J. Phys. Chem. C 2009, 113, 3419–3425
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Vacancy-Type Defects and Their Evolution under Mn Substitution in Single Crystalline ZnO Nanocones Studied by Positron Annihilation Tandra Ghoshal,†,§ Soumitra Kar,†,|,⊥ Subhajit Biswas,†,#,⊥ S. K. De,†,∇ and P. M. G. Nambissan*,‡ Department of Materials Science, Indian Association for the CultiVation of Science, JadaVpur, Kolkata 700032, India, and Nuclear and Atomic Physics DiVision, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064, India ReceiVed: June 25, 2008; ReVised Manuscript ReceiVed: December 23, 2008
Bipyramidal-shaped single crystalline nanocones of ZnO, doped with Mn2+ ions up to different concentrations, were synthesized through a solvothermal route and characterized by X-ray diffraction and transmission electron microscopy. The compositional analysis was also carried out by energy-dispersive analysis of X-rays (EDAX). Positron annihilation studies were carried out to extract information on the vacancy-type defect clusters and their evolution under doping, which may have a major influence on the physical properties of the material. In the undoped ZnO, trivacancy-type defects of the type VZn+O+Zn are present. Doping by Mn2+ ions reduced them to divacancies (VZn+O) as a result of the ion-vacancy complex formation. These were indicated by the measured positron lifetimes and coincidence Doppler broadening measurements. An interesting observation is the reduction in base diameters of the nanocones at high (>1 atom %) dopant concentrations, an effect of increased strain due to occupancy of Zn2+ vacancy sites by Mn2+ ions of slightly larger radius. As the diameters of the grains reduce to below the thermal diffusion lengths of positrons, significant number of annihilation events seemed to result from the surfaces of the nanocones. The intercrystalline regions also gave a favorable site for the formation and “pick-off” annihilation of orthopositronium atoms. Introduction Although in recent years there has been a considerable interest followed by extensive studies on the properties related to the application of zinc oxide (ZnO) in optical devices and hightemperature electronics,1,2 there still exists scope for studies of its properties likely to be modified by doping by elements like Ni, Cd, Mn, etc.3 The engineering of the properties of this semiconductor material has been highly promising both from physics and technology points of view and, in fact, even irradiation by particles has been attempted as one of the ways to achieve this goal.4,5 Talking about materials composed of nanocrystallites of various morphologies, it should be pointed out that the vacancytype defects both within and at the interfacial surfaces will play an important role in determining their characteristics. These defects therefore deserve systematic investigation well in advance before the said nanomaterial is considered for applications. Naturally the interaction of doped atoms with the defects will modify the properties of the material in different ways depending on the nature and concentration of the doped atoms. We are reporting here the results of an attempt in this direction. Positron annihilation spectroscopy has been used in this study due to its extreme sensitivity to the presence of vacancies in the material. The advantages of this technique over other more * To whom correspondence should be addressed. E-mail: pmg.nambissan@ saha.ac.in. Fax: 91-33-23374637. † Indian Association for the Cultivation of Science. ‡ Saha Institute of Nuclear Physics. § E-mail:
[email protected]. | E-mail:
[email protected]. ⊥ Present address: Nano Science Technology Center, University of Central Florida, Orlando, FL 32826. # E-mail:
[email protected]. ∇ E-mail:
[email protected].
