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Positron lifetime spectroscopy of defect structures in Cd1–xZnxTe mixed crystals grown by vertical Bridgman–Stockbarger method

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aDepartment of Material Physics, Institute of Physics, Maria Curie-Sklodowska University, 1 M. Curie-Sklodowskiej Sq., 20-031, Lublin, Poland, bDepartment of Physical Chemistry, Institute of Chemical Sciences, Maria Curie-Sklodowska University, 3 M. Curie-Sklodowskiej Sq., 20-031, Lublin, Poland, cDepartment of General and Coordination Chemistry and Crystallography, Institute of Chemical Sciences, Maria Curie-Sklodowska University, 3 M. Curie-Sklodowskiej Sq., 20-031 Lublin, Poland, and dInstitute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5/7, 87-100 Torun, Poland
*Correspondence e-mail: kamil@fizyka.umk.pl

Edited by R. B. Neder, University of Erlangen-Nürnberg, Germany (Received 27 March 2021; accepted 4 May 2021; online 6 July 2021)

Positron annihilation lifetime spectroscopy was used to examine grown-in defects in Cd1–xZnxTe mixed crystals as a function of Zn content (x = 0, 0.07, 0.11, 0.49, 0.9, 0.95, 1) and measuring temperature. All samples were prepared using the high-pressure modified vertical Bridgman–Stockbarger method. The crystal structure and material phase were characterized by X-ray diffraction. The positron lifetime spectra reveal the presence of both open volumes and shallow traps regardless of the sample composition. In particular, both average and bulk lifetimes are found to be much higher in ternary alloys (CdZnTe) than those in binary systems (CdTe and ZnTe). This originates from distinct differences in average electron densities and the nature of open-volume defects between binary and ternary samples. Competition in positron trapping with increasing Zn content is observed between defects characteristic for both structural systems. Moreover, a clear correlation is shown between defects and the lattice thermal conductivity of studied samples. The applicability of the positron trapping model to CdTe-based materials is discussed.

1. Introduction

Cadmium telluride (CdTe), zinc telluride (ZnTe) and cadmium zinc telluride (CdZnTe) are among the most frequently studied materials from the group of II–VI semiconductor compounds (Triboulet & Siffert, 2009[Triboulet, R. & Siffert, P. (2009). CdTe and Related Compounds; Physics, Defects, Hetero- and Nano-structures, Crystal Growth, Surfaces and Applications. Oxford: Elsevier.]). The great attention devoted to this class of materials is triggered by their potential applications of industrial significance such as nuclear radiation detectors (Szeles et al., 2002[Szeles, C., Cameron, S., Ndap, J. O. & Chalmers, W. (2002). IEEE Trans. Nucl. Sci. 49, 2535-2540.], 2008[Szeles, C., Soldner, S. A., Vydrin, S., Graves, J. & Bale, D. (2008). IEEE Trans. Nucl. Sci. 55, 572-582.]; Szeles, 2004[Szeles, C. (2004). Phys. Status Solidi B, 241, 783-790.]; Schlesinger et al., 2001[Schlesinger, T. E., Toney, J. E., Yoon, H., Lee, E., Brunett, B., Franks, L. & James, R. (2001). Mater. Sci. Eng. Rep. 32, 103-189.]; Bolotnikov et al., 2002[Bolotnikov, A. E., Boggs, S. E., Hubert Chen, C. M., Cook, W. R., Harrison, F. A. & Schindler, S. M. (2002). Nucl. Instrum. Methods Phys. Res. A, 482, 395-407.]; Sordo et al., 2009[Sordo, S. D., Abbene, L., Caroli, E., Mancini, A. M., Zappettini, A. & Ubertini, P. (2009). Sensors, 9, 3491-3526.]; Swain et al., 2014[Swain, S. K., Cui, Y., Datta, A., Bhaladhare, S., Rohan Rao, M., Burger, A. & Lynn, K. G. (2014). J. Cryst. Growth, 389, 134-138.]; Choi et al., 2015[Choi, H., Jeong, M., Kim, H. S., Kim, Y. S., Ha, J. H. & Chai, J. S. (2015). J. Korean Phys. Soc. 66, 27-30.]), solar cells (Fang et al., 2011[Fang, Z., Wang, X. C., Wu, H. C. & Zhao, C. Z. (2011). Int. J. Photoenerg. 2011, 297350.]; Gessert et al., 2013[Gessert, T. A., Wei, S. H., Ma, J., Albin, D. S., Dhere, R. G., Duenow, J. N., Kuciauskas, D., Kanevce, A., Barnes, T. M., Burst, J. M., Rance, W. L., Reese, M. O. & Moutinho, H. R. (2013). Solar Energy Mater. Solar Cells, 119, 149-155.]; Mathews et al., 2020[Mathews, I., Kantareddy, S. N. R., Liu, Z., Munshi, A., Barth, K., Sampath, W., Buonassisi, T. & Peters, I. M. (2020). J. Phys. D Appl. Phys. 53, 405501.]), electro-optic modulators (Nishimura et al., 1976[Nishimura, T., Aritome, H., Masuda, K. & Namba, S. (1976). Jpn. J. Appl. Phys. 15, 2283-2284.]) and photorefractive devices (Partovi et al., 1990[Partovi, A., Millerd, J., Garmire, E. M., Ziari, M., Steier, W. H., Trivedi, S. B. & Klein, M. B. (1990). Appl. Phys. Lett. 57, 846-848.]). CdTe-based materials combine a number of desirable properties including high atomic number, high quantum efficiency of photon-to-charge-carrier conversion, wide energy band gap in the optical range and relatively high electrical resistivity. Moreover, not only their superior optical, electrical and thermal properties over other competitive materials make them good candidates for some commercial devices, but also a great flexibility in engineering these properties. For example, unlike other II–VI compounds, CdTe can be amphoterically doped (Krause-Rehberg & Leipner, 1999[Krause-Rehberg, R. & Leipner, H. S. (1999). Positron Annihilation in Semiconductors: Defect Studies, Vol. 27 of Springer Series in Solid-State Sciences, 1st ed. Berlin: Springer-Verlag.]) giving a great control over p-type and n-type carrier concentrations. Alloying of CdTe with Zn enables, to some extent, the tuning of the energy band gap (Strzałkowski, 2016[Strzałkowski, K. (2016). J. Phys. D Appl. Phys. 49, 435106.]; Hsu et al., 2020[Hsu, H., Lin, D., Chen, C., Wu, Y., Strzałkowski, K. & Sitarek, P. (2020). J. Cryst. Growth, 534, 125491.]), unit-cell parameter and conductivity (Carvalho et al., 2010[Carvalho, A., Tagantsev, A. K., Öberg, S. & Briddon, P. R. (2010). J. Cryst. Growth, 81, 75215.]).

However, despite great research efforts, CdTe-based devices are hardly ever produced due to the technical difficulties and related high costs in fabrication of high-quality crystals. A fundamental feature of the II–VI compounds is a mixture of covalent and ionic bonds between adjacent atoms (Triboulet & Siffert, 2009[Triboulet, R. & Siffert, P. (2009). CdTe and Related Compounds; Physics, Defects, Hetero- and Nano-structures, Crystal Growth, Surfaces and Applications. Oxford: Elsevier.]). The ionic component gives rise to a range of native point defects and their associated complexes that substantially alter desired macroscopic properties degrading the expected performance of devices. Hence, understanding and controlling of defects is a key issue in the commercialization of CdTe-based materials. The problem is quite complex as each particular method for bulk crystal growth – melt, solution and vapour growth – introduce different compositions, densities and distributions of defects. Another issue is the identification and removal of extrinsic impurities introduced during the fabrication process (Triboulet & Siffert, 2009[Triboulet, R. & Siffert, P. (2009). CdTe and Related Compounds; Physics, Defects, Hetero- and Nano-structures, Crystal Growth, Surfaces and Applications. Oxford: Elsevier.]), which is a typical problem associated with semiconductor manufacturing technology. Moreover, the internal structure of CdTe-based materials is known to be very sensitive to the post-fabrication treatment of the crystal. Consequently, there is still insufficient knowledge about the relationship between the fabrication method, the processing, the structure and the properties of ternary CdZnTe alloys. In particular, the influence of lattice disorder on the properties of these materials and the evolution of related defects with the composition of alloys is still not fully understood.

