research papers
Local and electronic structure around Ga in CdTe: evidence of DX and Acenters
^{a}Vinča Institute of Nuclear Sciences, University of Belgrade, Belgrade, Serbia, ^{b}HelmholtzZentrum Berlin für Materialien und Energie GmbH, Berlin, Germany, ^{c}Chernivtsi National University, Chernivtsi, Ukraine, and ^{d}Freie Universität Berlin, Fachbereich Physik, Berlin, Germany
^{*}Correspondence email: vkotes@vin.bg.ac.rs
The lattice relaxation around Ga in CdTe is investigated by means of extended Xray absorption spectroscopy (EXAFS) and density functional theory (DFT) calculations using the linear augmented plane waves plus local orbitals (LAPW+lo) method. In addition to the substitutional position, the calculations are performed for DX and Acenters of Ga in CdTe. The results of the calculations are in good agreement with the experimental data, as obtained from
and Xray absorption nearedge structure (XANES). They allow the experimental identification of several defect structures in CdTe. In particular, direct experimental evidence for the existence of DXcenters in CdTe is provided, and for the first time the local bond lengths of this defect are measured directly.1. Introduction
CdTe has been researched extensively in the past owing to its interesting applications in optoelectronics. Various dopants are often introduced in CdTe in order to improve its optical and electrical properties. While the interest in CdTe used to be wide with respect to optoelectronic applications, with the characteristics of the basic material summarized by Rössler (1999), most recently the interest in CdTe has risen rather rapidly because of its high for X and γradiation for astronomy and medical imaging detectors (Del Sordo et al., 2009). Therefore, basic research for improving the preparation and processing of the basic material as well as the fabrication of thin film or nanostructures is receiving continuing attention (for example, see the monograph by Triboulet & Siffert, 2010). For optimal performance the incorporation of defects influencing the electrical behavior, e.g. the trapping of charge carriers, must be controlled and understood. The introduction of impurities in CdTe is in many cases followed by lattice distortions and the formation of defect complexes, which in turn influence the electronic features of the system (Koteski et al., 2005; Mahnke et al., 2005). Ga and In are highly soluble dopants in CdTe and this allows their solid solutions to be obtained up to a concentration of 10^{20} atoms cm^{−3} (Panchuk & Fochuk, 2010). The properties of CdTe:In crystals are well studied as published in various articles; however, gallium pointdefect structures have been investigated much less, especially at the hightemperature pointdefect equilibrium (Fochuk et al., 2002, 2004). In highly doped CdTe:Ga, besides the substitutional Ga_{Cd} position, Ga is primarily expected to form an Acenter (complex with a nearby cation vacancy) and a DXcenter (Chadi & Chang, 1988; Park & Chadi, 1995) (accompanied by significant lattice relaxation around the dopant). In addition, it was found that when Ga is incorporated into CdTe it may induce antisite defects of the type Cd_{Te}, leading to a compensating complex (Babentsov et al., 2001). When observed locally, these configurations are expected to differ considerably in their atomic arrangements, as compared with the pure undistorted crystal.
The DX and Acenter complexes (Fig. 1) are important types of defects, often held responsible for limiting the doping efficiency in a broad range of semiconductors. While their existence in most cases is confirmed only indirectly, there are several experimental studies with more direct measurements. Cd vacancies associated with the Acenter defects in CdTe have been confirmed by positron annihilation spectroscopy (Kauppinen et al., 1997). Large lattice instability, accompanied by the shortening of one of the four Cd nearestneighbor (NN) bond lengths, has been observed in the signal of heavily indiumdoped CdTe (Espinosa et al., 1997). In another Xray absorption study, the photoinduced lattice relaxation around indium is attributed to the presence of DXcenters, whereas the Acenter defects are considered to be dominant types of defects at lower dopant concentration (Espinosa et al., 2000). Other locally sensitive methods, such as perturbed angular correlations in combination with density functional theory (DFT) calculations (Lany et al., 2004), have also been employed to gather information about CdTe:In on the local scale. Here, the assignment of the measured electric field gradient to the defect in question was possible due to DFT calculations.
