PHYSICAL REVIE%' 8 VOLUME 34, NUMBER 4

Excitation and ionization of Mo and W in GaAs

N. MakiuchiDepartarnento de F&sica, Universidade de Brasilia, Brasilia, D.I"., Brazil

A. FazzioInstituto de F&sica, Uniuersidade de Sao Paulo, Caixa Postal 20516, Sao Paulo, Sao Paulo, Brazil

M. J. CaldasInstituto de Fisica, Universidade Estadual de Campinas, Carinas, Sao Paulo, Brazil

(Received 27 November 19S5)

%e study the electronic structure of the Mo 4d and % 5d impurities in GaAs, using the cluster

approach within the multiple-scattering Xa formalism; results are also given for the Cr 3d isovalent

impurity. Multiplet structures for the systems are evaluated through the approach of Fazzio, Cal-

das, and Zunger. Our results indicate that the Mo and % impurities will present a low-spin groundstate in the 2+ oxidation state {acceptor), and that the observed luminescence lines are not related tothe 'E ~'T& internal transition of the isolated substitutional Mo and %' impurities.

served in GaP:Cr + with a zero-phonon line (ZPL) at-0.87 eV.5 In the case of GaAs:Cr + the excited ~E stateis resonant at the conduction band; however, under hy-drostatic pressure (beyond -6 kbar) the state splits fromthe band and the luminescence can be seen with the ZPLat -0.82 eV.7 For InP:Cr + the excited state is alsoresonant at the conduction band, and only the absorptionis observed (locating the sE state at about 0.23 eV abovethe minimum of conduction bands).

Our aim here is to analyze the isovalent impurities Moand % in GaAs, vrith emphasis on the eventual similari-ties to GaAs:Cr. The mean-field results are obtainedthrough the multiple-scattering Xa method (MS-Xa)(Ref. 9) with an impurity-centered 17-atom cluster of Tdsymmetry, and with the Watson-sphere boundary condi-tion the same model is applied to the system GaAs:Cr,which will be referred to for comparison. Many-electroneffects within the d shell are then included using themodel recently proposed by Fazzio, Caldas, and Zunger(FCZ)." These effects will be seen to be relevant not onlyto analyze the internal transitions but also to allow us toestimate the position of acceptor levels in the band gap.

I. INTRODUCTION

II. EXPERIMENTAL SITUATION:MO AND W IN GaAs

The literature on main-body 4d and 5d impurities inGaAs is still scant, ' ' particularly so for Mo and W.The pioneering works on this subject are from Vavilovet al. ' for GaAs:Mo and from Ushakov and Gippius, ' 'who studied %'-related luminescence in GaAs. In the in-vestigation of GaAs:W, Ushakov and Gippius studied n

type samples with varying location of the Fermi level,with free-carrier densities from 2X10' to 2X10' cmIn the moderately n-type samples (low carrier densities) atliquid-He temperature, the authors observe a luminescencespectrum with a narrow ZPL at 0.678 eV and phonon re-plicas at 0.653 and 0.648 eV. %ith increasing carrier den-

We study in this work the electronic structure of thetransition metals (TM) Mo and W, from the second andthird series, as impurities in GaAs. TM impurities fromthe first series (3d-shell atoms) in semiconductors fromthe II-VI, III-V, and IV groups have been intensivelystudied from both the experimental and theoretical pointsof view. '2 The past ten years have seen, in particular, agreat progress in the understanding of systems of TM im-purities in III-V compounds, with emphasis on GaAs:Cr.Our aim is to analyze the behavior of Mo and W in GaAs,which have been less explored, and which share with Crthe valence shell d5s' in the neutral free-atom configura-tion. The technological importance of Cr-doped GaAshas motivated an increasing interest in this material, and alarge spectrum of different experimental techniques hasbeen used, ' including optical absorption, luminescence,electron paramagnetic resonance, Hall effect, photocon-ductivity, pressure, Zeeman effects, etc. The impurity canappear in GaAs in different charge states; the neutral Ao