In light of the above-mentioned problems, many efforts have been devoted to the defect characterization in CdTe-based materials [see Triboulet & Siffert (2009[Triboulet, R. & Siffert, P. (2009). CdTe and Related Compounds; Physics, Defects, Hetero- and Nano-structures, Crystal Growth, Surfaces and Applications. Oxford: Elsevier.]) and reference therein]. Among different approaches (Stavola et al., 1998[Stavola, M. R. K., Willardson, R. K. & Weber, E. R. (1998). Editors. Identification of Defects in Semiconductors, Vol. 51A of Semiconductors and Semimetals, 1st ed. San Diego: Academic Press.]), the positron techniques (Krause-Rehberg & Leipner, 1999[Krause-Rehberg, R. & Leipner, H. S. (1999). Positron Annihilation in Semiconductors: Defect Studies, Vol. 27 of Springer Series in Solid-State Sciences, 1st ed. Berlin: Springer-Verlag.]; Tuomisto & Makkonen, 2013[Tuomisto, F. & Makkonen, I. (2013). Rev. Mod. Phys. 85, 1583-1631.]) belong to the most sensitive methods. In particular positron annihilation lifetime spectroscopy (PALS) has the capability to identify particular point defects (Elsayed et al., 2015a[Elsayed, M., Arutyunov, N., Krause-Rehberg, R., Oganesyan, G. & Kozlovski, V. (2015a). Acta Mater. 100, 1-10.],b[Elsayed, M. Yu., Arutyunov, N., Krause-Rehberg, R., Emtsev, V., Oganesyan, G. & Kozlovski, V. (2015b). Acta Mater. 83, 473-478.]), because positron lifetime is very sensitive to the size and the charge state of open volume. Moreover the temperature dependence of positron lifetimes may reveal the presence of impurities at concentration levels inaccessible for other techniques. Therefore PALS has been used many times in the past for the study of the structure of point defects in CdTe/CdZnTe/ZnTe systems (Geffroy et al., 1986[Geffroy, B., Corbel, C., Stucky, M., Triboulet, R., Hautojärvi, P. J., Plazaola, F., Saarinen, K., Rajainmäki, H., Aaltonen, J., Moser, P., Sengupta, A. & Pautrat, J. L. (1986). Mater. Sci. Forum, 10-12, 1241-1246.]; Geffroy, 1988[Geffroy, B. (1988). Tech. Rep. CEA-R-5419. CEA - Commissariat à l'energie atomique et aux énergies alternatives, Centre d'Etudes Nucléaires de Saclay. https://inis.iaea.org/collection/NCLCollectionStore/_Public/19/058/19058061.pdf.]; Gely et al., 1989[Gely, C., Corbel, C. & Triboulet, R. (1989). C. R. Acad. Sci. Paris, 309II, 179-182.]; Gély Sykes et al., 1991[Gély Sykes, C., Corbel, C. & Triboulet, R. (1991). Solid State Commun. 80, 79-83.]; Corbel et al., 1993[Corbel, C., Baroux, L., Kiessling, F., Gély Sykes, C. & Triboulet, R. (1993). Mater. Sci. Eng. B, 16, 134-138.]; Polity et al., 1994[Polity, A., Abgarjan, T. & Krause-Rehberg, R. (1994). Mater. Sci. Forum, 175-178, 473-476.]; Kauppinen et al., 1997[Kauppinen, H., Baroux, L., Saarinen, K., Corbel, C. & Hautojärvi, P. (1997). J. Phys. Condens. Matter, 9, 5495-5505.]; Krause-Rehberg et al., 1998[Krause-Rehberg, R., Leipner, H. S., Abgarjan, T. & Polity, A. (1998). Appl. Phys. Mater. Sci. Process. 66, 599-614.]; Tessaro & Mascher, 1999[Tessaro, G. & Mascher, P. (1999). J. Cryst. Growth, 197, 581-585.]; Peng, 1999[Peng, Z. L., Simpson, P. J. & Mascher, P. (1999). Electrochem. Solid State Lett. 3, 150.]; Martyniuk & Mascher, 2001[Martyniuk, M. & Mascher, P. (2001). Physica B, 308-310, 924-927.]; Li et al., 2012[Li, H., Min, J. H., Wang, L. J., Xia, Y. B., Zhang, J. J. & Ye, B. J. (2012). J. Inorg. Mater. 27, 790-794.]; Liu et al., 2013[Liu, W., Min, J., Liang, X., Zhang, J., Sun, X., Wang, L., Ran, A. & Ye, B. (2013). J. Phys. Conf. Ser. 419, 012040.]; Elsharkawy et al., 2016[Elsharkawy, M. R. M., Kanda, G. S., Abdel-Hady, E. E. & Keeble, D. J. (2016). Appl. Phys. Lett. 108, 242102.]; Šedivý et al., 2016[Šedivý, L., Čížek, J., Belas, E., Grill, R. & Melikhova, O. (2016). Sci. Rep. 6, 20641.]; Dannefaer, 1982[Dannefaer, S. (1982). J. Phys. C. Solid State Phys. 15, 599-605.]; Keeble et al., 2011[Keeble, D. J., Major, J. D., Ravelli, L., Egger, W. & Durose, K. (2011). Phys. Rev. B, 84, 174122.]; Puska et al., 1989[Puska, M. J., Mäkinen, S., Manninen, M. & Nieminen, R. M. (1989). Phys. Rev. B, 39, 7666-7679.]; Plazaola et al., 1994a[Plazaola, F., Seitsonen, A. & Puska, M. (1994a). Mater. Sci. Forum, 175-178, 469-472.], 1994b[Plazaola, F., Seitsonen, A. P. & Puska, M. J. (1994b). J. Phys. Condens. Matter, 6, 8809-8827.]; Barbiellini et al., 1996[Barbiellini, B., Puska, M. J., Korhonen, T., Harju, A., Torsti, T. & Nieminen, R. M. (1996). Phys. Rev. B, 53, 16201-16213.]; Pareja & de la Cruz, 1993[Pareja, R. & de la Cruz, R. M. (1993). Phys. Status Solidi B, 178, K23-K25.]; Puff et al., 2002[Puff, W., Brunner, S., Balogh, A. & Mascher, P. (2002). Phys. Status Solidi B, 229, 329-332.]; Hamid et al., 2005[Hamid, A. S., Shaban, H., Mansour, B. A. & Uedono, A. (2005). Phys. Status Solidi A, 202, 1914-1918.]); however, the measured lifetimes have almost never been correlated with actual physical properties of samples.

In this work we report on an investigation of positron lifetimes in Cd1–xZnxTe as a function of both the composition and the measuring temperature (93 K–473 K). The lifetime results are analyzed using the simple trapping model (STM) (Krause-Rehberg & Leipner, 1999[Krause-Rehberg, R. & Leipner, H. S. (1999). Positron Annihilation in Semiconductors: Defect Studies, Vol. 27 of Springer Series in Solid-State Sciences, 1st ed. Berlin: Springer-Verlag.]; Stavola et al., 1998[Stavola, M. R. K., Willardson, R. K. & Weber, E. R. (1998). Editors. Identification of Defects in Semiconductors, Vol. 51A of Semiconductors and Semimetals, 1st ed. San Diego: Academic Press.]). The applicability of this approach to describe positron states in studied samples is discussed. Observed annihilation characteristics are correlated with thermal properties of studied samples. The importance of defect structure in forming the properties of CdTe-based materials is unambiguously demonstrated.

2. Sample preparation

Cd1–xZnxTe mixed crystals were grown by the modified high-temperature and high-pressure Bridgman–Stockbarger vertical technique under argon overpressure (about 150 atm). Several mixed crystals with different composition were grown between two binary parents (x = 0, 0.07, 0.11, 0.49, 0.9, 0.95, 1). The starting CdTe and ZnTe powders of high purity (6N) were mixed together in a graphite crucible in stoichiometric proportion and then put into the growth chamber. To remove the oxygen from the chamber, it was evacuated and filled with argon, then evacuated and filled again. After that the temperature (depending on the zinc content) in the range of 1150 to 1350°C was maintained for 5–6 h. Once the starting material was melted, the crucible was moved out from the hot zone at a rate of 2.4 mm h−1. After the cooling procedure, the crystal rods obtained (1 cm in diameter and 5–6 cm in length) were cut with a wire saw perpendicular to the growth axis into 1–1.5 mm-thick plates. To remove the damaged layer caused by cutting, the plates were first ground with 10 µm powder (Al2O3). The final polishing was performed with 1 µm Al2O3 powder until mirror-like surface quality was obtained. Such prepared specimens were investigated within this work. Careful inspection of studied crystals showed that they are not in the form of single crystals, but they are composed of two to three macroscopic grains merged together (each a few millimetres in diameter) (Hsu et al., 2020[Hsu, H., Lin, D., Chen, C., Wu, Y., Strzałkowski, K. & Sitarek, P. (2020). J. Cryst. Growth, 534, 125491.]). This is a typical problem associated with the high-pressure Bridgman technique, which usually produces large-grain polycrystalline ingots of Cd1–xZnxTe systems (Raiskin & Butler, 1988[Raiskin, E. & Butler, J. F. (1988). IEEE Trans. Nucl. Sci. 35, 81-84.]; Doty et al., 1992[Doty, F. P., Butler, J. F., Schetzina, J. F. & Bowers, K. A. (1992). J. Vac. Sci. Technol. B, 10, 1418-1422.]; Szeles & Eissler, 1997[Szeles, C. & Eissler, E. (1997). In MRS Online Proceedings Library, Vol. 484, Symposium F: Infrared Applications of Semiconductors II, pp. 309-318.]).