With progress both in the experimental determination of local structures by Xray absorption techniques and in theoretically modeling local structures with improved DFT calculations we are now able to report in this paper on a quite precise determination of the local structure around Ga in CdTe. _{Cd} fraction. Instead, we demonstrate that the superposition of at least three different local configurations is needed for a satisfactory fit to the measured data. Given that the absorption is measured at the Ga Kedge, the possible Cd on Te antisite defects, induced by the incorporation of Ga in Cd_{Te}, are of little concern for this study. We will not be sensitive enough to clearly distinguish a contribution from such a complex, but it may well be an additional fraction. By performing allelectron DFT calculations, we were able to obtain an accurate theoretical description of the local coordinations of the different defect structures, and use it as the starting point in our fitting of the data. Our results are also complemented by XANES model simulations, enabling an additional qualitative comparison with the experimental data.
spectra were obtained on samples doped with Ga under conditions that would make it feasible to achieve high concentrations of DX and Acenter defects, so that the contribution of these defect configurations to the total signal would be detectable. We show that the spectra of the highly doped Ga samples cannot be successfully fitted by assuming only one substitutional Ga2. Experimental and data processing
For our ^{18} atoms cm^{−3} in the melt. The other sample, S2, was made from CdTe〈Ga〉 additionally saturated by Ga at 1123 K over 1.5 months. The estimated Ga concentration of the S2 sample is ∼10^{20} atoms cm^{−3}. This concentration is suitable for studying DX and Acenter defects. Samples with higher concentrations than, for example, ∼10^{21} atoms cm^{−3} might lead to additional defect structures, making the physical picture even more complicated.
data acquisition we prepared two types of samples: one, designated as S1, was prepared from the top of the CdTe〈Ga〉 ingot with a gallium concentration of ∼9 × 10The Kedge in fluorescence mode with a sevensegment Ge detector at 90° and in line with the polarization vector of the incoming synchrotron radiation. After background reduction and normalization, the spectra were transformed to Rspace using the IFFEFIT package (Ravel & Newville, 2005).
measurements were performed at the A1 beamline of HASYLAB with the absorption spectra collected at 20 K, 80 K and room temperature. Absorption was measured at the GaSubsequent analysis and fitting was performed with Kaiser–Bessel windows with ramp width of 1.0 Å^{−1} from roughly 3.5 to 13 Å^{−1} for the S1 sample and 3.5 to 14 Å^{−1} for the S2 sample. The fitting procedure was carried out in Rspace from 1.25 to 3.9 Å^{−1}.
3. Ab initio calculations
Our calculations were performed using the linear augmented plane waves plus local orbitals (LAPW+lo) method, as implemented in the wien2k (Blaha et al., 2001) code. Starting from the optimized lattice parameter a = 6.63 Å of CdTe, we constructed a 2 × 2 × 2 in bodycentered cubic symmetry, wherein one Cd atom was replaced by Ga. This was used to model the various charge states of the substitutional, DX and Acenter configuration in the presence of a uniform compensating background charge of opposite sign. The Acenter defect was calculated after removing one metal atom from the nextnearestneighbor (NNN) shell, whereas for the DX structures Ga was displaced along the [] direction, breaking its pointgroup symmetry from T_{d} to C_{3v}. We relaxed all atoms in the along the predefined symmetry directions with a force criterion of 3 mRy a.u.^{−1} up to the third shell around Ga, the fourth shell being fixed to the lattice parameter owing to symmetry restrictions. Going to a larger 3 × 3 × 3 would bring certain improvements regarding the accuracy of the calculated distances. It would also increase the number of shells that could be relaxed around Ga. However, this would contain 216 atoms (38 nonequivalent) which would dramatically increase the computational overhead of the simulation. As far as our results are concerned, this improvement would not be crucial since the calculated distances are only used as starting values in the fit. In addition, our fit includes paths only from within the first three shells of each of the calculated defect structures, so the relaxation of the more distant shells is not needed.
In the LAPW+lo calculations, the basis set functions were expanded up to R_{mt}K_{max} = 7, with R_{mt} being the smallest radius of the atomic muffin tin (MT) spheres, and K_{max} the magnitude of the largest vector in the basis of plane waves. The radii of the MT spheres for Cd, Te and Ga were set to 2.5, 2.5 and 2.3 a.u., respectively. The irreducible part of the was sampled with 10 kpoints. We used the generalized gradient approximation in the PBE parameterization (Perdew et al., 1996). The charge difference of 0.00001 electrons between two consecutive iterations was chosen as the convergence criterion.
