PHYSICAL REVIEW B VOLUME 52, NUMBER 20 15 NOVEMBER 1995-II

Dielectric function and optical conductivity of TiO (Q.S ( x ( 1.3)determined from electron energy-loss spectroscopy

Shubha Gokhale*Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India

and Jamaharlal Nehru Centre for Advanced Scientific Research, Indian Institute of Science, Bangalore 560012, India

S. R. BarmanSolid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India

D. D. SarmatSolid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560019, India

and Jawaharlal Nehru Centre for Advanced Scientific Research, Indian Institute of Science, Bangalore 560012, India(Received 22 June 1995)

Re8ection electron energy-loss spectra are reported for the family of compounds TiO over theentire homogeneity range (0.8 & x & 1.3). The spectra exhibit a plasmon feature on the low-

energy side, while several interband transitions are prominent at higher energies. The real andimaginary parts of dielectric functions and optical conductivity for these compounds are determinedusing the Kramers-Kronig analysis. The results exhibit systematic behavior with varying oxygenstoichiometry.

I. INTRODUCTION

Titanium oxide has been a topic of interest for variousinvestigations, due to its physical and chemical propertieswhich are important from a technological point of view.Varying the oxygen content changes the conductivity ofthe sample from metallic (TiO) to a wide gap insulator(Ti02). TiO can be formed homogeneously over a widerange of x (0.8 & x & 1.3) retaining the rocksalt structureof the monoxide TiO. There have been many attempts toexperimentally and theoretically determine the electronicstructure of TiO . In contrast, there have been com-paratively few attempts to find the optical properties oftitanium oxide using diferent techniques. Plasma fre-quencies for different compositions of TiO (x=0.8, 1.0,and 1.2) have been determined using reflectance spec-troscopy. Subsequently, the dielectric functions of a cleantitanium surface and oxidized titanium surface between 2and 25 eV were obtained from reflectivity studies, how-ever, the exact stoichiometry of the oxide species presenton the surface was not known in this case. Dielectricfunctions have also been obtained for nominal TiO andTi02 from an analysis of transmission electron energy-loss spectra. While it is known that transport proper-ties are pronouncedly affected by changing the oxygencontent of TiO over the homogeneity range, there hasbeen no attempt to determine the dielectric function orthe optical conductivity of TiO with a systematic varia-tion of oxygen stoichiometry. Here, we report a reflectionelectron energy-loss spectroscopy (REELS) investigationof TiO with such a variation of oxygen content overthe entire homogeneity range (0.8 & x & 1.3). REELspectra obtained consist of plasmon features at lower en-ergies and interband transitions at higher energies. We

interpret our results on the basis of band structure calcu-lations carried out for this system. We believe that theband approach to explain the origin of loss features ob-served in the REEL spectra is more appropriate in thesebroadband systems compared to earlier approaches ' '

based on molecular orbital diagrams. Furthermore, wehave determined the real and the imaginary parts of thedielectric function &om Kramers-Kronig analysis of thespectra, corrected for multiple scattering eKects. Boththe components of dielectric functions show systematicvariations with varying oxygen stoichiometry. Opticalconductivities were obtained from the imaginary parts ofthe dielectric functions.

II. EXPERIMENT

TiO (0.8 & x & 1.3) samples were prepared by meltquenching a mixture of Ti and Ti02 in the required pro-portions using an arc furnace under argon atmosphere.The oxygen stoichiometry (x) was determined by mea-suring the increase in the weight of samples on oxidationto Ti02 at 1000 C in Howing oxygen. The estimatedcompositions were found to be TiOo 8~, TiOp g~, TiO] o3,TiOq q8, and TiOq 3p corresPonding to starting comPo-sitions of TiOo.s, TiOp g, TiOx. o& TiOq ~5, and TiOq 28,respectively.

