Positron annihilation spectroscopy of vacancy-related defects in CdTe:Cl and CdZnTe:Ge at different stoichiometry deviations

Positron annihilation spectroscopy (PAS) was used to examine the effect of defined Cd-rich and Te-rich annealing on point defects in Cl-doped CdTe and Ge-doped CdZnTe semi-insulating single crystals. The as-grown crystals contain open-volume defects connected with Cd vacancies . It was found that the Cd vacancies agglomerate into clusters coupled with Cl in CdTe:Cl, and in CdZnTe:Ge they are coupled with Ge donors. While annealing in Cd pressure reduces of the density, subsequent annealing in Te pressure restores . The CdTe:Cl contains negatively-charged shallow traps interpreted as Rydberg states of A-centres and representing the major positron trapping sites at low temperature. Positrons confined in the shallow traps exhibit lifetime, which is shorter than the CdTe bulk lifetime. Interpretation of the PAS data was successfully combined with electrical resistivity, Hall effect measurements and chemical analysis, and allowed us to determine the principal point defect densities.

is required for a good detector in order to reduce the dark current. Moreover a large mobility-lifetime product is desired to ensure that carriers generated by radiation in the whole detector volume can be collected by electrodes. Lattice defects form energy levels in the band gap and affect thereby the resistivity and the mobility lifetime product 9 . CdTe can be alloyed with Zn forming CdZnTe ternary compound. Alloying of CdTe with Zn strengthens the lattice and increases the band gap and thereby also maximum achievable resistivity 10 .
The electric properties are affected by lattice defects forming energy levels in the band gap 9 . The determination of the properties of native defects and their complexes is particularly important to understand their role in crystal growth and compensating of extrinsic defects 4 . In spite of extensive investigations the defects attached to distinct levels have in most cases not been completely identified. High purity CdTe/CdZnTe crystals are usually grown under Te-rich conditions because the Cd pressure required for Cd-rich conditions is as high as several atmospheres 11 . The CdTe/CdZnTe crystals grown under Te-rich conditions are typically characterized by low resistivity and p-type conductivity 4 due to Cd vacancies ( ) V Cd which are divalent acceptors with two ionization levels ( /−) 0 and (−/ −) 2 located below the mid-gap level 4,12 . To achieve high resistivity V Cd acceptors and residual impurities must be electrically compensated usually by doping using group III (Al, In, Ga) or group VIII (Cl) donors 4,12 .
Positron annihilation spectroscopy (PAS) including Positron lifetime (LT) and Coincidence Doppler broadening (CDB) spectroscopy was usually used for the study of the structure of point defects in CdTe/CdZnTe in the past [13][14][15][16][17][18] , but the link between defects and controlled annealing treatment has never been studied before. This work reports on an investigation of the influence of defined annealing in Cd or Te vapour on the defect structure of Cl-doped CdTe and Ge-doped CdZnTe semi-insulating single crystals. The defect structure is characterized by PAS before and after each annealing step. The results are compared with galvanomagnetic Hall effect measurements in the Van der Pauw configuration 19 .
The paper is organized as follows. In Section Experimental we introduce samples, show the impurity content and summarize technical details of experiments. In Section Theory, we introduce methods for lifetime calculations and discuss their limits. Section Results and Discussion presents galvanomagnetic, positron back-diffusion measurements and theoretical calculations of lifetimes of positrons captured in different point defects. The subsection Lifetime spectroscopy reports the results of temperature dependent positron lifetime spectroscopy and their analysis based on three-state simple trapping model. This subsection is divided to the three parts describing for the undoped CdTe, Cl-doped CdTe and Ge-doped CdZnTe. The next subsection contains the results of CDB spectroscopy and their interpretation.

Experimental
The Cl-doped CdTe (CdTe:Cl) and Ge-doped − Cd Zn Te , . x 0 035 (CdZnTe:Ge) single crystals were grown by the vertical gradient freeze method 20 (using 6N purity source elements). The annealing was done in the two zone furnace at 700 °C while the Cd or Te source temperature was 600 °C, which corresponds to Cd or Te pressure of 111 or 7.7 mbar, respectively. After annealing, the samples were cooled down at a cooling rate of 1 °C min −1 . Nominally undoped CdTe (u-CdTe) single crystal grown by the vertical gradient freeze method at fairly increased Cd overpressure 1.6 atm was used as a reference sample.
