- Email: [email protected]
On surface states of the LaB6 (001) face
Surface Science 0 North-Holland
100 (1980) Publishing
L454-L456 Company
SURFACE SCIENCE LETTERS ON SURFACE STATES OF THE LaB6 (001) FACE
M. TOMASEK and S. PICK J. Heyrovskj Institute of Physical Chemistry and Electrochemistry, Sciences, Mchova 7, 12138 Prague 2, Czechoslovakia
Received
22 April 1980; accepted
for publication
Czechoslovak Academy
of
14 July 1980
Simple qualitative reasoning is used to discuss the origin and the nature the (001) face of LaB6, found recently by Aono et al.
of surface
states on
Recently, Aono et al. performed very interesting angle-resolved UV photoemission experiments [ 1,2], which led to the conclusion that on the (001) surface of LaBc, there exist two pronounced peaks which can be ascribed to surface states, one just below EF [l] and the other (probably consisting of two features [3]) at a distance z2 eV below it. These states are of resonance character and at least one of them (e2 eV below EF) has been interpreted [2,3] as the expression of boronboron bonds broken at the surface (dangling bonds, Shockley surface states). The analysis of projections of bulk energy bands onto the (001) surface Brillouin zone of LaB, has shown [4] that hybridization gaps corresponding to boron-boron bonds lie at much lower energies (more than 4 eV below EF) and that (resonance) gaps in the energy region of interest (called U gaps in ref. [4]) are non-hybridizational gaps typical of heteroatomic lattices [S]. The latter divide boron sp-bands from d-bands of lanthanum, leading to a region of low density in the electronic density of states [6] which points clearly to the existence of a certain ionic component of the La-B bond [2,6]. The energy band structure of ref. [6] has recently been confirmed experimentally [ 11. As it is well known (see, e.g., p. 256 of ref. [5]), the above type of non-hybridizational gaps can contain a special kind of surface states called heteroatomic (HA) states. These states appear under the following conditions: Suppose in agreeement with experiment [7 $1, that La atoms form the surface. If the perturbation of these atoms caused by the surface formation is such that it brings their potentials nearer to those of the second layer B atoms, HA surface states are split from the bottom of the La band irrespective of how small this perturbation is. (Analogically, if the surface was formed by B atoms, HA states should appear above the bottom of the gap being split from the boron band.) Furthermore, the above gap can contain ah usual Tamm subsurface states [5] steming from B atoms, guaranteed that the perL454
M. TomdSek, S. Pick /Surface
states of LaB6 (001) face
IA.55
turbation in the second layer is still strong enough to invoke such states. Let us see whether the perturbations postulated above are physically reasonable and why they act in the supposed directions. The answer is based on the following reasoning (cf. ref. [9]). During the crystal surface formation, the local density of states n&5)
njj(E) = -77-l Im Gii(E) , on surface atoms (SDS) (where Gij is the matrix element of the respective Green function [lo] and the index stands for the position and type of the localized orbital) undergoes important changes, brought about by the fact that every surface atom has lost a certain number of neighbours as compared with the bulk. This leads to the effective narrowing of the width w (2nd moment of energy) Wj =
s
dE(E
-
j#i
hii)* nij(E) = C Ih,l* ,
of the respective energy bands near the surface and to the concentration sity more towards the SDS weighted average hii (1st moment of energy)
of the den-