Reflection electron energy-loss spectroscopy rnea-surements were carried out in a combined x-rayphotoemission spectroscopy —ultraviolet photoemissionspectroscopy —bremsstrahlung iso chromat spectroscopyspectrometer from VSW Scientific Limited, U.K. Thesample surface was cleaned by scraping with an aluminaflle in a vacuum of 5xl0 ' mbar. The cleanliness of

0163-1829/95/52(20)/14526(5)/$06. 00 52 14 526 1995 The American Physical Society

52 DIELECTRIC FUNCTION AND OPTICAL CONDUCTIVITY OF. . . 14 527

sample surfaces was checked by monitoring the 0 18 andC 18 core levels with x-ray photoemission spectroscopy.REELS spectra were collected using a hemispherical an-alyzer with constant pass energy of 10 eV. The primaryelectron beam with 0.4 eV full width at half maximum(FWHM) of elastic peak was incident on the sample sur-face at 45 angle with respect to the sample normal. TheREEL spectra were collected at normal emission withspectrometer energy resolution of 0.1 eV. Thus, the totalresolution for spectra reported here was limited by the en-ergy spread of the primary electron beam. Spectra wererecorded over a wide range of energy (0 —56 eV), includ-ing the elastic peak. The spectra were recorded at variousprimary energies, though only the results obtained with1500 eV are presented here. At this energy, we expect atypical mean free path of about 20 A. , which makes it arather surface sensitive probe. However, our recent com-parison of photoemission results with bulk band structurecalculations for these systems suggests that the elec-tronic structure is not greatly changed, due to surfaceeffects in these systems.

the real part of the inverse of the dielectric functionjRe(1/e(E))] vanishes at zero energy.

The normalized single scattering loss functionj= Im( —1/e(E))j thus obtained was used to determinethe real part of inverse of the dielectric function, usingthe Kramers-Kronig analysis.

E'Im /—

e(E) ~ E'2 —E2

where P denotes the principal part of Cauchy's integral.The integral was calculated numerically. Subsequently,ei = Re(e) and e2 ——Im(e) were determined by

Rei

(I (E) ~

+ I

and

III. DATA ANALYSIS ~2(E) =

( 1

(E)&

As recorded REELS spectra are dominated by the elas-tic peak. This peak was removed &om the raw data andthe spectrum was extrapolated to zero intensity at 0 eVloss energy by quadratic curve fit (uE + bE) between 0eV and about 1.5 eV, as was employed earlier in the caseof metallic cuprates. As this extrapolation is on a verynarrow frequency interval, its effect on the final result isnot very significant. Since the experimental spectra wererecorded over a finite frequency range (0—56 eV), the lossintensity was assumed to have a dependence of ~ 4 be-yond the experimentally obtained range on the basis offree electron gas approximation. This approxima-tion does not significantly affect the results of subsequentanalysis for energies less than about 50 eV. It is alsoknown that the REEL spectra can have prominent fea-tures arising &om surface plasmon excitations. We have,therefore, checked the REEL spectra from these com-pounds with various primary energies. With decreasingprimary energy, the surface sensitivity can be increased,thereby identifying the surface related features. This waywe have ensured that the spectral features obtained at1500 eV have minimal contributions from surface plas-mons and thus, have neglected any small contributionfrom this process in all data analysis. However, the spec-tra were corrected for multiple scattering effects, usingan iterative procedure; the convergence criterion ensuredthat the total squared error between the results of twoconsecutive steps is less than 10 on convergence.

The resultant single scattering loss function, S(E) wasnormalized with a factor C, where C is defined as

Using the imaginary part of the dielectric function, theoptical conductivity was determined from

X (d

4n

IV. RESULTS AND DISCUSSION

We show REEL spectra normalized to the elastic peakheights for TiO with different values of x in Fig. 1. Allthese spectra exhibit four prominent features at 2—4 eV,13—14 eV, 25—26 eV, 47—49 eV and match qualitativelywith the ones reported in Ref. 8 for nominal TiO usingtransmission-electron energy-loss spectroscopy (TEELS).The first loss feature appears at 3.9 eV in case of TiOp 8iand shifts gradually towards lower energy with increas-ing oxygen content. For TiO] 3p this feature is at 2.2eV. This feature is attributed to a plasmon loss. Earlierstudies reported a plasmon loss feature at about 3.8 eVfor nominal TiOy p and a reduction in plasmon &equencywith increasing oxygen content. The plasmon &equencyis indeed expected to decrease with a decreasing num-ber of conduction electrons. In the case of nearly &eeelectrons, the plasmon frequency uz is given by

