Angle resolved photoemission study and calculation of the electronic structure of the Pt(111) surface

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Surface Science 310 (1994) 155-162

Angle resolved photoemission study and calculation of the electronic structure of the Pt(111) surface V . M . T a p i l i n *, D . Y . Z e m l y a n o v ,

M.Y. Smirnov, V.V. Gorodetskii

Boreskov Institute of Catalysis, Novosibirsk 630090, Russia

(Received 7 September 1993; accepted for publication 21 December 1993)

Abstract -

-

D

Angle resolved photoemission spectra of Pt(111) were measured along the FK and FM direction of the surface Brillouin zone (SBZ). The electronic structure of a semi-infinite Pt(lll) crystal was calculated applying the LMTO-TB approximation to aid interpretation of the spectra. The experimental spectra are well described by the calculated bulk band structure. Both the experiment and calculation reveal a surface state near the Fermi level in the neighborhood of the K point of the SBZ.

1. Introduction Angle resolved photoemission spectroscopy (ARUPS) has proved itself as one of the most powerful probes of both bulk and surface electronic structure. For example, A R U P S combined with the corresponding electronic structure calculations have given us the most detailed and reliable data on the electronic structure of the low index faces of the noble and some transition metals, both clean and with adsorbed species (see, e.g. Refs. [1-5], and references therein). Surprisingly, there are no publications of A R U P S on clean Pt surfaces despite of the great importance of Pt in catalysis. This gap in the investigations of the Pt surface prompted us to perform an A R U P S study of P t ( l l l ) in combination with a theoretical calculation of the electronic structure of a semi-infinite P t ( l l l ) crystal.

* Corresponding author.

Details of the experiments and calculations are described in Sections 2 and 3, respectively. The experimental and theoretical results are discussed in Section 4.

2. Experiment The experiments were performed using a V G ADES-400 spectrometer (typical base pressure was better than 10 - l ° mbar) equipped with ARUPS, H R E E L S and TDS facilities. The P t ( l l l ) crystal was mounted on a V G UMD-20 manipulator with two-axis rotation and x, y, z translations. The surface was routinely cleaned in situ with cycles of Ar + sputtering, annealing in oxygen (Po2 = 1 0 - 6 mbar, T h = 950 K) and flashing up T = 1100 K in vacuum. This procedure has been described elsewhere [6]. Cleanliness was confirmed by H R E E L S (observation of a steep smooth intensity drop of the elastic peak and comparison of CO and N O loss spectra with

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V.M. Tapilin et al. / Surface Science 310 (1994) 155-162

previous studies on clean Pt(111)). The work function as obtained from the difference between the photon energy and the width of ARUPS was about 5.7 eV in good agreement with previous values for clean P t ( l l l ) . The ARUPS measurements were carried out at room temperature using He I radiation, hu = 21.2 eV. The incident angle to the surface normal was 0 i = 45 °. Photoemitted electrons were detected using a rotatable 150°-hemispheric deflector type analyzer at various polar emission angles 0d (with respect to the surface normal) with a resolution of +_1.5 °. The photon flux direction and the center of analyzer aperture were in the surface normal plane (photoemission plane). During data collection the base pressure in the spectrometer chamber increased to = 10 -s mbar due to helium leakage. ARUPS were taken along the two principal azimuths of the P t ( l l l ) surface, namely, the FM and FK crystal SBZ directions. The appropriate orientation was obtained with the aid of the L E E D method (an EMU-50 electron gun provided a source of monochromatic electron beam and the rotatable analyzer was used to measure diffracted beam intensities). The primary beam was aligned in the photoemission plane and the incident angle was 45 °. The analyzer was placed in the position where the (01) beam should be observed according to diffraction conditions, then the crystal was rotated around the surface normal until the (01) beam intensity was at a maximum, thus defining the FM direction of SBZ in the photoemission plane. The F K direction was obtained by rotating the crystal azimuthally by 30 ° from the FM direction. 3. Calculations

The LMTO-TB (linear muffin-tin orbitalstight-binding) approximation [7] has been applied to the surface electronic structure calculations in Refs. [8-10]. We will treat the surface of the P t ( l l l ) semi-infinite crystal as described in Ref. [9]. Matrix elements of the Hamiltonian in the LMTO-TB approximation are written in the form: t ~ R L , R ' L ' ""41/2 I' , H R L , R'L' = CI~RR'~LL' q- ~"/1/2K'