LT measurements were carried out using a digital spectrometer 21 with time resolution of 145 ps. 22 Na activity of 1 MBq deposited on a 2 μm thick Ti foil was used as a positron source. The LT measurements were performed at 295 K (room temperature -RT) and at 123 K (low temperature), respectively. In both temperatures typically, 10 7 positron annihilation events were collected in LT spectra, which were subsequently decomposed into exponential components. The contribution of positron annihilations in the source spot and in the covering foils were always subtracted. In addition, temperature-dependent LT measurements were carried out in the temperature range of 123-295 K at a heating rate of ~1 K hour −1 . Here the statistics of × 5 10 5 events was collected at each temperature step.
CDB spectroscopy 22 was employed for characterization of local chemical environment of vacancies. The CDB studies were performed at RT using the same positron source as in the LT measurements. A digital CDB spectrometer 23 equipped with two HPGe detectors and characterized by the energy resolution of 0.9 keV at the annihilation line and the peak-to -background ratio >10 5 was employed for the CDB studies. At least 10 8 annihilations were collected in each two-dimensional CDB spectrum. Subsequently the CDB spectra were reduced into one-dimensional cuts representing the resolution function of the spectrometer and the Doppler broadened annihilation peak. Normalized Doppler broadened peaks were divided by the normalized peak for the u-CdTe reference sample. Hence, in this paper the CDB results are presented as ratio curves with respect to u-CdTe.
Positron back diffusion measurement was performed on a continuous magnetically guided slow positron beam with energy of incident positrons adjustable in the range from 0.05 to 30 keV. Doppler broadening of the annihilation photopeak was measured by a HPGe detector with the relative efficiency of 35% and the energy resolution of ( . ± . ) 1 08 0 01 keV at 511 KeV. Shape of Doppler broadened annihilation photopeak was characterized using the S (sharpness) parameter 24 . The dependence of of the S parameter on positron energy was fitted using the VEPFIT code 25 .
Glow Discharge Mass Spectrometry (GDMS) was used for the chemical analysis. The concentrations of elements exceeding − 10 cm 15 3 for u-CdTe, CdTe:Cl and CdZnTe:Ge presented in Table 1 in units 10 15 cm −3 . A 30% error of GDMS analysis was declared.

Theory
Positron properties were calculated using density functional theory (DFT) within so-called standard scheme 26 . In this approximation positron density is assumed to be everywhere vanishingly small and not affecting the bulk electron structure. At first electron density ( ) n r in the material is solved without the positron. Subsequently, the effective potential for positron is constructed as   1  1  1  5  183  1  3  3   CdZnTe:Ge  3  5  3  3  1  8  1  7  20  3  1 3.5% 60 12 where r e is the classical electron radius, c is the speed of light, and γ denotes the electron enhancement factor describing the pileup of electrons at the positron site 26 . The electron-positrons correlation, i.e. the correlation potential ( ( )) V n r corr and the enhancement factor γ, were treated by two approaches: 1. local density approximation (LDA) utilizing the parametrization by Boroński and Nieminen 27 and taking into account incomplete positron screening 28 using a high frequency dielectric constant of = .
The electron density ( ) n r was constructed by superposition of atomic electronic densities calculated by a relativistic atomic code 31 . This approach called atomic superposition (ATSUP) 32 neglects the charge transfer, but it is computationally feasible and can be used even for very large supercells retaining full 3-D geometry of the problem. In the following text the approach employing LDA and GGA scheme with superimposed electron density is denoted ATSUP-LDA and ATSUP-GGA, respectively.
The ATSUP-LDA and ATSUP-GGA calculations of positron parameters were performed on × × 8 8 8 supercells containing 2048 Cd and 2048 Te atoms. Defects were modelled by removing the corresponding number of atoms from the supercell. Integration over the Brillouin-zone described in ref. 33 was used in calculations of positron parameters for defects.