47t neCdP m*

2y-'( ')dEp

This normalization procedure is consistent with themetallic ground state of these samples and ensures that

where n is the number of electrons and m* is the ef-fective mass. The number n of d electrons available inTiO is given by n = 4 —2x. We find that while w

exhibits the expected monotonic increase with n, the de-pendence differs considerably from the expected linear

14 S28 SHUBHA GOKHALE S, S. R. BARMAN AND D.. D. SARMA

~ w

20

10 -Q

5—

TiO„

1.30

1.18

1.03

a~—

%lying

0.91

x = 0.81

I I I I I I I I I I II I I I I I I I I I I I I I

20 30 40 50Loss energy (eVl

weighted average of S. Whsle we cannot 1

t~q e) for all an gular momentano ca cu ate transitio

differen l ~ l + 1 chion probabilities for

c annels and thustt t' tho t' ld

b d h~ ~

core &ca escription of ta

' eatures in the EELat qualitative fea)

fas pea positions must r ' r

eatures in the indi 'd 1

culated these an 1

in ivy ua S~~~gq e . T, a-us, we have cal-

p jo

der to compare thr o ave significant iintensities. In or-

e ese results with the exe'

e experimental ones,gy

is is necessitated b theld proximation calculation ten

fh e unoccupied states''d d h comparison of unoccccupied calculated DOS

F&C.. l. Electron enervalues of x

energy-loss spectra of TiOues o~ x normalized to the elastic e

h b 11ft de

v

1.03), 10.0 (z = 1.18)), and 14.0 (z = 1.30).

—total

TI STI 0'

------- 0 p—00'

behavior arisin frome'

g rom the uncertainties'

e peak positions.in ies xn determining

Hi h'gher energy-loss f tea ures arise &oband transitions. Is. n order to inter re

&om various inte-

report in Fig. 2&~aj~ therpret these features we

) using

shown earliers th t h s ructa t ese band structeen

a realistic descri trip ion of the electron's ructure results providvi e

compounds. Wh 1

c ronsc structure of these

the DOS shown i F'x e for the commonon range of energies

()n in tg. 2(a) is similar

)

h dff t t 1DOSdiscussion.

ar ia OS, relevant to the present

While band structure resultsious partial DOS 1could be directl co

s, xn terms of DOS andn var-

hcorrespond to tr 't

erse p otoemissions epectra, EEL spectransxtions between th e

unoccupied bands a deen e occupied and the

o the DOS. Howevero e irectly compared

tioowever, if we assume t

do' t th EEL...d h„...d th. t tra

e spectra at ta transition matrix e

ergy

fEF

Sl—+l~l(e) OC Pt (e )Pt+ x (e + e) tie

Q

a5

C/}0A 1—

tI ~

-10 -5

10

8

act

0h. 4

2

08

EF 5 10Energy (eV)

12 16 20

15

T1 p ~dOp s

Op d

20

where p~ andp~ d p~~q represent the ar '

corresponding to E ande partial density of states

Son y over the unoccu

ia

() vanous joint de)