(1)

where R describes the position of the atoms in the crystal, L(-- {l, m}) is the (collective) angularmomentum index, and SRL,R,L, is a matrix element of the screened structure matrix. The potential parameters c t and d t are expressed in terms of the parameters C t and At of the Hamiltonian in the nearly orthogonal representation ct = C l -

( Yl - a l ) ( Et - C l ) 2 / A l ,

d]/2 = A~/z + (3', - a t ) ( E , -

C,)/A~/2,

(2)

where a t are given in Ref. [7], Cz = E t + o~t( - ) ,

a, = s

)]

2(- )[1 -

/ [ 1 + (q62)o92( - ) ] 2 / 2 ,

(3)

Yt = q~t( -- ) / 2 ( 2 1 + 1) q~,( + ). All the values on the right-hand side of Eqs. (3) are given in Refs. [11,12]. The following approximation of the perturbation in the Dyson equations for a crystal with a surface will be used: Vni;m j = - H n i ; m j ,

for n < 0, m > 0,

Vni;mj = Vni;nianm~ij int outt~ q- Vnn -nm, •

(4a)

for n, m >/0, (4b)

where n, m label atomic planes, i, j label basis functions of a unit cell, n < 0 relates to the removed part of the crystal, Hni;m j is a matrix element of the unrestricted crystal, Vni;n int i describes a variation of the corresponding matrix element due change of the electronic states population inside the MT-sphere of layer n, and Vn°ut is a variation of the same matrix element due to a possible appearance of electric charges at other MT-spheres. Eq. (4a) is commonly accepted in the LCAO (linear combination of atomic orbitals) approximation for semi-infinite crystals. It creates the surface, but accurate calculations must be completed by the interaction of crystal and freespace electrons. Such interactions can be introduced as in Ref. [13] or by some other means. Eq. (4b) corresponds to the approximation of an extended Hiickel type used in quantum chemistry for complex systems. We have ignored variations in non-diagonal matrix elements and have taken

V.M. Tapilin et ul. /Surface Science 310 (1994) 155-162

previously calculated dependences of atomic level energies on populations which can be taken from experimental data or calculations for perturbations in the diagonal matrix elements. This considerably simplifies the procedure of self-consistency. Even though the approximation is crude it nevertheless guards against unrealistic charges at surface atoms which are eliminated in some calculations by force induced shifts of energy levels of surface atoms. The surface condition described above we label as I. Beside that, we shall consider another one which takes into account the free-space near the surface. For that we shall replace the matrix elements of the perturbations for surface MTspheres in (4b) by ones which follow from the difference between free electron and Pt L M T O potential parameters. This condition we label as II. Changes of electronic populations at a surface may be expressed through changes of the imaginary part of the corresponding diagonal matrix element of the G r e e n function Ao'ni;m =

-llmfEFdE(2~)2

1

s b × f dkll(G.i;m-G~i;ni),

(5)

where the superscripts s and b denote the Green function of the semi-infinite and infinite crystals, ktt is the surface parallel component of an electron wave vector, and E v is the Fermi energy. Direct integration in (5) causes serious difficulties because of singularities of the G r e e n function in both variables ktt and E. To avoid these difficulties we shall shift the integration path to the complex plane. Using the asymptotic expression for the G r e e n function

./;.,(k,,)] - 1,

s,b

[Z - HS b

Gni;ni(k]] , E ) ~

(6)

we obtain for the population of the (n, i)th state O~s'b l k ~ -

ni;ni\ 11]

s,b E v --H~,i,ni(kll )

1

1

2

7r

-

d E R e Gni;ni( s,b kll, EF -- i E ) .

arctg

•

157

The first two terms in (7) are received by integrating (6) along the circle I E I exp(i&) for 7r/2 ~< & ~< 7r and along the line Re E = EF, • ~< Im E < ~. The value of • is chosen from conditions of validity of the asymptotic expression for the G r e e n function

Gni:,,i(EF+ie)=[Ev+ie_H,,i;,,i ] i.

(8)

The integration in the last term of (7) causes no problems and may be carried out by the Simpson method. The populations ~r(ktt), resulting from integration over E, are smooth functions and may be integrated using the special points of the SBZ [14]. Populations of the two first Pt surfaces layers were obtained from the solution of non-linear set of equations

n = 1, 2; i = sp, d,

(9)

where ~r° is the population used for calculating the perturbation in the Dyson equations, and ~ is the population obtained by solving the Dyson equations.

