Self-compensation in chlorine-doped CdTe

Defect energetics, charge transition levels, and electronic band structures of several Cl-related complexes in CdTe are studied using density-functional theory calculations. We investigate substitutional chlorine (ClTe and ClCd) and complexes formed by ClTe with the cadmium vacancy (ClTe-VCd and 2ClTe-VCd) and the TeCd antisite (ClTe-TeCd). Our calculations show that none of the complexes studied induce deep levels in the CdTe band gap. Moreover, we find that ClTe-VCd and ClTe are the most stable Cl-related centers in n-type and p-type CdTe, under Te-rich growth conditions, showing shallow donor and acceptor properties, respectively. This result suggests that the experimentally-observed Fermi level pinning near midgap would be originated in self-compensation. We also find that the formation of the ClTe-TeCd complex passivates the deep level associated to the Te antisite in neutral charge state.


Results and Discussion
substitutional chlorine in Cdte. As an isolated substitutional impurity, chlorine can occupy only a Cd site or a Te site in CdTe. Our initial model was simply substitute a lattice atom with the neutral Cl impurity and left the system to relax. Figure 1(a) shows the equilibrium geometries and band structure of substitutional chlorine in CdTe in the neutral charge state. Our results for chlorine occupying a Te site (Cl Te ) indicate a four-fold coordinated impurity with almost undistorted geometry, preserving the T d symmetry. The Cd atoms next to the impurity relax outwards by about 3%, resulting in a Cd-Cl bond distance of 2.936 Å. The same configuration is observed in single positive charge state. The electronic properties indicate that Cl Te is a shallow donor, introducing an impurity level resonant in the conduction band (c 2 ). The squared wavefunction, or simply the charge density, corresponding to this level indicates a Cl-Cd antibonding character, as shown Fig. 1(a). The electronic structure shows a band gap of 1.40 eV, close to that calculated for pristine CdTe (1.44 eV). Figure 1(b) shows the equilibrium geometries and band structure of chlorine occupying a Cd site (Cl Cd ), revealing a strong relaxation from the T d symmetry. In the neutral charge state, the impurity has two-fold coordination, forming a bridge-like structure between two Te atoms. The Te-Cl bond distances are found to be of 2.627 Å with a Te-Cl-Te bond angle of 169°. Whereas, the two other Te atoms become three-fold coordinated at a distance of 3.75 Å from the Cl atom. The same configuration is observed in single negative charge state. It is interesting to note that the Cl Cd equilibrium configuration is similar to that expected for the V Cd -Cl i complex. The electronic properties of Cl Cd show that it is a shallow acceptor that introduces a strong perturbation on the top of the valence band. These states are associated with the three-fold coordinated Te atoms next to the Cl atom. In addition, an impurity level with an antibonding character (c 2 ) is found to be resonant in the conduction band, as shown Fig. 1(b).
The stability of substitutional chlorine in CdTe is obtained through formation energy calculations, as shown in Fig. 2. Our results indicates that Cl Te is the most stable impurity for both Cd-rich and Te-rich growth conditions. Moreover, the Cl Te impurity is a shallow donor with a ε(+/0) transition level at VBM + 1.29 eV, while Cl Cd is a shallow acceptor that introduces a ε(0/−) transition level at VBM + 0.15 eV. However, Cl Cd shows a high formation energy in comparison with Cl Te , suggesting that it would be unlikely to form at relevant concentrations.
the Cl te -V Cd complex in Cdte. The Cl Te -V Cd complex in CdTe is formed when a Cl atom replaces a Te atom nearest neighbor to a Cd vacancy 38 . Previous DFT calculations have identified the isolated Cd vacancy as the dominant intrinsic acceptor in CdTe [39][40][41] . We found that V Cd is stable in T d , D 2d , and C 2v symmetries, being the V Cd (C 2v ) configuration the global minimum. We also found that V Cd is stable in C 3v symmetry in the single-negative charge state, which is stabilized by a hole polaron, in good agreement with previous calculations 41 . In the neutral charge state, V Cd (T d ) and V Cd (D 2d ) are 0.64 and 2.11 eV higher in energy than V Cd (C 2v ), respectively. The V Cd (C 2v ) structure is characterized by the formation of a Te-Te dimer between two undercoordinated Te atoms neighboring to the vacancy. Our results show that this dimer has a bond distance of 2.773 Å, while the others Te atoms remain three-fold coordinated and are displaced inward the vacancy by about 0.24 Å with respect to their perfect crystal positions. Interestingly, the V Cd (C 2v ) in the neutral charge state exhibits a ground-state configuration with all the valence band filled and all the conduction bands empty. This result is in close agreement with recent DFT-HSE06 calculations, although the formation of the Te-Te dimer was not reported 42 . On the other hand, the V Cd (D 2d ) structure reveals the formation of two Te-Te dimers with bond distances of 2.765 Å, while its electronic structure indicates a double donor character.