3. Experimental

To verify the real composition of the grown crystals, as well as the radial and axial homogeneity, energy-dispersive X-ray spectroscopy (EDS) was applied. A Quantax 200 X-ray spectrometer and an EDX XFlash 4010 detector with 20 keV excitation energy were used in order to acquire characteristic radiation. For each sample the analysis was performed at three different places on a surface of area of ∼ 0.1 mm × 0.1 mm. The obtained results were averaged and given with standard deviation as uncertainty. Since the deviation was not large it was concluded the samples exhibit satisfactory radial uniformity. Since all elements present within our crystals are heavy enough to give a good quality signal, in this case, the standard uncertainty of the EDS method can be assumed to be about 1% of the measured value. Our samples are mixed crystals with a few or more atomic percent of added element, therefore, such accuracy is acceptable in this case. The obtained real compositions did not vary significantly from the starting contents and are used within this work. More details concerning the composition and basic characterization of the grown Cd1–xZnxTe ternary compounds can be found in previous work by Strzałkowski (Strzałkowski, 2016[Strzałkowski, K. (2016). J. Phys. D Appl. Phys. 49, 435106.]; Hsu et al., 2020[Hsu, H., Lin, D., Chen, C., Wu, Y., Strzałkowski, K. & Sitarek, P. (2020). J. Cryst. Growth, 534, 125491.]).

The X-ray diffraction (XRD) measurements were conducted on an PANalytical Empyrean diffractometer using a Cu anode which produced Cu Kα radiation (λ = 0.15406 nm). The measurements were performed in the 2θ angle range from 20° to 80°. The radiation source was equipped with a mirror to cut-off the Cu Kβ radiation. The input slit was 0.5 mm and both detector and source were equipped with Soller slits. The signals were recorded using a PixelX detector. The XRD analyses were performed on both the plates from crystal rods and powders from the powdered plates. Precise values of the dimensions of the crystalline cell were determined from the position of the Bragg reflections by using powder diffraction analysis ReX software (Bortolotti et al. 2009[Bortolotti, M., Lutterotti, L. & Lonardelli, I. (2009). J. Appl. Cryst. 42, 538-539.]), which is based on the Rietveld method.

Positron annihilation lifetime spectroscopy on Cd1–xZnxTe plates was performed in the laboratory at Lublin (Maria Sklodowska-Curie University, Poland) using a digital spectro­meter based on the Agilent U1065A (former DC252) digitizer with a sampling rate of 4 GS s−1. The data from the digitizer were analyzed in-flight by software using the algorithm developed by the Prague group (Bečvář et al., 2008[Bečvář, F., Čížek, J. & Procházka, I. (2008). Appl. Surf. Sci. 255, 111-114.]). The digitizer was triggered by the custom-made fast coincidence unit, and its inputs were collecting impulses from two gamma-ray detectors (ø 1.5′′ × 1′′ BaF2 scintillators combined with Hamamatsu R3377 photomultipliers). The detectors were placed in the immediate vicinity of the sealed sample chamber. The sample consisted of two identical crystals surrounding a positron source (22Na, 0.3 MBq) in a Kapton envelope. The pressure in the chamber was lowered to p < 10−4 Pa to obtain thermal insulation. This allowed the temperature of the sample to be controlled in the range 93–473 K with an accuracy of 0.1 K. Twenty spectra were collected for each sample at temperatures differing by 20 K. A single measurement lasted 6 h, during which about 6 × 106 counts were collected. The spectra were analyzed with PALSfit program (Olsen et al., 2007[Olsen, J. V., Kirkegaard, P., Pedersen, N. J. & Eldrup, M. (2007). Phys. Status Solidi C, 4, 4004-4006.]). The resolution function was well approximated by a single Gaussian with FWHM of about 210 ps.

Additional cross-check PALS measurements were carried out at room temperature (RT) (293 K) in the laboratory at Torun (Nicolaus Copernicus University, Torun, Poland) using conventional (analog) fast-fast coincidence ORTEC PLS system equipped with plastic scintillators (St. Gobain BC418) and RCA 8850 photomultipliers (Karbowski et al., 2011[Karbowski, A., Fidelus, J. D. & Karwasz, G. P. (2011). In Progress in Positron Annihilation, Vol. 666 of Mater. Sci. Forum, pp. 155-159 Trans Tech Publications Ltd.]). At least 2 × 106 total counts were accumulated in each measurement. These lifetime spectra were analyzed using the LT package (Kansy, 1996[Kansy, J. (1996). Nucl. Instrum. Methods Phys. Res. A, 374, 235-244.]). The RT results from two different experimental systems (and laboratories) are within 15% agreement in absolute values (both lifetimes and intensities). In particular the same trend in positron lifetimes measured as a function of Zn concentration (x) is observed.

4. X-ray diffraction results

The XRD patterns of Cd1–xZnxTe mixed crystals in a form of thick plates and powder are presented in Figs. 1[link](a) and 1[link](b), respectively. Characteristic diffraction reflections from (111), (200), (220), (311), (400), (331), (422) and (511) planes of the cubic phase (type of zinc blende structure) are clearly visible on the patterns of both CdTe and ZnTe in the form of the plates from crystal rods as well as their powders. Also, for Cd1–xZnxTe mixed crystals the same diffraction peaks are detected, however, they are shifted towards higher 2θ in comparison to the position of these signals in the CdTe sample without Zn. For powdered Cd1–xZnxTe the dominant diffraction reflection is (111). On the other hand, the intensity of diffraction reflections for Cd1–xZnxTe in the form of thick plates differs from the intensity of reflections for corresponding powders. This indicates the distinguished orientation of the crystallites in the plates, whereas the orientation is characteristic/specific to each plate. A broad reflection around 30° to 50° 2θ in the XRD patterns for Cd1–xZnxTe plates indicates a presence of an amorphous phase. It may be caused by the final polishing of the plates. The amorphous phase is not observed in the XRD patterns of powdered samples.

[Figure 1]
Figure 1
XRD patterns of Cd1–xZnx in the form of (a) plates from crystal rods and (b) powdered crystalline plates.

The increase of the Zn content in Cd1–xZnxTe causes a change of the crystal structure. The unit-cell parameter decreases linearly with increasing Zn concentration for both thick plates and powders (see Fig. 2[link]). This suggests that the unit-cell parameter (a) of Cd1–xZnxTe crystals as a function of the Zn concentration (x) follows Vegard's law (Stolyarova et al., 2008[Stolyarova, S., Edelman, F., Chack, A., Berner, A., Werner, P., Zakharov, N., Vytrykhivsky, M., Beserman, R., Weil, R. & Nemirovsky, Y. (2008). J. Phys. D Appl. Phys. 41, 065402.]): a = aCdTe(1−x) + aZnTex, where aCdTe ≃ 6.48 Å and aZnTe ≃ 6.10 Å. The absolute values of unit-cell length calculated by the Rietveld method are in good agreement with the values given in the literature [see Kosyak et al. (2016[Kosyak, V., Znamenshchykov, Y., Čerškus, A., Gnatenko, Y. P., Grase, L., Vecstaudza, J., Medvids, A., Opanasyuk, A. & Mezinskis, G. (2016). J. Alloys Compd. 682, 543-551.]) and references therein].

[Figure 2]
Figure 2
The unit-cell parameter (a) versus Zn content (x) in Cd1–xZnxTe in the form of plates from crystal rods and powdered plates. The lines obey Vegard's law: a = aCdTe(1 − x) + aZnTex.

Generally, the quality of a crystallographic structure can be judged from the shape and the intensity of X-ray diffraction peaks. In the case of ideal (defect-free) crystals, all the waves reflected at Bragg angles from parallel crystallographic planes interfere constructively to form narrow and intense peaks. On the other hand, in imperfect crystals the limited size of coherently scattered domains contributes to broad reflections. Usually, such crystals are highly defective. The intensities of XRD peaks (see Fig. 1[link]) are rather weak and broad for the sample with Zn content x = 0.49 when compared to other compositions (regardless of the sample form: powder or thick plate). This result implies that for intermediate Zn concentrations many small and highly defective domains are created during the crystal growth process. Moreover, the reflections are asymmetric, which indicates the coexistence of two phases with slightly different compositions. Interestingly, present XRD results are consistent with the behaviour of crystal quality versus Zn concentration observed for Cd1–xZnxTe thin films prepared by metal–organic chemical vapour deposition (Stolyarova et al., 2008[Stolyarova, S., Edelman, F., Chack, A., Berner, A., Werner, P., Zakharov, N., Vytrykhivsky, M., Beserman, R., Weil, R. & Nemirovsky, Y. (2008). J. Phys. D Appl. Phys. 41, 065402.]) and molecular-beam epitaxy (Reno & Jones, 1992[Reno, J. L. & Jones, E. D. (1992). Phys. Rev. B, 45, 1440-1442.]). The lowest quality of crystals in the middle of the alloy range was attributed to relatively large lattice mismatch between CdTe and ZnTe (Reno & Jones, 1992[Reno, J. L. & Jones, E. D. (1992). Phys. Rev. B, 45, 1440-1442.]).