4. R e s u l t s

The photoemission spectra for various polar angles (corresponding to the F K and F M directions) are shown in Figs. 1 and 2. For spectra analysis the Pt band structure was calculated in the direction perpendicular to the ( l l l ) - p l a n e for a set of ktl belonging to F K and FM. The results along F L of the bulk Brillouin zone (BBZ), which are necessary to explain the emission normal to (lll)-surface, are shown in Fig. 3. For the final photoemission states we use the free-electron approximation. Even this approximation sometimes leads to significant errors, however in our case as it will be seen below, it gives satisfactory results. The energy of a free electron, shifted down on the photon energy hu, we express as h2

(7)

Ef( k ) = ~ - ( k + K,l,)2 + Eb - hU, Am

(10)

V.M.

158

Tapilin et al. / Surface Science 310 (1994) 155-162

( K l l ~ is t h e smallest r e c i p r o c a l lattice v e c t o r p e r p e n d i c u l a r to the ( l l l ) - p l a n e a n d E b is t h e energy of the b o t t o m o f the lowest b a n d ) is also shown in Fig. 3. I n t e r s e c t i o n s o f this e n e r g y curve with the e n e r g y b a n d s give us t h e e n e r g i e s satisfying the c o n d i t i o n o f e l e c t r o n k-vector conservation d u r i n g p h o t o e x c i t a t i o n which m u s t b e ful-

FM

h g ~

e-

/////////////////

Od:

,~ hq~

o8

e"

FK

al,a" b2

,

c

,-;

36° 2.

7111117///////

b2,b3 , /

L

o b'l,

z

2

, ,b

~-

2&°

z

a2 ,, ,,, ~

,,rb 3

J

12°

J

"E

~

c

-

j A

.13

.... >.I--"

EF=0

6o 0°

i .... 5

i .... 10

i

15

Binding Energy (eV)

z I..d I.-Z

Fig. 2. As for Fig. 1, but along FM. Bars are labeled in accordance with the curves in Fig. 5. filled for t r a n s i t i o n s in t h e bulk. T h e s e e n e r g i e s w h e n going f r o m P p o i n t a l o n g F K a n d F M d i r e c t i o n s o f t h e S B Z a r e p l o t t e d in Figs. 4 a n d 5. T h e emission angle 0d, kll a n d the kinetic e n e r g y o f an e m i t t e d e l e c t r o n a r e r e l a t e d by t h e expression Eki n =

3.841kll12/sin20d,

(11) o

EF=O

5

10

15

Fig. 1. The Pt(lll) photoemission spectra taken along FK of the SBZ. Capital letters label the experimental peaks. The vertical bars show the energy position where interband transitions could contribute according to the calculations. Bars are labeled with small letters in accordance with the curves in Fig. 4.

1

w h e r e Eki n a n d kll a r e m e a s u r e d in e V a n d A - , respectively. A s follows f r o m (11), only for t h e n o r m a l emission d i f f e r e n t e n e r g y regions in t h e s p e c t r a have the s a m e I klll = 0. F o r o t h e r emission angles t h e e l e c t r o n s e m i t t e d u n d e r the s a m e angle with d i f f e r e n t kinetic e n e r g i e s have differe n t kll a n d m u s t b e t a k e n into a c c o u n t w h e n

V.M. Tapilin et al. / Surface Science 310 (1994) 155-162 /

0°

/

O---Tk ...... ~

0

L3 L'2

6°

5

,,

¢"

t

\

~,_

~

L1

10J,

MI

5 -

i

t

'~\ "

Fig. 3. The calculated bands along FL. The dashed line corresponds to the free-electron final-state band shifted down on the photon energy. The dashed-dotted line shows the position of the Fermi level. comparing experimental spectra and theoretical predictions. For that reason we plotted in Figs. 4 and 5 the dependence of the kinetic energy on klr given by (11), for a set of emission polar angles, which were used in the experiment. The intersections of these last curves with the ones representing the dependence of calculated peak positions on kip give us the calculated position of the photoemission peaks for the bulk transition in

0° 10° 20030040050o60° I I I w al/ja~ b1 ---I--..~"~-'~1I / ~'1

L.

.h~Ji / / .

LLI I I

c l

II !o~ ~

I/~

L

~5

2.4°

30 ° 36 °

! ~

.4",Ull

i ~

1

¢

I A b'

ki.,i X ,;,; /," l

2

\

'5it-

18 °

',, A 1

Ld

0

12 °

i

a

,-

159

i

,'X,'i/ vl ;,'I ,:i!