Next, we investigate the formation of the Cl Te -V Cd complex starting from the V Cd (T d ) geometry by substituting a neighboring Te atom by a Cl atom. Our results for the electronic band structure and the equilibrium geometry are shown in Fig. 3(b). We find that the neutral complex is stable in C 3v symmetry [hereafter referred as (Cl Te -V Cd ) (C 3v )], where the Cl Te impurity moves outward the vacancy by 0.5 Å, while the three-fold coordinated Te atoms relax inward by 0.29 Å with respect to their perfect crystal positions, as shown in Fig. 3(b). Moreover, neutral (Cl Te -V Cd )(C 3v ) has a hole at the VBM, indicating a shallow acceptor character in good agreement with previous theoretical 35,43,44 and experimental 32 results.
By taking into account the high stability of the V Cd (C 2v ) structure that form the Te-Te dimer, we construct another complex by substituting an under-coordinated Te atom by a Cl atom. Our results for the band structure and equilibrium geometry of this complex are shown in Fig. 3(a). We find that the new complex geometry preserves the Te-Te dimer of the V Cd (C 2v ) configuration with a bond distance of 2.771 Å. Moreover, we found that the substitutional chlorine moves outward the Cd vacancy by 0.5 Å. This complex has C s symmetry with only one symmetry plane [hereafter referred as (Cl Te -V Cd )(C s )], which is 0.73 eV higher in energy than the (Cl Te -V Cd ) (C 3v ) structure in the neutral charge state. It is worth noting that the Cl Te -V Cd complex was recently studied by   36 . They found two equilibrium geometries for this complex, which is stable in both C s and C 3v symmetries, in the neutral and in the negative charge state, respectively. Although the two configurations of the complex agree with our calculations, the equilibrium geometry of the neutral (Cl Te -V Cd ) (C s ) differs from our results. We find the formation of a Te-Te dimer, while Lindström et al. 36 found only a small approach between the same Te atoms, suggesting that its configuration may be a metastable state.
Our results shows that the (Cl Te -V Cd )(C s ) complex has a shallow donor property, in contrast to the (Cl Te -V Cd ) (C 3v ) complex, which is a shallow acceptor, as shown Fig. 3. Although with a higher formation energy, the (Cl Te -V Cd )(C s ) complex is likely to form in the single-positive charge state, which is a ground state configuration with all the valence band filled and all the conduction bands empty. Indeed, for the Fermi energy close to the VBM the [(Cl Te -V Cd )(C s )] + configuration has much lower energy than the [(Cl Te -V Cd )(C 3v )] − polaronic configuration found in ref. 36 , which acts as a harmful electron trap. Figure 4 shows the formation energies of (Cl Te -V Cd )(C s ) and (Cl Te -V Cd )(C 3v ), indicating that both complexes can coexist for the Fermi energy close to VBM + 0.33 eV, the energy at which their formation energies are equal, as indicated by the arrow. As the transition between the C 3v and C s geometries involves the formation of a Te-Te dimer, we want to know the energy needed to overcome the barrier between them, that is the activation energy, and if this process is likely to occur at the operational conditions. To do that, we calculate the minimum energy path (MEP) of neutral Cl Te -V Cd moving from C 3v to C s geometries, using the climbing-image nudged elastic band (NEB) method 45 . This method finds the MEP between two local minima previously obtained, by optimizing intermediate geometries called images. Then, the activation energy is obtained by calculating the difference between the lowest minimum and the saddle point. In our calculations we obtain the MEP using GGA-PBE functional, considering a 128-atom supercell with all atoms free to relax, and ten images between the C 3v and C s local minima. We obtain an activation energy of 0.64 eV, as shown in Fig. 5. www.nature.com/scientificreports www.nature.com/scientificreports/ To estimate the MEP using the hybrid HSE06 functional, which is the functional used throughout this work, we re-evaluated the GGA-PBE images previously found using now the HSE06 functional without allow the system to relax (single-point energy). It is important to note that NEB calculations using directly the HSE06 functional are not possible due to the huge computational time required. Our results show an activation energy of 0.85 eV, as shown in Fig. 5. The difference between both minimum energy paths is partially attributed to a residual strain in the single-point calculation and the inclusion of the fraction of exact exchange due to the hybrid functional. It is interesting to note that the larger difference between MEPs is obtained when the Te-Te dimer becomes to form. We believe that a realistic activation energy for transition between the C 3v and C s geometries should be something between GGA-PBE and HSE06 calculations. Experiments have measured activation energies for the chlorine diffusion in CdTe to be of 0.63 and 1.32 eV for a temperature range between 200 and 700 °C 46 . Therefore, the activation energy for the C 3v to C s transition in the neutral Cl Te -V Cd complex lies in the range of 0.64 to 0.85 eV, suggesting that it is likely to occur.