conventional methods have been subjects covered under several review articles.6 In a recent work reported by us, the ability of this technique to selectively annihilate at vacancy-type defects within as well as at the surfaces of undoped ZnO nanocones (referred to as “nanobipyramids” therein) has been demonstrated.7 Experimental Section ZnO nanocones were synthesized by using a solvothermal process.8,9 It was observed that an equal volume ratio of ethanol and water with a high pH value was the favorable solvent for the synthesis of ZnO nanocones. The sizes of the nanocones were sensitive to the synthesis temperature. The synthesis of the Mn-incorporated ZnO nanostructures is carried out following our published protocol.9 In short, appropriate amounts of zinc nitrate [Zn(NO3)2, · 6H2O], manganese acetate [Mn(CH3COO)2 · 4H2O], and NaOH were dispersed in an ethanol-water solvent mixture followed by heating in a closed Teflon-lined stainless steel chamber for 12 h at 413 K. A series of samples with varying Mn2+ content were synthesized by introducing different concentrations (0.1, 0.5, 1, 6, 10, and 15 atom %) of the manganese source. For the positron annihilation studies, the radioactive isotope 22 Na of strength 400 kBq served as the source of positrons. 22 NaCl in dilute HCl was deposited and dried on a thin (∼2 µm) Ni foil and folded to form the experimental source. It was kept immersed in the volume of the powdered sample taken in a glass tube and maintained under dry vacuum conditions during the experiments. The sample surrounded the source from all sides in sufficient thickness to ensure annihilation of positrons within it. The positron lifetime measurements were carried out using a slow-fast coincidence spectrometer, having a time
10.1021/jp805602f CCC: $40.75 2009 American Chemical Society Published on Web 02/10/2009
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Ghoshal et al. TABLE 1: Percentage of Mn2+ Ions Added during the Synthesis and the Actual Percentage Obtained from EDAX Analysis of the Different Samples
Figure 1. (a) X-ray diffraction patterns of the undoped and the 15 atom % Mn-doped ZnO nanocone samples.
Figure 2. EDAX spectra of the undoped and the 6 atom % Mn-doped ZnO nanocone samples.
resolution (fwhm) of 200 ps for prompt γ rays (from 60Co source) accepted under the normal experimental window settings. For Doppler broadening measurements, the positron annihilation gamma ray spectra were recorded using a HPGe detector with resolution 1.14 at 511 keV. This and another detector with identical resolution were used on either side of the source-sample assembly for coincidence Doppler broadening spectroscopy (CDBS) studies. Further details and the description of the method of data analysis are discussed later.
added concentration of Mn ions (atom %)
actual concentration of Mn ions (atom %)
0 (undoped) 0.1 0.5 1 6 10 15
0 0.1 0.44 0.89 5.8 9.72 14.58
The morphology and crystal structure of the as-synthesized Mn-doped ZnO nanoforms were studied by transmission electron microscopy (TEM). TEM images of the undoped ZnO and 1 and 15 atom % Mn-doped samples are shown in Figures 3a-c, respectively. The images clearly show that the nanocrystals are composed of double-sided cones with hexagonal cross-section. They are hereafter referred to as nanocones. These nanocones possessed a flat hexagonal base with six well-defined planes that merge at the vertex to form the prism-like structures. TEM studies revealed that the morphology remained unaltered but the size of the crystals varied with increase in Mn2+ concentration. For the undoped sample, the average base diameter of the nanocones is about 75 nm. Although no substantial change in diameter of the base of the nanocones was observed in the initial stage (0.1 and 0.5 atom %) of doping, on further doping to increased concentrations of 1, 6, 10, and 15 atom %, the average base diameter decreased gradually to 55, 40, 35, and 25 nm, respectively (Table 2). Figure 3d shows the high resolution TEM image of the vortex of 1 atom % Mn-doped ZnO nanocones. The clear lattice fringes illustrate that the nanocones are single crystalline. Positron Annihilation Studies. In a recent work on pure ZnO samples of nanocones and nanoparticles of various sizes, we have shown that the dominant positron trapping centers are the negatively charged vacancies created by the absence of Zn2+ ions (hereafter simply referred as “Zn vacancies” or VZn).7 This was verified from the analysis of the CDB spectra, which for the present samples are shown in Figure 4. As mentioned earlier, in this kind of experiment, both of the annihilation γ rays are
Results and Discussion Characterization of the Samples. The synthesized samples were initially characterized using X-ray diffraction (XRD, Seifert 3000P with Cu KR radiation) and transmission electron microscopy (TEM, JEOL 2010). The crystal structure and phase of all of the doped samples were determined. Figure 1 shows the XRD pattern of the undoped and 15 atom % Mn-doped samples. The diffraction peaks of all of the samples are indexed to the crystalline hexagonal wurtzite structure of ZnO (JCPDS card no. 36-1451). The patterns did not show any extra peaks, indicating that the samples are of sufficient purity in composition and there is no secondary phase formation. The compositional analysis of the Mn-doped ZnO samples was performed by energy-dispersive analysis of X-rays (EDAX, Kevex, Delta Class Ι). The EDAX spectra of the undoped and 6 atom % Mndoped ZnO samples are shown in Figure 2. In undoped ZnO, elemental Zn and O were found in near-stoichiometric ratio. In the Mn-doped samples, the amount of Mn detected by EDAX was almost the same as that actually added during synthesis (Table 1). For example, 14.58 atom % Mn was detected in the 15 atom % Mn-doped ZnO sample.