For our simulations of the XANES spectra we used the ab initio multiplescattering FEFF8 program (Ankudinov et al., 1998). FEFF8 is capable of performing fullmultiplescattering (FMS) calculations to improve the modeling of the nearedge region. Simulations were conducted on a cluster of roughly 200 atoms. The atoms in the vicinity of the absorbing atom (within a sphere of ∼11.5 Å) were arranged according to the calculated lattice relaxation, as obtained from our LAPW+lo calculations. The remaining atoms were fixed to their undistorted lattice positions. The potential was calculated selfconsistently (SCF card), and the FMS mode was turned on. Additionally, we introduced 0.5 eV broadening to account for the experimental resolution. Also, we improved the interstitial density of this relatively open system by using the INTERSTITIAL card. Putting extra charge on the central atom to account for the different charge states of the defect systems was found to have no practical effect on the calculated spectra, as the charge transfer between the neighboring atoms is obviously already taken care of with the use of the SCF capabilities of FEFF8.
4. Results and discussion
The upper panel of Fig. 2 depicts the Fourier transform (FT) of the kweighted experimental spectra χ(k). Qualitatively, in the heavily doped S2 sample we observe a decrease in magnitude of the most dominant peak with respect to the sample with lower Ga concentration. This peak is associated with the firstshell environment around the dopant and, in principle, all different Ga local arrangements contribute to its intensity. The distinctive shoulder that appears in the region from 2.7 to 3 Å is more pronounced in the S2 indicating that the addition of Ga strongly modifies the local environment in CdTe, and that contributions other than the substitutional are becoming visible in the signal.
Fig. 2 (lower part) depicts the temperature dependence of the data collected on the S2 sample. The decrease in amplitude in this case is due to the temperaturedependent Debye–Waller factors, and qualitative inspection shows that there are no indications of possible structural rearrangements of the local atomic coordinations with temperature. Furthermore, the positions of the main peaks seem to be temperatureindependent, indicating that there are virtually no changes in the nearest bond lengths within the investigated temperature range.
The experimental XANES spectra, along with our model XANES simulations, are shown in Fig. 3. The experimental S1 and S2 XANES curves, while matching each other relatively well beyond 10385 eV, exhibit some pronounced differences immediately at and above the edge step. In particular, the S2 sample shows a decrease in the whiteline intensity accompanied with an increase in the intensity of the nearest shoulder located at 10376 eV. Our model calculations for the substitutional and Acenter positions also predict an intense white line, more dominant in the latter case. The simulated XANES for the DXcenter configuration, however, exhibits a reduction in whiteline intensity, which is a hint that the observed whiteline intensity change of the S2 XANES could be associated with this type of defect. The only feature that our model computations completely fail to describe is the presence and behavior of the shoulder nearest to the white line.
While we were able to successfully fit the S1 ). For the heavily doped sample, the starting basis of our fitting model was deduced by qualitative comparison of the experimental S2 with the superposition of the theoretical FEFF path standards (see Fig. 5) for each of the three different local environments around Ga [according to the wien2k calculated fully relaxed structures (see below)].
spectrum by including only the substitutional model configuration [with the fitted NN distance of 2.64 (1) Å, and = 0.0023 (7) ], the satisfactory fit of the S2 spectrum required additional contributions (Fig. 4The sums of the most important theoretical scattering paths (up to a distance of 4.5 Å from the absorbing atom) for the DXcenter, Ga(Cd)_{DX}, Acenter, Ga(Cd)_{A}, and substitutional, Ga(Cd)_{subst}, local environments are presented in Fig. 5. They were obtained by running FEFF8 on a cluster of atoms in real space arranged according to the lattice relaxation calculated by wien2k. The amplitude reduction factor, S_{0}^{ 2}, for each path in the sum was set to 0.9, the energy shift, E_{0}, to 0, whereas the meansquared displacements, , were set to the values obtained from the Debye model.
Both Ga(Cd)_{subst} and Ga(Cd)_{A} environments contribute to the main peak; the former is more pronounced owing to the single fourfold coordinated Te NN shell. The first shell of the Ga(Cd)_{A} configuration is distorted and thus the resulting signal is smeared out. The Ga central atom in the Ga(Cd)_{DX} configuration is moved away from the threefoldcoordinated Te NN shell and therefore the contribution from this shell is dominant farther to the right, in the region of the righthand shoulder of the main peak. These three configurations, with fixed bond lengths according to our LAPW calculations (Table 1), were then given equal weighting, added together, and the amplitude of the total sum was adjusted to match those of the experimental spectrum.