charge state (relative to the lattice) corresponds to the oxi-dation state 3+, as the impurity substitutes for the ca-tion, and the first acceptor transition H(0/ ) is then-Cr + /Cr +. In GaAs, this level is at H (0/ )—=E„+0.735 eV, close to the middle of the band gap[(H(0/ —)=E„+1.125 eV in GaP and E„+0.95 eV inInP].3 The midgap acceptor level of Cr in GaAs can thusbe conveniently used to obtain a semi-insulating material(si-GaAs) with resistivities up to 10sQ cm ', much usedin substrates for electronic devices. As said above, apartfrom this acceptor level, Cr also introduces a donor level(Cr +/Cr +

) in GaAs and a second acceptor level(Cr +/Cr+), with a Mott-Hubbard energy U of -0.4 eV

[ U(Cr )] to -0.7 eV [ U(Cr +)]. It is, however, in theacceptor state Cr +d that the optical activity of thecenter has been most studied. A luminescence spectrumcorresponding to the intra-d transition E~ T2 is ob-

O~ 1986 The American Physical Society

EXCITATION AND IONIZATION OF Mo AND % IN GaAs

sity the intensity of these lines decreases, until they be-

come very difficult to detect at n=10' cm '. A dif-ferent spectrum, consisting of four lines with energies0.706, 0.701, 0.699, and 0.692 eV, begins to appear atn =5)& 10'5 cm and is the only one present at higher(n ~ 10' cm ) Fermi energies. The authors concludethat the first spectrum (0.678-eV ZPL) is related to inter-nal transitions of the neutral impurity, W +d, while thesecond group of lines originates from the acceptor stateW2+d4. Ushakov and Gippius use the Tanabe-Suganocrystal-field approach' to analyze the spectrum, and as-sign the luminescence to the transition Ti~ Ti forW +, and T&~ Tz or T2~ Tz in the case of W +.Vavilov et al. ' deto:t for GaAs:Mo a luminescence lineat -0.84 eV, which they assign to the E~ Ti intra-dtransition of Mo +, in close analogy to GaAs:Cr +.

From the assignments of Ushakov and Gippius, ' 'iand Vavilov et al. "the impurities would be present in thehigh-spin (weak-field) ground states Ti (W2+ and Moi+)and Ti (W +), within the band gap of GaAs.

III. THEORETICAL RESULTSA. Mean field

We use model clusters with a central impurity atom,Cr, Mo, and W, a first-neighbor shell of 4 As atoms and asecond-neighbor shell of 12 Ga atoms (1TM-4As-12Ga).The electronic structure is obtained through the MS-Xa(Ref. 9) method, with the Watson sphere saturation tech-nique. ' The MS-Xa method has already been used byHemstreet' to study GaAs:Cr, with the hydrogen-saturation boundary condition (1Cr—4As —12H). As forthe Mo and % impurities in a III-V compound, these cal-culations are, to our knowledge, the first electronic struc-ture calculations.

We present in Fig. 1 the results for the neutral impuri-ties (oxidation state 3+) around the band-gap region.The characteristic electronic structure is the "fingerprint"of a TM impurity in semiconductors ' a tz level fullyoccupied in the valence band, known as "crystal-fieldresonant" rz"", an e le'vel that for these impurities ap-pears within the gap, e "" of predominantly d (1=2)character; and finally a higher-lying t2 level [tq, which iscalled the "dangling-bond hybrid" DBH] with also a highI =2 character. These latter two levels would have occu-pation e t' in a Hund-rule, high-spin ground state for theneutral transition-metal impurities T +. The trend saithatomic number shows that the valence-band t2 levels ofthe heavier impurities Mo and W lie below the tz levelof Cr, while e and t2 rise in energy in going from3d~4d~5d. This behavior was also obtained by a re-cent study of the Cu 3d, Ag 4d, and Au 51 impurities inSi,' using a Green's-function technique, the quasibandcrystal field method' (QBCF).

