Angle resolved photoemission valence band dispersions E(k) for gaP.

~

Solid State Cormnunications, Vol.52,No.l, pp.37-40, 1984. Printed in Great Britain.

ANGLE

RESOLVED

PHOTOEMISSION

VALENCE

BAND

0038-I098/84 $3.00 + .00 Pergamon Press Ltd.

DISPERSION3

E(k)

FOR

GaP.

F. x

S o l a l x, G. J e z e q u e l xx, F. N o u z a y xxx, A. B a r s k i x and R. P i n c h a u x x = Laboratolre L.U.R.E. L.P. C N R S 008 B~t. 209 C, U n i v e r s i t ~ de P a r i s - S u d 91405 Orsay France xx Laboratoire de s p e c t r o s c o p l e , U n i v e r s i t 8 de R e n n e s I 3 5 0 4 2 R e n n e s F r a n c e x x x C N E T i0 Rue de P a r i s 9 2 2 2 0 B a g n e u x F r a n c e = and Laboratoire de Physique des Solides, Unlversit4 P. et M. Curie, Paris, France

(Received March 19, 1984 by O. Joffrin ; revised form July 2, 1984) We e x p e r i m e n t a l l y d e t e r m i n e d the v a l e n c e b a n d d i s p e r s i o n s E(k) a l o n g the s y m m e t r y d i r e c t i o n s rKX, rx, rL u s i n g a n g l e - r e s o l v e d photoemlsslon, r x , rKX and FL h a v e b e e n s t u d i e d b y o f f - n o r m a l emission process with photon energy between 31 e V a n d 44 eV, w h i l e FKX has a l s o b e e n s t u d i e d by n o r m a l e m i s s i o n p r o c e s s u s i n g p h o t o n e n e r g y f r o m 31 to 85 eV. The r e s u l t i n g d i s p e r s i o n curves E(k) are compared to p s e u d o p o t e n t i a l calculation. We used a d i r e c t t r a n s i t i o n m o d e l and a n e a r l y - f r e e electron final state approximation to i n t e r p r e t the m a i n e x p e r i m e n t a l features.

w e r e c l e a v e d at r o o m t e m p e r a t u r e in a n u l t r a h i g h v a c u u m c h a m b e r ( 10 -10 T o r r ) . T h e e x p e r i m e n t s w e r e d o n e at L U R E , the french synchrotron radiation center using the radiation emitted by the storage ring A.C.O. A spherical electron energy analyzer with I° angular resolution was used, this a n a l y z e r is m o v i n g a r o u n d the s a m p l e in the incidence plane, the over all instrumental resolution (monochromator + a n a l y z e r ) w a s 0 , 2 5 e V in t h e p h o t o n energy ranRe between 30 e V a n d 85 eV. T h e light was i n c i d e n t at 45 ° in o r d e r to equally excite all the v a l e n c e band ~tates.

INTRODUCTION Angular resolved phot oemission spectroscopy from single cristal is widely used for determining the electronic band structures of s o l i d s . O u r p u r p o s e is to g i v e a o n e e l e c t r o n band description for GaP from experimental measurements. We present h e r e a c o m p l e t e set of d a t a c o n c e r n i n g t h e v a l e n c e band d i s p e r s i o n E ( k ) of GaP a l o n g the s y m m e t r y l i n e s rX, F L , FKX. Similar studies have been successfully performed in t h e c a s e of m e t a l s (I) . F o r t r a n s i t i o n m e t a l s (2), it h a s b e e n necessary to take account of the correlations in the d b a n d . In the case of s e m i c o n d u c t o r s GaAs and GaSh for example have been successfully studied ( 3 , 4 ) . T h e s t u d y of s i l i c o n is more c o m p l e x and no s i m p l e i n t e r p r e t a t i o n of the d a t a is p o s s i b l e probably because of the g r e a t i n f l u e n c e of t h e s u r f a c e reconstruction which involves several atomic layers. For the study of GaP, the direct transition model appears to b e v a l i d , also the nearly-free final state approximation is sufficient to interpret the d a t a in the e n e r g y range t h a t we u s e d (3).

