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Unoccupied electronic band structure of graphite studied by angle-resolved inverse photoemission
~
Solid State Conanunications, Vol.61,No.6, pp.347-350, 1987. Printed in Great Britain.
0038-I098/87 $3.00 + .00 Pergamon Journals Ltd.
UNOCCUPIED ELECTRONIC BAND STRUCTURE OF GRAPHITE STUDIED BY ANGLE-RESOLVED INVERSE PHOTOEMISSION H. Ohsawa,
T. Takahashi,
T. Kinoshita,
D e p a r t m e n t of Physics,
Y. Enta, H.
Tohoku University,
Ishii ~, and T. Sagawa ~
Sendai
980,
Japan
( R e c e i v e d 22 O c t o b e r 1986 by T. Tsuzuki}
Angle-resolved inverse photoemission spectroscopy {ARIPES} in isochromat mode {~td = 9.5 eV} has been performed for highly oriented pyrolytic graphite. The unoccupied band structure of graphite could be mapped with considerable accuracy in the energy range of 0 - 21 eV above the Fermi level. The experimental results were compared with some previous ARIPES results and band calculations presented so far.
retical interpretation according to their gasadsorption experiment of graphite surface and rather associated It with the bottom of the interlayer band. In this letter, we report the results of our high-resolution angle-resolved inverse photoemlssion spectroscopy {ARIPES} for hlghly oriented pyrolytic 9Taphite (HOP(]). With ARIPES we cOuld map out the unoccupied band structure of graphite with considerable accuracy In the energy range of 0 - 21 eV above FT. By c o - - i n s the present experimental result with the two different theoretical calculations [4,5], we discuss the unoccupied band structure of graph Ite. The experiments were carried out with an ARIPES spectrometer constructed at ore" laboratory which has a Pierce-type electron gun and a Geiger-Milller-type counter. The typical electron current impinging on the sample was about 2 #A and the divergence of the incident electron beam was about 3 ° inferred from the observed polarangle dependence of ARIPES spectra, which results in the uncertainty of the wave vector parallel to the surface of at most 0.15 ~-I. In order to cancel the voltage drop across the filament of the electron gun which lowers the energy resolution of the primary etectrons, the electronic current to the filament was cyclically chopped and the data-acqulsltion system was operated only when the filament was off. Outcoming photons are focused by a concave mirror into the GM counter which detects photons with the energy of 9.Rt9.2 eV by the filter of a SrF2 window and iodine gas in It [II]. The overall energy resolution (electrons and
The electronic structure of graphite has been intensively studied both theoretically and experimentally; however, it was relatively recent that the overall valence band structure was established experimentally by angle-resolved ultraviolet photoelectron spectroscopy (ARUPS} [I-3]. In contrast to the valence states, the conduction {or unoccupied} band structure is still controversial [4-6I. The main point of the controversy is the energy position of an interlayer band, which has a three-dimensional character concentrating in the space between the carbon layers, and therefore plays an important role for intercalated graphite [6,7]. Tatar and Rabii [4] predicted theoretically the bottom of the interlayer band at about 7.5 eV above the Fermi level {F_~) while Holzwarth et al.[5] and Posternak et al.[6] placed it at about 4 eV above FT in their band calculations. Later, Fauster et al. I8] reported the first observation of a dispersive energy band a t 4 - 6 eV above F_~ n e a r t h e c e n t e r of t h e Brillouln zone using inverse pbotoemlssion s p e c t r o s c o p y {IPES) w i t h t u n a b l e p h o t o n e n e r g y , and t h e y a t t r i b u t e d i t t o t h e t h e o r e t i c a l l y p r e d i c t e d i n t e r l a y e r band. In a d d i t i o n t o t h e d i s p e r s i v e band, F a u s t e r e t a l . found a nond i s p e r s i v e f e a t u r e a t 3 . 6 eV above FT . P o s t e r n a k e t a l . I9] i n t e r p r e t e d i t as an i n t r i n s i c s u r f a c e state split-off from t h e i n t e r l a y e r band, although Reihl et al.[10] questioned the theo-