It is well known that LDA overestimates positron annihilation rates especially with d electrons 30 and the lifetimes calculated within the LDA approach are often shorter than the values measured in experiment. This shortcoming is to some extend compensated when LDA approach is used with electron density constructed by ATSUP 32,34 . On the other hand, the GGA approach when used with ATSUP electron density gives often lifetimes which are longer than the experimental values 35 . Hence, the lifetimes calculated using the LDA and the GGA approach can be considered as a lower and an upper bound of the interval where the actual lifetime falls. The GGA scheme is more sensitive to details of electronic structure than LDA 30 and the lifetimes calculated using the GGA approach are it the best agreement with experiment when used with a self-consistent electron density. For these reasons we performed also self-consistent electron density calculations for selected positron states. The self consistent valence electron density was calculated by the plane wave code VASP (Vienna ab-inito simulation package) 36,37 using projector augmented wave (PAW) potentials 38 . The s 5 2 , d 4 10 Cd electrons and s 5 2 , p 5 4 Te electrons were considered as valence electrons in the VASP calculations. The calculations were performed using 216 atoms based supercells and × × 2 2 2 k-point grids generated using the Monkhorst-Pack scheme 39 . The wave functions were expanded in a plane wave basis with the cut-of energy of 277 eV. The calculated CdTe lattice constant a = 6.60 Å is in a reasonable agreement with the experimental value of 6.48 Å. Ionic relaxations were not considered at the present stage of calculations. In construction of the positron potential the frozen core electron orbitals were added to the self-consistent valence electron density calculated by VASP. In the following text this approach is denoted VASP-GGA.
The momentum distribution of annihilating pairs was calculated employing the ATSUP-based approach described in refs 40 and 41. The electron-positron correlations were treated within the GGA approach. The contribution  ( ) , p i nl from the i-th atom and a shell characterized by principal (n) and orbital (l) quantum numbers is calculated by the formula where , N i nl denotes the number of electrons in the ( , ) n l shell, B l is the spherical Bessel function and − , R i nl and + R i denotes the electron and positron radial wave functions. The symbol γ , i nl stands for the state-dependent positron enhancement factor 41 . The momentum distribution of the annihilating electron-positron pairs is obtained by summing the partial contributions  Table 2. The properties of u-CdTe accord with its growth at Cd overpressure, where the V Cd -related defects are suppressed and the electron density is afforded by residual noncompensated donors. The as-grown CdTe:Cl and CdZnTe:Ge samples exhibit rather high resistivity, which is typical for the growth of Te-rich materials, where excess donors dominating above shallow acceptors are compensated by V Cd 8,42 . Annealing in Cd vapour leads to a decrease in resistivity for both samples. CdTe:Cl exhibited n-type conductivity due to the suppressed V Cd and dominating shallow donors Cl Te . The free carrier concentration of ~10 17 cm −3 therefore gives a lower limit for the concentration of Cl dopants in the sample 43 . Cd vapour annealing of CdZnTe:Ge yield p-type conductivity contrary to CdTe:Cl. Such a behaviour is well known in annealed undoped or weakly doped CdTe/CdZnTe 44 , where acceptor-like impurities are dominant after annealing. In our CdZnTe:Ge, the extrinsic shallow donor ((B) + (Al)) and shallow acceptor ((P) + (Au) + (Cu)) densities are similar, and weak excess acceptor contamination is assumed. Subsequent annealing in Te vapour produced p-type conductivity in both samples. This is in agreement with expected V Cd formation.  Table 3. Theoretical positron lifetimes available in literature are shown in Table 3 as well. The positron lifetimes calculated using the ATSUP-LDA and ATSUP-GGA schemes in the present work are in an excellent agreement with the lifetimes calculated in refs 15,45. One can see in Table 3 that positron lifetimes calculated using various approaches for the electron-positron correlation, i.e. the enhancement factor and the electron-positron correlation potential, differ. The positron lifetimes calculated using the LDA approach are always lower than those obtained by the GGA scheme. Moreover, calculated positron lifetimes vary depending whether superimposed or self-consistent electron density was used in the calculation. The bulk positron lifetime for CdTe calculated using the ATSUP-LDA approach is τ = 276  Table 4. The experimental bulk positron lifetimes for CdTe reported in literature fall into the range from 280 to 291 ps [13][14][15][16]18,46,47 . The VASP-GGA scheme which can be considered as the most precise approach used here yielded the CdTe bulk positron lifetime τ = 291 B ps which is comparable with the experimental values.