Figure 3. Transmission electron microscopic (TEM) images of the (a) undoped, (b) 1 atom % Mn-doped and (c) 15 atom % Mn-doped ZnO nanocone samples. (d) High resolution transmission electron microscopic (HRTEM) image of the vortex of the 1 atom % Mn-doped ZnO nanocone sample.
Vacancy-Type Defects and Their Evolution
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TABLE 2: Average Diameters of the Base of the ZnO Nanocones of Samples Doped with Different Concentrations of Mn2+ Ions, As Determined from Transmission Electron Microscopic Images concentration of Mn2+ ions (atom %)
nanocone base diameter (nm)
0 (undoped) 0.1 0.5 1 6 10 15
75 75 75 55 40 35 25
detected and recorded using the two HPGe detectors placed on either side of the source-sample assembly till approximately 7-8 million counts are obtained. A spectrum is simultaneously generated with the sum (E1 + E2)/2 and difference (E1 - E2)/2 of the energies E1 and E2 of the γ rays in the two coplanar perpendicular axes. The one-dimensional projection of (E1 + E2)/2 ) 511 ( 1.2 keV on the energy-difference ((E1 - E2)/2) axis is a spectrum of distribution of Doppler shifted energies free of resolution and background effects.10,11 As is the normal practice with the analysis of this type of spectra, a ratio curve is generated by dividing the spectra so obtained by the corresponding spectrum of a pure element (Si, in the present case) after normalizing the area under each spectrum to unity. The results shown in Figure 4 depict a remarkable difference in the position of the characteristic peak of ZnO from that of elemental Zn. This means the positrons in ZnO encounter with electrons of element different from Zn and they obviously are those of the oxygen ions. This is confirmed by also showing the corresponding spectra of MnO2 as well, whose peak also appears at the same position, identifying with an identical elemental environment. This apparently indicates that positrons are trapped at the Zn vacancies (VZn) in ZnO and is consistent with the fact that the oxygen ionic vacancies (VO) being positively charged cannot trap positrons due to Coulomb repulsion. The results of positron lifetime measurements also help to draw additional inferences on this aspect, which are discussed in the following paragraphs. The positron lifetime data were analyzed using the latest version of the PATFIT package, namely PALSfit.12 Initially, a spectrum of well-annealed single crystalline Si (the same sample
Figure 4. Ratio curves generated by dividing the CDBS spectra of undoped ZnO, MnO2, and 0.1 and 6 atom % Mn-doped ZnO nanocones by the spectra of pure annealed Si samples. The curves of elemental Zn and Mn are also shown.
that was used to obtain the reference spectrum for analysis of the CDB spectra) was recorded using the same source and a characteristic lifetime of 220 ps was obtained. The remaining two lifetimes, 100 and 500 ps with intensities 3.8% each, are contributions coming respectively from the Ni foil and the 22 NaCl source. This source correction is done in the subsequent analyses of the spectra of all of the experimental samples. The spectra of all the samples were fitted satisfactorily with variances of fit ∼1.05 ( 0.15 to a three-component exponential decay composed of lifetimes τ1, τ2, and τ3 with relative intensities I1, I2, and I3. The longest lifetime τ3 varied between about 600 ps and 1.6 ns, lifetimes typical of positrons annihilating at surfaces and as orthopositronium atoms in extended defects like cavities.13 Although its intensity I3 was small (∼0.5 to 5%), we still preferred not to ignore its presence to a two-component analysis of the spectrum. The origins of the other two lifetime components should arise from the structural and morphological features of the particular sample used. The shorter lifetime τ1 in the undoped ZnO sample was 133 ps while the other longer lifetime τ2 ) 310 ps. The intensity I2 was as high as 50.2%, and it indicated the trapping of positrons in large defects. Expectedly, the shorter lifetime τ1 at all stages of doping was less than the delocalized positron lifetime (variedly reported as τb ) 151,14,15 170,16 and 171 ps17 for bulk ZnO) in accordance with the two-state trapping model equation18
(
1 1 I23 1 1 ) + τ1 τb I1 τb τ23
)
(1)