We see that in the ). One has to bear in mind that the nonabinitio parameters obtained from the Debye model are not accurate, and that the relative ratio of the FT magnitude of the individual paths can change, as they indeed do in the actual fit (Fig. 4).
of the heavily doped Ga sample there are at least three local contributions, and the theoretical sum of these configurations (the distances were not allowed to vary from their computed values), even without fitting, matches the experimental data very well (Fig. 5Our calculations predict a sizeable bondlength contraction (2.72 Å) for the positively charged substitutional Ga(Cd)_{subst} position. The undisturbed CdTe bond length is 2.81 Å. As expected, the charge of the defect strongly influences the relaxation, which is reflected in the calculated neutral Ga(Cd)_{subst} NN distance of 2.83 Å. The NN distances of the negatively charged Ga(Cd)_{A} state are distributed in several subshells close to the bond length obtained for the substitutional position. Our calculations indicate that the lattice relaxation of the Ga(Cd)_{DX} position is also quite large. After bond breaking, a stable position of the impurity is found 0.99 Å from the original position in the [] antibonding direction. The [111] Te atom is also displaced in the same direction by 0.23 Å. The net effect is that the state has a markedly different local relaxation, with NN distances expanded by more than 0.2 Å compared with the substitutional position.
Given that the Rspace was from 1.25 to 3.9 Å. Owing to the fact that the bond lengths are virtually temperatureindependent within the measured range, the mutual parameters across the temperature data sets were the bond lengths for each of the paths, their corresponding parameters, as well as the ratio of the fractions. Owing to the different electronic structure around the impurity atom in the three contributions considered here, it is more favorable to assign a different to each fraction, instead of a single for the whole data set. The data sets were fitted with separate amplitude reduction factors, S_{0}^{ 2}, also leaving the parameters for each path as free variables. In order to further reduce the number of free parameters, some of the paths with lesser importance were excluded from the fit (see Table 2). In total, we used 27 variables to fit our data sets for the S2 sample. Because our fitting procedure was based on simultaneously fitting three data sets with 35 independent data points (Nyquist Formula) we had enough to accommodate this high number of free parameters. This fitting model, although somewhat rigid, was chosen in order to describe the physics of the system without introducing too many variables and keeping their correlations as low as possible. This strategy is supported by the quality of the fit (R_{factor} in FEFFIT) which came out within the limits of a good fit, comparable with the fit of the lowconcentration CdTe〈Ga〉 sample (S1) with the substitutional configuration only. The results of the fit are summarized in Table 2.
data were obtained at three different temperatures, we arranged a multiple data set fitting that allowed us to effectively limit the number of variables and their correlations and to improve the quality of the fit. In order to avoid the numerous contributions from the scattering paths in the region around 4.5 Å, the fitting range in

As can be seen, the best fit was found for 45% of Ga atoms occupying the substitutional, 25% the DXcenter and 30% the Acenter configuration. These figures for the fractions would presumably change if a fourth fraction was allowed for a possible Ga complex formed with a Cd antisite. All the fitted distances agree reasonably well with our calculated bond lengths. In particular, the NN Ga—Te bond length for the substitutional Ga position of 2.66 (4) Å is in relatively good agreement with our calculated value of 2.72 Å. As expected, it also agrees well with the corresponding value obtained for the S1 sample. Our fitted DX distances are larger by up to 0.15 Å compared with the calculated values, a discrepancy which is probably due to the limited
size.The evidence presented for the formation of A and DXcenters when Ga is introduced into CdTe resembles the situation with Br in CdTe (Mahnke et al., 2004, 2005). For Br in CdTe, careful analysis of the spectra revealed the occurrence of both Acenters and most likely DXcenters as well. However, for Br no reference sample was observed with only substitutional Br, although the concentration was comparable with the Ga in the CdTe sample S1 in our investigation. This was interpreted as resulting from the slight lattice expansion around a substitutional Br acting as the driving force for the formation of A and DXcenters. In the present case of Ga in CdTe, the relaxation around Ga facilitates the substitutional incorporation leading to additional A and DXcenters only at higher concentrations.
5. Conclusion
Relying on the theoretically predicted local configurations, the most likely reason for the decrease in i.e. DXconfigurations. Our analysis has been able to account for these configurations and for the first time directly extract the local structural parameters.
amplitude of the heavily Gadoped sample is the appearance of additional Acenter and DXcenter contributions, resulting in a less sharply defined fourfold neighborhood and a distorted NN shell. The shoulder around 3 Å has been traced down to contributions from local configurations which have undergone a deep relaxation,Our results indicate that the measured absorption spectra on the heavily doped CdTe:Ga sample cannot be explained using only one substitutional donor configuration, whereas the inclusion of additional DX and Acenter local environments considerably improves the fits. The additional indication of the validity of this model is the good agreement between the fitted and calculated bond lengths.