, R

Fig. 4. Energies of electronic condition of conservation of during photoexcitation (solid the dependence of energy on angles.

states along FK, satisfying the three-dimensional wave vector lines). Dashed lines represent k N for a set of emission polar

j---h~

/ f/ //

-7--- i \ t c /

I

i

i I

10

~'.,..4-.-.~l ,'

I I

l,~e

/ /.1'\I I

I

I

I

'1 I

I

I

F Fig. 5. As for Fig. 4, but along FM.

spectra taken under the corresponding polar angle. These calculated peak positions, shown as vertical bars in Figs. 1 and 2, must be compared with the experimental spectra. First of all, let us consider the normal emission. The calculation predicts three peaks at 2.0, 4.2 and 8.5 eV below the Fermi level. The bars, labeled a, b and c in accordance with Figs. 4 and 5, show the calculated peak positions in Figs. 1 and 2. The experimental spectrum has two peaks A and B at 1.7 and 4.2 eV which we match with the first two calculated peaks. The first peak arises mainly from dx2y2 and dz2 states and the second one from dxy, dy z and dxz states. The local densities of states (LDOS) at the F point of the SBZ are represented for the surface, subsurface and bulk layers in Fig. 6. It is shown that the LDOS from which the peak at 8.5 eV arises is very small, so this peak is difficult to observe above the background of the inelastically scattered electrons unless the transition probability is unusually high. Peak A has an excrescence on its left which we assign to the violation of the k j_-conservation during photoexcitation at the surface. The surface and subsurface LDOS, shown in Fig. 6, support this assumption.

V.M. Tapilin et al. /Surface Science 310 (1994) 155-162

160

Surface Layer

Subsurface Layer 5

,4 L_

U') O

!

BuLk Layer

cf .

EF=O

.

.

.

L

5

.

.

.

.

1

10

Binding Energy (eV) Fig. 6. LDOS at the P point of the SBZ for the surface, subsurface and bulk layers.

When going from the F point along F K and FM, the bands, shown in Fig. 3, change their position and are split. As a result of this splitting (see Figs. 4 and 5 we have curves a~ and a 2 with their origin at a, and bl, b 2 and b 3 with the origin at b. Because F K and FM of the SBZ are not symmetrical directions for the BBZ, the curves labeled a,' b ' and c' with corresponding subscripts appear in Figs. 4 and 5. This leads to changes in the positions and splitting of the photoemission peaks. Although the calculated and experimental peak positions differ significantly for some angles, for example, at 0d = 60 ° in the Fig. 1, the experimental and calculated spectra are in reasonable agreement. Let us compare the calculated and experimental results obtained for the F K direction in detail. At small polar angles the splitting of the peaks

manifest itself as a broadening of the experimental peaks. At 15 ° (Fig. 1) the splitting of peak A into two peaks A 1 and A 2 is clearly seen. We match this splitting with one between the a l and a 2 states of Fig. 4, although the experimental value of the splitting is bigger than the calculated one. Peak A 2 shifts towards peak B and for 25 ° becomes a shoulder AB of peak B. For that angle it consists of a 2 and bl split from B. In the spectrum for 40 ° the peak AB splits again into A 2 consisting of a 2 and B 1 consisting of b I and b'l states. At larger angles A 2 shifts above the Fermi level. At 60 ° we have B 1 which we believe, consists of the b 1 and b'~ states and a broad peak BC consisting of b2, b 3 and c states. The predicted position of the B1 peak is too high and we believe that a more accurate calculation would give the right result. A similar but more complex situation occurs for the F M direction (see Figs. 2 and 5). The calculated position of surface states and resonances are shown in Fig. 7. The calculations were performed for the two boundary conditions described in Section 3. Both calculations predict surface states in the gaps B and C although the positions of the levels are different. The surface state in gap A is obtained with the boundary condition I only. To reveal the surface states in the spectra we studied the dependence of the spectra on the

0-

c

> >-LDC CI z

~J/A .Y.//~ "////A

(IJ

LI-} w

10.

Fig. 7. The projected bulk P t ( l l l ) bands and predicted surface states and resonances. Dashed lines refer to surface condition I, solid lines to the surface condition II.