However, the activation energy for the inverse transition C s to C 3v , which would be the most probable direction, is just of 0.15 eV. Therefore, at the HSE06 level of calculation, the formation of the Cl Te -V Cd complex would start with a neutral V Cd vacancy with C 2v geometry. If a Cl impurity occupies the position of one of the two three-fold coordinated Te atoms surrounding the vacancy, a neutral (Cl Te -V Cd )(C s ) complex would form. According to Fig. 3(a), this complex is a shallow donor being likely to lose an electron, changing to the (Cl Te -V Cd ) (C 3v ) geometry after overcoming an energy barrier of 0.15 eV.
The 2Cl te -V Cd complex in Cdte. We subsequently investigate the possibility of a new complex consisting of two Cl atoms substituting two of the four undercoordinated Te atoms nearest neighbors to a Cd vacancy (hereafter referred as 2Cl Te -V Cd ). This complex was predicted in 1974 by Canali et al. 47 , suggesting that it would be likely to be found in high-resistivity donor-doped CdTe. After substituting the second Te atom by a Cl atom in (Cl Te -V Cd )(C 3v ) as shown in Fig. 3(b), we observe that the system relaxes to the 2Cl Te -V Cd configuration shown in  www.nature.com/scientificreports www.nature.com/scientificreports/ Fig. 6(a), exhibiting C 2v symmetry. The inclusion of the second chlorine fills the hole that (Cl Te -V Cd )(C 3v ), shows at the VBM, stabilizing the (2Cl Te -V Cd )(C 2v ) complex in neutral charge state. Moreover, the electronic structure of this complex shows that the neutral charge state is a ground-state configuration, that is with all the valence bands filled and all the conduction bands empty.
In addition, we find a second configuration for the 2Cl Te -V Cd complex, where the two adjacent undercoordinated Te atoms form a Te-Te dimer with a bond length of 2.771 Å, preserving the C 2v symmetry. In the neutral charge state, this complex has two excess electrons in the conduction bands, as shown in Fig. 6(b), indicating that 2Cl Te -V Cd is a double donor that would tend to transfer its excess electrons to uncompensated acceptors such as the V Cd . In this way, the ground-state configuration [2Cl Te -V Cd ] 2+ should be stabilized. Figure 7 shows the calculated formation energies for the two configurations of the 2Cl Te -V Cd complex as a function of the Fermi level, under both Te-rich and Cd-rich growth conditions. We find that the Te-Te dimer configuration, which will be referred as (2Cl Te -V Cd )(d), has the lowest formation energy for the Fermi level close to the VBM (n-type CdTe), being likely to be found under this condition. Whereas for other Fermi level positions, the complex configuration with the separated Te atoms is the most stable. Thus, the crossing point of formation energy lines, indicated by arrows in Fig. 7, shows that 2Cl Te -V Cd introduces a shallow transition level ε(2 + /0) at VBM + 0.1 eV. Interestingly, this complex exhibits the same defect formation energies under both Te-rich and Cd-rich growth conditions. the Cl te -te Cd complex in Cdte. We now turn to examine the complex formed by the substitutional chlo- www.nature.com/scientificreports www.nature.com/scientificreports/ which are stable in T d , C 3v and C s symmetries, respectively. We found similar results, but according to our formation energy calculations only + Te Cd 2 and Te Cd 0 would be stable, as shown in Fig. 8. The discrepancy can be attributed to finite size effect, as the authors of ref. 52 applied a potential alignment scheme in a 128-atom supercell, in contrast to our formation energy calculations performed with a larger 250-atom supercell. It is interesting to note that Te Cd shows higher formation energies than Cl Te for all values of the Fermi energy in the band gap, as can be seen by comparing Figs 8 and 2, suggesting that the chlorine impurity would be energetically favorable over any native defect. Moreover, the Te Cd defect exhibits a negative-U behavior, where the single-positive charge state is never stable, in agreement with previous calculations 40,50,52,53 . Hence, the Te Cd defect shows a ε(2 + /0) transition level at VBM + 0.4 eV. However, in a previous work using accurate quasiparticle DFT + GW calculations we found this state at VBM + 1.0 eV 53 . The electronic structure of + Te Cd 2 shows an empty t 2 level in the higher part of the CdTe band gap. After capturing two electrons, the defect experiences a Jahn-Teller distortion, which is characterized by the breaking a Te-Te bond, lowering the symmetry from T d to C 3v . In this way, the t 2 level split into a fully-occupied a 1 level and an empty e level, which are represented by v 1 and c 2 levels in the Te Cd 0 band structure, shown in Fig. 9(a).