Here, hij is the matrix element of the hamiltonian in the localized function basis utilized. For the boron energy band, the weighted average is situated below EF, whereas for the La band, it lies above EF. As a result, the electronic charge on La atoms decreases and that on B atoms (supposing non-negligible interactions between boron cages) increases. Naturally, these changes are artificial and have to be corrected by respecting charge self-consistency. The latter works in the opposite direction to bring back the situation with approximately the same charges on La and B atoms as in the bulk. One can understand this trend by realizing that the artificial changes in surface atomic charges have to be removed by screening properties of mobile (conducting) electrons. The situation resembles. that well known with metal surfaces, where local charge neutrality condition is used to guarantee surface charge self-consistency [9]. To be more explicative, at present exact experimental or theoretical information on the magnitudes of the resulting charges seems to be missing. Then, naturally, the question arises how to prescribe correctly those charges, at which the self-consistent process actually stops. With metals, the prescription requires the system to be locally electroneutral. In the bulk of conducting systems exhibiting partial ionicity, a balance between the latter and the screening effects has been achieved, leading to the effective bulk atomic charges. The artificial increase of ionicity at the surface, which would arise due to the surface formation, should then be screened and the situation should return back close to that in the bulk. This picture generalizes slightly Friedel’s ideas well known from the theory of metals [ll]. Since the Fermi energy is fixed and the same for both the bulk and the surface, the prescribed charge on the La surface atom can be achieved by enlarging the
L456
I% Tomi~ek, S. Pick / Sur.face states of LaB, (001) face
occupied (below EF) part of the local density of states of this atom at the expense of unoccupied states. This leads to the flow of charge back to the La atom, while for B atoms of the second Layer an opposite effect occurs. These flows correspond to such changes in the surface potential, as postulated above for the appearance of both the HA surface and the Tamm subsurface states. Namely, for states with energies near EF, the electrons feel the surface potential more attractive while on La atoms and more repulsive while on B atoms. The changes in the potential (perturbations) can be large for boron atoms due to their low density of states near EF [6] leading to small flow of electrons. Our reasoning concerning HA surface states gives the same results as the simple Madelung potential approach ]12] (which assumes exactly the same charges on surface and bulk atoms, but uses purely electrostatic arguments). However, the latter is applicable only to non-metalic systems. Summarizing, it appears that the surface states just below Er: are HA states localized on La surface atoms, whereas those at a2 eV below Et: are Tamm states from boron subsurface atoms. The present Letter improves and complements the interpretation of ref. f4] to conform with the new experiments ]1,2].
References [ l] M. Aono, T.-C. Chiang, J.A. Knapp, T. Tanaka and D.E. Eastman, Solid State Commun. 32 (1979) 271. [2] R. Nishitani, S. Kawai, H. Iwasaki, S. Nakamura, M. Aono and T. Tanaka, Surface Sci. 92 (1980) 191. [3] M. Aono,T. Tanaka, E. Bannai, S. Oshima and S. Kawai, Phys. Rev. B16 (1977) 3489. [4] M. TomfZek and S. Pick, Czech. 3. Phys. B29 (1979) 557. [S] M. Tomis’ek and J. Koutecky, Intern. 1. Qu~tum Chem. 3 (1969) 249. [6] A. Hasegawa and A. Yanase, J. Phys. F7 (1977) 1245. (71 M. Aono, C. Oshima,T. Tanaka, E. Bannai and S. Kawai, .I. Appl. Phys. 49 (1978) 2761. [S] B. Goldstein and D. Szostak, Surface Sci. 74 (1978) 461. [9] M. Tomas’ek and S. Pjck, Czech. .I. Phys. B29 (1979) 933. [lo] M. Tomis’ek and L. Sroubkovi, in: Proc. 7th Intern. Vacuum Congr. and 3rd Intern. Conf. on Solid Surfaces, Vienna, 1977 fBerger, Vienna, 1977) p. 521. Ill) See, e.g., J. Friedel, in: Theory of Magnetism in Transition Metals, Proc. Intern. School on Physics “Enrico Fermi”, 1966, Ed. W. Marshall (Academic Press, New York, 1977) especially ch. II; D.J. Thouless, The Quantum Mechanics of Many-Body Systems, 2nd. ed. (Academic Press, New York, 1972) especially ch. 6. [12] S.G. Davison and J.D. Levine, in: Solid State Physics Vol. 25, Eds. H. Ehrerueich, I‘. Seitz and D. Turnbull (Academic Press, New York, 1970) p. 2, especiaIly ch. 10, p. 84.