V.M. Tapilin et al. /Surface Science 310 (1994) 155-162

angle of incidence of the radiation on the surface for fixed polar angles of the electron emission and the effect of CO adsorption on the spectra. Increasing the incident angle increases the photon run in the surface region and the surface contribution to the spectra. Unfortunately, for the unpolarized light the relative intensity of the s- and p-polarized components will change with angle of incidence due to the response of the surface [15] which can cause the changes in both surface and bulk contributions to the spectra. Under these circumstances one must adduce arguments in favour of the surface origin of the spectra modifications. Series of experiments were performed at various polar angles in the interval 0d -- 25-70 ° for the F K direction and 0d ~ 20-50 ° when the F M direction was studied. The only changes in the spectra we could find, occur in the interval 0d = 55-65 ° along FK. A set of spectra obtained at 0d = 60 ° is presented in Fig. 8. We can see the growth of the electron emission in the neighborhood of 1.2 eV with increasing incidence angle. It is difficult to perceive that the change of relative intensity of s- and p- polarized components effects in such narrow energy a n d kll region. Indeed, the change of polarization varies the relative contributions to the spectra of different muffin-tin orbitals constructed a crystal orbital. As follows from calculations the crystal orbitals, in the energy and kll region in which the spectra modifications occur, have no special properties explaining their peculiar behaviour. We will label this peak S. In Fig. 9 the energy bands beneath the Fermi level normal to the surface direction at the K point of the SBZ are plotted. Though electrons emitted under a fixed polar angle with different kinetic energies have different kll this plot together with Fig. 4 helps us to conceive the origin of the photoemission peaks in the 0~ = 60 ° spectra. The letters C and B mark the band gaps as in Fig. 7. To examine the surface localization of the S peak the effect of CO adsorption on its intensity has been studied. Fig. 10 shows spectra taken at an incidence angle of 0 i = 80 ° and 0d = 60 ° (the conditions are precisely the same as for the upper spectrum in Fig. 8) for clean and CO covered surfaces. It is seen that CO adsorption causes

161

@

U/////////

ei

//// //////,

b ~ 8

~

~d

-~

45 °

I

r

0

,

~

,

Binding Energy(eV)

I

5

Fig. 8. Photoemission spectra for different radiation incident angles and fixed emission angle 0d = 60 ° along FK. The bars s and b I and b~ show the calculated position of the transitions from the surface state and bulk states.

p e a k S to vanish, whereas other spectral features Bt and B 2 persist without significant change. A broad intensive peak at 9 eV should be assigned

ILl

K.L

Fig. 9. The calculated bands in normal to the surface direction for Y-, point. The dashed lines correspond to the free-electron final-state band shifted down on the photon energy. S labels the surface state, C and B label the band gaps as in Fig. 7,

k ± = 2 7 r / a [ ( ~ , O , - 3 ) + ( x , x , x ) ] , -~<~ x <~½.

V.M. Tapilin et aL / Surface Science 310 (1994) 155-162

162

COad

2

y "

"~

-)

,

I

I

i

'

i

CO ot300 K

~'

, ~,aFr ~'~"

2 c

j

+3L

clean

./

Pt(111)

f ~

o I

o

0-

/////////////////////

J

three-dimensional wave vector during the electron excitation. At the same time, the use of grazing incident angles revealed a surface state in the spectra in the neighborhood of the K point of the SBZ which is predicted by the calculations. The L M T O - T B approximation in the electronic structure calculations gives us a reasonable guide for analysis of angle resolved photoemission spectra.

i

I

I

I

3

6

9

12

Acknowledgement We are grateful to the Russian Foundation of Fundamental Research for the financial support of this work under Grant 93-03-4761.

Binding Energy(eV) Fig. 10. The photoemission spectra taken at grazing incidence angle for the clean and CO covered P t ( l l l ) surfaces. S, B x and B 2 denote the same spectra features as in Fig. 8, s, b 1 and b'1 are the calculated positions of the surface state and the bulk peaks, respectively.

to the combination of the 1~- and 5tr molecular orbitals of CO, in accordance with Ref. [16]. We assign the photoemission peak S observed experimentally in the interval 0 a - - 5 5 - 6 5 ° to the surface state in the band gap C (Figs. 7 and 9) found with the calculation. The predicted position of the peak is shown in Fig. 8 with a bar. The predicted positions of the bulk transitions b I and b'1 which, as it has been discussed above, refer to the B~ experimental peak, are also shown in Fig. 8. No other spectral features sensitive to the incidence angle of the radiation were observed. The surface state in gap C at K point mainly consists of equal parts of dxy, d y z a n d dxz states.

5. Conclusion The main features of the P t ( l l l ) photoemission spectra can be understood in terms of the bulk band structure and the conservation of the

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