~Present address: Nippon Kokan K.K., Shinminato, Toyama 934, Japan. ~-~He died on 27th of September, 1986. 347
348
GRAPHITE STUDIED BY ANGLE-RESOLVED INVERSE PHOTOEMISSION
p h o t o n s ) was e s t i m a t e d t o be 0.5 - 0.6 eV. The vacuun i n t h e s p e c t r o m e t e r was l x l 0 -9 T o r t
Graphite(HOPG)
d u r i n g t h e measurements. In o r d e r t o o b t a i n a c l e a n and a t o m i c a l l y f l a t (0001) s u r f a c e of g r a p h i t e , s e v e r a l s u r f a c e l a y e r s of h i g h l y o r i e n t e d p y r o l y t i c g r a p h i t e (HOPG) sample was p e e l e d o f f w i t h an a d h e s i v e t a p e in t h e s p e c t r o m e t e r . The p o l a r a n g l e 8 of t h e i n c i d e n t e l e c t r o n beam r e l a t i v e t o t h e sample s u r f a c e was d e t e r m i n e d by t h e p o l a r - a n g l e d e p e n d e n c e o f t h e &qIPF_.S s p e c t r a . We o b s e r v e d no a z i m u t h a l - a n g l e d e p e n d e n c e of t h e ARIPES s p e c t r a b e c a u s e t h e a n i s o t r o p y around t h e c a x i s i s a v e r a g e d o u t i n HOP6. ARIPF__.Ss p e c t r a were Deasured i n t h e r a n g e o f t h e p o l a r a n g l e from t h e normal (8 =0°} t o 0 ffi about 70 ° w i t h an i n t e r v a l o f 2 . 5 °. The Fermi l e v e l (EF) o f t h e sample was r e f e r r e d t o t h a t o f a s i l v e r f i l m d e p o s i t e d o n t o t h e sample s u r f a c e . The u n c e r t a i n t y o f t h e e n e r g y P o s i t i o n o f EF due t o t h e n o n - s h a r p r i s e n e a r F~ in an IPES s p e c t r u m of s i l v e r may be 0.1 eV. No n o t i c e a b l e e f f e c t o f o x i d a t i o n o f t h e sample s u r f a c e was d e t e c t e d d u r i n g t h e measurements. F i g u r e I shows a n g l e - r e s o l v e d i n v e r s e p h o t o e m l s s l o n {ARIPES) s p e c t r a o f g r a p h i t e (llOPG) a t ~a = 9.5 eV. P o l a r a n g l e r e f e r r e d t o t h e s u r f a c e normal i s i n d i c a t e d on each s p e c trum, These ARIPES s p e c t r a show a p r o m i n e n t a n g u l a r d e p e n d e n c e which r e f l e c t s t h e u n o c c u p i e d band s t r u c t u r e o f g r a p h i t e . For t h e normal e m i s s l ~ s p e c t r u m , we f i n d t h r e e d i s t i n c t s t r u c t u r e s a t alxmt 4, 9, and 20 eV. The f i r s t peak a t 4 eV i s much n a r r o w e r t h a n t h e o t h e r two and shows a c l e a r upward e n e r g y d i s p e r s i o n w i t h t h e p o l a r a n g l e . This peak c o r r e s p o n d s t o t h e d i s p e r s i v e band which F a u s t e r e t a l . [ 8 ] found a t 4 eV above Ep n e a r t h e r p o i n t in t h e l r p h o t o n - e n e r g y t u n a b l e ARIPES o f g r a p h i t e . The most r e m a r k a b l e f e a t u r e in t h e s p e c t r a i s a s e r i e s o f s t r o n g peaks which appear In t h e h i g h p o l a r a n g l e s (above 30 ° ) and show a p r o m i n e n t downward e n e r g y d i s p e r s i o n w i t h t h e p o l a r a n g l e in t h e lowe n e r g y r e g i o n ( 3 - 8 eV). These s t r o n g s t r u c t u r e s in t h e ARIPES s p e c t r a a r e a s c r i b e d t o t h e l o w e s t u n o c c u p i e d n band. In F i g . 2 we p l o t t h e energy p o s i t i o n s (E c)
Vol. 61, No. 6
59
2
55
C
A
I 5o
2 m
~.5
C
c
4 ,
25~ 20~ 15__
i°=y 0
~ ....
m ....
I ....
t
....
10 15 20 25 Energy relative to EF (eV)
Fig. 1 Angle-resolved inverse photoemission s p e c t r a of highly o r i e n t e d p y r o l y t i c g r a p h i t e (HOPG) a t fw = 9.5 eV. P o l a r a n g l e r e l a t i v e t o t h e s u r f a c e normal i s i n d i c a t e d on each s p e c trum.