In order to compare positron lifetimes for various defects with the experimental values we use ratios τ τ / D B of the calculated lifetime τ D to the bulk lifetime τ B calculated by the same approach. These ratios are listed in Table 5. Cd-annealed 4.9 × 10 −2 n 9.7 × 10 16 Te-annealed 6.9 × 10 3 p 8.5 × 10 12 CdZnTe:Ge as-grown 1.8 × 10 9 n 6.1 × 10 6 Cd-annealed 3.0 × 10 4 p 3.2 × 10 12 Te-annealed 2.5 × 10 3 p 4.0 × 10 13  The differences between various theoretical schemes are to a large extend cancelled using τ τ / D B ratios and the τ τ / D B values exhibit relatively low sensitivity to the approach used for electron-positron correlation 30,33 . While V Te is believed to be positively charged in CdTe, V Cd is either neutral ( ) depending on the Fermi level position 12 . Hence, positrons are repelled by V Te while V Cd represent trapping sites for positrons. This is illustrated in Fig. 1 presenting the positron density in the (001) plane calculated by the ATSUP-GGA approach. Figure 1a shows the positron density in a perfect CdTe crystal where positron is de-localized in the lattice. The positron density calculated for a CdTe crystal containing V Cd is plotted in Fig. 1b. Obviously the positron is localized in V Cd . Experimental evidence for positron trapping in V Cd has been reported by many authors [14][15][16]18,46 . The lifetimes of positrons trapped V Cd determined experimentally fall into the range from 320 to 325 ps which corresponds to τ τ / D B falling into the interval 1.11-1.15, see Table 4. The ATSUP-LDA and ATSUP-GGA calculations for positrons trapped at V Cd resulted in τ τ , which is remarkably lower than the experimental values. On the other hand, the VASP-GGA approach yielded τ τ / = . 1 12 D B which is close to the values measured in experiment. This indicates that charge transfer which was neglected in ATSUP calculations leads to a slight decrease of electron density in V Cd and consequently an increase of the lifetime of trapped positrons.
Positron lifetime was calculated also for V Cd associated with Te anti-site Te Cd and with various impurities. One can see in Table 3 Table 3 indicate that replacement of Te nearest neighbours of V Cd by Cl atoms increases the lifetime of trapped positron. This effect is caused by smaller size of Cl atoms compared to Te ones. Hence replacement of a Te nearest neighbour of V Cd by a Cl impurity increases the open volume of vacancy. This is illustrated in Fig. 1c    the (001) plane for a positron trapped at A C defect. One can see in the figure that positron density in A C becomes asymmetric since it expanded towards the Cl nearest neighbour.
Lifetime spectroscopy. The results of LT measurements, i.e. lifetimes τ i and relative intensities I i resolved in LT spectra for u-CdTe, CdTe:Cl and CdZnTe:Ge samples, are summarized in Table 6 for temperatures 295 and 123 K, respectively. The temperature dependences of the mean positron lifetime τ τ = ∑ I i i i are presented in Fig. 2. Undoped CdTe. The u-CdTe crystal exhibits a single component LT spectrum (except of the source contribution) with lifetime of ~290 ps, which fits in the CdTe bulk lifetimes reported in literature, see Table 4. Hence, the concentration of positron traps in the u-CdTe crystal is very low (below the sensitivity threshold of LT spectroscopy) and virtually all positrons are annihilated in the de-localized state. Low temperature LT measurements of the u-CdTe crystal yielded practically the same results as the measurement at RT.
Results of positron back-diffusion measurement, i.e. dependence of the S parameter on the energy E of incident positrons in plotted in    denote the probabilities that a positron is at time t de-localized in the free state or trapped in a shallow or deep trap, respectively. K d1 and K d2 stand for the positron trapping rates for the shallow and the deep traps, respectively, and δ d1 is the de-trapping rate from the shallow traps. The lifetimes of positrons trapped at the shallow and the deep traps, i.e. inverse of the annihilation rates of trapped positrons, are denoted τ d1 and τ d2 , respectively. Solution of the differential equations (6) gives the decay spectrum of positrons is the number of positrons annihilated in various times and is obtained as a negative time derivative of the decay spectrum ( ) Hence the lifetimes τ 1 , τ 2 , τ 3 of the exponential components resolved in experimental LT spectra and their relative intensities I 1 , I 2 , I 3 can be interpreted within 3-STM using Eqs (8)(9)(10). Note that for a high concentration of shallow or deep positron traps the lifetime τ 1 becomes extremely short and its intensity I 1 diminishes. In such case it is not possible to resolve the first component in LT spectrum due to limited resolution of LT spectrometer. This situation happened here in the case of low temperature LT spectra for CdTe:Cl. The short lived component could not be resolved in LT spectra due to very high density of shallow traps in this sample as will be shown in the following text.