where the second term on the right-hand side of the equation gives the rate of trapping of positrons into the defects. Note that, in order to do these calculations (and also those mentioned later), the weighted average τ23 ) (τ2 I2 + τ3 I3)/I23 and I23 ) I2 + I3 are used in place of τ2 and I2 in the appropriate equations. This is justified since positronium is formed by a fraction of the positrons, which are trapped in the defects on the grain surfaces. Although positronium formation is not generally reported for metallic or semiconductor systems of the macroscopic grain size owing to the high electron densities involved, there lies a distinct possibility for the same in the case of nanomaterial systems as the grain surfaces and interfaces are sites of very low electron density and which can probably act as favorable sites for a fraction of the positrons to form positronium. Since the samples used in the present study are all of nanometer dimensions, it is not possible to get a direct estimation of the bulk lifetime τb using the above equation. Hence to estimate the same, we have used the positron lifetimes reported in ref 7 for a sample composed of nanocones of base diameter 200 nm in which the thermal diffusion of positrons to the surfaces could be neglected. That lead to a value of τb ) 179 ps using eq 1 above and is very much in agreement with the calculated value of 177 ps reported by Tuomisto et al.16 and further used by Zubiaga et al.17 and Tuomisto et al.19 in the interpretation of the results of their subsequent experiments. In this context, it is worth mentioning here that the bulk positron lifetime in ZnO is still a debatable issue, as is evident from the large spread in the values reported by several authors. We have summarized them in Table 3. Brauer et al.14,15 have reported the lowest value of 151 ps, with which several authors have disagreed. In particular, this value has been strongly refuted by Zubiaga et al.17 on the grounds that the said lifetime 151 ps had been estimated from a spectrum dominated by a high intensity vacancy-related lifetime component. Besides, the references quoted by Brauer et al.15 in support of their finding contained erroneous results and wrong interpretations. The value
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TABLE 3: Summary of the Positron Lifetimes in Bulk (τb), Zn Monovacancies (τ1V), and ZnO Divacancies (τ2V) As Reported in Literature by Different Research Groups and the Respective Difference and Ratios with Respect to the Bulk Valuea ref
τ2V - τb τb τ1V τ2V τ1V - τb (ps) (ps) (ps) (ps) τ1V/τb (ps) τ2V/τb
Brauer et.al.14,15 151 Tuomisto et al.16 170 177c Zubiaga et al.17 171 177c Tuomisto et al.19 177 Puff et al.20 173 Brunner et al.21 173 Chen et al.25 158c 188 a
229 237
257
230 230 210 175c
260 260 215c
78 67 60 53
1.52 1.39 1.34 1.30
53
1.30
37 17
1.21 1.10
106
1.70
87 87 57
1.50 1.50 1.36
Superscript c indicates the calculated value.
of 179 ps obtained in the present work, on the other hand, finds better agreement with that of Toumisto et al.16 and has also been reproduced by repeated measurements. The lifetimes of trapped positrons, which eventually annihilate within the defects, would be larger than τb and characteristic of the density of electrons available at the defect sites. The intermediate lifetime τ2 ) 310 ps represents the trapping of positrons in vacancy-type higher order defects present in abundance (I2 ) 50.2%) within the constituent nanocones of the samples. In bulk ZnO, the most dominant positron trapping site has been recognized by many authors as the negatively charged monovacancies (VZn) created by the missing Zn2+ ions and different authors have reported the positron lifetime in such a vacancy as differently as 229 ps,15 237 ps16 and 230 ps.19 The value of τ2 ) 310 ps obtained in the undoped sample is larger than the positron lifetimes in Zn vacancies and in fact even larger than the positron lifetime reported for divacancies (VZn+O) in ZnO (∼ 257 ps,14 260 ps,20,21 273 ps6). The attribution of a measured positron lifetime to vacancy-type defect of a given size based on simple numerical agreement with a reported value in literature may be misleading due to the differences and discrepancies existing among the values quoted by many authors regarding the positron lifetimes in the various kinds of defects in ZnO. In Table 3, we have included these values as well and see that the ratio of positron lifetimes in the defect (τd) and the bulk (τb) is a more acceptable parameter in view of the vast disagreement related to the value of τb in ZnO. Thus there seems to be general agreement on τd/τb lying between 1.30 and 1.52 for a Zn monovacancy and between 1.50 and 1.70 for a Zn-O divacancy (Table 3). (The insignificant overlap between the upper limit of the former and lower limit of the latter arises from the standard errors in the lifetimes obtained from the PALSfit analysis.) Another point to consider is the effects of relaxation of neighboring atoms around vacancy-type defects in ZnO. However, even after incorporating these effects into the estimation of the positron lifetimes using the atomic superposition method, Brauer et al.15 has obtained a positron lifetime of 1.74 times the bulk value in VZn+O divacancies. In our work, the positron lifetime τ2 ) 310 ps in the defects is 1.73 times larger than the bulk value of 179 ps and hence it may suggest that the vacancy-type defects are divacancies. On the other hand, if the enhancement in lifetime τd - τb is considered, we observe a difference of 131 ps compared to 117 ps reported in Brauer et al.’s work.15 As discussed below shortly, the evidence from CDBS experiments is more in favor of attributing the τ2 ) 310 ps component to trivacancies rather than divacancies. It should be mentioned here that the positron
