PHYSICAL REVIEW B VOLUME 39, NUMBER 14

Charge transfer and core-hole screening in PbTe

15 MAY 1989-I

S. D. Waddington and P. WeightmanDepartment ofPhysics and Interdisciplinary Surface Science Centre, The University ofLiuerpool,

Oxford Street, P.O. Box 147, Liuerpool L693BX, United Kingdom

l. A. D. MatthewDepartment ofPhysics, Uniuersity of York, Heslington, York Y01 5DD, United Kingdom

A. D. C. GrassieDepartment ofMathematical and Physical Sciences, Uniuersity ofSussex, Brighton BNI 9QH, United Kingdom

(Received 14 October 1988)

An analysis of the Auger-parameter shifts between PbTe and the pure elements is shown to yield

insight into mechanisms of core-hole screening and charge transfer in the ground state. Aparametrized treatment of the Auger-parameter shifts in which the screening terms are treated in

terms of a Jost-cavity model shows that the ground-state charge transfer in PbTe is less than0.30e+0.06e. It is shown that core holes are screened more efficiently on Pb sites than on Te sites in

PbTe, and that Te core holes are screened more efficiently in pure Te than in PbTe.

I. INTRODUCTION

It was shown in a previous paper' that the ground-statecharge distribution in alloys, and in particular the extentof charge transfer, can be obtained from an analysis ofAuger-parameter shifts. ' This approach was shown tobe superior to methods in which core-ionization-energyshifts are analyzed in terms of potential models.

In this work we extend the analysis of Auger-parameter shifts to semiconducting systems and considercontributions from the incomplete screening of core holesand their polarization of the atomic environment. Thetechnique is applied to PbTe, which is a member of animportant class of polar semiconductors in which the bal-ance between the ionicity and covalency of the bondsinfluences the mobility of carriers by their interactionwith optical phonons and is also thought to be an impor-tant determinant of lattice instability. ' We show thatan analysis of the Auger-parameter shifts between thepure elements and the compound provides an upper limiton the charge transfer in PbTe and gives insight into therelative efBciency of the screening of core holes on Pbsites in PbTe and Te sites in PbTe and pure Te.

contamination-free surfaces with a composition represen-tative of the bulk.

The experiments were designed to measure the changein the Auger parameter n of Pb and Te between each ofthe pure elements and PbTe. As discussed earlier' hacan be accurately determined from the change in core-level ionization energies, I„and the kinetic energies ofcore-core-core Auger energies, K, according to

ha=hI+AK . (l)

The core-level ionization energies measured relative tothe Fermi level of Pb or the top of the valence bands ofPbTe and Te are given by

I, =KF —K, ,

where KF is the energy of the Fermi level or top of thevalence band and K, the energy of the core level, eachmeasured on the energy scale of the instrument. In thesemeasurements the spectra were excited by monochromat-ed Al Ka x rays. The kinetic energies of the core-core-core Auger lines are determined with respect to the ap-propriate reference level using

K~ =1486.55+K~ —K, —I, (3)II. KXPKRIMKNT AND RESULTS

The PbTe specimen (doped with 4 at. % of Tl) was pro-duced by radio-frequency melting of appropriate amountsof the pure elements in an evacuated quartz ampoule.The x-ray photoelectron (XPS) and Auger electron spec-tra of PbTe and specimens of the pure elements weremeasured using a modified KRATOS ES200 spectrome-ter equipped with a multidetector system. The experi-mental procedure, including the results of XPS measure-ments confirming the composition of the PbTe specimen,is described in an earlier paper. The early work also de-scribes the specimen cleaning procedures which yielded

where K„and K, are the kinetic energies of the Augerand core-level XPS lines measured on the instrumentalenergy scale when excited by unmonochromated Al Karadiation the average energy of which is accuratelyknown to be 1486.55 eV. The Te M45N4~N45 and PbM5N6 7N6 7 Auger transitions were chosen for these mea-surements since they involve deep levels and should begood probes of the potential in the core of the elementsconcerned. These transitions also have relatively narrowspectral components and the Auger spectral profiles ob-served from PbTe were identical with those observedfrom the pure elements. The narrow Pb 4f and Te 3d

39 10 239 1989 The American Physical Society

10 240 WADDINGTON, WEIGHTMAN, MATTHEW, AND GRASSIE 39

III. THEORY

The aim of this work is to use accurate measurementsof the change in the Auger parameter of Pb and Te on

TABLE I ~ Core ionization, Auger, and Auger-parametershifts. All shifts are for the given element in the compound rel-

ative to the pure material (eV).