o f peaks (m) and s h o u l d e r s (x) in t h e ARIPES s p e c t r a v e r s u s t h e wave v e c t o r p a r a l l e l t o t h e s u r f a c e k, using the following formula, /ikll = [ 2m (fro + Ec - ~ ) ] l / 2 sinO, (1)
g r a p h i t e (4.7 eV), and 0 t h e polar' a n g l e r e l a t i v e t o t h e s u r f a c e normal. In F i g . 2, t h e e x p e r i m e n t a l r e s u l t s a r e compared w i t h t h e band c a l c u l a t i o n by T a t a r and Rabii [43. The same e x p e r i m e n t a l r e s u l t s were p l o t t e d f o r t h e two d i f f e r e n t d i r e c t i o n s in t h e B r i l l o u i n zone (F~C and i%11 b e c a u s e t h e a z i m u t h a l dependence is a v e r a g e d o u t in HOPG. In Fig. 3, we show a s i m i l a r comparison of t h e p r e s e n t e x p e r i m e n t a l r e s u l t w i t h t h e band c a l c u l a t i o n by Holzwarth e t a l . [ 5 ] . I t is n o t e d t h a t t h e y c a l c u l a t e d t h e
where m i s t h e mass of an e l e c t r o n , f~o t h e p h o t o n e n e r g y m o n i t o r e d w i t h t h e C/~ c o u n t e r (]~o = 9.5 eV), Ec t h e e n e r g y p o s i t i o n of c o n d u c t i o n (or u n o c c u p i e d ) b a n d s , 0 t h e work f u n c t i o n of
e n e r g y bands up t o o n l y about 12 eV above EF. In F i g . 2 we c a n n o t f i n d a good agreemenl between t h e e x p e r i m e n t and t h e c a l c u l a t i o n e x c e p t f o r a q u a l i t a t i v e agreemeni of t h e
Vol.
61, No. 6
349
GRAPHITE STUDIED BY ANGLE-RESOLVED INVERSE PHOTOEMISSION
~
20
xxx xx~Xx
x~eeeee x x
2
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x:r x x xxx~,x,c'k
/
M
tvl
F i g . 2 E x p e r i m e n t a l u n o c c u p i e d band s t r u c t u r e of g r a p h i t e {HOP(;}; f i l l e d c i r c l e s and c r o s s e s r e p r e s e n t peaks and s h o u l d e r s in ARIPES s p e c t r a , r e s p e c t i v e l y . I t i s n o t e d t h a t t h e same e x p e r i mental r e s u l t s a r e p l o t t e d b o t h f o r t h e IX and FM d i r e c t i o n s . S o l i d and broken l i n e s a r e a and n bands c a l c u l a t e d by T a t a r and Rabii [ 4 ] . The vacuum l e v e l i s i n d i c a t e d by E v a c . .
d i s p e r s i v e f e a t u r e o f t h e l o w e s t - l y i n g n band and an a l m o s t n o n - d i s p e r s i v e band a t about 21 eY. The l a r g e s t d i s c r e p a n c y i s t h e e n e r g y p o s i t i o n of t h e bottom o f t h e u n o c c u p i e d bands a t t h e F p o i n t . As shown in F i g . 2, we c l e a r l y o b s e r v e d a d i s p e r s i v e band a t about 4 eV above EF a t t h e P p o i n t , w h i l e t h e c a l c u l a t i o n o f T a t a r and Rabii [4] p l a c e d i t a t about 7.5 eV above EF. an e x p e r i m e n t a l band l o c a t e d a t 12 17 eV w i t h a d i s t i n c t e n e r g y d i s p e r s i o n has no t h e o r e t i c a l c o u n t e r p a r t s in t h e c a l c u l a t i o n of T a t a r and R a b i i [ 4 ] . Weak n o n - d i s p e r s i v e f e a t u r e s a t about 2 eV in t h e e x p e r i m e n t a l band s t r u c t u r e may be due t o t h e i n d i r e c t t r a n s i t i o n from t h e n band a t t h e ~ p o i n t . In F i g . 3, on t h e o t h e r hand, we f i n d an e x c e l l e n t agreement between t h e e x p e r i m e n t and t h e c a l c u l a t i o n , p a r t i c u l a r l y in t h e d i s p e r s i v e f e a t u r e o f t h e l o w e s t d i s p e r s i v e band n e a r t h e P p o i n t . This e x c e l l e n t a g r e e m e n t s t r o n g l y s u g g e s t s t h a t t h e i n t e r l a y e r band i s l o c a t e d a t about 4 eV above EF a t t h e F p o i n t , as p r e d i c t e d by Holzwarth e t a l . [ 5 ] . However, i t may be necessary to consider another effect to the a p p e a r e n c e o f t h e d i s p e r s i v e band n e a r t h e F p o i n t ; t h e band may be an image p o t e n t i a l s t a t e a l r e a d y r e p o r t e d in many m e t a l s [12], which i s a weakly-bound s t a t e n e a r t h e s u r f a c e and shows a nearly-free-electron-like energy d i s p e r s i o n
Fig. 3 Comparison of the present experimental results (filled circles and crosses} with the band calculation o F graphite by Bolzwarth et al.[5]. The calculation is shown in the energy range up to about 12 eV above E F.