In Fig. 2 we show the percentage of / =2 charge withinthe impurity muffin-tin sphere (radius 2.4 a.u.). We no-tice that the d character, as might be inferred from acharge analysis, changes very little for the e orbital ingoing from 31~4d ~51„while the tz"" orbital shows adelocalization with atomic number. The behavior of thee orbital in this respect is consistent with the fact that

GaAs(MS-Xo)

—20-l.O—

g oo-LUw -I,0-45

-2.0—

ta

FIG. 1. Relevant d-related mean-field levels introduced byCr, Mo, and W impurities in GaAs. The impurities are in theneutral-charge state relative to the lattice, and the occupation{indicated for the Cr'+ impurity) corresponds to the high-spinconfiguration. VBM and CBM are the valence- andconduction-band minima, respectively.

70—0~0

60—& so-n. 40-xCA

30—20—

FIG. 2. Charge in percents within the impurity muffin-tinsphere for the d-related orbitals t2, e, and t2 {see notation inFig. l) for Cr+, Mo +, and W + in GaAs (solid lines}. Thepercentage of charge spread out in the interstitial region isshown as the dashed line for the valence band t2 orbital.

it interacts only with the second-neighbor shell of atoms,and should present an almost unperturbed d character.The t2"" orbital is less localized on the impurity alreadyfor the Cr atom in agreement with previous calculationsin GaAs:Cr the decrease of charge within the centralsphere with atomic number has two origins. We can notefirstly that the 4d and 5d orbitals are naturally more ex-tended than the 3d orbital ( (r )3d ~ ( r )4d & (r )5d ); conse-quently, the t2 components (d„„,d~„and d~) suffer astronger interaction with the ligands' hence a strongerdelocalization. The second reason is tied to the method(MS-Xa) used here: What we show in Fig. 2 is the total1 =2 charge within the muffin-tin sphere, with a radius of2.4 a.u. , approximately equal to the covalent radius ofMo. We should then expect the decrease of charge in thecentral sphere to be accompanied by an increase of chargein the interatomic region. In Fig. 2 we also show (dashedline) the prcentage of charge in this interstitial volume,for the tz"", and we can note the marked increase withprincgial quantum number. A similar analysis holds forthe t2 orbital.

2692 N. MAKIUCHI, A. FAF~IO, AND M. J. CAI.DAS 34

(,ee ~1/r (ee},(dd i

1/ridd };,„

{3)

8- Excitation axle 10QizatloB energies

We use the FCZ (Ref. 11) model to estimate ionizationenergies for the first acceptor states, and excitation ener-

gies within the d shell for different charge states of Moand W in GaAs. A similar application to 3d impurities inGaP has been recently carried out by Singh and Zunger. '

The first acceptor ionization energy ( T +/T +) can bewritten as

H"( —/0) =H MF( —/0)

+ [~E'J'(~ —,T'+) —~E"'(a', T'+ }],where 8MF( —/0) is the mean-field energy needed to ion-ize (capture a valence-band electron) orbital p, which canbe ec" or t; and hE'i'(A, T +) and hE'"(Ao, T +)are the multiplet corrections affecting the fmal and initialterms I J (of d ) and I'; (of d ), respectively. In comput-ing HMF{ —/0) one uses (for the "vertical" piece, as wecomment below ) the Slater transition-state construct.

The internal or intra-d transition occurs within a fixedcharge state, often referred to as d ~(d }', and can bedescribed by

hE"'[d (d )']=5,f{m',n', m, n)+5"' . (2}

Here the effective crystal-field splitting h,Qm', n', m, n} isthe mean-field energy required to excite the system from aconfiguration e~t" to e™r",with m'+n'=m+n=¹The energy 5MC is the multiplet correction to the excita-tion energy, which cannot be computed within mean-fieldtheory; it accounts for the electron repulsion splitting forthe terms I i and I k, coming predominantly from themean-field configurations (m', n') and (m, n).