total EEL speciensities of states. Th

ec rum consists of a ts. e

a transition probability-

00 10 20

Energy (eV)30

FIG. 2. (a) Total ando a and some selecteda es In TiO obtain d fine rom LMTO

parti. al densities fs 0

tion probabilities f0 calculations. (b Tra

in TiO calculated withci a xons or selected channels

on the basis of thwi zn an ap roxim

e results shownown in a .ee ext

52 DIELECTRIC FUNCTION AND OPTICAL CONDUCTIVITY OF. . . I4 529

with the bremsstrahlung isochromat (BI) spectra of TiOpresented in Ref. 3. With this single adjustable parame-ter to expand the energy axis, we find that the calculatedresults in Fig. 2(b) provide a very good description forthe experimentally observed features. For example, allthe three transitions, namely, Ti p ~ d, 0 p —+ 8, and0 p —+ d, exhibit promjnent feature around 13 eV cor-responding to the experimentally observed EELS featureat about the same loss energy. Even the weaker featuresin the calculated results at about 5.5 and 18.5 eV mayhave weak corresponding features in some of the experi-mental spectra shown in Fig. 1 at about the same energy,arising from primarily Ti p ~ d and 0 p —+ 8 transitions,respectively. Similarly, a comparision of EELS data inFig. 1 and the calculated plots in Fig. 2(b) suggest thatthe second prominent experimental feature at about 26eV arises from an oxygen p —+ d interband transition.This interpretation is in contrast to the assignment ofthis peak in Ref. 8 to a collective excitation of the totalvalence electrons. However, there can be a contributionto this loss feature from excitations of oxygen 28 elec-trons to oxygen p states just above the Fermi energy. Itis interesting to note that there appears to be a system-atic variation in the energy position of this loss featurewith changing oxygen content in TiO; thus, the peakappears at about 24.5 eV for TiOq 8q and at about 26 eVfor TiOi 3. Since no major changes are observed in x-ray photoemission and BI spectra of these compounds,these small changes may indicate minor rearrangementsof the unoccupied oxygen p partial density of states withchanging oxygen content.

The fourth feature is in the form of a very broad humpcentered around 48 eV. This feature is accompanied bya shoulder at about 37 eV, which is more prominent forsamples with higher oxygen contents. These high energy-loss features cannot be explained on the basis of the cal-culation of joint density of states presented in Fig. 2(b).The main feature at 48 eV is possibly due to electronictransitions from the Ti 3p to unoccupied Ti 3d level. Theorigin of the shoulder, however, remains unclear.

In Figs. 3 and 4, we show the real (eq) and theimaginary (e2) parts of the dielectric function over awide energy range for these compounds obtained by theKramers-Kronig analysis of loss functions shown in Fig.1. Overall shapes of ei and e2 are very similar for differ-ent compounds in this series.

The eq(w) curves are mainly dominated by a peak atabout 7 eV. At higher energies, there are broad featuresappearing at about 18 eV, 35 eV, and 41 eV. These highenergy features arise due to interband transitions as dis-cussed above in detail. The value of ei at 7 eV system-atically increases &om 1.5 for TiOO Sq to 1.85 in case ofTiOq 30, while the other features have almost the sameintensity for different compositions. The imaginary partof dielectric function, e2 represents the dissipative part.The e2(u) curves (Fig. 4) show the first feature at about10 eV. At higher energy, two broad features appear atabout 21 eV and 43 eV. The amplitude of the peak at10 eV decreases from 1.5 for Ti00 8g to 1.15 for TiO] 30.The amplitude of the remaining features remains moreor less constant over the entire range of oxygen content.

~ ~

-;i~0

Il~si~ ~

~ ~'g

1.30

1.18

1.03

0.91

~ ~

~ ~ ~

x = 0.81

0 I I I 5 I I I I I I I 1 I 1 I I I I I I I j I I ! I I I

0 10 20 30 40 50Energy (eV)

60

FIG. 3. Real parts of the dielectric functions for TiO forvarious values of x. The plots have been shifted along the yaxis for clarity by the following amounts: 0.0 (x = 0.81), 0.5(x = 0.91), 1.0 (x = 1.03), 1.5 (x = 1.18), and 2.0 (x = 1.30).

1.30

1.18

1.03

x = 0.81

I I I I I I I I I I 1 I I I I I I I I I 3 I I I I I I I I00 10 20 30 40 50

Energy (eV)60

FIG. 4. Imaginary parts of the dielectric functions for TiOfor various values of x. The plots have been shifted along the

y axis for clarity by the following amounts: 0.0 (x = 0.81),0.5 (x = 0.91), 1.2 (x = 1.03), 1.7 (x = 1.18), and 2.2 (x =1.30).