The probability that a positron trapped in a shallow trap will escape by thermal excitation decreases with falling temperature. Hence the positron de-trapping rate from shallow traps δ d1 depends on temperature 53 where ⁎ m is the effective positron mass 26 , k B the Boltzmann constant, [c] the concentration of shallow traps, and E b the positron binding energy to the shallow traps. The temperature dependence of the mean lifetime τ τ = ∑ = I i i i 1 3 was fitted using 3-STM with K d1 , K d2 , [c] and E b as fitting parameters. If the sample contains shallow traps, then the mean positron lifetime τ varies with temperature due to the temperature dependence of δ d1 . Figure 2 shows that τ for CdTe:Cl decreases with temperature, which testifies to the presence of shallow traps in this sample. The temperature dependence of τ can be explained by the formation of series of attractive shallow Rydberg states connected with negatively-charged defects 54,55 . Since the positron binding energy of the shallow Rydberg states is rather small (typically ≤ 0.1 eV), they act as efficient positron traps at low temperatures only where the positron may not escape by thermal excitation 54 .
Hence, to describe LT spectra measured at RT 3-STM can be simplified by elimination of the shallow traps, i.e. by setting in Eqs (6)(7)(8)(9)(10). This leads to the following rate equations The LT spectrum ( ) Decomposition of LT spectrum of the as-grown CdTe:Cl measured at RT revealed two exponential components, see Table 6 Table 5. Extended investigations of CdTe:Cl with chlorine content from 100 to 3000 ppm performed by Krause-Rehberg et al. 13  , which was assigned to clusters of ( ) V 2Cl Cd Te neutral complexes. The concentration of both defects increased with Cl content, testifying that they are associated with chlorine. Our CdTe:Cl sample exhibits a smaller lifetime τ 3 than 450 ps. This could be due to significantly lower Cl concentration leading to the formation of V 2Cl Cd Te clusters of smaller size. The analysis of the LT spectrum of the as-grown CdTe:Cl measured at 123 K revealed a new component with lifetime τ = ( ) 281 9 2 ps, which is shorter than the bulk positron lifetime (290 ps) and dominates the spectrum with 94% intensity, see Table 4. Taking into account the temperature dependence of τ in Fig. 2 54,55 . Depending on the local electron density the lifetime of positrons confined at low temperatures in shallow traps can be either higher or lower than the bulk positron lifetime. The latter case has been recently reported for Cu in-diffused GaAs:Te crystals 56 . Low temperature LT studies of Cu in-diffused GaAs:Te revealed shallow traps characterized by a lifetime of 220 ps, which is about of 8 ps shorter than the GaAs bulk lifetime of 228 ps 56  CdZnTe:Ge as-grown V Cd Ge Cd 2.6(2) × 10 16 Cd-annealed -< 1 × 10 15 Te-annealed V Cd Ge Cd 2.7(2) × 10 16 Table 7. The concentration of defects calculated from the LT data. The neutral defects at CdTe:Cl and at CdZnTe:Ge, negatively-charged A-centres and shallow Rydberg states associated with negatively-charged Acentres are symbolized by V Cd 2Cl Te , V Cd Ge Cd , A C , A C R , respectively.
Scientific RepoRts | 6:20641 | DOI: 10.1038/srep20641 Cu-indiffused GaAs:Te were identified as Cu Ga ions coupled with Ga vacancies ( ) V Ga . At RT positrons in the Cu-indiffused GaAs:Te sample are trapped at deep traps identified as V Cu Ga Ga complexes and characterized by a positron lifetime of 280 ps. At low temperatures positrons are confined predominantly in Rydberg states associated with Cu Ga ions and characterized by a positron lifetime of 220 ps, which is shorter than the bulk lifetime 56 . Thus, it seems that positron trapping in the CdTe:Cl sample is to some extent analogous to that in Cu-indiffused GaAs:Te: at RT positrons are trapped at deep traps (vacancy clusters) while at low temperatures positrons are confined at Rydber states associated with Coulomb field around negatively charged A-centers and characterized by a positrons lifetime ≈280 ps, which is about of ≈10 ps shorter than the CdTe bulk lifetime of ≈290 ps measured on the u-CdTe sample, see Table 4. We assume that the reduced lifetime of the positron in the Rydberg state comparing to the bulk lifetime may stem from a lattice relaxation and enhanced mass density in the vicinity of the vacancy, at the radius about 1 nm, where the positrons in Rydberg state mostly occur.