PbTe —Pure element

b,I(Pb:4f)"EI(Te:3d)g~(pb;~, ~, 7+6 7)AK(Te;M4 A%4, X4, )"Aa{pb)'ha(Te)'

—0.04+0. 16—0.90+0.05—0.51+0.17+0.10+0.05—0.55+0.07—0.80+0.07

'Result influenced by the unknown systematic error arisingfrom the difterence in the bias applied to Pb and PbTe.Result inAuenced by the unknown systematic error arising

from the difference in the choice of reference energy for thethree materials.'The systematic errors afT'ecting the separate determinations ofbI and AK cancel as do some of the other sources of error.

XPS lines were used in the measurements of core-levelshifts. A bias of +1000 V was required to bring the PbAf $N{j 7 N6 7 Auger electrons within the energy range ofthe instrument. The Pb 4f XPS lines excited by Al Ka xrays were measured while the specimen was under thesame bias as that employed in the Auger measurements.The bias then cancels in (3) and does not need to beknown accurately. The results for AI and AK are shownin Table I. These results are sensitive to systematic errorsarising from the difference in the choice of reference levelbetween Pb and the two semiconducting materials and inthe difference in the bias applied in the Pb measurementson PbTe and the pure element. These systematic errorscan be eliminated in the determination of Aa as can beseen by subtracting the results obtained for pure Pb fromthose obtained for PbTe. Using (3) this gives

bE~ ='[K~(PbTe) —E„(Pb)]—[K,(PbTe ) —K, (Pb ) ] EI, —

Using (2) for the XPS results on the same two materialsgives

ha = [Kz (PbTe) —K„(Pb)]—[K,(PbTe) —K, (Pb)] (5)

with a similar expression for the comparison between Teand PbTe. Provided the spectra of the core lines andAuger lines are measured with the same bias in the exper-iments on each material any difference in the bias appliedto the two materials will be eliminated together withdifferences arising from the difFerent choice of referenceenergy. Furthermore, the accuracy of the differencedetermination can be improved by matching the actualAuger and photoelectron spectra of each material, mea-sured on the instrumental energy scale, against each oth-er. This procedure yields the results for Aa shown inTable I. They are free of the systematic errors whichaffect the results for 4K and AI.

going from the pure elements to PbTe to give informationon the local charge distribution in the compound. Weanticipate that, as in the alloy study, this approach willhave advantages over attempts to deduce information onlocal electronic structure solely from the results of XPSexperiments.

In order to simplify the analysis we first make the as-sumption that the local valence s orbitals around Pb andTe sites in the pure elements and in PbTe can be con-sidered to be full and that differences in the loca1 electroncon6gurations of Pb and Te between the pure elementsand PbTe can be discussed solely in terms of changes inthe amount of valence charge of p character. This is areasonable assumption for PbTe and pure Te since the re-sults of band-structure calculations' ' and valence-band photoelectron spectra show that the Te 5s and Pb6s bands are both filled in PbTe and that the Te 5s band isfull in pure Te. The assumption might be questioned forPb on the grounds that the intensities of the peaks ob-served in the photoelectron spectrum of the 6p bandshow the infIuence of s-p mixing. ' However, in view ofthe high binding energy of the 6s band, =6—12 eV, andthe 2-3-eV splitting between the 6s and 6p bands in purePb it is reasonable to consider the local 6s orbitals asfilled. "

We adopt the expression relating Aa, in eV, to parame-ters linking the potential in the atomic core with changesin valence charge and 1ocal environment that was derivedfrom the work of Thomas' and which is discussed in pre-vious work

Aa =A[q (dk/dN)+ (k —2dk/dN)(dq/dN)+d U/dN],

(6)

where q is the valence charge on the atom of interest, k isthe change in the core potential when a valence electronis removed, N is the occupation number of core orbitals,and U is the contribution to the core potential made bythe atomic environment. In the derivation of (6) it is as-sumed" that k and q vary linearly with N.