against the wave vector parallel to the surface in the center of the Brlllouin zone. As found in Fig. I, the first peak at 4 eV in the normal emission spectrum is much narrower than the other structures in the spectrum. This is one of the typical features observed in an image potential state [12]. Very recently Sch~fer et al. [13] reported a similar dispersive band In their ARIPES o f ~ and associated it with an image potential state. So, the final characterization of the lowest-lying dispersive band observed near the r point cannot be reached at present stage, while the observed excellent agreement between the experiment and the calculation in Fig. 3 favours the model of Holzwarth et al.[5] where the interlayer band is located at about 4 eV above F_~ at the P point. In order to make this point clearer, an ARIPES with a singlecrystal Iine graphl te is necessary because the energy dispersion of the interlayer band is different for the two azimuthal direction {I"K and I-M) as shown in Fig. 3 while an image potential state disperses as a nearly-free-electronlike state independent of the azimuthal direction. In conclusion, we have performed angleresolved inverse photoemission spectroscopy (ARIPES) in isochromat mode {~ito= 9.5 eV) for graphite {HOP(;) and succeeded in mapping out the unoccupied band structure in the energy range of 0 - 21 eY above E F. The band calculation of tlolzwarth et al. [5], where the interlayer band is situated at about 4 eV above E~ at the F point, shows the excellent agreement to the &
350
GRAPHITE STUDIED BY ANGLE-RESOLVED INVERSE PHOTOEMISSION
present experimental result, although the possibility that the observed lowest-lyln9 dispersive band near t h e F p o i n t may be an image p o t e n t i a l s t a t e c a n n o t be r u l e d o u t . For more d e t a i l e d d i s c u s s i o n of t h e u n o c c u p i e d band s t r u c t u r e of 9 r a p h l t e , ARIPES w i t h a s i n g l e - c r y s t a l l i n e graphite is desired.
Vol. 6 I , No. 6
Acknowledgment - We thank Prof. H. Suematsu, The U n i v e r s i t y of Tsukuba, f o r s u p p l y i n 9 a HOPG sample. We a l s o t h a n k Dr. S. Suzuki f o r h i s c o l l a b o r a t i o n i n c o n s t r u c t i n g t h e ARIPES s p e c trometer. T h i s work was f i n a n c i a l l y s u p p o r t e d by t h e K u r a t a F o u n d a t i o n and t h e M i n i s t r y of Education, Japan.
References
1 2
3 4 5 6
7
T. T a k a h a s h i , H. T o k a i l i n , and T. Sagawa, S o l i d S t a t e C o m u n . 52, 765 (1984). D. Marchand, C. F r ~ t i g n y , M. Lagu~s, F. B a t a l l a n , Ch. Simon, I . Rosenman, and R. P i n c h a u x , Phys. Rev. B 30, 4788 (1984). A.R. Law, J . J . B a r r y , and H.P. Hughes, Phys. Rev. B 28, 5332 (1983). R.C. T a t a r and S. R a b i i , Phys. Rev. B 25, 4126 ( 1 9 8 2 ) . N.A.W. H o l z v a r t h , S . 6 . L o u i e , and S. R a b i i , Phys. Rev. B 26, 5382 (1982). M. P o s t e r n a k , A. B a l d e r e s c h i , A.J. Freeman, E. W i m e r , and M. W e i n e r t , Phys. Rev. L e t t . 50, 761 ( 1 9 8 3 ) . H. Kamimura, h n n a l de Phys. (Paris) II, 39 (1986).
8
9
10 11 t2 13
Th. F a u s t e r , F . J . Himpsel, J . E . F i s c h e r , and E.W. Plummer, Phys. Rev. L e t t . 51, 430 (1983). M. P o s t e r n a k , h. B a l d e r e s c h i , A.J. Freeman, and E. Wimmer, Phys. Rev. L e t { . 52, 863 (1984). B. R e i h l , O.K. Gimzewski, J.M. N i c h o l l s , and E. T o s a t t i , Phys. Rev. B 33, 5779 (1986). A. Goldmann, M. Donath, W. Altmann, and V. Dose, Phys. Rev. B 32, 837 (1985). For example, V. Dose, Surf. Sci. Rep. 5, 337 (1985). I. S c h ~ f e r , M. S c h l O t e r , and M. S k i b o w s k i . Extended A b s t r a c t of I n t . Conf. Vacuum U l t r a v i o l e t R a d i a t i o n P h y s i c s (Lund, 1986), p.529.