Concerning Cl Te -Te Cd , our results suggests that this complex only exists in single positive charge state with similar formation energy than the Te Cd antisite, as shown Fig. 8. Figure 9(b) shows the band structure calculations of this complex, indicating a shallow donor character, without exhibiting deep levels in the band gap. This result  Interstitial chlorine in Cdte. In an earlier paper 54 , we discussed the role of interstitial chlorine in CdTe (Cl i ). In that study we found that Cl i is stable in at least five distinct interstitial sites with close formation energies. Moreover, this impurity introduces shallow energy levels that may lead to a donor-acceptor compensation mechanism. Nevertheless, the dominant configurations of Cl i have a formation energies higher than Cl Te and the 2Cl Te -V Cd complex for values of the Fermi level near midgap, under both Te-rich and Cd-rich growth conditions. We refer the interested reader to ref. 54 , the work of Lindström et al. 36 , and the topical review of Yang et al. 44 . self-compensation in chlorine-doped Cdte. Figure 10 summarizes the formation energies Cl-related defects in CdTe, which are likley to be formed due to their low formation energies. For values of the Fermi level in the lower part of the band gap (n-type CdTe), we observe that (Cl Te ) + is the most relevant defect under both Te-rich and Cd-rich growth conditions, acting as the dominant donor. Whereas, for the Fermi level in the higher part of the band gap (p-type CdTe), the relevant defect is the complex [(Cl Te -V Cd )(C 3v )] − , which is the dominant acceptor. Therefore, in the Te-rich limit, the closed-shell (Cl Te ) + donor would be compensated by the [(Cl Te -V Cd ) (C 3v )] − acceptor after transferring its electron in excess, leading to the Fermi level pinning at VBM + 0.92 eV, as indicate the arrow in Fig. 10(a).
Interestingly, at the crossing point between (Cl Te ) + and [(Cl Te -V Cd )(C 3v )] − in Te-rich CdTe, the complex 2Cl Te -V Cd is only 0.05 eV higher in energy [see Fig. 10(a)]. Thus, the existence of 2Cl Te -V Cd complexes will contribute to stabilize the charge neutrality condition, allowing the Fermi level pinning in CdTe:Cl without introducing a compensating deep level at variance of the cases of CdTe:Sn 27 and CdTe:Ge 55 . These results are in good agreement with the earlier work of Höschl et al. 56 , who suggested that Cl Te -V Cd and 2Cl Te -V Cd dominate (59% and

summary
In summary, we have investigated the electronic structure, formation energies, and transition states of substitutional chlorine Cl Te and Cl Cd , and the complexes formed by Cl Te with the most probable defects found in Te-rich CdTe, namely the Cd vacancy and the Te antisite. We find that the Cl Te -V Cd complex can exist in two geometries, with C s and C 3v symmetries, showing shallow donor and acceptor properties, respectively. We also identify a second complex containing two substitutional chlorine neighboring to the cadmium vacancy 2Cl Te -V Cd , which also can exist in two geometries, both with C 2v symmetry. The latter is found stable only in double positive charge state for n-type CdTe, while the former exhibits a ground-state configuration. Concerning the Cl Te -Te Cd complex, our results suggest that it is stable only in single positive charge state with similar formation energy than the Te Cd antisite. For a Fermi energy close to the middle of the CdTe band gap, the three complexes show formation energies of around 1 eV under Te-rich condition, as shown in Fig. 10(a), suggesting that they are equally likely to be found. Table 1 compares the formation energy values for all the Cl-related defects studied under Te-rich and Cd-rich conditions for the Fermi energy at the VBM.