Annealing the CdTe:Cl sample in Cd vapour led to a significant reduction of the intensity of the long-lived defect component and shortening of its lifetime down to τ = ( ) 328 7 3 ps at RT. The ratio τ τ / = . ( ) is close to the value calculated for A C or single V 2Cl Cd Te complex The reduction of this component is clearly caused by the removal of V Cd by Cd annealing and the reduction in cluster size. Ensuing analysis within 2-STM proves the depression of the density of V Cd related defects, see Table 7. The Cd-annealed CdTe:Cl is characterized by very low resistivity and n-type conductivity, caused by + Cl Te shallow donors which in contrast to the as-grown sample are not compensated by − V Cd 2 shallow acceptors. In spite of significant V Cd depreciation the sample measured at low temperature again exhibits a remarkable contribution of A C R , see Table 6. The temperature dependence of τ plotted in Fig. 2 is similar to the as-grown sample just shifted to lower values due to the suppressed contribution from neutral clusters. Since the lifetime of positrons localized in the shallow traps is lower than the CdTe bulk lifetime, τ decreases below the bulk lifetime value at low temperatures where almost all positrons are confined in the shallow traps. Referring to similar concentration of defects at RT and at low temperature, see Table 7, we deduce that τ 3 in the Cd-annealed CdTe:Cl sample is associated with A C only.
Subsequent annealing of a CdTe:Cl sample in Te vapour leads to the appearance of a defect component with lifetime τ ≈ -316 320 3 ps, which corresponds to negatively-charged A C and neutral V 2Cl Cd Te defects. Unlike the as-grown CdTe:Cl crystal, the V 2Cl Cd Te complexes formed after Te-annealing are isolated and do not agglomerate into clusters. This could be caused by the fact that during Te-annealing the sample was kept at a lower temperature than during crystal growth, and the mobility of the V 2Cl Cd Te complexes was therefore lower. The analysis of LT spectra measured at 123 K revealed that the positron trapping in A C R dominates at low temperatures in a similar way as in the Cd-annealed crystal. The temperature dependence of τ presented in Fig. 2 again shows a drop with decreasing temperature in a similar manner as for the Cd-annealed sample.
Referring to the concentration of defects (Table 7), we can deduce that the defects observed at RT in the Te-annealed sample are associated with V 2Cl . Again this value is in very reasonable agreement with the total Cl density determined by GDMS.
The as-grown CdTe:Cl crystal was characterized also by positron back-diffusion measurement on the slow positron beam. The dependence of the S-parameter on the energy E of incident positrons for the as-grown CdTe:Cl crystal is plotted in Fig. 3. Obviously the ( ) S E curve for the as-grown CdTe:Cl sample exhibits similar features as the curve for the u-CdTe crystal, namely a maximum at low energies (≈ 2 keV) followed by a gradual decrease down to a plateau value at high energies where virtually all positrons are annihilated inside the CdTe:Cl region. However the plateau value at high energies for the as-grown CdTe:Cl sample is remarkably higher than that for the u-CdTe. The ( ) S E curve was fitted in the similar manner as the curve for u-CdTe sample, i.e. using a two-layer model consisting of a thin surface oxide layer and the bulk CdTe:Cl region. The model curve calculated by VEPFIT 25 is plotted by solid line in Fig. 3 Table 7.
CdZnTe:Ge. At RT the CdZnTe:Ge as-grown crystal exhibits a defect component with lifetime τ = ( ) 327 8 3 ps falling into the range -320 330 ps commonly attributed to − V Cd 2 shallow acceptors or complexes of − V Cd 2 associated with donors, see Table 4. The lifetime τ 3 at 123 K is practically the same as in RT, and τ remains constant apart from the statistical scattering in the whole temperature range of 123-295 K, see Fig. 2. A similar result was observed 17 for undoped CdZnTe. The temperature independence of τ observed in CdZnTe:Ge crystal testifies that (i) the defects responsible for the lifetime τ 3 in this sample are mostly electrically neutral, and (ii) unlike CdTe:Cl, the CdZnTe:Ge crystal does not contain shallow traps in detectable concentration.