5. Positron lifetime spectroscopy results

After subtracting the source correction, all experimental positron lifetime spectra N(t) were resolved into two exponential decay components for all studied samples at all temperatures:

[N(t) = {{I_{1}} \over {\tau_{1}}}\exp\bigg(-{t \over {\tau_{1}}}\bigg)+{{I_{2} } \over {\tau_{2}}}\exp\bigg(-{{t} \over {\tau_{2}}}\bigg), \eqno(1)]

where τ1 and τ2 are the individual lifetimes and I1 and I2 are the corresponding intensities. The two-term decomposition is a typical result for CdTe-based samples in the bulk form (Geffroy et al., 1986[Geffroy, B., Corbel, C., Stucky, M., Triboulet, R., Hautojärvi, P. J., Plazaola, F., Saarinen, K., Rajainmäki, H., Aaltonen, J., Moser, P., Sengupta, A. & Pautrat, J. L. (1986). Mater. Sci. Forum, 10-12, 1241-1246.]; Geffroy, 1988[Geffroy, B. (1988). Tech. Rep. CEA-R-5419. CEA - Commissariat à l'energie atomique et aux énergies alternatives, Centre d'Etudes Nucléaires de Saclay. https://inis.iaea.org/collection/NCLCollectionStore/_Public/19/058/19058061.pdf.]; Gely et al., 1989[Gely, C., Corbel, C. & Triboulet, R. (1989). C. R. Acad. Sci. Paris, 309II, 179-182.]; Gély Sykes et al., 1991[Gély Sykes, C., Corbel, C. & Triboulet, R. (1991). Solid State Commun. 80, 79-83.]; Corbel et al., 1993[Corbel, C., Baroux, L., Kiessling, F., Gély Sykes, C. & Triboulet, R. (1993). Mater. Sci. Eng. B, 16, 134-138.]; Polity et al., 1994[Polity, A., Abgarjan, T. & Krause-Rehberg, R. (1994). Mater. Sci. Forum, 175-178, 473-476.]; Kauppinen et al., 1997[Kauppinen, H., Baroux, L., Saarinen, K., Corbel, C. & Hautojärvi, P. (1997). J. Phys. Condens. Matter, 9, 5495-5505.]; Krause-Rehberg et al., 1998[Krause-Rehberg, R., Leipner, H. S., Abgarjan, T. & Polity, A. (1998). Appl. Phys. Mater. Sci. Process. 66, 599-614.]; Tessaro & Mascher, 1999[Tessaro, G. & Mascher, P. (1999). J. Cryst. Growth, 197, 581-585.]; Peng, 1999[Peng, Z. L., Simpson, P. J. & Mascher, P. (1999). Electrochem. Solid State Lett. 3, 150.]; Martyniuk & Mascher, 2001[Martyniuk, M. & Mascher, P. (2001). Physica B, 308-310, 924-927.]; Li et al., 2012[Li, H., Min, J. H., Wang, L. J., Xia, Y. B., Zhang, J. J. & Ye, B. J. (2012). J. Inorg. Mater. 27, 790-794.]; Liu et al., 2013[Liu, W., Min, J., Liang, X., Zhang, J., Sun, X., Wang, L., Ran, A. & Ye, B. (2013). J. Phys. Conf. Ser. 419, 012040.]; Elsharkawy et al., 2016[Elsharkawy, M. R. M., Kanda, G. S., Abdel-Hady, E. E. & Keeble, D. J. (2016). Appl. Phys. Lett. 108, 242102.]; Šedivý et al., 2016[Šedivý, L., Čížek, J., Belas, E., Grill, R. & Melikhova, O. (2016). Sci. Rep. 6, 20641.]), though Krause-Rehberg et al. (1998[Krause-Rehberg, R., Leipner, H. S., Abgarjan, T. & Polity, A. (1998). Appl. Phys. Mater. Sci. Process. 66, 599-614.]) reported the lifetime spectra composed of the very high number of annihilation events (more than 107) that revealed the presence of a third component in CdTe:Cl samples.

The average positron lifetime [\tau_{\rm avg}] was calculated from the decomposition of the lifetime spectra as:

[\tau_{\rm avg} = I_{1}\tau_{1}+I_{2}\tau_{2}. \eqno(2)]

The average positron lifetime is always accurately determined despite of the spread in distribution of intensities and lifetimes among the components.

Typically for these types of samples, the experimental data are analyzed considering the one defect simple trapping model (1D-STM) (Krause-Rehberg & Leipner, 1999[Krause-Rehberg, R. & Leipner, H. S. (1999). Positron Annihilation in Semiconductors: Defect Studies, Vol. 27 of Springer Series in Solid-State Sciences, 1st ed. Berlin: Springer-Verlag.]; Tuomisto & Makkonen, 2013[Tuomisto, F. & Makkonen, I. (2013). Rev. Mod. Phys. 85, 1583-1631.]). In this approach, after the thermalization, the positrons may annihilate in the defect-free bulk of the sample (i.e. from delocalized state) with characteristic lifetime τb or they can be captured by a single open-volume defect, where they annihilate after characteristic (longer) lifetime τd. The 1D-STM model is applicable even if the material actually has more types of defects than a single one, but with comparable lifetimes that cannot be separated experimentally. In such a case the model allows the weighted average annihilation characteristics to be quantified (Berre et al., 1995[Le Berre, C., Corbel, C., Saarinen, K., Kuisma, S., Hautojärvi, P. & Fornari, R. (1995). Phys. Rev. B, 52, 8112-8120.]). If the 1D-STM is applicable, the bulk and defect lifetimes can be calculated from the experimental lifetime components using (Krause-Rehberg & Leipner, 1999[Krause-Rehberg, R. & Leipner, H. S. (1999). Positron Annihilation in Semiconductors: Defect Studies, Vol. 27 of Springer Series in Solid-State Sciences, 1st ed. Berlin: Springer-Verlag.]; Tuomisto & Makkonen, 2013[Tuomisto, F. & Makkonen, I. (2013). Rev. Mod. Phys. 85, 1583-1631.]):

[\tau_{\rm b} = \bigg({{I_{1}} \over {\tau_{1}}}+{{I_{2}} \over {\tau_{2}}}\bigg)^{-1},\, \,\tau_{\rm d} = \tau_{2}. \eqno(3)]

Although the crystals studied here are composed of few merged macroscopic grains, the likelihood of annihilation of positrons at grain boundaries is negligibly small due to large grain dimensions (Staab & Krause-Rehberg, 1997[Staab, T. & Krause-Rehberg, R. (1997). Mater. Sci. Forum, 255-257, 479-481.]). Hence, the lifetime τd is related only to defects located within the internal structure of grains.

5.1. Room-temperature results

Fig. 3[link] shows the experimental lifetimes (τ1 and τ2 = τd) measured at room temperature (∼293 K) as well as the corresponding positron mean (τavg) and STM bulk (τb) lifetimes as a function of Zn content in the Cd1–xZnxTe samples (x = 0, 0.07, 0.11, 0.49, 0.9, 0.95, 1).

[Figure 3]
Figure 3
Positron lifetimes at room temperature (T ≃ 293 K) τ1 and τ2 = τd, average τavg and STM bulk τb as functions of the Zn content (x in BCd1–xZnxTe).