Finally, we find that neither the complexes under study nor the substitutional Cl impurity induce deep level in the CdTe band gap. Therefore, our calculations suggest that self compensation between Cl-induced shallow donors and acceptors should be responsible for the high resistivity observed in detector-grade CdTe:Cl, usually grown in a Te-rich environment, in agreement with previous hypothesis 35 . Particularly, the (Cl Te ) + shallow donor would be compensated by the [(Cl Te -V Cd )(C 3v )] − shallow acceptor, leading to the Fermi level pinning at VBM + 0.92 eV. In addition, our results show that the formation of the Cl Te -Te Cd complex passivates the deep level associated to the Te antisite (Te Cd ), confirming to some extent the beneficial effect of chlorine in CdTe.

Methods
We performed first-principles calculations based on the density functional theory (DFT) 57,58 , as implemented in the Vienna Ab Initio Simulation Package (VASP) 59 . We used the Heyd-Scuseria-Ernzerhof (HSE06) 60,61 hybrid functional with the standard mixing parameter α = 25%, a plane-wave basis set with a cutoff energy of 285 eV. The core-valence interaction is described by the projector augmented-wave mathod 62 . Our calculations were performed using large 250-atom supercells, which were fully relaxed until the forces on each atom were less than 0.025 eV/Å. Our computational approach improves previous theoretical works in which smaller 64-atom supercell were used 36,44,63 , despite the fact that the convergence of hybrid functionals with respect to the supercell size may be slower than its local and semi-local counterparts 15,64,65 . Additionally, due to the high computational cost of the HSE06 calculations, only the Γ point was used for the Brillouin zone sampling, whereas band structures calculations were performed using a 128-atom supercell.
The formation energy (ΔH f ) of a defect in charge state q can be written as a function of the Fermi level (E F ) and the chemical potentials of the atomic species (μ i ) as follows 66 : are the total energy of the system with a defect in charge state q and the pristine system, respectively. E VBM is the energy of the valence band maximum. n i is the number of atoms of type i that have added or removed from a pristine system. For instance, in the case of Cl substituting a Cd atom in the charge state q, the formation energy can be obtained as: where E tot (Cd n Te n ) is the total energy of a supercell containing n primitive cells of CdTe and E tot (Cd n−1 Te n Cl) q is the energy of the same supercell with one Cd atom replaced by a Cl atom with q electrons removed. For Cl substituting a Te atom in charge state q (Cl q Te ), the same procedure is applied, just exchanging Te by Cd in Eq. (2). The chemical potentials in Eq. (2) are defined as: , with X {Cd, Te, Cl}, where E X is the energy per atom of bulk-phase Cd and Te, and gas-phase Cl (Cl 2 ). In addition, the thermodynamic equilibrium requires the following restrictions to the chemical potentials: Inequalities (4) and (5) represent necessary conditions to avoid that elements and compounds segregate, whereas Δμ Cd = 0 and Δμ Te = 0 represent Cd-rich and Te-rich conditions, respectively. ΔH(CdCl 2 ) and ΔH(CdTe) are the heats of formation of CdCl 2 and CdTe. The numerical values of heats of formation are obtained from HSE06 calculations. Relations (4) and (6) impose that both Δμ Cd and Δμ Te are larger than ΔH(CdTe). Others expressions like (5) can be set to avoid the formation of other compounds like TeCl 4 and Te 3 Cl 2 , but in practice (5) sets the maximum possible value for Δμ Cl in equilibrium with CdTe. E tot (Cd n Te n Cl) q in Eq. (2) includes size corrections for electrostatic interactions between nearest-neighbor images in the supercell calculation 67 . No additional corrections for band filling are needed 67 , as we used only the Γ point for the Brillouin zone sampling.