In the analysis of the Mo and W impurities, we mustkeep in mind four main points: (i) Our mean-field resultsindicate that b,rr is roughly constant for the three impuri-ties Cr, Mo, and W (although the absolute values we ob-tain for h, rr are overestimated, we may extract from theresults the trend for the effective splitting with the princi-pal quantum number). According to a simple point-ionmodel, the Tanabe-Sugano crystal-field splittingshould increase in the column 3d~4d~5d. 's (ii) The dcharacter remains virtually unaltered for the e ""orbitalsof the three impurities, while decreasing with the atomicnumber for the tz orbitals. (iii) The tz orbital in-

creases in energy when we follow the series Cr~Mo~W;the same behavior has been obtained through the QBCFmethod for the tz orbitals of the series Cu, Ag, and Ausubstitutional in Si.' (iv) According to the well-established experiinental facts regarding Cr in GaAs,under normal conditions, the E excited state of Cr + isresonant at the conduction-band miiumum, with the ab-sorption band T2~ E peaking at -0.9 eV (Ref. 6}{0.82eV ZPL), and the first acceptor level is located atH( —/0) =E„+0.732 eV.

Based on the premises in (i) and (ii), we calculate themultiplet structure for Mo and W in GaAs using lL,rf andA,, obtained for GaAs:Cr +. The parameter A,, is de-fined" as

and measures the interelectronic repulsion in the solid(sol} relative to the free ion. The other constraint comesfrom (ii) in the choice of A,, (defined for the ti orbitalin analogy to A,, ): we expect A,, (3d)&A, ,(4d)&A, ,(5d). '

The limiting parameters h,g, k„and k, are those ob-tained by Caldas et al. (E,it=0.65 eV, A,,=0.872, andA,, =0.778) and we use the atomic Racah parametersgiven in Ref. 22.

Our results predict for Mo + and W + the !oiv spi-n

ground state 'Ai, even ivith the (Cr +) limiting parameters, since the interelectronic repulsions (as incorporatedin 8 and C) are weaker for the heavier impurities. Weshow in Fig. 3 the multiplet spectrum obtained for Mo +

in GaAs; we may remark that the transition energyE~ Ti is (accidentally) quite close to the energy detect-

ed in luminescence. '

We argue in what follows that the luminescence detect-ed for GaAs:Mo at -0.84 eV is unlikely to be related tothe E~'Tq decay of Mo2+. We suppose first that theground state of Mo + is the high-spin term Tz. The ion-ization transition Mo +/Mo + would then involve thestates Ti(T +,e t') and 'Tz(T +,e t2}, characterizingthe first acceptor state in the form of Eq. (1) as a captureof an electron at the t q level [mean-field pieceHMF( —/0)]. The multiplet correction energies [withinbrackets 6n the right-hand side of Eq. (1)], still with theoverestimated parameters A,, and A., obtained for Cr +,would result in —0.28 eV for Mo and —0.27 eV for W.These values are much smaller than the correction to thefirst acceptor of Cr, —0.51 eV. If we now use the prem-ises (iii) and (iv), we conclude that the acceptor level forMo and W should be located well above the middle of theband gap. This conclusion can be made clear writing theequation for H( —/0) as

g /

/

/

/X

FIG. 3. Estimated multiplet spectrum obtained for the Moimpurity in the 2 + oxidation state (acceptor), relative to the en-

ergy of the 'A l(e ) ground state (see text). Note the large ener-

gy separation for the states 'T2 (high spin), '3l (low spin).