Taking into account electrical neutrality of defects and positron lifetime comparable to − V Cd 2 the component with the lifetime τ 3 can be attributed to positrons trapped at electrically neutral − + V Ge Cd 2 Cd 2 complexes which are likely formed in CdZnTe:Ge. Table 7 shows the concentration of − + V Ge Annealing of CdZnTe:Ge crystal in Cd vapour led to the disappearance of the defect component with lifetime τ 3 , and the LT spectrum became single-component with the lifetime τ ≈ 295 1 ps, which is close to the bulk lifetime of 292(1) ps measured in the u-CdTe, see Table 6. Hence, virtually all positrons in the Cd-annealed CdZnTe:Ge sample are annihilated in the de-localized state. This result proves that V Cd annihilation is due to Cd-annealing. Slightly higher value of the bulk positron for CdZnTe:Ge compared to that for u-CdTe could be caused by lower electron density in CdZnTe compared to that in CdTe. Temperature-dependent measurements did not reveal any temperature dependence of LT results for the Cd-annealed CdZnTe:Ge sample, see Fig. 2 and Table 6, which is in accordance with the assignment of the τ 1 component to the free positrons.
The subsequent annealing of CdZnTe:Ge in Te vapour resulted in the restoration of the defect component with lifetime τ ≈ 320 3 ps, which shows the re-emergence of V Cd . The LTs obtained after annealing are very similar to those measured in the as-grown CdZnTe:Ge, including the temperature independence of τ in Fig. 2, which testifies to positron trapping in electrically neutral − + V Ge CDB spectroscopy. The CDB spectroscopy was employed in order to obtain direct information about chemical environment of V Cd in CdTe:Cl and CdZnTe:Ge crystals. Figure 4 shows the momentum distribution of annihilating electron-positron pairs measured in the u-CdTe reference sample. The calculated momentum distribution for a perfect CdTe crystal is plotted in the figure as well. One can see in the figure that the momentum distribution calculated using the ATSUP-GGA approach agrees well with the experimental points in the high momentum range ( > × ) where the contribution of positrons annihilated by core electrons dominates. This is caused by the fact that core electrons in the inner shells retain their atomic character are almost not influenced by crystal bonding. On the other hand the ATSUP-based approach is not able to describe accurately the momentum distribution in the the low momentum region ( < × ) − p mc 15 10 z 3 0 where the contribution of positrons annihilated by valence electrons becomes dominating. For this reason the calculated momentum distributions will be compared with the experimental data in the high momentum region only. Figure 5a shows the experimental CDB ratio curves related to the u-CdTe reference for the CdTe:Cl sample in the as-grown state and after annealing in Cd and Te vapour, respectively. The calculated CDB curves related to a perfect CdTe crystal for V Cd , A C and V 2Cl Cd Te defects are plotted in Fig. 5b. From inspection of Fig. 5 it becomes clear that the CDB curve for CdTe:Cl annealed in Cd vapour is almost flat (except of statistical scattering) and close to unity in the whole momentum range testifying that the momentum distribution for the Cd-annealed CdTe:Cl is very similar to that in the u-CdTe reference. This confirms the picture that positron traps were removed by annealing in Cd vapour and virtually all positrons in the Cd-annealed sample are annihilated in the free state. On the other hand, the CDB ratio curves for the as-grown CdTe:Cl and the sample annealed in Te vapour clearly differ from unity and exhibit a distinct peak in the high momentum range at ≈ × − p m c 25 10 z 3 0 . Similar peak is observed in the CDB curves calculated for positrons trapped in A C and V 2Cl Cd Te defects in Fig. 5b. This testifies to positron trapping in defects associated with chlorine in the as-grown and Te-annealed CdTe:Cl sample.