Solid State Conanunications, Vol.61,No.6, pp.347-350, 1987. Printed in Great Britain.
0038-I098/87 $3.00 + .00 Pergamon Journals Ltd.
UNOCCUPIED ELECTRONIC BAND STRUCTURE OF GRAPHITE STUDIED BY ANGLE-RESOLVED INVERSE PHOTOEMISSION H. Ohsawa,
T. Takahashi,
T. Kinoshita,
D e p a r t m e n t of Physics,
Y. Enta, H.
Tohoku University,
Ishii ~, and T. Sagawa ~
Sendai
980,
Japan
( R e c e i v e d 22 O c t o b e r 1986 by T. Tsuzuki}
Angle-resolved inverse photoemission spectroscopy {ARIPES} in isochromat mode {~td = 9.5 eV} has been performed for highly oriented pyrolytic graphite. The unoccupied band structure of graphite could be mapped with considerable accuracy in the energy range of 0 - 21 eV above the Fermi level. The experimental results were compared with some previous ARIPES results and band calculations presented so far.
retical interpretation according to their gasadsorption experiment of graphite surface and rather associated It with the bottom of the interlayer band. In this letter, we report the results of our high-resolution angle-resolved inverse photoemlssion spectroscopy {ARIPES} for hlghly oriented pyrolytic 9Taphite (HOP(]). With ARIPES we cOuld map out the unoccupied band structure of graphite with considerable accuracy In the energy range of 0 - 21 eV above FT. By c o - - i n s the present experimental result with the two different theoretical calculations [4,5], we discuss the unoccupied band structure of graph Ite. The experiments were carried out with an ARIPES spectrometer constructed at ore" laboratory which has a Pierce-type electron gun and a Geiger-Milller-type counter. The typical electron current impinging on the sample was about 2 #A and the divergence of the incident electron beam was about 3 ° inferred from the observed polarangle dependence of ARIPES spectra, which results in the uncertainty of the wave vector parallel to the surface of at most 0.15 ~-I. In order to cancel the voltage drop across the filament of the electron gun which lowers the energy resolution of the primary etectrons, the electronic current to the filament was cyclically chopped and the data-acqulsltion system was operated only when the filament was off. Outcoming photons are focused by a concave mirror into the GM counter which detects photons with the energy of 9.Rt9.2 eV by the filter of a SrF2 window and iodine gas in It [II]. The overall energy resolution (electrons and
The electronic structure of graphite has been intensively studied both theoretically and experimentally; however, it was relatively recent that the overall valence band structure was established experimentally by angle-resolved ultraviolet photoelectron spectroscopy (ARUPS} [I-3]. In contrast to the valence states, the conduction {or unoccupied} band structure is still controversial [4-6I. The main point of the controversy is the energy position of an interlayer band, which has a three-dimensional character concentrating in the space between the carbon layers, and therefore plays an important role for intercalated graphite [6,7]. Tatar and Rabii [4] predicted theoretically the bottom of the interlayer band at about 7.5 eV above the Fermi level {F_~) while Holzwarth et al.[5] and Posternak et al.[6] placed it at about 4 eV above FT in their band calculations. Later, Fauster et al. I8] reported the first observation of a dispersive energy band a t 4 - 6 eV above F_~ n e a r t h e c e n t e r of t h e Brillouln zone using inverse pbotoemlssion s p e c t r o s c o p y {IPES) w i t h t u n a b l e p h o t o n e n e r g y , and t h e y a t t r i b u t e d i t t o t h e t h e o r e t i c a l l y p r e d i c t e d i n t e r l a y e r band. In a d d i t i o n t o t h e d i s p e r s i v e band, F a u s t e r e t a l . found a nond i s p e r s i v e f e a t u r e a t 3 . 6 eV above FT . P o s t e r n a k e t a l . I9] i n t e r p r e t e d i t as an i n t r i n s i c s u r f a c e state split-off from t h e i n t e r l a y e r band, although Reihl et al.[10] questioned the theo-