thermal diffusion length in ZnO has been variedly reported for samples treated under different temperatures, with a maximum around 52 nm.22-24 Therefore, in the case of nanosystems with any physical dimensions less than this length, a significant fraction of the positrons, after their initial thermalization, will diffuse out to the surfaces to get annihilated with an enhanced lifetime owing to the reduced electron density over there. (The lower-than-average electron density is to be attributed to the increased disorder in atomic arrangement on the surfaces.) From Figure 3a, we note that the base diameter of the nanocones of the undoped sample is around 75 nm, and hence, the contribution from positron annihilation at surfaces is rather small. The measured value of τ2 (310 ps) is larger than the reported lifetime in divacancies (26020,21 and 273 ps6) by the same magnitude as the difference between the positron lifetimes in divacancies and Zn monovacancies (237 ps16). For smaller vacancy clusters, theoretical calculations by Chen et al.25 showed a linear variation of the positron lifetime with the increase in size of the vacancy clusters, although the magnitudes of the positron lifetimes reported by these calculations are much smaller than the experimental values.16,17,19-21 These are also reasons behind our attribution of the lifetime τ2 ) 310 ps in the undoped sample to the trivacancy-type defect generated by the absence of neighboring Zn-O-Zn atoms. This argument is also in agreement with the conclusion derived from CDBS spectra that the annihilation predominantly occurs from the electrons of oxygen ions. It should also be noted that, since the Zn ion is positive and oxygen ion negative in ZnO, the corresponding vacancies will be oppositely charged. It is then easy to understand that a trivacancy of the VO+Zn+O type will be positively charged and hence cannot trap positrons as a result of Coulomb repulsion. On the other hand, VZn+O+Zn trivacancy is negatively charged, and positron trapping and subsequent annihilation are highly favored. Zubiaga et al.17 had discussed about the possibility of positron trapping at hydrogen-like Rydberg states around negative ionic centers. This is, however, significant only at low temperatures (T < 200 K) and does not influence the results of the present experiment in which all the measurements have been carried out at room temperature. The evolution of the defects under increased Mn-doping is monitored from the variation of the various positron annihilation parameters. A sensitive parameter, denoted as S, that varies in accordance with the changes in size and concentration of the defects in solids is derived from the Doppler broadened gamma ray spectral line shape. It is defined as the counts under the energy interval of 511 ( 0.64 keV when the total area under the spectrum is normalized to unity after the subtraction of the background and represents the fraction of low momentum (valence) electrons annihilated by positrons. In Figure 5, the variation of the S parameter as a function of the input concentration of Mn2+ ions is shown. (In this and the following figures, the values shown against x ) 0.01 refer to the undoped sample.) Note that S exhibits remarkable changes as the doping is increased. Three distinct stages can be identified from the figure. The initial rise is followed by a flat response in the region of change of Mn2+ concentration from 0.1 to 1 atom % and then a subsequent sharp rise till the highest concentration used in the present work. A look at the sharp decrease of the lifetime τ2 and its intensity I2 in the initial stage of variation (Figure 6) reveals the partial occupation of the trivacancy clusters by Mn2+ ions. To explain the behavior of S, we once again focus attention on the CDB spectra shown in Figure 4. The peaks of the spectra of the Mn-doped samples (even of concentration 0.1 atom %) shifts to coincide with that of elemental Mn and subsequently
Vacancy-Type Defects and Their Evolution
Figure 5. S parameter vs the input Mn2+ concentration in the ZnO nanocone samples. (The value shown against x ) 0.01 refers to the undoped sample.)