METHOD The e n e r g y r a n g e t h a t we u s e d a l l o w s to consider the case of nearly free-electron final state for the direct transition model. Using the three-step process model (5) initial and final states are eigen-states of the i n f i n i t e s o l i d a n d a r e t h e n B l o c h states. In the e x t e n d e d zone scheme the final B l o c h s t a t e s E (k) are d l s c r i b e d by ~2k~" ~2k~-EF(k) = EO + --~--m4 2m

(I) where ~

and k ~

are the momentum components parallel and perpendicular to the s u r f a c e , E o is the "bottom of t h e m u f f i n - t l n " with respect to the top of the valence band. The energy and momentum conservation ( d i r e c t t r a n s i t i o n m o d e l ) l e a d to :

EXPERIMENTAL G a P h a s the fcc zinc b l e n d s crystal structure with a lattice constant a ~ 5 , 4 5 ~. The c l e a v a g e f a c e is ( i i 0 ) , the symmetry lines FX, ~, FKX are p a r a l l e l to the s u r f a c e . We s t u d i e d the whole band-structure by collecting off-normal photoemission from this surface. The FKX llne has also been s t u d i e d at n o r m a l e m i s s i o n . T h e s a m p l e s

EF(k) = El(k) + h~ El(k ) : initial 37

(2) Bloch

States

Vol. 52, No. l

PHOTOEMISSION VALENCE BAND DISPERSIONS E(k) FOR GaP

38 The measured momentum (k) by ,E K = E F - e 0 =

kinetic energy (Ek) and in the v a c u u m a r e r e l a t e d 42. 2 ~2K2 # r,..~.. + 2m 2m

o

I

(3)

The conservation of the parallel component of the momentum during the whole process ( K # = k//)and e q u a t i o n s (I), (2), (3) l e a d to hkll = (2mE k) I/2sin 0

(4)

= (2m(E i + hW - e0)) I/2 sin O ~kj. = (2m(EkCOS20 - V)) I/2

(5)

= (2m((E i + hw - e~)cos20 - Vo)) I/2 where Vo = Eo - e ~ the inner potential O is the plan emission angle with respect to t h e n o r m a l to the sample surface At n o r m a l e m i s s i o n (4) a n d (5) r e d u c e to k~, = 0 (4') i~kt = ( 2 m ( E + h v - Eo))I/2(5 ')

,4--o = m

e-

t._

= m

.0

The Umklapp processes are not t a k e n i n t o a c c o u n t in this d e s c r i p t i o n , t h e y l e a d at r a t h e r high energies to non dispersive structures emphasizing the high densities of states at c r i t i c a l p o i n t s of B r i l l o u i n zone.

t_

<

RESULTS All the spectra are referenced to the valence band maximum, which was determined by t h e G a 3 d 5 / 2 line at 18,6 eV below the top of the valence band. The 3d 5/2 and 3d3/2 splitting was well resolved for photon energies from 36 eV to 6 0 e V , t h e energy p o s i t i o n w a s a l s o c h e c k e d at d i f f e r e n t emission angle. Normal emission W e s t u d i e d the b a n d s t r u c t u r e a l o n g FKX at n o r m a l e m i s s i o n u s i n g p h o t o n energy f r o m h v = 31 e V to h ~ = 85 eV. The promlnant peaks denoted i to 3 in Fig i are dispersive when changing h~. These dispersion curves are consistent w i t h a d i r e c t t r a n s i t i o n m o d e l and w e r e interpreted using equation (4)' and (5)' , t h e y d e s c r i b e the v a l e n c e bands in the s e c o n d B r i l l o u i n zone Non dispersive weaker structures emphasize the h i g h d e n s i t y of s t a t e s at critical points X5 , Emi n and X 3 (see F i g . l ) and a r e p r o b a b l y associated to Umklapp processes. The positions of t h e c r i t i c a l points and the photon energy values of the turning points of dispersion corresponding to B r i l l o u i n zone center and boundary crossings lead to an experimental v a l u e for E o o f - 9 , 5 eV. A l l the d i s p e r s i v e structures have been then interpreted with a photothreshold of 5 , 4 5 e V and an i n n e r p o t e n t i a l of Vo = - 1 4 , 9 5 eV. The o b t a i n e d E(k) curves a r e g i v e n in Fig. 3.

-IO

Energy Fig. I

-5

above

8

VBM

eV

Photoemission spectra at normal emission with photon energy from 31 ev to 85 ev. Dispersive structures are denoted I to 3. Non dispersive structures are denoted with respect to the critical points X3, min X 5 .