~Present address: Nippon Kokan K.K., Shinminato, Toyama 934, Japan. ~-~He died on 27th of September, 1986. 347
348
GRAPHITE STUDIED BY ANGLE-RESOLVED INVERSE PHOTOEMISSION
p h o t o n s ) was e s t i m a t e d t o be 0.5 - 0.6 eV. The vacuun i n t h e s p e c t r o m e t e r was l x l 0 -9 T o r t
Graphite(HOPG)
d u r i n g t h e measurements. In o r d e r t o o b t a i n a c l e a n and a t o m i c a l l y f l a t (0001) s u r f a c e of g r a p h i t e , s e v e r a l s u r f a c e l a y e r s of h i g h l y o r i e n t e d p y r o l y t i c g r a p h i t e (HOPG) sample was p e e l e d o f f w i t h an a d h e s i v e t a p e in t h e s p e c t r o m e t e r . The p o l a r a n g l e 8 of t h e i n c i d e n t e l e c t r o n beam r e l a t i v e t o t h e sample s u r f a c e was d e t e r m i n e d by t h e p o l a r - a n g l e d e p e n d e n c e o f t h e &qIPF_.S s p e c t r a . We o b s e r v e d no a z i m u t h a l - a n g l e d e p e n d e n c e of t h e ARIPES s p e c t r a b e c a u s e t h e a n i s o t r o p y around t h e c a x i s i s a v e r a g e d o u t i n HOP6. ARIPF__.Ss p e c t r a were Deasured i n t h e r a n g e o f t h e p o l a r a n g l e from t h e normal (8 =0°} t o 0 ffi about 70 ° w i t h an i n t e r v a l o f 2 . 5 °. The Fermi l e v e l (EF) o f t h e sample was r e f e r r e d t o t h a t o f a s i l v e r f i l m d e p o s i t e d o n t o t h e sample s u r f a c e . The u n c e r t a i n t y o f t h e e n e r g y P o s i t i o n o f EF due t o t h e n o n - s h a r p r i s e n e a r F~ in an IPES s p e c t r u m of s i l v e r may be 0.1 eV. No n o t i c e a b l e e f f e c t o f o x i d a t i o n o f t h e sample s u r f a c e was d e t e c t e d d u r i n g t h e measurements. F i g u r e I shows a n g l e - r e s o l v e d i n v e r s e p h o t o e m l s s l o n {ARIPES) s p e c t r a o f g r a p h i t e (llOPG) a t ~a = 9.5 eV. P o l a r a n g l e r e f e r r e d t o t h e s u r f a c e normal i s i n d i c a t e d on each s p e c trum, These ARIPES s p e c t r a show a p r o m i n e n t a n g u l a r d e p e n d e n c e which r e f l e c t s t h e u n o c c u p i e d band s t r u c t u r e o f g r a p h i t e . For t h e normal e m i s s l ~ s p e c t r u m , we f i n d t h r e e d i s t i n c t s t r u c t u r e s a t alxmt 4, 9, and 20 eV. The f i r s t peak a t 4 eV i s much n a r r o w e r t h a n t h e o t h e r two and shows a c l e a r upward e n e r g y d i s p e r s i o n w i t h t h e p o l a r a n g l e . This peak c o r r e s p o n d s t o t h e d i s p e r s i v e band which F a u s t e r e t a l . [ 8 ] found a t 4 eV above Ep n e a r t h e r p o i n t in t h e l r p h o t o n - e n e r g y t u n a b l e ARIPES o f g r a p h i t e . The most r e m a r k a b l e f e a t u r e in t h e s p e c t r a i s a s e r i e s o f s t r o n g peaks which appear In t h e h i g h p o l a r a n g l e s (above 30 ° ) and show a p r o m i n e n t downward e n e r g y d i s p e r s i o n w i t h t h e p o l a r a n g l e in t h e lowe n e r g y r e g i o n ( 3 - 8 eV). These s t r o n g s t r u c t u r e s in t h e ARIPES s p e c t r a a r e a s c r i b e d t o t h e l o w e s t u n o c c u p i e d n band. In F i g . 2 we p l o t t h e energy p o s i t i o n s (E c)
Vol. 61, No. 6
59
2
55
C
A
I 5o
2 m
~.5
C
c
4 ,
25~ 20~ 15__
i°=y 0
~ ....
m ....
I ....
t
....
10 15 20 25 Energy relative to EF (eV)
Fig. 1 Angle-resolved inverse photoemission s p e c t r a of highly o r i e n t e d p y r o l y t i c g r a p h i t e (HOPG) a t fw = 9.5 eV. P o l a r a n g l e r e l a t i v e t o t h e s u r f a c e normal i s i n d i c a t e d on each s p e c trum.