Figure 6. Positron lifetimes τ1 and τ2 and relative intensity I2 vs the input Mn2+ concentration in the ZnO nanocone samples. (The values shown against x ) 0.01 refer to the undoped sample.) The lines are drawn only to guide the eyes.
the falling parts of the spectra merge with that of Mn at higher momentum regions. This suggests that positrons are now able to annihilate with the electrons of Mn in the doped samples. In Figure 6, we notice a characteristic fall of the positron lifetime τ2 with the addition of 0.1 atom % Mn to ZnO and this directly speaks about a reduction of the size of the positron trapping sites. It can be conjectured that the doped Mn2+ ions combine with the trivacancy defect VZn+O+Zn and reduces it to a divacancy of the form VZn+O. In other words, one Zn monovacancy (VZn) constituting the original trivacancy is now occupied by the doped Mn2+ ion, thus forming a Mn-vacancy complex in the immediate neighborhood of the transformed divacancy. The positron getting trapped into the VZn+O divacancy will now be able to interact and annihilate with the electrons of Mn2+ ion. Both Zn2+ and Mn2+ ion cores have got the outermost electrons in their 3d orbits, but because of the reduced nuclear charge, the electrons of Mn2+ are less tightly bound and hence more delocalized in r space. Therefore, the peak of the CDBS curve
J. Phys. Chem. C, Vol. 113, No. 9, 2009 3423 for Mn2+ will be in the lower momentum side of that of the curve of Zn2+, as seen in Figure 4. Further rise in the S parameter with increasing Mn2+ concentration beyond 1 atom % is attributed to the effect of size of the nanocones on the positron annihilation characteristics. From the TEM figures, the base diameters of the nanocones in the different Mn-doped samples have been estimated and the results are shown in Table 2. It is observed that the base diameters of the nanocones reduce monotonically with increasing concentrations of the dopant ions (Figures 3(a)-3(c)). This indicates that Mn2+ ions have a restricting effect on the growth of the Mn-doped ZnO nanocones. This could be attributed to the lattice strain induced in the doped crystals caused by the mismatch of ionic radii between the host (Zn2+) and dopant (Mn2+) cations. The ionic radius of Mn2+ (0.80 Å) is about 10% larger than that of Zn2+ (0.74 Å)26 and hence the substitution of the smaller Zn2+ ions by the larger Mn2+ ions forced a lattice distortion in the ZnO nanosystems. Larger the concentration of Mn2+ ions, larger is the induced strain. Also the lattice distortion is larger in crystals with larger sizes. Thus the incorporation of more and more Mn2+ ions in the host lattice introduced more and more strain, which in turn increased the internal energy of the crystals. The doped crystal will then prefer to minimize its lattice strain by reducing the size of the crystallites. It can also be noted that the lattice strain will be more if the dopant ions are inside the crystal compared to the case where the dopant ions are at the surface. The smaller the particle size, the larger the surface to volume ratio and, therefore, the larger the chance of hosting the dopant ions at the surface. This could be a reason for the reduction of the cone size with increased dopant ion concentration. The decrease in the base diameters continues to values less than the thermal diffusion length for positrons (∼52 nm;22-24 Table 2). In such a situation, a fraction of the positrons will reach the nanocone surfaces. Thus positrons are now getting trapped not only in the defects within the nanocones but also on their surfaces. The availability of additional trapping centers (i.e., at the surfaces of nanocones) is also indicated by the variation of the intensity I2 (Figure 6) that exhibits a sudden increase when the nanocone diameters fall just below the positron thermal diffusion length. Subsequently the recombination of vacancies within the nanocones due to the increasing number of Mn2+ ions reverses the trend and it falls and saturates at around 40%. The rise of the lifetime τ2 beyond the original 310 ps limit at higher Mn2+ concentrations (>1 atom %) is also understood as the result of positron annihilation in the defects on the surfaces. The same is responsible for the monotonous rise of the longest lifetime τ3 (Figure 7). Note that at the highest Mn2+ concentrations (10-15 atom %) when the dimensions of the nanocones are the minimum, τ3 approaches a value of ∼1.6 ns, a lifetime typical of orthopositronium atoms undergoing annihilation via the so-called “pick-off” process.6,13 Although the corresponding intensity I3 is rather small (only 0.5%; Figure 7), it points out to the very large intercrystalline space available by virtue of the shrinking dimensions of the nanocones. As explained earlier, the increasing strain in the lattice due to the incorporation of increasing concentration of Mn2+ ions leads to the shrinkage of the nanocone dimensions at this stage. Finally, we used the three-state trapping model to calculate the positron trapping rates due to defects on the surfaces and within the interior of the nanocones (i.e., the vacancy clusters).6,18 These are given by the equations