In order to make use of (6) in interpreting the mea-sured Aa's it is necessary to derive values of k and of itsderivative with respect to core occupancy. Our assump-tion that the local valence orbitals of s character are filledrestricts the k and q parameters, and their derivativeswith respect to N, to orbitals of p character. Thomas andWeightman' have discussed the various ways in whichthese parameters can be derived from atomic structurecalculations and we follow their procedures, making useof the Dirac-Pock code of Desclaux. ' We equate k withthe difference between the Koopmans's energy of therelevant core orbital in the neutral and valence-ionizedatoms. Values of dk /dN were determined in twodifferent ways using the expressions'

dk/dN =2(k EI), —

atom kcore-ionized atom

where

CHARGE TRANSFER ANI3 CORE-HOLE SCREENING IN PbTe 10 241

and I„, is the core-ionization energy determined from adi6'erence in the total energy of the atom in its groundstate and core-ionized state. I;,„ is the correspondingquantity for an atom that has lost the outermost valenceelectron.

The results for k and dkjdN determined using theDirac-Fock code of Desclaux' are shown in Table II.The two ways of determining dkjdN give similar valuesfor this parameter for both the Pb 4f and Te 3d levels.

In analyzing the local electronic structure of solids it isnecessary to consider the changes in the potential in thecore caused by the compression of the valence electronwave functions. To take account of this we modify thepotential parameters using the renormalization methodof Watson and co-workers. ' In this procedure thevalence wave functions are truncated at a radius ap-propriate to a sphere of equal volume to the Wigner-Seitzcell of the pure elemental solids. The wave functions arethen renormalized such that the probability of finding thevalence electron i+side such a sphere is unity. In follow-ing this prescription we used the wave function ofClementi and Roetti' for the Te 5p orbital and the wavefunction for the Pb 6p orbital obtained from a Dirac-Fock calculation. ' The potential parameters are thencorrected for the eFects of compression of the valenceelectron wave functions using

k'=k(( 1 jr ),„/(1/r )„, ),1k' IdN = ( k ' Ik)( dk /dN),

where ( 1/r )„, and ( 1/r ),„are the expectation valuesof 1jr for the atomic and renormalized valence electronwave functions, respectively. The modified parametersare also shown in Table II. As discussed by Thomas andWeightman' this renormalization procedure probablyoverestimates the e6'ect of valence wave-functioncompression so the true potential parameters lie betweenthe values found from the free atom and renormalized ap-proaches.

question concerns the precise balance between the ionici-ty and covalency of the bonding. The rocksalt structureof PbTe suggests that the material is strongly ionic andthis view is supported by the band-structure calculationsof Martinez, Schluter, and Cohen an analysis based ontouching ionic spheres yielding a charge transfer from Pbto Te of 1.5e. This result is in keeping with the positionof PbTe on empirical ionicity scales deduced from XPSmeasurements by Kowalczyk, Ley, McFeely, and Shir-ley' and Shalvoy, Fisher, and Stiles. " Kowalczyket aI. ' based their analysis on the separation of the twomost bound peaks in the valence-band spectrum, a pro-cedure which avoids the problems of energy referencingand the separation of initial- and final-state contributionsto XPS results. Shalvoy et al. " analyzed core peaks interms of a potential model having deduced from a limitedamount of Auger data that corrections for final-state con-tributions were small. Recent work ' ' has tended torevise these estimates of the charge transfer downwardsto values more in keeping with the estimate of 0.18e ob-tained from an analysis of the inhuence of optical pho-nons on caIrier mobilities.