o f peaks (m) and s h o u l d e r s (x) in t h e ARIPES s p e c t r a v e r s u s t h e wave v e c t o r p a r a l l e l t o t h e s u r f a c e k, using the following formula, /ikll = [ 2m (fro + Ec - ~ ) ] l / 2 sinO, (1)
g r a p h i t e (4.7 eV), and 0 t h e polar' a n g l e r e l a t i v e t o t h e s u r f a c e normal. In F i g . 2, t h e e x p e r i m e n t a l r e s u l t s a r e compared w i t h t h e band c a l c u l a t i o n by T a t a r and Rabii [43. The same e x p e r i m e n t a l r e s u l t s were p l o t t e d f o r t h e two d i f f e r e n t d i r e c t i o n s in t h e B r i l l o u i n zone (F~C and i%11 b e c a u s e t h e a z i m u t h a l dependence is a v e r a g e d o u t in HOPG. In Fig. 3, we show a s i m i l a r comparison of t h e p r e s e n t e x p e r i m e n t a l r e s u l t w i t h t h e band c a l c u l a t i o n by Holzwarth e t a l . [ 5 ] . I t is n o t e d t h a t t h e y c a l c u l a t e d t h e
where m i s t h e mass of an e l e c t r o n , f~o t h e p h o t o n e n e r g y m o n i t o r e d w i t h t h e C/~ c o u n t e r (]~o = 9.5 eV), Ec t h e e n e r g y p o s i t i o n of c o n d u c t i o n (or u n o c c u p i e d ) b a n d s , 0 t h e work f u n c t i o n of
e n e r g y bands up t o o n l y about 12 eV above EF. In F i g . 2 we c a n n o t f i n d a good agreemenl between t h e e x p e r i m e n t and t h e c a l c u l a t i o n e x c e p t f o r a q u a l i t a t i v e agreemeni of t h e
Vol.
61, No. 6
349
GRAPHITE STUDIED BY ANGLE-RESOLVED INVERSE PHOTOEMISSION
~
20
xxx xx~Xx
x~eeeee x x
2
eee 10
.~
x:r x x xxx~,x,c'k
/
M
tvl
F i g . 2 E x p e r i m e n t a l u n o c c u p i e d band s t r u c t u r e of g r a p h i t e {HOP(;}; f i l l e d c i r c l e s and c r o s s e s r e p r e s e n t peaks and s h o u l d e r s in ARIPES s p e c t r a , r e s p e c t i v e l y . I t i s n o t e d t h a t t h e same e x p e r i mental r e s u l t s a r e p l o t t e d b o t h f o r t h e IX and FM d i r e c t i o n s . S o l i d and broken l i n e s a r e a and n bands c a l c u l a t e d by T a t a r and Rabii [ 4 ] . The vacuum l e v e l i s i n d i c a t e d by E v a c . .
d i s p e r s i v e f e a t u r e o f t h e l o w e s t - l y i n g n band and an a l m o s t n o n - d i s p e r s i v e band a t about 21 eY. The l a r g e s t d i s c r e p a n c y i s t h e e n e r g y p o s i t i o n of t h e bottom o f t h e u n o c c u p i e d bands a t t h e F p o i n t . As shown in F i g . 2, we c l e a r l y o b s e r v e d a d i s p e r s i v e band a t about 4 eV above EF a t t h e P p o i n t , w h i l e t h e c a l c u l a t i o n o f T a t a r and Rabii [4] p l a c e d i t a t about 7.5 eV above EF. an e x p e r i m e n t a l band l o c a t e d a t 12 17 eV w i t h a d i s t i n c t e n e r g y d i s p e r s i o n has no t h e o r e t i c a l c o u n t e r p a r t s in t h e c a l c u l a t i o n of T a t a r and R a b i i [ 4 ] . Weak n o n - d i s p e r s i v e f e a t u r e s a t about 2 eV in t h e e x p e r i m e n t a l band s t r u c t u r e may be due t o t h e i n d i r e c t t r a n s i t i o n from t h e n band a t t h e ~ p o i n t . In F i g . 3, on t h e o t h e r hand, we f i n d an e x c e l l e n t agreement between t h e e x p e r i m e n t and t h e c a l c u l a t i o n , p a r t i c u l a r l y in t h e d i s p e r s i v e f e a t u r e o f t h e l o w e s t d i s p e r s i v e band n e a r t h e P p o i n t . This e x c e l l e n t a g r e e m e n t s t r o n g l y s u g g e s t s t h a t t h e i n t e r l a y e r band i s l o c a t e d a t about 4 eV above EF a t t h e F p o i n t , as p r e d i c t e d by Holzwarth e t a l . [ 5 ] . However, i t may be necessary to consider another effect to the a p p e a r e n c e o f t h e d i s p e r s i v e band n e a r t h e F p o i n t ; t h e band may be an image p o t e n t i a l s t a t e a l r e a d y r e p o r t e d in many m e t a l s [12], which i s a weakly-bound s t a t e n e a r t h e s u r f a c e and shows a nearly-free-electron-like energy d i s p e r s i o n
Fig. 3 Comparison of the present experimental results (filled circles and crosses} with the band calculation o F graphite by Bolzwarth et al.[5]. The calculation is shown in the energy range up to about 12 eV above E F.