EXCITATION AND IONIZATION OF Mo AND %' IN GaAs

(~E(5') ~E(4T) )) (5)

The quantity b, eI' involves the difference in mean-fieldionization energies HMF( —/0), using the transition-stateconcept

«»"= [HMF( —/o)]M. —[HMF( —/o)]c.

and QEtt' measures the differences in lattice relaxation orJahn-Teller energies in the transition Ti (e2t ')«T2(e t2), between Mo and Cr. It may be noted thatwe have no reason to believe in any large net relaxationenergies for this particular transition d «d . v Insertingthe obtained values in Eq. (4), we are led to

[H( —/0)]M.=[H( —/0)]c.+(~Ea")Mo,c.+o 5 eV .

Hence, if the luminescence at 0.84 eV were related toE«Ti transition of Mo + in GaAs (in which case

Mo + would have the T2 ground state}, (&&q' )M, c,u)ould have to be larger (in absolute value) than 0.5 eV; ifnot, the E excited state of Mo + would certainly beresonant in the conduction band, making it very difficultto observe direct luminescent decay. As shown by Eaveset »tl. , subsequent to the photocreation of the E excitedstate of Cr + an electron is self-ionized to the conductionband, producing a photocurrent. Two processes are thencompeting in the decay mechanism: the direct radiativerecombination E«Tz (internal luminescence), and thecapture of a conduction-band electron by the (neutral)center, yielding a broader recombination luminescenceband —conduction band to level —which dominates theprocess. Furthermore, in the case of GaAs:Cr, lumines-cence 'E«'Tt has to be photoexcited with above-gaplight even with hydrostatic pressure applied to the sam-ple. The creation of the E state involves thus the cap-ture of an exciton, and the recombination should bedescribed schematically as

['~i(e't') ]c»+(e+e } ['«e 't')]c»

«['Tt(e t )]+I»v(0.82 eV) .

Summarizing our results for the case of a high-spinMo2+ ground state, we may say that (i) unless very largerelaxation energies are involved in the transitionMo +/Mo +, which does not seem probable, the acceptorlevel would be closer than 0.75 eV to conduction band, orin other words, (ii) the E state would be resonant in theband, as for GaAs:Cr +, and the E«T2 decay wouldprobably be masked by band-to-level luminescence.

We suggest two other possible origins for the 0.84 eV

[H ( —/0}]M.

=H( —/0)]c, +(ddIMc+he»' +DE»(' )M, c, , (4)

where [H ( —/0)]M, and [H( —/0)]c„denote the acceptorlevel measured from the top of valence band; ~Mcstands for the difference in multiplet correction to thefirst acceptor energy (d «d ) between Mo and Cr:

34i}HMc =(~E

luminescence band of GaAs:Mo +, supposing an intra-dtransition is involved. The first possibility is to ascribe itto a (d )'«d decay, however to the low-spin 'A)(e )

ground state. In this case the acceptor transition wouldinvolve, in mean-field language, capture of an electron atthe e ""orbital; the first acceptor H'( —/0) could thenbe located slightly belo(v the middle of the band gap andthe luminescent transition could originate from the terms(

' T, or 3T2 )« 'A) (see Fig. 3).

The other possibility is that the transition occurs in theneutral charge state Mo +, with ground state T) (weakfield) or even E (strong field).

In the case of GaAs:W, we have to analyze two groupsof luminescence lines, one occurring at "low" carrier con-centration and the other at high carrier densities. Al-though we can make at best a rough estimate for themean-field parameters to be used for a T + impurity,over a reasonable range our results seem to support thesuggestion of Ushakov and Gippius' ascribing theluminescence to the internal transition T&~ T&, whichinvolves energies around 0.7 eV. %e must mention, lastly,that we have also estimated the influence of relativistic ef-fects for the heavier W impurity. In this case, the elec-tronic structure is solved with an impurity core potentialobtained through the Hartree-Fock-Dirac-Slater formal-ism; the relevant quantities are not significantly affect-ed. We find that b,,tt is virtually unaltered, the energies ofthe gap levels suffering an uniform, very slight( &0.05 eV) upward shift which, if anything, stresses thetrend already discussed above.