The non-dispersive p e a k s p r o v i d e a good set of d a t a for the c r i t i c a l points of the B r i l l o u i n zone. Off normal emission By using photoemission at o f f - n o r m a l angles we followed the valence band a l o n g FKX, FL, FK u s i n g photon energy f r o m 31 e V to 44 eV. In a d d i t i o n to its opportunity to s t u d y several symmetry lines from a single surface the off-normal photoemission involves a smaller photon energy range than normal photoemission. Off normal emission spectra are obtained fixing the perpendicular component of t h e e l e c t o n k~at a zone center while varying the parallel

VoI: 52, No. 0

PHOTOEMISSION VALENCE BAND DISPERSIONS E(k) FOR GaP

I p

t

X

K

P

~ xxx >

5-

> 0 e~ 0

ID

C W

nP

x"

r

~

r

We have interpreted all t h e s t r u c t u r e s in the d a t a w i t h kj_ = 2 F K X +_ 0 , 0 0 7 2 ~/a in an extended zone scheme ( the experimental value f o r kj. is o b t a i n e d from equation (5) w i t h m e a s u r e d values of El, hV, a n d 8 f o r e v e r y structures in e a c h s p e c t r u m ) , they are represented by spots in Fig 2 (black or white respectively for intense and weak features). The strutures with measured k I o u t of t h i s r a n g e a r e r e p r e s e n t e d by squares and are usually weaker than previous structures. The dispersive structures are all represented by spots while the others a r e of t h r e e k i n d s : - three non-dlsperslve structures emphasize the h i g h d e n s i t i e s of states at -3eV, -4eV, and -6,8 eV below the t o p of the v a l e n c e - b a n d corresponding to c r i t i c a l p o i n t s XS, E m i n a n d X 3. a non-dlsperslve structure at - 2 e V w h e r e no h i g h d e n s i t y of state exists ( s e e t a b l e I). It h a s b e e n prooved by F. S e t t e et al (6) to b e a s u r f a c e state. - a dispersive structure between 0 et - l e V w h i c h e x h i b i t s the s y m m e t r y of t h e C L I O ) s u r f a c e Brillou~in z o n e a n d no dispersion at normal emission when changing photon energy. W e h a v e p r o v e d the d i s p e r s i v e structure to be a s u r f a c e state b y at l e a s t two ways • this state appears at normal emission at p h o t o n e n e r g i e s from 52 e V a n d s h o w s no d i s p e r s i o n up to h ~ = 8 5 eV it h a s b e e n s t u d i e d s y s t e m a t i c a l l y a t h ~ = 64 e V c h a n g i n g the emission angle from O ° to 1 8 ° a n d O ° to 24 ° respectively for 1"X'and F X directions of the surface Brillouin zone. This s t u d y l e a d s to E ( k ) curves similar to previous ones. The symmetry of t h e s e curves is the main argument to c o n c l u d e to a s u r f a c e state • However, this structure shows very little sensitivity to oxygen being reduced by o n l y 15 % of t h e i n t e n s i t y for a 13000 L exposure to o x y g e n . As t h e s t i c k i n g coetficient of ~ on G a P is so l i t t l e , we had problem to conclude to a s u r f a c e state for the -2 eV s t r u c t u r e , which does not appear at normal emission and can not also be characterizled by the symmetry of t h e E(k) curve because it shows no dispersion. Performing resonant photoemlssion from GaP (ii0) surface, S e t t e at a l h a s 46) shown strong resonance from initial state at -2 eV , this resonance disappears with 2 ~ of Silicon evaporation on the s u r f a c e . They notice that such a silicon coverage does not remove hulk GaP emission. This surface s t a t e at -2 eV is a l s o c o n s i s t e n t with the optical data (7), whlch shows a s t r o n g f e a t u r e at h ~ = 3,5 e V r e s u l t i n g from transition from initial state at -

Fig. 2

All detected structures from off normal emission process along TL, TKX, TX. The dispersive surface state between Oev and -lev is in a different figure in order to show the symetry in the surface Brillouin zone.

-

-2

=m, >

o

-

8

>" -I0 e- -42 UJ L

A

S

P

A

X

U,K

E

r

normal emission off normal emission

Fig. 3

Electronic band structure of GaP by normal and off - normal photoemission processes. Only the dispersive structures are reported,

component k~, which is o b t a i n e d by choosing accordingly h~ and emission angle, 8 . In p r i n c i p l e eq.(4) a n d (5) provide the relations between h~ a n d 8 for a n y p o i n t of t h e B r i l l o u i n zone. It is u s e f u l l to n o t i c e two points whlch make this choice easy. - the width of the experimental structures is a b o u t i eV which is equivalent to A k I 0 , 0 0 5 2 w/a - E i ( k ) a l o n g the s y m m e t r y lines is stationary w i t h r e s p e c t to k

39

40

PHOTOEMISSION VALENCE BAND DISPERSIONS E(k) FOR GaP

-2 eV to the first e m p t y s u r f a c e state in the gap. These two surface states a re in r e l a t i v e good a g r e e m e n t with Calandra et al c a l c u l a t i o n (8).

