atom in OH BC adopts a puckered configuration, making a Si-H-Si angle of 1368 after structural relaxation. This means that some of the compressive strain, which is present in isolated Si-H þ BC -Si and Si-O-Si defects along their 111 bond directions, is released in OH þ BC and that corresponds to a calculated binding energy of 0.30 eV. The binding energy of atomic H À to interstitial O (with OH À AB as a reaction product) is estimated as 0.47 eV after considering independent supercells with H À T and O i defects. Here, the negatively charged hydride ion establishes an ionic bond with the oxidized (positively charged) silicon atom that is connected to oxygen. The above figures match the experimentally determined binding energies of 0.29 and $0.5 eV for defects which give rise to the E3 00 and AT 00 signals [10,11], assigned to oxygen perturbed (0/þ) and (À/0) transitions of bond-centered and tetrahedral hydrogen, respectively.
Further confirmation of the above model comes from the calculated electrical levels. In this case, isolated atomic H is expected to do a good job as marker. Accordingly, we place OH BC (0/þ) and OH T/BC (À/0) transitions at E c À 0.16 eV and E c À 0.69 eV, respectively, in excellent agreement with the measured E3 00 and AT 00 signals with levels at E c À 0.17 eV and E c À 0.68 eV, respectively.

Carbon-oxygen-hydrogen complex
In line with Ref. [7], we found that in the ground state of the CO complex, the O atom is located at the BC2-site with respect to carbon (see Fig. 2(a)). CO BC1 and CO BC4 configurations were metastable by 1.23 and 0.15 eV, respectively. The binding energy of CO BC2 (against formation of uncorrelated substitutional carbon and interstitial oxygen impurities) was found to be 0.51 eV. Inspection of the band structure revealed a clean band gap and no electrical levels were found.
The CO complex gives rise to three C-related LVM absorption bands at 589, 640, and 690 cm À1 , respectively 18 cm À1 below and 33 and 83 cm À1 above the unperturbed C s -related triplet mode at 607 cm À1 . It also produces an Orelated band at 1104 cm À1 , 32 cm À1 below the prominent 1136 cm À1 band from interstitial O [5,6]. LVM frequency calculations for the CO BC2 model give C-modes at 557, 608, and 663 cm À1 plus one O-mode at 1074 cm À1 . The C-modes are 18 cm À1 below and 34, and 88 cm À1 above the calculated 575 cm À1 mode of isolated carbon. Analogously, we find the calculated O-mode frequency at 1074 cm À1 , 20 cm À1 below that of isolated O (calculated at 1094 cm À1 ). These figures improve previous modeling results [7], account very well for the observations, and provide undisputable evidence for the correctness of the atomistic model. For the interaction of H with CO, we found several lowenergy configurations, which differ on the defect charge state. For a negatively charged COH (which should be stable under equilibrium in n-type material) we found that the structure shown in Fig. 3(a) and labeled COH AB , is distinctly stable. Analogously to OH À AB , the H À anion is attached to the electron-depleted Si atom, which in this case is further oxidized due to the bond with an electronegative C atom.
For the neutral defect, we found the COH BC1 configuration shown in Fig. 3(b) to be the ground state. COH 0 AB is now metastable by 0.18 eV. The BC1 structure is made of a CH BC1 defect perturbed by a nearby interstitial O atom, so it is expected to show rather similar electronic properties to CH BC1 . Another low energy configuration was COH 0 BC2 (0.05 eV above the ground state), which is depicted in Fig. 3(c).
Finally, for positively charged COH, the ground state configuration is now COH BC2 (Fig. 3(c)), which resembles an OH þ BC complex stabilized by a nearby tensile C s defect. Another stable structure is COH þ BC1 (0.08 eV above the BC2 ground state). Now we proceed to the calculation of the electrical levels of COH. On this report, we will focus on the acceptor activity only. Accordingly, the relevant acceptor transitions are COH AB (À/0), COH AB/BC1 (À/0) and COH AB/BC2 (À/0). While the last two involve electronic states similar to that of the H T/BC (À/0) marker, the COH AB (À/0) direct transition finds no resemblance with either H T/BC (À/0) or VOH(À/0). Conversely, the OH AB (À/0) transition (observed at E c À 0.79 eV [11]) should closely describe the COH AB (À/0) level. Hence, we obtain indirect COH AB/BC1 (À/0) and COH AB/BC2 (À/0) levels at E c À 0.81 eV and E c À 0.76 eV, respectively, that is, E v þ 0.31 eV and E v þ 0.36 eV if we consider 1.12 eV for the band gap of Si. We also find a direct COH AB (À/0) at E c À 0.80 eV.
Although all three calculated levels agree very well with the location of the H 1 /H 2 hole traps, we note that we have two rather different mechanisms that could explain the recombination activity. These are (i) a direct COH AB (À/0) transition, or (ii) a mechanism involving indirect COH AB/BC1 (À/0) and COH AB/BC2 (À/0) levels which imply a structural change in the neutral charge state. A deeper understanding of the above processes will involve the calculation of the potential energy surface between the AB, BC1, and BC2 configurations. We leave this for a future report to be published elsewhere.
The structural distinction between the H 1 and H 2 traps is also an open question. Until now, we have considered the interactions between single C, O, and H species. It is possible that one of these traps involves two O or H atoms, and we intend to look at this problem in the near future.

Conclusions
We presented a joint theoretical and experimental study of the interaction of H with carbon-and oxygen-related defects in silicon. For convenience, we summarize all calculated levels and experimental assignments in Table 1.
We started by reporting on the interaction of H with a C s impurity, where based on the total energies and calculated levels, we confirm the support from first-principles theory to the assignment of CH II and CH I DLTS signals in Ref. 12 to carbon-hydrogen defects with the H atom on the firstand second-neighboring BC sites with respect to a C s impurity, respectively. We did not find any CH defect with two or less H atoms, which could give rise to a donor transition above H BC (0/þ). This suggests that the CH B level at E c À 0.14 eV reported in Ref. [13] could be related to a CH n complex involving n > 2 hydrogen atoms.
The calculations support the interpretation of earlier experimental work [11], according to which H can bind to interstitial oxygen to from either OH þ or OH À with negative-U ordering of the donor and acceptor levels. We found that for the positive charge state H is nearly bondcentered forming a Si-H þ BC -Si-O i -Si zig-zag chain (like the O-dimer in Si), while the negative defect adopts an antibonding configuration that results in a nearly trigonal H À AB -Si-O-Si linear defect. The calculated binding energies and electrical levels are in excellent agreement with the observations.  We finally investigated the CO complex and its interaction with H. We confirm that C and O atoms in CO are bound to a common Si atom À no direct C-O bond is established. The calculated local vibrational mode frequencies for this complex account very well for all four bands observed by infra-red absorption measurements.
The COH complex is predicted to adopt different configurations in all three charge states that were investigated (À, 0, and þ). In the negative charge state, and particularly in n-type material, the complex takes the form of an OH À AB defect perturbed by a nearby C s impurity, being therefore referred to as COH À AB . We suggest that this structure, shown in Fig. 3(a), corresponds to the observed hole-trapping center reported in Section 3. The neutral charge state was found to have several virtually degenerate configurations with the H atom either connected to the C atom, or at a nearby BC site (see Fig. 3(b) and (c)). Several calculated electrical levels are close to the observed H 1 /H 2 traps, although further work is needed in order to understand eventual defect transformations upon carrier trapping/ emission events.