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τ1(λb - I23λ23) - I1 τd - τ1
(2)
I23 (λ - λ23 + κsurface) I1 b
(3)
κsurface )
τcal 1 )
and
κcluster )
1+
(
κcluster κsurface 1+ λ1 λb - λ23 + κsurface λb + κsurface + κcluster
)
(4)
and is clearly visible as observed in Figure 6. Summary and Conclusions
Here the annihilation rates (λ) are the corresponding reciprocals of the positron lifetimes (τ). The saturation lifetime τd contributing to the vacancy clusters is taken as 310 ps. Consistent with the arguments we made in the preceding paragraphs, the positron trapping at the surfaces of the nanocones is initially negligible but increased in samples where their base diameters are less than the positron thermal diffusion length (i.e., at Mn2+ ion concentrations larger than 1 atom %) (Figure 8). The positron trapping in the vacancy clusters rapidly decreased owing to the two reasons explained earlier (Figure 8). First, as the vacancy clusters are reducing in size due to partial occupancy by the doped Mn2+ ion, the trapping rate is also reduced. Second, increasing fractions of positrons manage to reach the surfaces of smaller nanocones. The rise of the lifetime τ1 at higher Μn2+ ion concentrations is then in accordance with the equation
The main conclusions from this work are related to the effects of doping nanoconical ZnO single crystals by Mn2+ ions that were found to significantly modify the inherent structural defects within and at the surfaces. The doping has also certainly modified the defect environments of the surfaces of the nanocrystalline systems, as was evident from the sharp rise of the Doppler broadened line shape parameter when the positrons could thermally diffuse out and reach the surfaces. Positron annihilation spectroscopy is successfully used in identifying the vacancy-type defects within the nanosystems. The measured positron lifetimes and the results of coincidence Doppler broadening measurements indicated the presence of trivacancytype defects of the form VZn+O+Zn in the undoped ZnO sample and they were converted to the divacancy-type defects VZn+O due to the formation of Mn-vacancy complex by the doped Mn2+ ions. The signature for positron annihilation with the Mn2+ ions is found vividly reflected in the coincidence Doppler broadened spectra. At the initial doping concentrations, the base diameter of the nanocones did not vary much. However, further doping resulted in increased strain within the crystals and at the surfaces due to the larger ionic radius of Mn2+ and the reduction of the base diameters resulted from the effort to minimize the additional energy introduced. The positron annihilation parameters varied in accordance with the expected trend. As for example, the defect-related positron lifetimes increased when a fraction of the positrons could diffuse out to the surfaces of nanocones with dimensions less than their diffusion length. Simultaneously, the largest lifetime component further increased to reach the value corresponding to positronium formation and annihilation at the intercrystalline region that increased in volume owing to the shrinkage of the nanocones.
Figure 7. (a) Longest positron lifetime component τ3 and (b) its intensity I3 vs the input Mn2+ concentration in the ZnO nanocone samples. (The values shown against x ) 0.01 refer to the undoped sample.)
Acknowledgment. The authors would like to pay their rich tributes to the memory of late Prof. Subhadra Chaudhuri of the Indian Association for the Cultivation of Science, who had inspired and motivated them to undertake this work. One of them (T.G.) also gratefully acknowledges the financial support received from Council of Scientific and Industrial Research, New Delhi (India). References and Notes
Figure 8. Positron trapping rates κsurface and κcluster vs the input Mn2+ concentration in the ZnO nanocone samples. (The values shown against x ) 0.01 refer to the undoped sample.)
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