We now consider the contribution that can be made tothe understanding of the electronic structure of PbTe byan analysis of the Auger-parameter shifts of Table I. Inthe work on alloys it was possible to simplify Eq. (6) byconsidering the effects of the efficient local screening ofcore holes in metals. Thus it was argued that the core-hole screening charge would be localized in the elementalvalence levels in metals so that dq/dN is unity for bothalloy and element and b, (dqjdN) is zero for a comparisonof two metals. Similarly the polarization of the surround-ings by the core hole, represented by the d UjdN term, iszero in conductors and so could be ignored. Thus, inwhat will be termed the perfect local screening model,Eq. (6) reduces to

b,a = b,q (dk IdN),

IV. DISCUSSION

The electronic structures of PbTe and related materialshave been the focus of interest for some time. Early workis summarized in Ref. 20. An important and unresolved

giving a direct connection between the Auger-parametershift and the ground-state charge transfer. The extent towhich this model is appropriate to PbTe and Te will bediscussed later. We now apply it as a useful first approxi-mation to the data of Table I.

TABLE II. Theoretical estimates of potential parameters in eV.

Core level

Pb(4f, 6p)Te(3d, 5p)

8.16'8 99'

9.58939

dk /dN

—1 73'—1.79e

dk /dN

—1.66—1.72d

dk'/dN

—2.03'—1.87'

dk'/dN

—1.95'—1.80

'From the di6'erence in the Koopmans's energy of the core level between the neutral atom and valence-ionized atom.Based on renormalization of the valence wave functions to give unit charge within the %'igner-Seitz

sphere. See text.'dk/dN=2(k —AI) with EI found from an evaluation of Eq. (7) using Dirac-Fock calculations (Ref.17).ddk /dN = katom keore-ionized atom'dk'/dN = (k'/k)dk /dN using c.'dk'/dN = (k'/k)dk /dN using d.

10 242 WADDINGTON, WEIGHTMAN, MATTHEW, AND CiRASSIE 39

A. Perfect local screening model

q"=(1—I/e. )q' . (13)

This induced charge may be interpreted in one of twoways. (a) We associate the charge at the surface of thecavity as appearing on the outer surface of the atom.Then

and

dq/dN = 1 —1/e

b, (dq/dN) = —6(1/e) . (14)

In this approach the rest of the environment does notcontribute to the potential at the atom and we can setdU/dN =Q. Now Eq. (6) becomes

We first note that as the change in a between PbTe andthe pure elemental solids is negative for both elementsand since dk/dN is also negative the ground-state chargetransfer accompanying the formation of PbTe will be pos-itive for each element, i.e., the change in core potentialfor both Pb and Te in PbTe is that expected from a lossof valence electrons. From the data of Tables I and II wededuce core charges of +0.30+0.06 for Pb and+0.45+0.06 for Te in PbTe, the uncertainty in the re-sults coming equally from the experimental uncertaintiesin the ha measurements and the spread in the values ofthe parameters dk/dN and dk'/dN (Table II). This is asurprising result particularly as Te, conventionally con-sidered to be the more electro-negative element, is pre-dicted to lose more valence charge than Pb on the forrna-tion of the compound. However, it should be remem-bered that Auger-parameter shifts essentially reQectchanges experienced in the core of the atoms concernedand in a covalent material such as PbTe it is not clearhow charge donated to covalent bonds would affect themeasurements. It may be possible to interpret the resultsof applying the perfect local screening model to theAuger-parameter shifts of PbTe in terms of differentialdonation of charge from the atomic cores to covalentbonds but it is clearly important to consider first theinfluence of the terms omitted from (6) in the perfect lo-cal screening model.