100 (1980) Publishing
L454-L456 Company
SURFACE SCIENCE LETTERS ON SURFACE STATES OF THE LaB6 (001) FACE
M. TOMASEK and S. PICK J. Heyrovskj Institute of Physical Chemistry and Electrochemistry, Sciences, Mchova 7, 12138 Prague 2, Czechoslovakia
Received
22 April 1980; accepted
for publication
Czechoslovak Academy
of
14 July 1980
Simple qualitative reasoning is used to discuss the origin and the nature the (001) face of LaB6, found recently by Aono et al.
of surface
states on
Recently, Aono et al. performed very interesting angle-resolved UV photoemission experiments [ 1,2], which led to the conclusion that on the (001) surface of LaBc, there exist two pronounced peaks which can be ascribed to surface states, one just below EF [l] and the other (probably consisting of two features [3]) at a distance z2 eV below it. These states are of resonance character and at least one of them (e2 eV below EF) has been interpreted [2,3] as the expression of boronboron bonds broken at the surface (dangling bonds, Shockley surface states). The analysis of projections of bulk energy bands onto the (001) surface Brillouin zone of LaB, has shown [4] that hybridization gaps corresponding to boron-boron bonds lie at much lower energies (more than 4 eV below EF) and that (resonance) gaps in the energy region of interest (called U gaps in ref. [4]) are non-hybridizational gaps typical of heteroatomic lattices [S]. The latter divide boron sp-bands from d-bands of lanthanum, leading to a region of low density in the electronic density of states [6] which points clearly to the existence of a certain ionic component of the La-B bond [2,6]. The energy band structure of ref. [6] has recently been confirmed experimentally [ 11. As it is well known (see, e.g., p. 256 of ref. [5]), the above type of non-hybridizational gaps can contain a special kind of surface states called heteroatomic (HA) states. These states appear under the following conditions: Suppose in agreeement with experiment [7 $1, that La atoms form the surface. If the perturbation of these atoms caused by the surface formation is such that it brings their potentials nearer to those of the second layer B atoms, HA surface states are split from the bottom of the La band irrespective of how small this perturbation is. (Analogically, if the surface was formed by B atoms, HA states should appear above the bottom of the gap being split from the boron band.) Furthermore, the above gap can contain ah usual Tamm subsurface states [5] steming from B atoms, guaranteed that the perL454
M. TomdSek, S. Pick /Surface
states of LaB6 (001) face
IA.55
turbation in the second layer is still strong enough to invoke such states. Let us see whether the perturbations postulated above are physically reasonable and why they act in the supposed directions. The answer is based on the following reasoning (cf. ref. [9]). During the crystal surface formation, the local density of states n&5)
njj(E) = -77-l Im Gii(E) , on surface atoms (SDS) (where Gij is the matrix element of the respective Green function [lo] and the index stands for the position and type of the localized orbital) undergoes important changes, brought about by the fact that every surface atom has lost a certain number of neighbours as compared with the bulk. This leads to the effective narrowing of the width w (2nd moment of energy) Wj =
s
dE(E
-
j#i
hii)* nij(E) = C Ih,l* ,
of the respective energy bands near the surface and to the concentration sity more towards the SDS weighted average hii (1st moment of energy)
of the den-