The positions of the features reported here are in agree-ment with the results obtained from reHectivity spectraby Wall et al. in case of an oxidized surface, which theyidentify as TiO.

Figure 5 depicts the optical conductivity cr(u) of thesesamples as a function of energy. Prominent features inthese plots appear at about 3 eV, 10 eV, 23 eV, and45 eV. The low intensity feature at about 3 eV closelymatches in energy to the feature in EEL spectra (Fig.1) attributed to a plasmon loss. Furthermore, this fea-ture in cr(u) shows a systematic shift to lower energy

14 530 SHUBHA GOKHALE, S. R. BARMAN, AND D. D. SARMA 52

1.30

1.18

1.03

0.91

x =0.81I I r I I i & & I s I I I I & I I I I I

10 20 30 40Energy (eV)

50 60

FIG. 5. Optical conductivities of TiO for various valuesof x. The plots have been shifted along the y axis for clarityby the following amounts: 0.0 (x = 0.81), 0.5 (z = 0.91), 1.2(x = 1.03), 1.7 (x = 1.18), and 2.2 (x = 1.30).

with increasing oxygen content in the sample, which isthe same behavior as in the case of the plasmon loss fea-ture in EEL spectra. The pronounced peak in cr(~) atabout 10 eV most probably arises from oxygen p to ti-tanium d transition, the energy difFerence between thesebands [Fig. 2(a)] being in good agreement with the en-ergy of this feature. The feature near 23 eV can be at-tributed to oxygen p—oxygen d excitations [Fig. 2(b)]and to oxygen 28—Ti d and oxygen p admixed states just

above Ey. The higher energy features in o (E) at about37 eV and 45 eV probably arise from Ti 3p core excita-tions. Though the value of conductivity remains almostunaltered between difFerent samples on the higher-energyside, the first feature at 3 eV shows a decrease in inten-sity with increasing oxygen content. This trend is similarto that of dc conductivities reported by Banus et al. forTiO (0.86 ( z ( 1.17). Hence at lower energies, wherethe free electrons in the system govern the data, there isa systematic change observed in the conductivity. Athigher energies, where the interband transitions domi-nate the loss spectrum, the conductivity remains almostunaltered with oxygen content.

In conclusion, we have presented electron energy-lossspectra of TiO for five compositions with 0.81 & z (1.3. Various features in the spectra have been inter-preted with the help of ab initio band structure calcu-lations. Real and imaginary parts of the complex dielec-tric function have been obtained from the loss spectraby Kramers-Kronig analysis; optical conductivity of thesamples have been calculated from the dielectric func-tion. The low-energy part of the optical conductivity isfound to decrease systematically with increasing oxygencontent in the samples similar to dc conductivity results.

ACKNOWLEDGMENTS

We thank Professor C.N.R. Rao for his continued sup-port. Support for this work from the Homi Bhabha Fel-lowship Council and the Department of Science and Tech-nology, Government of India, is gratefully acknowledged.S.R.B. is thankful for support from the Council for Sci-entific and. Industrial Research, Government of India.

* Present address: Physik Department E-20, Technische Uni-versitat Munchen, D 85747 Garching, Germany.

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J. Yuan, L.M. Brown, and W.Y. Liang, J. Phys. C 21, 517(1988).H. Ibach and D.L. Mills, in Electron Energy Loss Spec-troscopy and Surface Vibrations (Academic Press, New

York, 1982).H. Raether, in Excitation of Plasmons and Interband Transitions by Electrons, Springer Tracts in Modern PhysicsVol. 88 (Springer-Verlag, Berlin, 1980); Springer Tracts inModern Physics (Springer-Verlag, Berlin, 1965), Vol. 38, p.85.J. Daniels, C.V. Festenberg, H. Raether and K. Zeppen-feld, Springer Tracts in Modern Physics (Springer-Verlag,Berlin, 1970) Vol. 54, p. 77.M.D. Banus, T.B. Reed, and A.J. Strauss, Phys. Rev. B 5,2775 (1972).