The High-Resolution Electron-Energy-Loss Spectrum of TiO2 (110)

Journal of Electron Spectroscopy and Related Phenomena, 39 (1986) 117-126 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

THE HIGH-RESOLUTION ELECTRON-ENERGY-LOSS SPECTRUM OF Ti0

P.A.

cox l ,

2 2, R.G. EGDELL S. ERIKSEN and W.R.

117

2(llO)

l FLAVELL

lInOrganic Chemistry Laboratory, South Parks Road, Oxford OXI 3QR (U.K.) 2Department of Chemistry, Imperial College, London SW7 2AY (U.K.)

ABSTRACT High-resolution electron-energy-loss spectra of Ti02(llO) are presented and compared with model calculations of dielectric loss functions. The influence of crystal anisotropy on loss spectra is rather small, producing only minor changes in the relative intensities of loss peaks. By contrast, electronic excitations associated with surface oxygen vacancy defects exert a major influence on the vibrational loss spectra and lead to pronounced changes in peak intensities and positions. INTRODUCTION One of the pioneering applications of high-resolution electron-energy-loss spectroscopy

~HREELS)

was to the study of surface optical phonons (ref. 1) first

predicted theoretically by Fuchs and Kliewer (Ref. 2) as elementary excitations of finite ionic crystals.

The loss

spectra for ZnO (Ref. 1) and other oxide

materials (ref. 3) can be described well in terms of semiclassical theories based on the dielectric response of the crystal surface to the potential of the incident electron via long-range dipole coupling, although the treatment appropriate to anisotropic materials has only been developed very recently (ref. 4,5). The surface modes excited strongly in near-specular scattering have a long characteristic penetration depth and thus the related loss spectra are generally believed to be insensitive to details of surface structure.

However, modifica-

tion of surface dielectric properties can lead to pronounced changes in the loss spectra.

Thus in the case of ZnO formation of an accumulation layer on the sur-

face leads to the appearance of coupled 2-D plasmon/phonon excitations with screening of the phonon modes (ref. 6).

A similar attenuation of phonon loss

intensity was recently noted by GBpel and coworkers (ref. 7) as a result of formation of oxygen vacancy defects at the (110) surface of rutile (Ti0 2). In the present paper we .extend this earlier work by a stUdy of more highly defective Ti0 2(llO) surfaces and show how the changes in the HREEL spectra can be understood quantitatively in terms of modification of the surface dielectric function by a contribution from a polaronic excitation associated with the oxygen vacancies.

At the same time we clarify the assignment of the HREELS of Ti0

2(110)

118 in terms of simple group theoretical arguments and consider in detail the possible influence of crystal anisotropy upon HREEL spectra.

EXPERIMENTAL AND RESULTS A single crystal of Ti0 with a lcm x lcm (110) face was obtained from 2 Hrand Djevahindjian SA (Monthey, Switzerland) and polished to an optically smooth finish with progressively finer diamond pastes down to Lum, crystal was then rinsed in isopropanol and distilled

The

water and heated in air at

1,000oC for two days to oxidise away residual diamond and anneal out polish damage. HREEL spectra were measured in a Leybold-Heraues ELS 22 spectrometer mounted -10 in an ion pumped chamber (base pressure 10 torr) equipped additionally with front view LEED optics and a Leybold-Heraues EAlO/100 100mm hemispherical analyser and 5kV electron gun for N(E) Auger spectroscopy and low-resolution electron energy loss spectroscopy (ELS). The crystal was mounted on a tantalum tray spot welded to tantalum wires held between two support rods.

The crystal could be heated either by electron

bombardment of the tray or by the passage of current through the support wires: temperature was monitored by a chromel-alumel thermocouple pressed by a Ta clip against the front face of the crystal, were

~xplored

Severa~

different cleaning procedures

but eventually it was found that clean, defect-free surfaces could

be produced by 2kV Ar+ bombardment at 10-20\lA for 10 minutes, followed by resistive annealing at 700 well-defined

(1

0C

for periods up to 70 hours.