Here, hij is the matrix element of the hamiltonian in the localized function basis utilized. For the boron energy band, the weighted average is situated below EF, whereas for the La band, it lies above EF. As a result, the electronic charge on La atoms decreases and that on B atoms (supposing non-negligible interactions between boron cages) increases. Naturally, these changes are artificial and have to be corrected by respecting charge self-consistency. The latter works in the opposite direction to bring back the situation with approximately the same charges on La and B atoms as in the bulk. One can understand this trend by realizing that the artificial changes in surface atomic charges have to be removed by screening properties of mobile (conducting) electrons. The situation resembles. that well known with metal surfaces, where local charge neutrality condition is used to guarantee surface charge self-consistency [9]. To be more explicative, at present exact experimental or theoretical information on the magnitudes of the resulting charges seems to be missing. Then, naturally, the question arises how to prescribe correctly those charges, at which the self-consistent process actually stops. With metals, the prescription requires the system to be locally electroneutral. In the bulk of conducting systems exhibiting partial ionicity, a balance between the latter and the screening effects has been achieved, leading to the effective bulk atomic charges. The artificial increase of ionicity at the surface, which would arise due to the surface formation, should then be screened and the situation should return back close to that in the bulk. This picture generalizes slightly Friedel’s ideas well known from the theory of metals [ll]. Since the Fermi energy is fixed and the same for both the bulk and the surface, the prescribed charge on the La surface atom can be achieved by enlarging the
L456
I% Tomi~ek, S. Pick / Sur.face states of LaB, (001) face
occupied (below EF) part of the local density of states of this atom at the expense of unoccupied states. This leads to the flow of charge back to the La atom, while for B atoms of the second Layer an opposite effect occurs. These flows correspond to such changes in the surface potential, as postulated above for the appearance of both the HA surface and the Tamm subsurface states. Namely, for states with energies near EF, the electrons feel the surface potential more attractive while on La atoms and more repulsive while on B atoms. The changes in the potential (perturbations) can be large for boron atoms due to their low density of states near EF [6] leading to small flow of electrons. Our reasoning concerning HA surface states gives the same results as the simple Madelung potential approach ]12] (which assumes exactly the same charges on surface and bulk atoms, but uses purely electrostatic arguments). However, the latter is applicable only to non-metalic systems. Summarizing, it appears that the surface states just below Er: are HA states localized on La surface atoms, whereas those at a2 eV below Et: are Tamm states from boron subsurface atoms. The present Letter improves and complements the interpretation of ref. f4] to conform with the new experiments ]1,2].
References [ l] M. Aono, T.-C. Chiang, J.A. Knapp, T. Tanaka and D.E. Eastman, Solid State Commun. 32 (1979) 271. [2] R. Nishitani, S. Kawai, H. Iwasaki, S. Nakamura, M. Aono and T. Tanaka, Surface Sci. 92 (1980) 191. [3] M. Aono,T. Tanaka, E. Bannai, S. Oshima and S. Kawai, Phys. Rev. B16 (1977) 3489. [4] M. TomfZek and S. Pick, Czech. 3. Phys. B29 (1979) 557. [S] M. Tomis’ek and J. Koutecky, Intern. 1. Qu~tum Chem. 3 (1969) 249. [6] A. Hasegawa and A. Yanase, J. Phys. F7 (1977) 1245. (71 M. Aono, C. Oshima,T. Tanaka, E. Bannai and S. Kawai, .I. Appl. Phys. 49 (1978) 2761. [S] B. Goldstein and D. Szostak, Surface Sci. 74 (1978) 461. [9] M. Tomas’ek and S. Pjck, Czech. .I. Phys. B29 (1979) 933. [lo] M. Tomis’ek and L. Sroubkovi, in: Proc. 7th Intern. Vacuum Congr. and 3rd Intern. Conf. on Solid Surfaces, Vienna, 1977 fBerger, Vienna, 1977) p. 521. Ill) See, e.g., J. Friedel, in: Theory of Magnetism in Transition Metals, Proc. Intern. School on Physics “Enrico Fermi”, 1966, Ed. W. Marshall (Academic Press, New York, 1977) especially ch. II; D.J. Thouless, The Quantum Mechanics of Many-Body Systems, 2nd. ed. (Academic Press, New York, 1972) especially ch. 6. [12] S.G. Davison and J.D. Levine, in: Solid State Physics Vol. 25, Eds. H. Ehrerueich, I‘. Seitz and D. Turnbull (Academic Press, New York, 1970) p. 2, especiaIly ch. 10, p. 84.