VOLUME 77, NUMBER 10 P H Y S I C A L R E V I E W L E T T E R S 2 SEPTEMBER1996

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Increased Elemental Specificity of Positron Annihilation Spectra

P. Asoka-Kumar,1 M. Alatalo,1 V. J. Ghosh,1 A. C. Kruseman,2 B. Nielsen,1 and K. G. Lynn11Brookhaven National Laboratory, Upton, New York 11973

2IRI, Delft University of Technology, Mekelweg 15, NL-2629JB Delft, The Netherlands(Received 28 March 1996)

Positron annihilation spectroscopy (PAS) is a sensitive probe for studying the electronic structuredefects in solids. We show that the high-momentum part of the Doppler-broadened annihilation specan be used to distinguish different elements. This is achieved by using a new two-detector coincidsystem to examine the line shape variations originating from high-momentum core electrons. Becathe core electrons retain their atomic character even when atoms form a solid, these resultsbe directly compared to simple theoretical predictions. The new approach adds increased elemspecificity to the PAS technique, and is useful in studying the elemental variations around a defect[S0031-9007(96)01120-9]

PACS numbers: 78.70.Bj, 71.60.+z

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Positron annihilation spectroscopy (PAS) is a sensitprobe for studying defects in solids [1,2]. The methrelies on the propensity of positrons to become localizat open-volume regions of a solid and the emissionannihilation gamma rays that escape the test system wout any final state interaction. These gamma rays hinformation about the electronic environment around tannihilation site. PAS measurements for defect charterization generally utilize two observables: positron liftime and the conventional Doppler broadening of tannihilation gamma rays using a single detector. Bof these techniques are not very sensitive to elemtal variations around an annihilation site, such asone occurring when a material is lightly doped with aother or when a vacancy is tied with an impurity atomA third observable, angular correlation of annihilatioradiation, can overcome this deficiency. However, tobservable is not used routinely in defect spectroscoowing to the difficulties associated with the low countinrates at many of the existing facilities. Here we presthe results from a new two-detector setup that measuthe elemental variations around the annihilation site. Tnew setup improves the peak to background ratio inannihilation spectrum to,105, and as a result the variations of the Doppler-broadened spectra resulting fromnihilations with different core electrons can be mappeBecause the core electrons retain their atomic charaeven when atoms form a solid, the new results can beily verified with straightforward theoretical calculationIn the past, Lynnet al. have shown the advantage of uing a two-detector setup in a study of thermal generatof vacancies in aluminum [3,4].

Upon entering the solid, positrons lose most of theirnetic energy and reach thermal equilibrium with the homaterial (within about 10 psec). In a crystal, the thermazed positrons experience a periodic repulsive potenthat is centered on the ionic cores, and their wave functis confined to the interstitial region. Their subsequent m

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tion is dominated by phonon scattering, and in the abseof an overall electric field in the medium, this motionnearly an isotropic random walk. Open-volume defeand negative charge centers provide isolated minimathe potential and localize positrons. Eventually positrolocalized at defects or not, annihilate with electrons pducing predominantly two gamma rays, necessitatedenergy-momentum conservation during annihilation. Bcause the positrons are thermalized, the total energy oannihilation gamma rays is given by2m0c2 2 EB, wherem0c2 is the electron rest mass energy andEB is the elec-tron binding energy (neglecting the thermal energieschemical potentials). When there is a net center of menergy associated with the annihilating pair, this totalergy is not split equally among the two gamma rays. Ogamma ray is upshifted while the other is downshiftfrom the center energy ofm0c2 2 EBy2 by an amountgiven by DE ­ s1y2dpLc, wherepL is the longitudinalcomponent of the electron-positron momentum alongdirection of the gamma ray emission. Since the directof the gamma ray emission is random, a detector locain a given direction will record both upshifted and dowshifted gamma rays. This produces an overall Doppbroadening, and characterizing this broadening provia sensitive way of examining the electronic environmaround the annihilation site.

Annihilations with core electrons produce largDoppler shifts compared to valence electrons. Therefthe tail region of the Doppler-broadened curve cbe analyzed to obtain the momentum distributionthe core electrons. In traditional Doppler-broadenmeasurements, a single detector records the energthe annihilation gamma rays. The spectrum collecwith a single detector suffers from high backgroucontributions (peak to background ratio,200), whicharise mostly from incomplete charge collection on the lenergy side and pileup and sum events on the high enside. When positronium is formed, annihilation into thr

© 1996 The American Physical Society 2097

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gamma rays also can contribute to the low energy sAs a result, the line shape variations arising from the ctribution of the core electrons cannot be easily extractOn the other hand, if the energies of both gamma r(from each annihilation event) are recorded, the signabackground ratio can be dramatically improved in the tregion.