against the wave vector parallel to the surface in the center of the Brlllouin zone. As found in Fig. I, the first peak at 4 eV in the normal emission spectrum is much narrower than the other structures in the spectrum. This is one of the typical features observed in an image potential state [12]. Very recently Sch~fer et al. [13] reported a similar dispersive band In their ARIPES o f ~ and associated it with an image potential state. So, the final characterization of the lowest-lying dispersive band observed near the r point cannot be reached at present stage, while the observed excellent agreement between the experiment and the calculation in Fig. 3 favours the model of Holzwarth et al.[5] where the interlayer band is located at about 4 eV above F_~ at the P point. In order to make this point clearer, an ARIPES with a singlecrystal Iine graphl te is necessary because the energy dispersion of the interlayer band is different for the two azimuthal direction {I"K and I-M) as shown in Fig. 3 while an image potential state disperses as a nearly-free-electronlike state independent of the azimuthal direction. In conclusion, we have performed angleresolved inverse photoemission spectroscopy (ARIPES) in isochromat mode {~ito= 9.5 eV) for graphite {HOP(;) and succeeded in mapping out the unoccupied band structure in the energy range of 0 - 21 eY above E F. The band calculation of tlolzwarth et al. [5], where the interlayer band is situated at about 4 eV above E~ at the F point, shows the excellent agreement to the &
350
GRAPHITE STUDIED BY ANGLE-RESOLVED INVERSE PHOTOEMISSION
present experimental result, although the possibility that the observed lowest-lyln9 dispersive band near t h e F p o i n t may be an image p o t e n t i a l s t a t e c a n n o t be r u l e d o u t . For more d e t a i l e d d i s c u s s i o n of t h e u n o c c u p i e d band s t r u c t u r e of 9 r a p h l t e , ARIPES w i t h a s i n g l e - c r y s t a l l i n e graphite is desired.
Vol. 6 I , No. 6
Acknowledgment - We thank Prof. H. Suematsu, The U n i v e r s i t y of Tsukuba, f o r s u p p l y i n 9 a HOPG sample. We a l s o t h a n k Dr. S. Suzuki f o r h i s c o l l a b o r a t i o n i n c o n s t r u c t i n g t h e ARIPES s p e c trometer. T h i s work was f i n a n c i a l l y s u p p o r t e d by t h e K u r a t a F o u n d a t i o n and t h e M i n i s t r y of Education, Japan.
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3 4 5 6
7
T. T a k a h a s h i , H. T o k a i l i n , and T. Sagawa, S o l i d S t a t e C o m u n . 52, 765 (1984). D. Marchand, C. F r ~ t i g n y , M. Lagu~s, F. B a t a l l a n , Ch. Simon, I . Rosenman, and R. P i n c h a u x , Phys. Rev. B 30, 4788 (1984). A.R. Law, J . J . B a r r y , and H.P. Hughes, Phys. Rev. B 28, 5332 (1983). R.C. T a t a r and S. R a b i i , Phys. Rev. B 25, 4126 ( 1 9 8 2 ) . N.A.W. H o l z v a r t h , S . 6 . L o u i e , and S. R a b i i , Phys. Rev. B 26, 5382 (1982). M. P o s t e r n a k , A. B a l d e r e s c h i , A.J. Freeman, E. W i m e r , and M. W e i n e r t , Phys. Rev. L e t t . 50, 761 ( 1 9 8 3 ) . H. Kamimura, h n n a l de Phys. (Paris) II, 39 (1986).
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Th. F a u s t e r , F . J . Himpsel, J . E . F i s c h e r , and E.W. Plummer, Phys. Rev. L e t t . 51, 430 (1983). M. P o s t e r n a k , h. B a l d e r e s c h i , A.J. Freeman, and E. Wimmer, Phys. Rev. L e t { . 52, 863 (1984). B. R e i h l , O.K. Gimzewski, J.M. N i c h o l l s , and E. T o s a t t i , Phys. Rev. B 33, 5779 (1986). A. Goldmann, M. Donath, W. Altmann, and V. Dose, Phys. Rev. B 32, 837 (1985). For example, V. Dose, Surf. Sci. Rep. 5, 337 (1985). I. S c h ~ f e r , M. S c h l O t e r , and M. S k i b o w s k i . Extended A b s t r a c t of I n t . Conf. Vacuum U l t r a v i o l e t R a d i a t i o n P h y s i c s (Lund, 1986), p.529.