Consider the second term of Eq. (6). For environmentsof less than perfect screening dq/dN may be less than 1

and the difference in this term between two environmentsmay not cancel out. This is an important considerationsince the values of the potential parameters (Table II) in-dicate that the coefficient in front of b, (dq/dN) in Eq. (6)is considerably larger than dk/dN, the coefficient of thefirst term. It is thus important to have some way of es-timating h(dq/dN), the environmental dependence of thechange in the local valence charge accompanying coreionization. Let us consider an extreme model of theatomic environment in which the ionized atom is as-sumed to sit in the center of a Jost-like spherical cavity inan infinite medium of dielectric constant e and radius R.Assume initially that the medium is unpolarized but thatwhen a core hole, giving a charge q', is introduced on theatom a polarizing charge q" is induced on the innerboundary of the cavity,

ha =6 q (dk/dN) (—k 2d—k/dN)b (1/e)

and there are two contributions to Aa, one directly relat-ed to the ground-state ionicity and arising from thedependence of the intra-atomic relaxation on the chargestate and the other dependent on the efficiency of the en-vironment in transferring charge to the vicinity of thecore hole or core holes. The values of the parameters list-ed in Table II indicate that Aa will be more sensitive tochanges in I/e than in q. In metallic alloys where thescreening is very good and effective values of e very largethe difFerence in 1/e between metallic environments willbe negligibly small, justifying the neglect of this contribu-tion in the earlier work. ' However, this term could be animportant contribution to our analysis of the semicon-ductors Te and PbTe where ha may be as muchinfluenced by the efficiency of transferring charge in-duced by the core hole as it is to the ground-state chargetransfer.

Before applying this model in detail we first consideran alternative interpretation of the charge induced on ourhypothetical Jost cavity. (b) We can associate the polar-ization charge with the medium rather than the atom.Then dq /dX =0 and the important environmentalcorrection term becomes b(dU/dN). In the Jost-cavitymodel the polarization of the environment now yields acontribution 27.21(1/R )(1—I /e) to the relaxation energyand (6) becomes

ba=bq(dk/dN)+27. 2lb[(1/R)(l —1/e)], (16)

R being measured in atomic units. For a perfect ionicsystem hq =0 and we obtain an expression which isclosely related to Citrin and Thomas's analysis ' of polar-ization contributions to ionic systems.

Equations (15) and (16) are not as different as at firstmight appear. The Jost radius R is closely related to thesize of the atom or ion containing the core hole, andmight to first order be thought of as an atomic and/orionic property, though one that will depend somewhat onthe initial state of the system. If R is regarded as a con-stant, then the second terms of both expressions scale as6(1/e). Furthermore if R is of the order of the atomicand/or ionic radius 27.21/R is similar in magnitude to(k —2dk/dN). Whether the polarization process is re-garded as a charge transfer to the site of the ionized atomor as a charge redistribution in the medium is somewhatarbitrary, depending on how Wigner-Seitz cells aredrawn, but both viewpoints lead to similar conclusions,i.e., that in environments of limited screening efficiency itis dielectric differences that may dominate ho; ratherthan ground-state charge transfer, although of course thetwo processes are not totally uncorrelated.

We now have two expressions, (15) and (16), which canbe applied to the analysis of environmental contributionsto the Auger-parameter shifts though we should note thatour parametrization of the environment terms dq/dXand dU/dN of Eq. (6) is much cruder than our treatmentof the charge transfer term and the results of applyingthese expressions will be correspondingly less precise.

39 CHARGE TRANSFER AND CORE-HOLE SCREENING IN PbTe 10 243

B. Limited screening model

In order to use Eq. (15) to interpret the experimentalmeasurements of the Auger-parameter shifts we need thedielectric constants for these materials. These are shownin Table III where we have listed values for both thelow-frequency and high-frequency dielectric constants, eoand e„, respectively. For Pb metallic screening impliesthat we should regard both quantities as infinite. PbTehas a large static dielectric constant indicating that thescreening of low-frequency changes in local core charge,such as the difFerence in local charge on an ionized im-purity and a host lattice site, is very good in this material.The high-frequency dielectric constant of PbTe is similarto those of elemental Te, the latter being an anisotropicmaterial whose dielectric constants show very little fre-quency dependence.