For all samples the average positron lifetime is clearly above the bulk lifetime indicating that positrons are trapped at defects. The measured bulk lifetimes in binary CdTe and ZnTe crystals are 279 (1) ps and 260 (1) ps, respectively. These results are in very good agreement with previous experimental and theoretical works showing that τb of CdTe is in the range 276–292 ps (Geffroy et al., 1986[Geffroy, B., Corbel, C., Stucky, M., Triboulet, R., Hautojärvi, P. J., Plazaola, F., Saarinen, K., Rajainmäki, H., Aaltonen, J., Moser, P., Sengupta, A. & Pautrat, J. L. (1986). Mater. Sci. Forum, 10-12, 1241-1246.]; Geffroy, 1988[Geffroy, B. (1988). Tech. Rep. CEA-R-5419. CEA - Commissariat à l'energie atomique et aux énergies alternatives, Centre d'Etudes Nucléaires de Saclay. https://inis.iaea.org/collection/NCLCollectionStore/_Public/19/058/19058061.pdf.]; Gely et al., 1989[Gely, C., Corbel, C. & Triboulet, R. (1989). C. R. Acad. Sci. Paris, 309II, 179-182.]; Gély Sykes et al., 1991[Gély Sykes, C., Corbel, C. & Triboulet, R. (1991). Solid State Commun. 80, 79-83.]; Corbel et al., 1993[Corbel, C., Baroux, L., Kiessling, F., Gély Sykes, C. & Triboulet, R. (1993). Mater. Sci. Eng. B, 16, 134-138.]; Polity et al., 1994[Polity, A., Abgarjan, T. & Krause-Rehberg, R. (1994). Mater. Sci. Forum, 175-178, 473-476.]; Kauppinen et al., 1997[Kauppinen, H., Baroux, L., Saarinen, K., Corbel, C. & Hautojärvi, P. (1997). J. Phys. Condens. Matter, 9, 5495-5505.]; Krause-Rehberg et al., 1998[Krause-Rehberg, R., Leipner, H. S., Abgarjan, T. & Polity, A. (1998). Appl. Phys. Mater. Sci. Process. 66, 599-614.]; Tessaro & Mascher, 1999[Tessaro, G. & Mascher, P. (1999). J. Cryst. Growth, 197, 581-585.]; Peng, 1999[Peng, Z. L., Simpson, P. J. & Mascher, P. (1999). Electrochem. Solid State Lett. 3, 150.]; Martyniuk & Mascher, 2001[Martyniuk, M. & Mascher, P. (2001). Physica B, 308-310, 924-927.]; Li et al., 2012[Li, H., Min, J. H., Wang, L. J., Xia, Y. B., Zhang, J. J. & Ye, B. J. (2012). J. Inorg. Mater. 27, 790-794.]; Liu et al., 2013[Liu, W., Min, J., Liang, X., Zhang, J., Sun, X., Wang, L., Ran, A. & Ye, B. (2013). J. Phys. Conf. Ser. 419, 012040.]; Elsharkawy et al., 2016[Elsharkawy, M. R. M., Kanda, G. S., Abdel-Hady, E. E. & Keeble, D. J. (2016). Appl. Phys. Lett. 108, 242102.]; Šedivý et al., 2016[Šedivý, L., Čížek, J., Belas, E., Grill, R. & Melikhova, O. (2016). Sci. Rep. 6, 20641.]; Dannefaer, 1982[Dannefaer, S. (1982). J. Phys. C. Solid State Phys. 15, 599-605.]; Keeble et al., 2011[Keeble, D. J., Major, J. D., Ravelli, L., Egger, W. & Durose, K. (2011). Phys. Rev. B, 84, 174122.]; Puska et al., 1989[Puska, M. J., Mäkinen, S., Manninen, M. & Nieminen, R. M. (1989). Phys. Rev. B, 39, 7666-7679.]; Plazaola et al., 1994a[Plazaola, F., Seitsonen, A. & Puska, M. (1994a). Mater. Sci. Forum, 175-178, 469-472.],b[Plazaola, F., Seitsonen, A. P. & Puska, M. J. (1994b). J. Phys. Condens. Matter, 6, 8809-8827.]; Barbiellini et al., 1996[Barbiellini, B., Puska, M. J., Korhonen, T., Harju, A., Torsti, T. & Nieminen, R. M. (1996). Phys. Rev. B, 53, 16201-16213.]), while τb of ZnTe lies between 254 and 266 ps (Krause-Rehberg et al., 1998[Krause-Rehberg, R., Leipner, H. S., Abgarjan, T. & Polity, A. (1998). Appl. Phys. Mater. Sci. Process. 66, 599-614.]; Tessaro & Mascher, 1999[Tessaro, G. & Mascher, P. (1999). J. Cryst. Growth, 197, 581-585.]; Peng, 1999[Peng, Z. L., Simpson, P. J. & Mascher, P. (1999). Electrochem. Solid State Lett. 3, 150.]; Plazaola et al., 1994a[Plazaola, F., Seitsonen, A. & Puska, M. (1994a). Mater. Sci. Forum, 175-178, 469-472.]; Pareja & de la Cruz, 1993[Pareja, R. & de la Cruz, R. M. (1993). Phys. Status Solidi B, 178, K23-K25.]; Puff et al., 2002[Puff, W., Brunner, S., Balogh, A. & Mascher, P. (2002). Phys. Status Solidi B, 229, 329-332.]; Hamid et al., 2005[Hamid, A. S., Shaban, H., Mansour, B. A. & Uedono, A. (2005). Phys. Status Solidi A, 202, 1914-1918.]). This indicates that the 1D-STM model is applicable for both binary samples at room temperature (T = 293 K).

The current measured defect-related component of CdTe at room temperature is τd = 361 (1) ps (63%). The presence of native open-volume defects in as-grown undoped CdTe crystals was also found in lifetime spectra reported by Geffroy et al. (1986[Geffroy, B., Corbel, C., Stucky, M., Triboulet, R., Hautojärvi, P. J., Plazaola, F., Saarinen, K., Rajainmäki, H., Aaltonen, J., Moser, P., Sengupta, A. & Pautrat, J. L. (1986). Mater. Sci. Forum, 10-12, 1241-1246.]), Geffroy (1988[Geffroy, B. (1988). Tech. Rep. CEA-R-5419. CEA - Commissariat à l'energie atomique et aux énergies alternatives, Centre d'Etudes Nucléaires de Saclay. https://inis.iaea.org/collection/NCLCollectionStore/_Public/19/058/19058061.pdf.]), Corbel et al. (1993[Corbel, C., Baroux, L., Kiessling, F., Gély Sykes, C. & Triboulet, R. (1993). Mater. Sci. Eng. B, 16, 134-138.]) and Tessaro & Mascher (1999[Tessaro, G. & Mascher, P. (1999). J. Cryst. Growth, 197, 581-585.]). The early work of the Gif-sur-Yvette group (Geffroy et al., 1986[Geffroy, B., Corbel, C., Stucky, M., Triboulet, R., Hautojärvi, P. J., Plazaola, F., Saarinen, K., Rajainmäki, H., Aaltonen, J., Moser, P., Sengupta, A. & Pautrat, J. L. (1986). Mater. Sci. Forum, 10-12, 1241-1246.]) revealed that the defect lifetime takes two values ∼330 ps (in n-type crystals) or ∼385 ps (in p-type or semi-insulating materials) – the difference was initially attributed to the position of the Fermi level rather than to the growing conditions of the materials and post-fabrication treatment of the samples. However, more careful study carried out later by the same group (Geffroy, 1988[Geffroy, B. (1988). Tech. Rep. CEA-R-5419. CEA - Commissariat à l'energie atomique et aux énergies alternatives, Centre d'Etudes Nucléaires de Saclay. https://inis.iaea.org/collection/NCLCollectionStore/_Public/19/058/19058061.pdf.]) showed that the longer component is related to the near-surface defects (such as dislocations and large open volumes) and oxygen impurities (near surface oxidation). The proof was based on the chemical etching of a 10 µm surface layer which resulted in significant reduction of this component. Indeed, considering an approximate positron implantation profile from a 22Na source (Dryzek & Singleton, 2006[Dryzek, J. & Singleton, D. (2006). Nucl. Instrum. Methods Phys. Res. B, 252, 197-204.]): n(z) = [n_{0}\exp(-12.6\rho Z^{0.17}z/0.545^{1.28})] with density ρ = 5.85 g cm−3 and effective atomic number Z ≈ 49 for a CdTe crystal, up to 30% of implanted positrons n0 can annihilate within z = 10 µm depth from the surface. This is comparable with the intensity of the ∼385 ps component measured by Geffroy (1988[Geffroy, B. (1988). Tech. Rep. CEA-R-5419. CEA - Commissariat à l'energie atomique et aux énergies alternatives, Centre d'Etudes Nucléaires de Saclay. https://inis.iaea.org/collection/NCLCollectionStore/_Public/19/058/19058061.pdf.]). Hence, one can expect that contribution of the near-surface defects (if present) to the annihilation signal cannot be neglected in CdTe-based materials. Depth-resolved Doppler broadening measurements (Peng et al., 1999[Peng, Z. L., Simpson, P. J. & Mascher, P. (1999). Electrochem. Solid State Lett. 3, 150.]) of as-grown CdTe:Cl crystals confirmed the presence of a higher density of defects and larger open volumes in the near-surface region (in a few micrometre depth range). The importance of near-surface defects induced by mechanical grinding of CdTe-based crystals has been also noticed in the more recent work of the Prague group (Šedivý et al., 2016[Šedivý, L., Čížek, J., Belas, E., Grill, R. & Melikhova, O. (2016). Sci. Rep. 6, 20641.]). The presence of such defects is clearly related to the crystal growth method and post-fabrication treatment of the sample.

Other experimental studies of native defects in undoped as-grown CdTe crystals report only the presence of an ∼320–330 ps lifetime component (Corbel et al., 1993[Corbel, C., Baroux, L., Kiessling, F., Gély Sykes, C. & Triboulet, R. (1993). Mater. Sci. Eng. B, 16, 134-138.]; Tessaro & Mascher, 1999[Tessaro, G. & Mascher, P. (1999). J. Cryst. Growth, 197, 581-585.]) or no defects at all (only annihilation from the delocalized states) (Polity et al., 1994[Polity, A., Abgarjan, T. & Krause-Rehberg, R. (1994). Mater. Sci. Forum, 175-178, 473-476.]; Kauppinen et al., 1997[Kauppinen, H., Baroux, L., Saarinen, K., Corbel, C. & Hautojärvi, P. (1997). J. Phys. Condens. Matter, 9, 5495-5505.]; Krause-Rehberg et al., 1998[Krause-Rehberg, R., Leipner, H. S., Abgarjan, T. & Polity, A. (1998). Appl. Phys. Mater. Sci. Process. 66, 599-614.]; Šedivý et al., 2016[Šedivý, L., Čížek, J., Belas, E., Grill, R. & Melikhova, O. (2016). Sci. Rep. 6, 20641.]; Dannefaer, 1982[Dannefaer, S. (1982). J. Phys. C. Solid State Phys. 15, 599-605.]). Theoretical calculations of positron lifetimes in CdTe (Keeble et al., 2011[Keeble, D. J., Major, J. D., Ravelli, L., Egger, W. & Durose, K. (2011). Phys. Rev. B, 84, 174122.]; Puska et al., 1989[Puska, M. J., Mäkinen, S., Manninen, M. & Nieminen, R. M. (1989). Phys. Rev. B, 39, 7666-7679.]; Plazaola et al., 1994a[Plazaola, F., Seitsonen, A. & Puska, M. (1994a). Mater. Sci. Forum, 175-178, 469-472.],b[Plazaola, F., Seitsonen, A. P. & Puska, M. J. (1994b). J. Phys. Condens. Matter, 6, 8809-8827.]) indicate the Cd monovacancy (VCd) as a potential trapping site responsible for an ∼320 ps component. This open-volume defect is a good candidate since it can be either in neutral or in negatively charged state (dependently on the carrier concentration, i.e. the Fermi level), so it is detectable with positron techniques. On the other hand, the competing VTe vacancy (characterized by slightly larger open volume than VCd) is excluded as an effective trap due to the net positive charge resulting in a much lower trapping coefficient. The lifetime spectra measured in electron irradiated CdTe samples (Szeles et al., 2002[Szeles, C., Cameron, S., Ndap, J. O. & Chalmers, W. (2002). IEEE Trans. Nucl. Sci. 49, 2535-2540.]; Sen Gupta et al., 1989[Sen Gupta, A., Moser, P. & Pautrat, J. (1989). Phys. Lett. A, 141, 429-432.]) confirmed that ∼320 ps lifetime is related to rather small open volumes. The latest DFT calculations (Elsharkawy et al., 2016[Elsharkawy, M. R. M., Kanda, G. S., Abdel-Hady, E. E. & Keeble, D. J. (2016). Appl. Phys. Lett. 108, 242102.]) show that different Cd vacancies (VCd, [{\rm V}_{\rm Cd}^{-1}], [{\rm V}_{\rm Cd}^{-2}]) and vacancy-interstitial configurations of TeCd antisite defects ([{\rm Te}^{0}_{\rm Cd}], [{\rm Te}^{-2}_{\rm Cd}]) may also act as effective positron traps with lifetimes comparable to ∼320 ps.