Figure 1 shows a two-dimensional spectrum recordwith a 30 keV positron beam striking a Si(100) targeFor every coincident event, the energies of both gamrays (denoted byE1 and E2) are registered in two highpurity Ge detectors arranged at 180± to each other. Theseenergies form the horizontal and vertical axes, andcount corresponding to eachE1 and E2 combination isindicated in color, depending on their absolute valuThere is an intense central peak centered atE1 ­ E2 ­511 keV, which corresponds to annihilations with thvalence electrons. On either side of this central peak,spectrum shows horizontal and vertical bands. The lenergy bands (horizontal withE1 , 511 keV or verticalwith E2 , 511 keV) are produced mostly by events iwhich one Ge detector records a photon in the photopewhile the other records the energy of the second pho(from the same annihilation event) at a lower value dueincomplete charge collection. Typical absolute photopeefficiency of the detectors used for these measuremen,0.2% at 511 keV at a source-detector distance of 25 cThe high energy bands (horizontal withE1 . 511 keVor vertical with E2 . 511 keV) correspond to an evenin which one detector records the gamma ray energythe photopeak and the other records a piled-up evThe elliptical region extending diagonally withE1 1

E2 ø 2m0c2 ­ 1022 keV originates from annihilationswith high momentum electrons, and this region is neabackground free. A cut along the diagonal can th

FIG. 1(color). A two-dimensional display of coincident evencollected with a Si(100) target. The spectrum contains a toof 15 3 106 events.

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be analyzed to observe variations in shape due tocontributions of core electrons.

In Fig. 2, we show the results obtained with a trditional setup using a single Ge detector and a twdetector coincidence system. The coincidence rescorresponds to a projection ontoE1 2 E2 s­ 2DE ­pLcd axis from Fig. 1. The projection includes eventsa window along the diagonal with2m0c2 2 2.4 keV ,

E1 1 E2 , 2m0c2 1 2.4 keV. The width of the sum-energy window is selected to exclude horizontal avertical bands depicted in Fig. 1 and to include regiocorresponding to the deficit in sum energies arising oof electron binding energies. Increasing the sum-enewindow to 2m0c2 6 4.8 keV did not change the shapof the annihilation spectrum, apart from an increasethe background. The plot reveals the increased sensity of the new method to high momentum contributionAs shown, a small improvement can also be made witsingle Ge detector in coincidence with ag-ray detector(such as a NaI detector). Recently this later approachbeen used by some authors [5–7].

Figure 2 also compares results for Si and Ge and shoshape variations arising from core annihilations. Tsamples used in the present study are high-purity sincrystals and are “defect free” as seen by positrons. Tspectra correspond to an incident positron beam energ30 keV and correspond to a mean penetration depth,4 mm in Si and ,1.7 mm in Ge, deep enough toexclude s,1%d positron diffusion to the surface ansubsequent annihilation from the surface states. Sithe spectrum is symmetric with respect toE1 2 E2 ­ 0,

FIG. 2(color). The comparison of the Doppler-broadenspectrum of Si collected with three different arrangementssingle detector (black), a single detector in coincidence wa NaI detector (red), and two detectors in coincidence (bluThe difference between the two coincident arrangementsthat in the first case the energy of only one of theg rays isrecorded. The plot also includes data from Ge (magenta).

VOLUME 77, NUMBER 10 P H Y S I C A L R E V I E W L E T T E R S 2 SEPTEMBER1996

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the next figure displays the results by folding it aboE1 2 E2 ­ 0 and averaging.

As already discussed in Ref. [7], the larger amplitudethe Ge curve stems from the fact that the outermost cshell in the case of Ge is3d, which is highly occupiedand spatially extended. Therefore the annihilation rwith 3d electrons in Ge is high. Being rather localizein r space,3d electrons produce a wide distribution in thmomentum space. This is better seen in Fig. 3, whwe present the experimental data for Al, Si, and Gtogether with the theoretical curves, calculated usingmethod described in more detail in Ref. [7]. Figure 3 alshows the partial contribution from the individual shellsGe. The total contribution has been convoluted with tdetector resolution.

The momentum distribution for each core electron stis calculated within the independent particle model uing free atom wave functions. These individual contbutions are then summed up by using state dependenhancement factors obtained by calculating the positwave function and the ensuing annihilation rate usithe method of superimposed atoms in solving the thr

FIG. 3. The comparison of the experimental and theoretiannihilation probability densities for Al, Si, and Ge. Tharea under the experimental data is normalized to unity. Tcalculated curves have been normalized to the quantitylcyltot,wherelc and ltot are the annihilation rate with core electronand the total annihilation rate, respectively.