Since we are interested in the response of the local elec-tronic structure of these materials to rapid changes in lo-cal charge, of the order of = 10 ' sec for photoelectronand Auger electron emission, the correction for limitedscreening should employ the high-frequency dielectricconstants e . The data of Table III indicate that thelargest effect of the correction for limited screeningrepresented by the second term of Eq. (15) will be on thecalculation of the charge on a Pb core in the ground statein PbTe. The evaluation of the second term of Eq. (15)using the data of Tables I, II, and III leads to a reductionin the estimated charge on the Pb core in PbTe to+0.09+0.06. The analysis is less clear for Te since al-though the low-frequency dielectric constant of PbTe andTe are very different the high-frequency dielectric con-stants are very similar (Table III). It is not even clearfrom the data for e whether the correction for limitedscreening should produce an increase or a decrease in theestimated core charge on a Te site in PbTe. Taking theextremes of the differences in high-frequency dielectricconstants shown in Table III gives predictions of thecharge on a Te core in PbTe of either +0.54+0.06 or+0.42+0.06. If the low-frequency values are used weobtain an estimated core charge of =+0.6. The quoteduncertainties arise from the spread in the data shown inthe tables and will be exceeded by errors arising from thecrudity of the treatment of the environmental contribu-tion to (15).

We conclude that the correction for the imperfect

screening of changes in core charge by the local environ-ment represented by Eq. (15) gives a significant reductionin the estimate of the Pb charge in the ground state inPbTe. It does not, however, change the conclusion thatthe conventionally more electro-negative element, Te,loses a significant amount of negative charge on the for-mation of PbTe.

In an effort to find the cause of this anomalous resultfor the charge on the Te core in PbTe we can impose thecondition that, irrespective of its magnitude, the electrondeficit Aq of the Pb core in the ground state in PbTeshould be balanced by an equal and opposite electrongain hq Te by the Te core;

Pb gq Te (17)

C. Differential screening model

Equation (16) overs a way, through the radius R of theJost cavity, that we can parametrize any difFerence in thescreening of core holes on the Pb and Te sites in PbTe.In order to simplify the discussion we introduce screeningparameters C„, proportional to the eSciency with whicha core hole on site x is screened in a medium y. In theJost-cavity model we equate C" with the appropriate(1/R)(1 —I/e) Using the d.ata of Tables I and II we get

O. 3O= aq" —14.8(C,"„,—C,'b ),Te 15 1(CTe CTe )

(18)

We find that the expressions obtained by applying Eqs.(15) and (17) to the data for Pb and Te are only cornpati-ble if the high-frequency dielectric constant of PbTe is re-duced from the value shown in Table III to = 14. Inspec-tion of these expressions shows that this result is a conse-quence of the implicit assumption made in deriving (15)that the screening around a Pb site in PbTe is the same asthat around a Te site in PbTe. This assumption might beexpected to be incorrect since although each element inPbTe has six nearest neighbors of the opposite species theTe neighbors should be more polarizable than the Pbneighbors, a difference which would be enhanced by anycharge transfer in the ground state. This suggests that weshould employ a differential screening model. Mott andGurney came to a similar conclusion many years ago inevaluating environmental contributions to the energies ofcation and anion vacancies in alkali-metal halides.

TABLE III. Dielectric constants.

Material

Pb

Te

PbTe

Static eo

30'43'

1181-16552710-3535"

High-frequency e„

23'36'

32.8'293

'Dependent on crystal direction. Values from Ref. 23.Values from Ref. 24.

'Experimental value, Ref. 25.Theoretical value, Ref. 13.

A number of useful conclusions can be made from thesimultaneous application of expressions (17), (18), and(19).

(i) Since a core hole on a Pb site will be better screenedin the pure metal than in PbTe then CpbT, —Cpb will benegative. Equation (18) thus puts an upper limit of 0.30for the ground-state charge transfer in PbTe.