These surfaces exhibited

x 1) LEED patterns, gave Auger spectra free of carbon and other

contaminant signals and·ELS with no electronic losses in the bandgap region. Defective surfaces were produced either by 2kV Ar+ bombardment or by 2kV electron bombardment.

The latter was explored principally as a means of annealing the

crystal: the dominant electron flux was onto the Ta tray and it was not possible to quantify the electron flux onto the sample itself.

In figure 1 we show HREEL

spectra of the annealed crystal and of three different damaged surfaces, ponding ELS spectra are shown in figure 2,

Corres-

The latter show that damage of the

surface is associated with growth of an electronic loss in the bandgap region close to the elastic peak. DISCUSSION Symmetry considerations in the HREELS of Ti0 2(110) The tetragonal structure of Ti02 contains two formula units per cell and 14 belongs to the space group D The 15 normal modes of non-vanishing frequency 4h, at k = 0 may be shown to span irreducible representations r as follows:

r =

(1)

119

a)

(0)

x3

b)

(b)

x 10

c)

(c)

d)

-0·1

o

0·1

0·2

Energy Loss leV

0·3

15

10

5

o

Energy Loss leV

Figure 1. (Left hand panel.) HREEL spectra of rutile(llO) excited by 7.35eV electron beam, specular mode, 30 0 incidence angle. (a) Ordered annealed surface. Electron beam along [OOlJ azimuth. Note single phonon losses at 44meV (shoulder), 52meV and 94meV together with combination and overtone peaks at higher energy. (b) Electron bombarded surface 20mAj2kV for 2 hours onto Ta backing plate. Note losses at 46meV, 53meV and 86meV. (c) Argon ion bombarded surface. 0.OOI5C 2kV ions onto crystal surface. Note losses at 50meV (i1ldefined) and 88meV. (d) Argon ion bombarded surface. 0.0060C 2kV ions onto crystal surface. Note ill-defined shoulder at 80meV. Elastic neak count rates: a) 3 x 10 4 s-l b) 2 x 104 s-l c) 1.5 x 10 3 s-l d) 7.5 x 102 . . Figure 2. (Right hand panel.) ELS spectra excited with unmonochromatised 500eV electron beam incident at 45 0 to crystal surface with analysis of specular electrons. (a) Ordered annealed surface as in (a) above. (b) Argon ion bombarded surface as in (c) above. (c) Argon ion bombarded surface as in (d) above. Note growth of loss peak at 1.3eV with increasing bombardment.

120 Only the modes of E and A symmetry involve the dipole moment change necessary 2u u for activity in HREELS or infrared spectroscopy and for the mode in question to contribute to the dielectric function of the material.

In the complex oscillator

analysis dielectric functions may be written in the form:

n £(W)

£(00)

+

L

2

W j

j=l

2

- W

(2) + iWY

j

Where £(00) is the high frequency dielectric constant arising from interband and other electronic excitations at higher energies and P • -W and Y,i are respecj j tively the dipole strength, transverse frequency and damping constant for the jth oscillator.

For Ti0

the summation in (2) for the dielectric function parallel 2 to the c-axis Ell (w) contains only the single term associated with the A mode 2u whereas for the perpendicular dielectric function E~(W) the summation extends over the three E modes. Parameter values derived from an oscillator analysis u of the infrared reflectivity of Ti0 (ref. 8,9) are ~iven in table I, along with 2 corresponding longitudinal phonon frequencies and calculated surface frequencies. TABLE 1 Parameter values from a complex oscillator analysis of the infrared reflection spectrum of Ti0 Calculated surface mode energies are also given. 2.