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dimensional Schrödinger equation [8]. Since the coelectrons retain their atomic character even when atoform a solid, atomic wave functions provide an accurate description of the core electron states. Atomic wafunctions, however, are not an accurate descriptionthe valence electrons. Annihilations with valence eletrons produce smaller Doppler shiftss&20 3 1023m0cdthan annihilations with core electrons. Since the treament of the valence electrons is only approximately corect, their contributions to the Doppler broadening is nadded to the total. Experimentally, the present approacannot resolve the partial contributions. However, by dtecting the Auger electrons or x rays generated from tcore-hole decay in coincidence with the two annihilation photons, these partial contributions can be measudirectly.

Since the counts vs energy curves span several ordof magnitude, the shape difference between them canseen more easily after normalizing the measured spectrto a reference spectrum. In this Letter, we chose Althe reference spectrum. Figure 4(a) shows the normalizdata set for several elements. The normalization involvthe following steps: For each element, the area undercurve (after folding) is normalized to unity. The unityarea curves are smoothed (16 point averaging consis

FIG. 4(color). The spectrum for different elements after nomalizing to Al: (a) experiment and (b) theory. The theoreticcurves for pL , 20 3 1023m0c [dashed line in (b)] are notaccurate.

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with the system resolution) and divided by the Al curvCorresponding theoretical curves are shown in Fig. 4(Because our calculations do not treat contributions frvalence electrons accurately, the theoretical curveslow 20 3 1023m0c are not reliable. As can be seen, thagreement between theory and experiment is only qutative. At high pL values, where the theoretical curveshow many interesting features, the present experimevalues are not reliable due to low statistics. Neverthelethe theoretical curves also show elemental specificity,there are some qualitative trends that are worth noticiFor example, both the calculated and experimental curfor W show a valley at,20 3 1023 m0c and a peak(arising from4f electrons) at,32 3 1023 m0c.

It is interesting to note that there are small differenc[,20%, Fig. 4(a)] between elements that are adjacin the periodic table. The difference between Si aAl arises mainly from the different lattice structure. Ifcc Al the interstitial space is reduced compared wSi having diamond structure, and therefore the overof the positron wave function (which is more confineto the interstitial region due to the Coulomb repulsioof the ionic core) with core electron wave functionslarger. This increase in overlap produces the increin the ratio curve seen at higher Doppler shifts [.7 3

1023 m0c, see Fig. 4(a)]. Because of the similar costructure, however, the shape of the core distributioarising from Al and Si is very similar. Therefore, it mighbe hard to distinguish them in situations such as Si dowith Al. Nevertheless, differences between elements tare not adjacent in the periodic table are significaenough to conclude that the technique can be appto examine elemental variations around an open-voludefect site, such as an impurity-vacancy complex. Inrelated study using a single Ge detector in coincidenwith a NaI detector, Szpalaet al. recently showed thatthe binding of Sb to vacancies in Si can be easobserved [6].

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In conclusion, we have shown that a two-detectcoincidence system can improve the sensitivity of tpositron annihilation measurements. The increased setivity compared to the previous Doppler-broadening mesurements allows us to extract the chemical identity ofatoms. The method can be used to study a wide varietyproblems, like simple open-volume defects, open-voludefects decorated with foreign elements, and vacanciedifferent sublattices of a stoichiometric compound. Walso show that simple theoretical models can be usedinterpret these results.

We thank F. M. Jacobsen, M. J. Puska, P. Mijnarenand T. Korhonen for various discussions. This wowas supported in part by U.S. DOE under Contract NDE-AC02-76CH00016. One of us (ACK) thanks thNetherlands Organization for Scientific Research (NWfor a travel grant.

[1] P. J. Schultz and K. G. Lynn, Rev. Mod. Phys.60, 701(1988).

[2] M. J. Puska and R. M. Nieminen, Rev. Mod. Phys.66, 841(1994).

[3] K. G. Lynn, J. R. MacDonald, R. A. Boie, L. C. Feldman, J. D. Gabbe, M. F. Robbins, E. Bonderup, aJ. Golovchenko, Phys. Rev. Lett.38, 241 (1977).

[4] K. G. Lynn, J. E. Dickman, W. L. Brown, M. F. Robbinsand E. Bonderup, Phys. Rev. B20, 3566 (1979).

[5] M. Alatalo, H. Kauppinen, K. Saarinen, M. J. PuskaJ. Mäkinen, P. Hautojärvi, and R. M. Nieminen, PhyRev. B 51, 4176 (1995).

[6] S. Szpala, P. Asoka-Kumar, B. Nielsen, J. P. PenS. Hayakawa, K. G. Lynn, and H.-J. Gossmann, Phys. RB (to be published).

[7] M. Alatalo, B. Barbiellini, M. Hakala, H. Kauppinen,T. Korhonen, M. J. Puska, K. Saarinen, P. Hautojärvi, aR. M. Nieminen, Phys. Rev. B54, 2397 (1996).

[8] M. J. Puska and R. M. Nieminen, J. Phys. F13, 333(1983).