(ii) If we assume perfect screening of a core hole in me-tallic Pb then Cpb = 1/R. Assuming R is constant,equating CpbT, with (1/R)(1 —1/e) for a Pb site in PbTeand using a value of 30 (Table III) for e then yields asimple relationship between R and hq . For values ofthe initial-state charge transfer of 0.0, 0.1, 0.2, and 0.3 we

10 244 WADDINGTON, WEIGHTMAN, MATTHEW, AND GRASSIE 39

Te Te Pb PbCpbTC CTe & CpbTe Cpb (20)

Since for each element the screening efficiency of coreholes on an elemental site decreases on going from thepure element to PbTe, Eq. (20) shows that this decrease isgreater for Te than for Pb. Since the screening in Pb willbe more eflicient than in Te Eq. (20) also shows that coreholes are screened more efficiently on Pb sites than on Tesites in PbTe.

It is difficult to interpret the radius of a Jost cavity inan anisotropic material like Te which has a hexagonalchainlike structure with each site having two nearestneighbors in the same chain at a distance of 2.86 A andfour neighbors from different chains at a distance of 3.74A, but the screening may be rather better than that sug-gested by the macroscopic dielectric constant. However,for Te in PbTe the nearest-neighbor positive Pb atomsand/or ions may be less polarizable than the second-neighbor negative Te atoms and/or ions. This may leadto an increase in the effective screening radius R and therequired decrease in screening efficiency.

V. CONCLUSIONS

We have shown that the analysis of the Auger-parameter shifts of PbTe, and probably of semiconductorsystems generally, must include considerations of thescreening of core holes by the local environment as well

obtain values for R of 0.9 A, 1.3 A, 2.7 A, and ~, respec-tively. These should be compared with the Pb environ-ment of six Te neighbors at an interatomic distance of3.23 A in PbTe and a nearest-neighbor distance in metal-lic Pb of 3.50 A.

(iii) Since Aq' lies in the range 0 to —0.3 (19) shows

that CpbT, —CT', is negative, which means that core-holescreening is more effective on Te sites in pure Te than inPbTe. Equation (19) also implies that the larger theground-state charge transfer the greater this difference incore-hole screening on the two sites. Independently ofthe value of the ground-state charge transfer we candeduce from the three equations that

as the environmental dependence of intrasite screeningassociated with ground-state charge transfer.

The environmental screening terms present in theparametrized treatment of Auger-parameter shiftsdeveloped earlier' have been evaluated for PbTe in termsof a Jost-cavity model.

It has been established that the charge transfer in theground state of PbTe, defined in terms of its influence onthe potential in the atomic cores, is less than0.30e+0.06e. This result is in keeping with recentwork ' on the nature of the bonding in PbTe and isquite consistent with the result of 0.18e deduced fromconsiderations of the inhuence of optical phonons on car-rier mobilities.

We have shown that core holes are screened moreefficiently on Pb sites than on Te sites in PbTe and thatTe core holes are screened more efficiently in pure Tethan in PbTe. These conclusions can be readily under-stood in terms of the difference in the polarizability of Pband Te neighbors and the tendency of ground-statecharge transfer to increase this difference.

The analysis of the environment of a core-ionized Pbsite in PbTe in terms of a Jost cavity leads to the con-clusion that, for a ground-state charge transfer of 0.2e,the effective screening radius is 2.7 A, 81 fo of thenearest-neighbor distance. This result is comparable withvalues of the static screening radius of vacancies inalkali-metal halides. It is more difficult to interpret theresults of a Jost-cavity treatment of the environment of acore-ionized Te site in PbTe, but the requirement of anenhanced Jost-cavity radius R may be associated with alower polarizability of neighboring electron deficient Pbatoms. Clearly both the environmental screening modelspresented here are very primitive but they do give insightinto the interplay of ground-state charge transfer(inAuencing intrasite screening) and extra-atomic screen-ing.

We suggest that systems like PbTe, but involvinglarger charge transfer, where it is possible to obtainAuger-parameter shifts from both species in condensedphase, provide good test cases for investigating screeningprocesses.

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