The CDB results for CdZnTe:Ge samples are presented in Fig. 6. The experimental CDB curves for the as-grown and Cd or Te-annealed CdZnTe:Ge are plotted in Fig. 6a while Fig. 6b shows the CDB ratio curves calculated for positrons trapped at V Cd and V Ge Cd Cd defects. The CDB ratio curve for Cd-annealed CdZnTe:Ge sample is again almost flat and close to unity indicating that the momentum distribution in this sample is similar to that in the u-CdTe reference. A slight enhancement in the momentum range ( )× − m c 10 30 10 3 0 is most probably due to positrons annihilated by electrons belonging to Zn. Annealing in Te vapour modified the momentum distribution of CdZnTe:Ge sample. Shape of the ratio curve for the Te-annealed sample is very similar to the curves calculated for positrons trapped at V Cd and V Ge Cd Cd defects. Hence, in accordance with the results of LT spectroscopy the CDB data in Fig. 6 indicate that positrons in CdZnTe:Ge annealed in Te vapour are trapped at defects containing V Cd . Very similar CDB curve was observed also in the as-grown sample. However, CDB spectroscopy does not allow to discern positrons trapped in isolated V Cd from those trapped in V Ge Cd Cd complexes due to very similar CDB ratio curves for both defects, see Fig. 6b.
In spite of extensive research, the basic properties of native point defects in CdTe/CdZnTe are still far from agreed understanding. Both formation and ionization energies are not settled and analyses based on various defect models or experimental data produce incompatible defect characteristics 8 . Nowadays, it is generally assumed that the difficulties in detecting of native point defects ensue from their reactivity and fast diffusion at elevated temperature. During cooling to room temperature native defects are supposed to migrate and interact with charged impurities. As a result, various types of associates and precipitates are formed 58,59 . The remaining isolated V Cd mostly annihilate during cooling at surface or dislocations and the final room temperature density of V Cd comes out very low 42 . Evidently, such premise is in pure agreement with evaluated defect structure both in CdTe:Cl and CdZnTe:Ge. Analysis of PAS data suggests that all detected V Cd are incorporated in various complexes stabilizing them in the lattice.
Detailed characterization of defect structure of CdTe:Cl and CdZnTe:Ge samples summarized in Table 7 raises a query on the unambiguity of the presented defect model. We believe that the comprehensive exploration of CdTe:Cl and CdZnTe:Ge samples, which were studied both in Cd-and in Te-rich state by multiple techniques, LT, CDB and galvanomagnetic measurements, and characterized by GDMS, allowed us the interpreting of measured data by rather unique way. In view of the fact that the defect densities in Te-rich state significantly exceed the densities of obvious residual extrinsic acceptor, we may conclude that V Cd is the only candidate for the acceptor defect at these conditions. Similarly, the intentional doping by Cl or Ge donors supplied the only extrinsic elements with the large enough concentration to arrange the detected density of revealed A-centres and complexes. Nevertheless, suggested interpretation of the defect structure of complexes does not represent the only possibility to create neutral or acceptor-type complex in CdTe and CdZnTe. An analogous defect might be created also without participation of extrinsic atoms taking only native point defects into account. That is the complex of Cd vacancy and Te anti-site defect ( ) V Te Cd Cd predicted in ref. 60. Such complex was not identified in experiments yet and its electrical properties are not known. The reason, why we favour the structure of complex related to extrinsic Cl or Ge donors rises from the proximity of the evaluated complex densities in Te-annealed samples and respective element concentrations revealed by GDMS. The density of V Te Cd Cd complexes appears significantly below extrinsic-donor-related complexes and does not manifest in presented measurements. This picture is supported also by theoretical calculations in Table 3 since the V Te Cd Cd complex is characterized positron lifetime which is slightly lower that the lifetime for isolated V Cd . But such trend was not observed in experimental lifetimes. Conclusions Point defects in CdTe:Cl and CdZnTe:Ge crystals have been characterized by LT and CDB spectroscopies combined with galvanomagnetic measurements. The as-grown CdTe:Cl crystal exhibits larger point defects with open volume comparable with several vacancies. The low temperature LT studies in CdTe:Cl have proved the existence of negatively-charged shallow traps interpreted as Rydberg states associated with Cl-related A-centres. These shallow traps are able to confine positrons at low temperatures only when thermal de-trapping becomes sufficiently small. The lifetime of positrons localized in the shallow traps is shorter than the CdTe bulk lifetime. The as-grown CdZnTe:Ge crystal contains − V Cd 2 shallow acceptors forming neutral complexes with + Ge Cd 2 deep donors. It has been confirmed that Cd-rich annealing of both CdTe:Cl and CdZnTe:Ge crystals suppresses the concentration of V Cd , which are created again during subsequent Te-rich annealing.