Mode

t (E l u) t 2(E u) t 3(E u) t 4(A 2u)

Energy -n:w (eV)

Absorption strength 41T P

0.0227

Parameter y/1iw

Dampin~

j

81,5

0.0481

0.1

1.08

0.0620

0.03

2.00

0.0207

0.025 0.025 *

165 Surface mode

Energy'flw (eV)

0.0462

sl

0.0468

12(E u)

0.0568

s2

0.0573

l3(E u)

0.0999

s3

0.0945

1 (A 4 2 u)

0.1006

s4

0.0903

11 (E

u)

Dielectric constants

*estimated

£

(00)

..L

6.0

E

II

(00)

8.4

121 The theory of HREELS for anisotropic materials (ref. 4) applied to the particular case of the (110) surface of a tetragonal crystal shows that the loss function is determined by an effective dielectric function

r

1

k

[f-

~

given by:

+

(3)

.1

where k

and k are the components of the total momentum transfer k parallel and x y perpendicUlar to the c-axis respectively. Thus we can envisage two limiting loss functions that could be observed in off-specular scattering

w~thin

the plane of

incidence.

One is determined by r (w) and requires the electrop beam to be in

~1~

azimuth (to ensure dominant momentum transfer perpendicular to the c

the

axis).

.

.1

The other is determined by

to be in the c axis.

;l ~O~

I r (w)£

-l

II

(w) and requires the electrom beam

azimuth (to ensure dominant momentum transfer parallel to the

In figure 3 we show the loss functions

l/wImC:1/~(w)

+

~

for these two

limiting cases and, for comparison, a hypothetical loss function determined by £

II

E

(w).

The 'perpendicular' loss function contains contributions only from the

modes and the highest energy peak at 94.5meV (Table 1) falls just below the

u corresponding longitudinal phonon frequency of 99.9meV.

is at the lower energy of 90.3meV. by

Ir

-l

(w)£

11

The A loss of r (w) Zu II In the 'parallel' loss function determined I

(w) it is no longer possible to make rigorous symmetry assignments

of the losses, although clearly the two lower energy peaks correlate strongly with the lower energy E

losses of r~ (w): the energies are shifted upwards by u almost negligible increments of 0.3meV and 1.ZmeV. The hi~h energy loss has composite A and E character and peaks at the intermediate energy of 91.5meV: Zu u the high energy shoulder reflects its mixed ch~racter. A further subtle effect

is that introduction of the A mode leads to additional screening of the low Zu modes which are relatively weaker than in the 'perpendicular' spectrum. u However the differences between 'parallel' and 'perpendicular' spectra become energy E

almost insignificant after convolution with instrument broadening and allowance for the range of momentum transfer allowed by our analyser system.

In prelim-

inary experiments we have been unable to achieve adequate count rates to allow off-specular experiments which might distinguish between the two limiting spectra.

In specular

scatteri~~

experiments, the non-vanishing angular accept-

ance of the analyser system allows both k and k transfer. However the spectra x y are adequately represented by the 'perpendicular' loss function and we use this function to explore the effects of detects on the HREEL spectra (see below). To summarise, the effects of crystal anisotropy on the HREELS of TiO Z(ll0) are rather small, the main effect being to introduce mixed Eu/AZu character into the highest energy loss peak.

Loss peaks occur at energies close to those

122

0)

b)

c)

o

0-05

0-15

0-1

En£'rgy loss I£'V

Figure 3. Loss functions for rutile(110) calculated (a) from the perpendicular dielectric function E (w) (b) from Ell (w) and (c) from the square root dielec1 tric function sqrt[E1(W) Ell (W) The energies of the peaks in (a) and (b) are given in table 1.

J.

of longitudinal optical phonons, although their energies are Ultimately determined by the traverse resonance frequencies.

In this sense the earlier

assignments of refs. 7 and 10 are misleading when they imply that the lowest loss has predominant Eu(TO) character whereas the two higher losses have Eu(LO) and A character respectively. 2 u(LO) The influence of defects on the HREELS of Ti02(110) It is well established that argon ion bombardment of rutile causes preferential sputtering of oxygen and introduction of occupied Ti:3d states as a result of oxygen deficiency (refs. 7,

11-~3).

Electron bombardment leads to oxygen

desorption through Knotek-Feibe1mann and related mechanisms (ref. 14).

The

123 Ti:3d states give rise to a new electronic loss feature in the bandgap region, although there is no general consensus as to the energy of the loss.