Acknowledgements
VK and JBC would like to acknowledge the help of the Serbian Ministry of Science and Education, under Grant No. ON171001. This work was largely supported by the former Hahn–MeitnerInstitut, now the Helmholtz–Zentrum Berlin für Materialien und Energie GmbH, when VK as a visiting scientist and HEM as a senior scientist were members of the institute. Finally the authors gratefully acknowledge the hospitality and help they experienced at HASYLAB at DESY, especially from E. Welter.
References
Ankudinov, A. L., Ravel, B., Rehr, J. J. & Conradson, S. D. (1998). Phys. Rev. B, 58, 7565–7576. Web of Science CrossRef CAS Google Scholar
Babentsov, V., Corregidor, V., Castaño, J. L., Fiederle, M., Feltgen, T., Benz, K. W. & Diéguez, E. (2001). Cryst. Res. Technol. 36, 535. Web of Science CrossRef Google Scholar
Blaha, P., Schwarz, K., Madsen, G., Kvasnicka, D. & Luitz, J. (2001). Wien2k, An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties. K. Schwarz, Technische Universität Wien, Austria. Google Scholar
Chadi, D. J. & Chang, K. J. (1988). Phys. Rev. Lett. 61, 873–876. CrossRef PubMed CAS Web of Science Google Scholar
Del Sordo, S., Abbene, L., Caroli, E., Mancini, A. M., Zappettini, A. & Ubertini, P. (2009). Sensors, 9, 3491. Web of Science CrossRef PubMed Google Scholar
Espinosa, F. J., de Leon, J. M., Conradson, S. D., Peña, J. L. & ZapataTorres, M. (2000). Phys. Rev. B, 61, 7428–7432. Web of Science CrossRef CAS Google Scholar
Espinosa, F. J., Mustre de Leon, J., ZapataTorres, M., CastroRodriguez, R., Peña, J. L., Conradson, S. D. & Hess, N. J. (1997). Phys. Rev. B, 55, 7629–7632. CrossRef CAS Web of Science Google Scholar
Fochuk, P., Korovyanko, A., Turkevich, I. & Panchuk, O. (2002). Inorg. Mater. 38, 350–354. Web of Science CrossRef CAS Google Scholar
Fochuk, P., Panchuk, O. & Korovyanko, O. (2004). J. Alloys Compd. 371, 10–14. Web of Science CrossRef CAS Google Scholar
Kauppinen, H., Baroux, L., Saarinen, K., Corbel, C. & Hautojärvi, P. (1997). J. Phys. Condens. Matter, 9, 5495. CrossRef Web of Science Google Scholar
Koteski, V., Haas, H., HolubKrappe, E., Ivanovic, N. & Mahnke, H.E. (2005). Phys. Scr. T115, 369. CrossRef Google Scholar
Lany, S., Wolf, H. & Wichert, T. (2004). Phys. Rev. Lett. 92, 225504. Web of Science CrossRef PubMed Google Scholar
Mahnke, H.E., Haas, H., HolubKrappe, E., Koteski, V., Novakovic, N., Fochuk, P. & Panchuk, O. (2005). Thin Solid Films, 480–481, 279–282. Web of Science CrossRef CAS Google Scholar
Mahnke, H.E., Haas, H., Koteski, V., Novakovic, N., Fochuk, P. & Panchuk, O. (2004). Hyperfine Interact. 158, 353–359. Web of Science CrossRef CAS Google Scholar
Panchuk, O. & Fochuk, P. (2010). CdTe and Related Compounds; Physics, Defects, Heteroand Nanostructures, Crystal Growth, Surfaces and Applications, edited by R. Triboulet and P. Siffert, pp. 309–362. Amsterdam: Elsevier. Google Scholar
Park, C. H. & Chadi, D. J. (1995). Phys. Rev. B, 52, 11884–11890. CrossRef CAS Web of Science Google Scholar
Perdew, J. P., Burke, K. & Ernzerhof, M. (1996). Phys. Rev. Lett. 77, 3865–3868. CrossRef PubMed CAS Web of Science Google Scholar
Ravel, B. & Newville, M. (2005). J. Synchrotron Rad. 12, 537–541. Web of Science CrossRef CAS IUCr Journals Google Scholar
Triboulet, R. & Siffert, P. (2010). Editors. CdTe and Related Compounds; Physics, Defects, Hetero and Nanostructures, Crystal Growth, Surfaces and Applications. Amsterdam: Elsevier. Google Scholar
Rössler, U. (1999). Editor. LandoltBörnstein, Numerical Data and Functional Relationships in Science and Technology, Group III: Condensed Matter, Suppl. to III/17b, 22a, Vol. 41. Berlin, Heidelberg: Springer. Google Scholar
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