We did not include spin-orbit (SO) corrections, whichcould in principle affect the results. The SO interactionproduces, to first order, an upward shift of the e ""level

(upon the contraction of the d states) and a smaller shiftof the t2 level together with a splitting t2«I s+I'7.The t2-level splitting is expected to be very small due tothe delocalization of the wave function. The dominant ef-fect of the SO interaction would be to reduce b„tt, and in-crease A,

Our results should then be checked against variations ofthe FCZ parameters. %e explored moderate joint varia-tions of the three parameters ( —15%) and extreme varia-tions of a single parameter. The ground state remainslow-spin 'A

i for both impurities for b,,tt down to 0.36 eVfor Mo + and 0.38 eV for W +( -45% variation), and forA.

»=1 or»)(,, =1, the maximum values of the hybridization

parameters. Now, if we lower b,,tt sufficiently to obtainthe Tz ground state, the transition E~'T2 occurs at-0.46 eV for W + and -0.5 eV for Mo2+, too far fromthe detected luminescence lines (-0.7 and -0.84 eV,respectively}. Even then, the multiplet corrections to theacceptor level do not exceed the value for Cr +/Cr +, andsince the t2 levels rise in energy from Cr~Mo~W,we may safely assume that our conclusions are not affect-ed by reasonable variations of the FCZ parameters.

IV. SUMMARY

%'e may summarize our results to the isovalent impuri-ties Cr, Mo, and W in GaAs as follows: (i) there is no sig-

N. MAKIUCHI, A. FAZZIO, AND M. J. CALDAS 34

nificant changes in the mean-field results for the three im-purities, apart from the expected delocalization of the dorbitals, in going from 31~4d ~5d; (ii) however, due toweaker electron repulsion energies within the d shell ofthe heavier ions, the multiplet structure is changed yield-ing low-spin ground states for both Mo + and W2+ (ac-ceptor state), even if we overestimate the values for theinternal parameters A,, and A,

From this, we conclude that the acceptor levelsH( —/0) for the isolated impurities Mo and W should be

located at higher energies compared to the Cr level; hence,the observed luminescence lines are most probably not re-lated to the E~ T2 transition of single isolated substitutiona/ Mo + or % +. %'e propose that the luminescencelines are related to transitions entirely within the low-spinregime to the 'A&(e ) ground state of the impurities, al-though one should also consider the possibility of complexformation (pairing the TM off with another deep-level de-fect, such as an anion vacancy), which is known to in-duce a downward shift of the acceptor level for Cr +.

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9K. H. Johnson and F. C. Smith, Jr., Phys. Rev, B 5, 831 (1972).A. Fazzio and J. R. Leite, Phys. Rev. B 21, 4710 (1980).

"A. Fazzio, M. J. Caldas, and Alex Zunger, Phys. Rev. B 29,5999 {1984);30, 3430 (1984).

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~The value of the parameter A., cannot be taken directly fromQMr(t2 "', the amount of d charge within the impuritysphere for the t2

" state. Ho~ever, due to the delocalizedcharacter of this state, we may infer that a decrease inQMt(tt) will imply a reduction of J, This can be verifiedfrom a comparison of the empirical A, , values [A. Zunger,Solid State Physics, Ref. 2, Table XII; A. Fazzio, M. J. Cal-das, and Alex Zunger, Phys. Rev. 8 30, 3430 (1984), Fig. 2. ]with calculated spin-restricted QMr(t2) values for the samesystems {A. Fazzio, unpublished results, see also Ref. 17 for3d impurities in GaP). Although the same trend is notpresent for the more localized e " state, the maximum varia-tion of empirical A,, values is less than 7% for 3d impuritiesin III-V compounds.

22J. S. Griffith, Thp Theory of Transition Metal Ions (Cam-bridge University Press, London, 1971).

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