Thus

Henrich (ref. 11) and Somorjai (ref. 12) observed defect induced losses on Ar

+

bombarded Ti0 and Ti0 at respective energies of 1.geV and 1.6eV, 2(100) 2(110) both measuring spectra in the dN/dE mode. By contrast Gapel (refs 7, 13) found defect induced losses at 0.8eV using a monochromated 20eV exciting beam in conjunction with a HREELS analyser with an angular acceptance of about 1.4

0

.

It is beyon'd the scope of this short paper to discuss in detail possible reasons for the differences between these earlier values for the loss energy and our own measured value of 1.3eV (figure 2): although the bulk defect absorption energy in Ti0 shifts to higher energy with increasing degree of reduction (ref. 15) we 2 believe that the use of differing electron excitation energies and differing modes of energy analysis of the scattered electrons is of major importance here. The issue of the nature of the excitation process responsible for the new loss is also controversial.

For argon ion bombarded surfaces there is clearly major

surface disorder, so that assignments referred to well-defined defect geometries are somewhat hazardous.

In fact the physical origin of the surface excitations

is not crucial to our central argument that their effect on vibrational HREEL spectra can be understood simply in terms of modification of the dielectric function close to the crystal surface, although on balance we believe the ex3 citations to be polaronic in nature (possibly involving bipolaronic Ti + pairs). In our model a Lorentzian oscillator term with parameter values P we and Y is e e, added to the summation in equation 2 to represent the defect excitations: the defects are thus assumed to extend into the bulk of the solid below the selvedge to at least the penetration depth of the surface phonon excitations. vibrational region where We »

In the

w the effect of the electronic term is essentially

to increase the value of the background dielectric constant by an amount P e To explore the influence of defects on vibrational HREELS we have therefore carried out some simple calculations of the 'perpendicular' loss function

l/WIm~l/£L(W) + ~ treating the background dielectric constant as a variable parameter.

The results of these calculations are summarised in figure 4.

The main features to emerge are as follows.

The energy and intensity of

the highest energy E loss peak decreases as the background dielectric constant u increases due to screening of the vibrational mode by the electronic excitation. The intensities and energies of the lower energy E sitive to the variation in

£(00),

losses are much less senu reflecting the fact that the dominant screening

of these modes always comes from the higher energy E intensity of the lower energy E constant.

u

mode.

Thus the relative

modes increases with increasing dielectric

u All of these features of the model calculations are found in the

experimental spectra of figure 1, where it is seen that electron or argon ion

124

Figure 4. (Left hand pane L) (a) Peak positions of two highest energy loss features in loss function for rutile(110) calculated from parameter values of table 1 with variable background dielectric function. Only Eu terms included in dielectric function. (b) Maximum peak intensities of losses as in (a). The intensities have been normalised to the intensity of the higher energy loss at E(OO) = 6.0. Solid lines s3 : dash-dot lines s2'

Figure 5. Simulated HREEL spectra of rutile(l10). (a) Defect free surface. Parameter values from table l. (b) e - bombarded surface. Y1 = 0.005eV, Y2 = 0.005eV, Y3 = O.OleV, i'l:we = 1.4eV, Ye = 2.2eV, 411Pe = 7.65. Other parameters as in table 1. (c) Lightly Ar+ bombarded surface Y1 = O.OleV, Y2 = O.OleV, Y3 = 0.015eV, i'l:We = 1.4eV, Ye = 2.2eV, 411Pe = 5.10. Other parameters as in table 1. (d) Heavily Ar+ bombarded surface. Y1 = O.02eV, Y2 = 0.02eV, Y3 = 0.025eV, i'l:we = 1.4eV, Ye = 2.2eV, 411P e = 8.67. Other parameters as in table 1. The increased Y values for phonon modes in defective samples allow for inhomogeneous line broadening.

125 bombardment

lead~

to a pronounced attenuation of the

together with a marked downward shift in its energy. shift is not observed for the lower energy faces the spectra are generally

highe~t

energy phonon loss,

A corresponding downward

For argon ion bombarded sur-

peak~.

well-defined than for annealed or electron

les~

bombarded surfaces both due to degradation in the resolution on the elastic peak and ~pecific broadening of the phonon losses. Guided by model simulate the loss.

calculation~

~pectra

of the

los~

functions, we have attempted to

using Fourier transform techniques to convolute in

instrumental broadening and the effects of the

~equential

inelastic

that leads to the appearance of overtone and combination peake

~cattering

16, 17).