Defect lifetime of CdTe [τd = 361 (1) ps] measured at room temperature in this work is clearly higher than ∼320 ps and lower than ∼385 ps. Hence, we cannot attribute it to Cd monovacancy. Moreover, the high intensity of this component (>60%) suggests that this defect is present in the entire volume of material, so we cannot locate it only in the near-surface region. Regarding the defect size, the experimental ratio τd/τb = 1.29 ± 0.02 is in perfect agreement with theoretical estimation (Elsharkawy et al., 2016[Elsharkawy, M. R. M., Kanda, G. S., Abdel-Hady, E. E. & Keeble, D. J. (2016). Appl. Phys. Lett. 108, 242102.]; Keeble et al., 2011[Keeble, D. J., Major, J. D., Ravelli, L., Egger, W. & Durose, K. (2011). Phys. Rev. B, 84, 174122.]; Plazaola et al., 1994b[Plazaola, F., Seitsonen, A. P. & Puska, M. J. (1994b). J. Phys. Condens. Matter, 6, 8809-8827.]) for neighbouring divacancies VCdVTe in CdTe monocrystals. This ratio is clearly distinguishable from analogous ratios for single vacancies and vacancy-interstitial configurations (Elsharkawy et al., 2016[Elsharkawy, M. R. M., Kanda, G. S., Abdel-Hady, E. E. & Keeble, D. J. (2016). Appl. Phys. Lett. 108, 242102.]; Šedivý et al., 2016[Šedivý, L., Čížek, J., Belas, E., Grill, R. & Melikhova, O. (2016). Sci. Rep. 6, 20641.]).

Here, the measured defect lifetime of ZnTe is 335 (1) ps (70%) at room temperature. This lifetime is clearly higher than theoretical estimations for monovacancies: 261 ps for VZn and 291 ps for VTe (Plazaola et al., 1994b[Plazaola, F., Seitsonen, A. P. & Puska, M. J. (1994b). J. Phys. Condens. Matter, 6, 8809-8827.]). For the 2VZn divacancy it is 276 ps (Hamid et al., 2005[Hamid, A. S., Shaban, H., Mansour, B. A. & Uedono, A. (2005). Phys. Status Solidi A, 202, 1914-1918.]). Note that the bulk and the VZn lifetimes in ZnTe are very close to each other, so they are expected to be indistinguishable using the PALS technique. The measured lifetime here is in excellent agreement with the theoretical value for the VZnVTe divacancy (Plazaola et al., 1994b[Plazaola, F., Seitsonen, A. P. & Puska, M. J. (1994b). J. Phys. Condens. Matter, 6, 8809-8827.]). The corresponding ratio between positron lifetimes at the defect and in bulk is τd/τb = 1.29 (1), so it is exactly the same as for the VCdVTe divacancy in the CdTe sample. An identical ratio has been also obtained experimentally for proton-irradiated ZnTe crystals (Puff et al., 2002[Puff, W., Brunner, S., Balogh, A. & Mascher, P. (2002). Phys. Status Solidi B, 229, 329-332.]). So, both binary systems studied here, CdTe and ZnTe, are characterized by rather large open-volume defects.

In the ternary systems Cd1–xZnxTe, the τd/τb ratio is between 1.15 (3) and 1.22 (3) indicating the presence of smaller (monovacancy-size) open volumes when compared to binary crystals. The defect-related τ2 component decreases rather slowly with increasing Zn content from 361 ps in CdTe to 335 ps in ZnTe, see Fig. 3[link]. This is consistent with similar PALS measurements reported by Martyniuk & Mascher (2001[Martyniuk, M. & Mascher, P. (2001). Physica B, 308-310, 924-927.]), who attributed this change to the decrease of open-volume sizes caused by the unit-cell parameter reduction with the increase of Zn content. In contrast, the STM bulk lifetime τb does not agree with results reported by Martyniuk & Mascher (2001[Martyniuk, M. & Mascher, P. (2001). Physica B, 308-310, 924-927.]), where a smooth linear decrease of τb from values typical for CdTe to those for ZnTe was observed with increasing composition x [crystals reported by Martyniuk & Mascher (2001[Martyniuk, M. & Mascher, P. (2001). Physica B, 308-310, 924-927.]) were grown by similar Bridgman technique]. In the present work, τb is clearly higher in ternary systems when compared with binary CdTe and ZnTe crystals. The most significant changes of τb are at the beginning (the rise for x from 0 to 0.1) and at the end of the composition curve (the decrease for x from 0.9 to 1), while in the middle there is a plateau (for x between 0.1 and 0.9). Since the bulk lifetime is inversely proportional to average electron density (Krause-Rehberg & Leipner, 1999[Krause-Rehberg, R. & Leipner, H. S. (1999). Positron Annihilation in Semiconductors: Defect Studies, Vol. 27 of Springer Series in Solid-State Sciences, 1st ed. Berlin: Springer-Verlag.]; Tuomisto & Makkonen, 2013[Tuomisto, F. & Makkonen, I. (2013). Rev. Mod. Phys. 85, 1583-1631.]) in the material, the present results suggest that effective electron density `seen' by positrons is not directly proportional to Zn content and it is much lower in ternary samples when compared with binary crystals. Clearly, it is related to higher lattice disorder for Zn compositions in the middle of the alloy range as proved by XRD (see Fig. 1[link]).

The change in STM bulk lifetime τb with Zn content is directly linked with the variations of the reduced bulk lifetime component τ1 derived from experimental spectra (see Fig. 3[link]). According to the 1D-STM model, both lifetimes are connected through the relation (Krause-Rehberg & Leipner, 1999[Krause-Rehberg, R. & Leipner, H. S. (1999). Positron Annihilation in Semiconductors: Defect Studies, Vol. 27 of Springer Series in Solid-State Sciences, 1st ed. Berlin: Springer-Verlag.]; Tuomisto & Makkonen, 2013[Tuomisto, F. & Makkonen, I. (2013). Rev. Mod. Phys. 85, 1583-1631.]):

[\tau_{1} = {{1} \over {\tau_{\rm b}^{-1}+\kappa_{\rm d}}}, \eqno(4)]

where the positron trapping rate [\kappa_{\rm d}] is proportional to the defect concentration Cd:

[\kappa_{\rm d} = \mu_{\rm d}C_{\rm d}, \eqno(5)]

with μd denoting the trapping coefficient (or the specific trapping rate).

Fig. 4[link] shows the positron trapping rate κd calculated from equation (4[link]) as a function of Zn content. Similarly, as for τ1 and τb lifetimes, the largest variations of κd are observed for small (x < 10%) and large Zn content (x > 90%), while a broad plateau is present for middle x values. Interestingly, similar variations of the thermal lattice conductivity in studied samples have been reported by Strzałkowski (2016[Strzałkowski, K. (2016). J. Phys. D Appl. Phys. 49, 435106.]), as shown in Fig. 4[link]. The direct correlation between the positron trapping rate and the thermal conductivity demonstrates that thermal properties of studied samples are strongly governed by the quality of crystallographic structure. Since the fundamental theories of heat transport in solid bodies predict the reduction of thermal conductivity with the rise of defect concentration due to the phonon scattering (Scott et al., 2018[Scott, E. A., Hattar, K., Rost, C. M., Gaskins, J. T., Fazli, M., Ganski, C., Li, C., Bai, T., Wang, Y., Esfarjani, K., Goorsky, M. & Hopkins, P. E. (2018). Phys. Rev. Mater. 2, 095001.]; Stern et al., 2018[Stern, R., Wang, T., Carrete, J., Mingo, N. & Madsen, G. K. H. (2018). Phys. Rev. B, 97, 195201.]), we can explain observed correlation by the change of defect composition with Zn content. In other words, the positron data presented in Fig. 4[link] manifest rather the changes in the (weighted average) specific trapping rate (μd) than the changes in concentration of defects (Cd), see equation (5[link]). Adding Zn to CdTe crystal (i.e. increasing x) creates new types of defects in addition to defects characteristic for CdTe, while the overall defect concentration is not altered substantially. The number of new defects increases rapidly with the value of x and saturate for x > 0.1. Further increase in the Zn content does not change the defect spectrum significantly up to x = 0.9. For very high x, the composition of defects tends towards the one characteristic for ZnTe crystals. Based on such interpretation we conclude from the results in Fig. 4[link] that the open-volume defects in ternary CdZnTe alloys are characterized by much lower specific trapping rates than those in CdTe and ZnTe samples studied in this work.