Vol. 52, ND. ]

and XPS, UPS and o p t i c a l measurements (11,12, 13). The uncertainty between all these r e s u l t s is less than 0,5 eV. CONCLUSION

DISCUSSION T h e c o m p l e t e band s t r u c t u r e is c o m p a r e d Fig. 4 to the pseudopotential c a l c u l a t i o n by C h e l i k o w s k y et al (9). The agreement is very good, particularly along FL , t h e main d i f f e r e n c e being a r o u n d ~ and a l o n g FX and F K X . The results a l o n g FKX a r e c o n s i s t e n t for normal and off-normal emission processes. The results at c r i t i c a l point are c o n s i s t e n t for m e a s u r e m e n t s a long d i f f e r e n t s y m m e t r y lines. In table I, we c o m p a r e the r e s u l t s at critical points with LCGO calculation (i0), p s e u d o p o t e n t l a l calculation (9)

The c o n s i s t e n c y of the r e s u l t s proves t h a t the d i r e c t transition m o d e l and the a p p r o x i m a t i o n of the final state as a nearly free electron state are adequate. The a g r e e m e n t b e t w e e n our results and self-consistent calculation s h o w s the capability of this technique to describe fondamental states from m e a s u r e m e n t s on e x c i t e d states. The identification of s u r f a c e state from the s y m m e t r y of the e x p e r i m e n t a l E(k) curves c o n f i r m s this t e c h n i q u e as a g o o d t o o l in the s t u d y of s u r f a c e electronic properties.

REFERENCES i°

For example G.V. H a n s s o n p S.A. F l o d s t r o m Phys. Rev. B 1572 (1978), P. Thiry, D. C h a n d e s r i s , J. L e c a n t e ~ C. G u i l l o t , R. P i n c h a u x , Y. P e t r o f f . P h y s . Rev. Lett. 43 (I) 82 (1979) 2. D. C h a n d e s r l s , J. L e e a n t e et Y. P e t r o f f Phys. Rev. B 27 2630 (1983) 3. T.C. Chiang, J.A. Knapp, M. Aono and D.E. E a s t m a n Phys. Rev. B 21 (8) 3513 (1980) 4. T.C. C h l a n g and D.E. E a s t m a n Phys. Rev. B 2 2 (6) 2940 (1980) 5. For a w h o l e d e s c r i p t i o n of the p r o c e s s see for example. B. F e n e u b a c h e r and R.F. W i l l i s J. Phys. C. Solid State Phys. 9 (1976) 169 6. F. Sette, P. P e r f e t t l , F. P a t e l l a , C. Q u a r e s i m a , C. C a p a n o , M. C a p o z l and A. S a v o v a Phys. Rev. B 28 (8) 4882 (1983). 7. P. C h l a r a d l a , G. C h l a r o t t l , P. C i c c a c c l , R. Memeo, S. N a n n a r o n e , P. S a s s a r o l l and S. Selcl Surf. Scl. 99 70 (1980). 8. F. M a n g h l , C.M. B e r t o n i , C. C a l a n d r a and E. M o l l n a r l P h y s . Rev. B 24 (I0) 6029 (1981) 9. J.R. C h e l l k o w s k y , D.J. C h a d l , M . L . C o h e n P h y s . Rev. B 8 2 7 8 6 ( 1 9 7 3 ) a n d Chellkowsky's thesis. I0. S. Wang, B.M. K l e i n Phys. Rev. B 24 3393 (1980) ii. L. L e y , R . A . P o l l a k , R . R . Mc P e e l y , S.P. K o w a l c z y k P h y s . Rev. B 9 600 (1974). 12. D.E. E a s t m a n , W.D. G r o b m a n , J.L. F r e e o u f and M. E r b r c a k Phys. Rev. B 9 3473

(1974). 13.

C. V a r e a de A l v a r e z , Rev. B 6 1412 (1972)

J.P.

Walter,

M.L.

Cohen,

J.

Stokes

and Y.R.

Shen

Phys.