(ref~.

In these calculations parameters for the electronic excitation were constrained to reproduce the peak shape and position of the experimental ELS feature, although a major contribution to the ELS intensity under 500eV excitation appears to come from impact scattering mechanisms that are not included in calculation~

in figure 5.

of dipole

los~

Sample theoretical

intensitie~.

~pectra

are

~hown

In general these bear a close resemblance to the experimental

spectra of figure 1.

The major deficiency is that we are unable to reproduce

the change in intensity of the highest energy phonon loss without introducing an unduly large downward

~hift

in phonon energy.

models in which the defect concentration

i~

We are currently exploring

allowed to vary as a function of

depth below the surface in order to overcome this problem.

CONCLUDING REMARKS The present study has lead to a more detailed understanding of the HREELS of defect free Ti0

than ha~ been achieved previously. 2(110) important conclu~ion ot the pre~ent work i~ that the major

spectra resulting from the introduction of

~urface

repre~enting

change~

in the HREEL

defects can be understood

in terms of modification of the dielectric function of the introduction of a term

However the most

~urface

layer by

the defect electronic excitations.

been suggested previously that highly detective Ti0

surfaces are

It has

es~entially

2 (ref. 11). However our modified dielectric function 203 differs from that expected for metallic Ti The downward ~hift in phonon 203. frequency ~~ociated with the defects contrasts with the small upward ~hift identical to those of Ti

found on going from non-metallic to metallic oxides (ref. 16).

ACKNOWLEDGEMENTS The equipment was funded in part by the SERC.

We are indebted to

Dr. D. Chadwick and Dr. K. Senkiw for their invaluable assistance in commissioning the HREEL spectrometer.

126 REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

H. Ibach, Phys. Rev. Lett., 24 (l970) l16. R. Fuchs and K.L. Kliewer, Phys. Rev., l40 (1965) A2076. R.G. Egdell in M. Che and G.C. Bond (eds), Adsorption and Catalysis on Oxide Surfaces, Elsevier, Amsterdam, 1985, pp. 173-l82. A.A. Lucas and J.P. Vigneron, Solid State Commun., 49 (1984) 327. M. Liehr, P.A. Thiry, J.J. Pireaux and R. Caudano, J. Vac. Sci. Technol. A, 2 (1984) 1079. J.I. Gersten, I. Wagner, A. Rosenthal, Y. Goldstein, A. Many and R.E. Kirby, Phys. Rev. B, 29 (1984) 2458. G. Rocker, J.A. Schaefer and W. GBpel, Phys. Rev. B, 30 (1984) 3704. W.G. Spitzer, R.C. Miller, D.A. Kleinman and L.E. Howorth, Phys. Rev., l26 (1962) 1710. D.M. Eagles, J. Phys. Chem. Solids, 25 (1964) 1243. L.L. Kesmodel, J.A. Gates and Y.W. Chung, Phys. Rev. B, 23 (l981) 489. V.E. Henrich, G. Dresselhaus and H.J. Zieger, Phys. Rev. Lett., 36 (l976) 1335. W.J. Lo, Y.W. Chung and G.A. Somorjai, Surf. Sci., 71 (1978) 199. W. G6pe1, J.A. Andersen, D. Frankel, M. Jaehnig, K. Phillips, J.A. Schaefer and G. Rocker, Surf. Sci., l39 (1984) 333. M.L. Knotek and P.J. Feibelman, Phys. Rev. Lett., 40 (1978) 964. D.C. Cronemayer, Phys. Rev., 113 (1959) l222. P.A. Cox, M.D. Hill, F. Peplinskii and R.G. Egdell, Surf. Sci., l41 (l984) 13. P.A. Cox, W.R. Flavell, A.A. Williams and R.G. Egdell, Surf. Sci., l52/l53 (1985) 784.