[Figure 4]
Figure 4
Positron trapping rate at room temperature (T ≈ 293 K) as a function of the Zn content (x) in Cd1–xZnxTe samples compared with measured lattice thermal conductivity (Strzałkowski, 2016[Strzałkowski, K. (2016). J. Phys. D Appl. Phys. 49, 435106.]).

5.2. Temperature dependence of positron lifetimes

Fig. 5[link] presents the temperature dependencies of experimentally resolved positron lifetime components τ1 and τ2 and corresponding intensities I1 and I2 for all studied samples. In all cases the defect-related component τ2 varies rather randomly (within 20 ps–30 ps range) with the measurement temperature around some mean value, hence τ2 can be considered as temperature-independent in studied temperature range. Similar behaviour is observed for τ1 component, except ZnTe and Cd0.05Zn0.95Te samples, where a distinct fall of this lifetime with increasing temperature is observed. The latter change is accompanied by the most substantial and systematic increase (decrease) in I1 (I2) with reducing temperature among all studied samples, see the insets in Fig. 5[link].

[Figure 5]
Figure 5
Temperature dependencies of experimentally resolved lifetimes components τ1 and τ2 for different Cd1–xZnxTe alloys. The insets show the corresponding intensities I1 and I2. For figures clarity, the error bars are not shown. The figure in the right bottom corner shows the temperature dependence of average positron lifetimes τavg (included error bars demonstrate typical uncertainties in the determination of τavg).

For samples with small (x < 0.1) and large (x > 0.9) Zn content, the value I1 is much lower than I2 in the entire temperature range. On the other hand, for x between 0.1 and 0.9, both intensities become comparable with each other. Clearly, this is a fingerprint of the change in the defect composition in these samples as discussed in the previous paragraph. The reduction of defect average size and specific trapping rates for samples with Zn content in the middle of the alloy range results in lower defect-related intensities.

The plots in the bottom-right corner of Fig. 5[link] show the temperature dependencies of mean positron lifetime for all samples. The observed reduction in τavg at low temperature reveals positron trapping in defects with low binding energy and high trapping rate instead of trapping in monovacancy-size and divacancy-size defects observed at high temperature (Saarinen et al., 1989[Saarinen, K., Hautojärvi, P., Vehanen, A., Krause, R. & Dlubek, G. (1989). Phys. Rev. B, 39, 5287-5296.]). The presence of shallow traps can be related to (i) the attractive Rydberg potential of negatively charged open-volume defects such as vacancies or (ii) to the attractive Coulomb potential of negatively charged non-open-volume defects (Saarinen et al., 1989[Saarinen, K., Hautojärvi, P., Vehanen, A., Krause, R. & Dlubek, G. (1989). Phys. Rev. B, 39, 5287-5296.]) such as intrinsic antisites and interstitials or extrinsic acceptor impurities [such as the oxygen impurity (Akimoto et al., 1992[Akimoto, K., Okuyama, H., Ikeda, M. & Mori, Y. (1992). Appl. Phys. Lett. 60, 91-93.]; T-Thienprasert et al., 2010[T-Thienprasert, J., Limpijumnong, S., Janotti, A., Van de Walle, C., Zhang, L., Du, M.-H. & Singh, D. (2010). Comput. Mater. Sci. 49, S242-S245.]; Mendis et al., 2015[Mendis, B. G., Gachet, D., Major, J. D. & Durose, K. (2015). Phys. Rev. Lett. 115, 218701.])]. Since τavg tends clearly toward the bulk lifetime at low temperatures, the annihilation from non-open-volume traps is a plausible explanation (Corbel et al., 1992[Corbel, C., Pierre, F., Saarinen, K., Hautojärvi, P. & Moser, P. (1992). Phys. Rev. B, 45, 3386-3399.]). The observed temperature dependencies of the average lifetime τavg stem out from the thermal excitation of positrons from shallow defects. The positron de-trapping rate is given by the thermodynamic approach (Krause-Rehberg & Leipner, 1999[Krause-Rehberg, R. & Leipner, H. S. (1999). Positron Annihilation in Semiconductors: Defect Studies, Vol. 27 of Springer Series in Solid-State Sciences, 1st ed. Berlin: Springer-Verlag.]; Tuomisto & Makkonen, 2013[Tuomisto, F. & Makkonen, I. (2013). Rev. Mod. Phys. 85, 1583-1631.]):

[\delta = {{\kappa_{\rm st}} \over {C_{\rm st}}}\bigg({{m^{*}k_{\rm B}T} \over {2\pi\hbar^{2}}} \bigg)\exp\bigg(-{{E_{\rm b}} \over {k_{\rm B}T}}\bigg), \eqno(6)]

where m* is the effective positron mass [around 1.2 of the electron rest mass for both CdTe and ZnTe (Abbar et al., 2013[Abbar, B., Méçabih, S., Amari, S., Benosman, N. & Bouhafs, B. (2013). Commun. Theor. Phys. 59, 756-762.]; Benosman et al., 2014[Benosman, F., Benosman, N., Méçabih, S., Ruterana, P., Abbar, B. & Bouhafs, B. (2014). Comput. Mater. Sci. 93, 22-28.])], kB is Boltzmann constant, Cst is the concentration of the shallow traps, κst is the positron trapping rate to the shallow traps and Eb is the positron binding energy to the shallow traps. Hence, the probability that a positron trapped in shallow states will escape by thermal excitation decreases with decreasing temperature. Consequently, at very low temperatures almost all positrons are expected to be trapped in shallow states. The temperature dependence of positron lifetimes due to the positron detrapping from the shallow traps in CdTe-based materials has been already reported in other works (Geffroy et al., 1986[Geffroy, B., Corbel, C., Stucky, M., Triboulet, R., Hautojärvi, P. J., Plazaola, F., Saarinen, K., Rajainmäki, H., Aaltonen, J., Moser, P., Sengupta, A. & Pautrat, J. L. (1986). Mater. Sci. Forum, 10-12, 1241-1246.]; Gely et al., 1989[Gely, C., Corbel, C. & Triboulet, R. (1989). C. R. Acad. Sci. Paris, 309II, 179-182.]; Corbel et al., 1993[Corbel, C., Baroux, L., Kiessling, F., Gély Sykes, C. & Triboulet, R. (1993). Mater. Sci. Eng. B, 16, 134-138.]; Polity et al., 1994[Polity, A., Abgarjan, T. & Krause-Rehberg, R. (1994). Mater. Sci. Forum, 175-178, 473-476.]; Krause-Rehberg et al., 1998[Krause-Rehberg, R., Leipner, H. S., Abgarjan, T. & Polity, A. (1998). Appl. Phys. Mater. Sci. Process. 66, 599-614.]; Elsharkawy et al., 2016[Elsharkawy, M. R. M., Kanda, G. S., Abdel-Hady, E. E. & Keeble, D. J. (2016). Appl. Phys. Lett. 108, 242102.]; Šedivý et al., 2016[Šedivý, L., Čížek, J., Belas, E., Grill, R. & Melikhova, O. (2016). Sci. Rep. 6, 20641.]). Generally, the effect is explained with the help of the two-defect simple trapping model (2D-STM) (Krause-Rehberg et al., 1998[Krause-Rehberg, R., Leipner, H. S., Abgarjan, T. & Polity, A. (1998). Appl. Phys. Mater. Sci. Process. 66, 599-614.]; Elsharkawy et al., 2016[Elsharkawy, M. R. M., Kanda, G. S., Abdel-Hady, E. E. & Keeble, D. J. (2016). Appl. Phys. Lett. 108, 242102.]; Šedivý et al., 2016[Šedivý, L., Čížek, J., Belas, E., Grill, R. & Melikhova, O. (2016). Sci. Rep. 6, 20641.]). Assuming an independent one shallow binding energy trap and one deep defect, the experimental lifetime spectrum should be composed of three lifetime components (Krause-Rehberg & Leipner, 1999[Krause-Rehberg, R. & Leipner, H. S. (1999). Positron Annihilation in Semiconductors: Defect Studies, Vol. 27 of Springer Series in Solid-State Sciences, 1st ed. Berlin: Springer-Verlag.]; Tuomisto & Makkonen, 2013[Tuomisto, F. & Makkonen, I. (2013). Rev. Mod. Phys. 85, 1583-1631.]):

[\tau_{1}^{\prime} = {{2} \over {\Lambda+\Xi}},\,\,\tau_{2}^{\prime} = {{2} \over {\Lambda -\Xi}}\,\,\rm {and}\,\,\tau_{2} = \tau_{d}, \eqno(7)]

with intensities:

[\eqalign{ I_{1}^{\prime}& = 1-(I_{1}^{\prime\prime}+I_{2}),\cr I_{1}^{\prime\prime}& = {{\tau_{\rm st}^{-1}+\delta-{{1} \over {2}}(\Lambda-\Xi)} \over {\Xi}}\cr&\times\Bigg[1+{{\kappa_{\rm st}} \over {\tau_{\rm st}^{-1}+\delta- {{1} \over {2}}(\Lambda-\Xi)}}+{{\kappa_{\rm st}} \over {\tau_{\rm d}^{-1}-{{1} \over {2}}(\Lambda -\Xi)}}\Bigg],\cr I_{2}& = {{\kappa_{\rm d}\big[\delta+\tau_{\rm st}^{-1}-\tau_{\rm d}^{-1}\big]} \over { \big[\tau_{\rm d}^{-1}-{{1} \over {2}}(\Lambda+\Xi)\big]\big[\tau_{\rm d}^{-1}-{{1} \over {2}}(\Lambda-\Xi)\big] }} .}\eqno(8)]

where

[\eqalign{\Lambda &= \tau_{\rm b}^{-1}+\kappa_{\rm st}+\kappa_{\rm d}+\tau_{\rm d}^{-1}+\delta,\cr \Xi &= \Big[{(\tau_{\rm b}^{-1}+\kappa_{\rm st}+\kappa_{\rm d}+\tau_{\rm d}^{-1}- \delta)^{2}+4\kappa_{\rm d}\delta} \Big]^{1/2}.} \eqno(9)]

Here, τst denotes the positron lifetime for shallow traps. Since there is no open volume associated with these traps, the latter quantity is expected to be close to the bulk lifetime, i.e. τstτb. Note that for high concentration of shallow or deep positron traps the lifetime [\tau_{1}^{\prime}] becomes extremely short and its intensity [I_{1}^{\prime}] small (Šedivý et al., 2016[Šedivý, L., Čížek, J., Belas, E., Grill, R. & Melikhova, O. (2016). Sci. Rep. 6, 20641.]). In such a case it is not possible to resolve this component in LT spectra due to limited resolution of the LT spectrometer. This situation happened here in the case of all studied samples since only two components were found in the spectra: (τ1[\tau_{1}^{\prime\prime}], I1[I_{1}^{\prime\prime}]) and (τ2, I2) at all temperatures. Note also that at room temperature the trapping to shallow defects can be neglected κst = δ = 0 and the 2D-STM model is simplified to the 1D-STM model [equations (3[link]) and (4[link])] used in the previous paragraph.

The solid line in Fig. 6[link](a) represents the fit of 2D-STM mean lifetime: [\tau_{\rm avg} = I_{1}^{\prime}\tau_{1}^{\prime}+I_{1}^{\prime \prime}\tau_{1}^{\prime\prime}+I_{2}\tau_{2}] to experimental values for CdTe with κst, κd, Cst and Eb as fitting parameters. The STM bulk lifetime τb = 279 ps determined at room temperature and the mean value of experimental defect-related lifetime τd = 351 ps were used in equations (6[link]), (7[link]), (8[link]) and (9[link]) to reduce the number of fitting parameters. Though the fit to τavg is relatively good (κst ∼ 10 ns−1, κd ∼ 1 ns−1, Cst ∼ 1017 cm3 and Eb ∼ 50 meV), the model is able to explain thermally induced variations of experimental components τ1 and I1 (and I2) only down to about 200 K, see Figs. 6[link](b) and 6[link](c). It is well known that the 1D-STM and 2D-STM models are valid when the bulk lifetime defined in equation (3[link]) provides a correct value of positron lifetime in a defect-free sample. For CdTe this is a case for temperatures higher than 200 K, as shown in Fig. 6[link](d). The bulk lifetime remains relatively constant (274–280 ps) within experimental errors at high temperatures (> 200 K), while a noticeable decrease is observed at low temperatures. If we assume that the trapping process is not diffusion limited (Würschum et al., 2018[Würschum, R., Resch, L. & Klinser, G. (2018). Phys. Rev. B, 97, 224108.]) (no extended defects, no migration of defects), the only explanation for this deviation is the fact that the measured lifetimes are actually mixtures of at least two unresolved components including negatively charged open-volume defects combined with shallow traps. Similar results to those shown in Fig. 6[link] were obtained for all other samples studied in this work.

[Figure 6]
Figure 6
(a) Temperature dependence of the mean positron lifetime for CdTe (empty dots). The line represents the fit using the STM model presented in equations (6[link]), (7[link]), (8[link]) and (9[link]). (b) Temperature dependence of experimental lifetime components [\tau_{1}] and τ2 (squares and dots respectively). Lines for [\tau_{1}^{\prime}] and [\tau_{1}^{\prime\prime}] represent the STM model, while the solid line for τ2 is the mean of experimental values. (c) Temperature dependence of intensity components I1 and I2 (squares and dots respectively). Lines represent the STM model. Since the theoretical [I_{1}^{\prime}] component is very small ( << 1%), it is not shown in the plot. (d) Temperature dependence of the STM bulk lifetime (empty dots). The dashed line is a guide for the eyes.

6. Summary

In this paper we have systematically studied defect structure in bulk Cd1–xZnxTe alloys as a function of Zn content (x = 0, 0.07, 0.11, 0.49, 0.9, 0.95 and 1). All studied crystals were grown by modified high-pressure Bridgman–Stockbarger method. X-ray diffraction measurements revealed the increase in lattice disorder created during the crystal growth for sample with the middle Zn concentration, x = 0.49. The positron lifetime measurements were performed over the temperature range of 93  K to 473 K. Despite only two lifetime components resolved in all spectra, all samples were found to be quite abundant in defects including open volumes and shallow traps. Moreover, the measurements below 200 K show that the simple trapping model (STM) is not sufficient to explain the thermally induced variations of experimental results. This suggests that the measured lifetimes are mixtures of at least two unresolved defect-related components. These results are in agreement with the latest DFT calculations (Elsharkawy et al., 2016[Elsharkawy, M. R. M., Kanda, G. S., Abdel-Hady, E. E. & Keeble, D. J. (2016). Appl. Phys. Lett. 108, 242102.]) showing that many native defects with similar positron lifetimes can contribute to the PALS spectrum of CdTe-based materials. Nevertheless, despite a complex composition of defects, the one-defect trapping model (1D-STM) is still able to retrieve bulk lifetimes and defects-related weighted average components in binary CdTe and ZnTe samples at higher temperatures (>200 K) where the trapping to shallow states is negligible. Applying this model to ternary alloys Cd1–xZnxTe showed that the bulk lifetime and also the average electron density are not linearly proportional to Zn content. The bulk positron lifetime is clearly longer in ternary compounds when compared to binary compositions. Moreover defects in ternary alloys are characterized rather by monovacancy-size open volumes on average, while those in binary systems have divacancy sizes. The study of the lifetimes as a function of x in Cd1–xZnxTe revealed a kind of competition in positron trapping between open-volume defects characteristic for binary samples and those for ternary systems. It is particularly visible for small (<0.1) and large (>0.9) x where rapid modifications of annihilation characteristics are observed with the change of Zn content. For intermediate x between 0.1 and 0.9 a similar defect composition is observed since the change in Zn amount does not modify the lifetimes significantly. The evolution of defect types with x is clearly related to the lattice disorder introduced during the crystal growth process. Furthermore we have shown that such peculiar behaviour of defects as a function of x is reflected in the thermal properties of the studied samples, because their lattice thermal conductivity plotted versus Zn content follows exactly the same trend as observed for the positron trapping rate obtained using the STM model. This suggests that defects in ternary systems are characterized by much lower (on average) positron specific trapping rates than those in binary samples.

To summarize, the present results confirmed great sensitivity of Cd1–xZnxTe properties to the defect composition. A great flexibility in engineering physical properties of CdTe-based materials is accompanied by easiness in defect formation during the crystal growth procedure and post-fabrication treatment. The capability of the PALS technique to identify particular point defects in such complex systems as ternary alloys of II–VI semiconductor compounds has been proved many times [see e.g. Krause-Rehberg & Leipner (1999[Krause-Rehberg, R. & Leipner, H. S. (1999). Positron Annihilation in Semiconductors: Defect Studies, Vol. 27 of Springer Series in Solid-State Sciences, 1st ed. Berlin: Springer-Verlag.]); Šedivý et al. (2016[Šedivý, L., Čížek, J., Belas, E., Grill, R. & Melikhova, O. (2016). Sci. Rep. 6, 20641.])]. Despite the fact that the compositions of defects in the samples studied here allows us to reveal only the averages of positron states, we showed that the PALS technique still provides very useful insights into the nature of the defect structure in Cd1–xZnxTe mixed crystals.

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