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The electronic configuration of Si(111) (2 × 1) reconstructed surfaces
Volume 53A, number 3
PHYSICS LETTERS
16 June 1975
THE ELECTRONIC CONFIGURATION OF Si (111) (2 x 1) RECONSTRUCTED SURFACES* M. SCHLUTER*, James R. CHELIKOWSKY and Marvin L. COHEN Department of Physics, University of California, and Inorganic Materials Research Division, Lawrence Berkeley Laboratory, Berkeley, California 94720, USA Received 15 April 1975 Self-consistent pseudopotential calculations are presetned for Si(111) (2 X 1) reconstructed surfaces based on Haneman’s model. Infrared absorption and recent angular resolved photo-emission data are discussed in the light of these calculations.
We have calculated the electronic structure of a 12 layer fihn representing (2 X 1) reconstructed Si(lll) surfaces. The calculations are done by a recently developed self-consistent pseudopotential method [1] and complement earlier preliminary calculations performed on a 6 layer film. We have used a surface structural model based on Han~man’smodel [2] for the (2 X 1) reconstruction, which consists of altematingly raising and lowering rows of surface atoms. A further important concept of the model is to approximately preserve the bond lengths of all bonds by slight lateral shifts of the atoms in the second layer. Changes in the electronic structure after reconstruction are attributed to changes in bond angles rather than bond lengths. The two main results of the calculation are: (a) a splitting of the dangling bond surface band into two bands cornbined with a shift to lower energies and (b) a rise of the back-bond surface states to the top of valence bands where they overlap with the lower (occupied) dangling bond band. Fig. 1 shows the calculated density of states in the vicinity of the valence band edge. The lower peak labelled d0~~ is fully occupied, the upper peak (d1~) empty, creating a semiconducting surface. The question about the distribution of the dangling bond electrons in real space on a (2 X 1) reconstructed surface is explored by considering charge density plots. Thus in fig. 2 we present charge density contour plots for electrons occupying the lower peak labelled d0~t(left plot) and *
Supported in part by the National Science Foundation Grant DMR72-03206-A02.
*
Swiss National Science Foundation fellow,
I v,~bands
~
~ \
-
d00~
d~0
-
P
2
-
I
-
E
Iv 0
0.1
I 0.2
I 0.3
0.4
0.5
ENERGY (eV) Fig. 1. Calculated density of states for a 12 layer Si(111) film with (2 X 1) reconstructed surfaces. The energy zero is taken at the bulk valence band edge.
for electrons hypothetically excited into the unoccupied states labelled ~ (right plot). The effect of reconstruction is to transfer about one dangling bond electron from every lowered atom to its raised neighboring atom. This leaves the Si (2 X 1) surface ionic. Conversely, excited electrons are localized around the lowered atoms only. The infrared absorption [3] is therefore described by a charge transfer from raised to lowered atoms. However, the net charge transfer obtained in our calculation is presumably too large and would be decreased by correlation effects. These effects can be considerable for bands of 0.3 eV width, since they are not properly included in our calculation, the results are of more qualitative nature. It can be seen that the electronic charge which is localized around the raised atoms partially leaks Into the back bonds between the first, second and third layers. The origin for this is the lowering in energy of these dangling bond states and the rising of the back 217
Volume 53A, number 3
16 June 1975
PHYSICS LETTERS
a) Si (111) SURFACE, (2x1) RECONSTRUCTED STATES AT 0 eV (d 0~,)
b) Si (111) SURFACE, (2><1) RECONSTRUCTED~ STATES AT 0.35 eV )d1~)
Fig. 2. Charge density plots for states labelled d0~tand din in fig. 1. The plots are shown in a (110) plane intersecting the (111) surface at right angles.
bond states such that overlap occurs. This observation could explain the three-fold rotational pattern of photoelectrons originating from an energy interval between 0 and —1.3 eV observed by angular resolved photoemission [4]. Part of this work was supported by the U.S. Energy Research and Development Administration.
References ~iJ M.L. Cohen,
M. SchlUter, J.R. Chelikowsky and S.G. Louie, to be published; M. SchiUter, J.R. Chelikowsky, S.G. Louie and M.L. Cohen, to be published. [21 A. Taloni and D. Haneman, Surf. Sci. 10 (1968) 215. [3] G. Chiarotti, S. Nannarone, R. Pastore and P. Chiaradia, Phys. Rev. B4 (1971) 3398. [4] J.E. Rowe, M. Traum and N.y. Smith, Phys. Rev. Lett. 33 (1974) 1335.
218
PHYSICS LETTERS
16 June 1975
THE ELECTRONIC CONFIGURATION OF Si (111) (2 x 1) RECONSTRUCTED SURFACES* M. SCHLUTER*, James R. CHELIKOWSKY and Marvin L. COHEN Department of Physics, University of California, and Inorganic Materials Research Division, Lawrence Berkeley Laboratory, Berkeley, California 94720, USA Received 15 April 1975 Self-consistent pseudopotential calculations are presetned for Si(111) (2 X 1) reconstructed surfaces based on Haneman’s model. Infrared absorption and recent angular resolved photo-emission data are discussed in the light of these calculations.
We have calculated the electronic structure of a 12 layer fihn representing (2 X 1) reconstructed Si(lll) surfaces. The calculations are done by a recently developed self-consistent pseudopotential method [1] and complement earlier preliminary calculations performed on a 6 layer film. We have used a surface structural model based on Han~man’smodel [2] for the (2 X 1) reconstruction, which consists of altematingly raising and lowering rows of surface atoms. A further important concept of the model is to approximately preserve the bond lengths of all bonds by slight lateral shifts of the atoms in the second layer. Changes in the electronic structure after reconstruction are attributed to changes in bond angles rather than bond lengths. The two main results of the calculation are: (a) a splitting of the dangling bond surface band into two bands cornbined with a shift to lower energies and (b) a rise of the back-bond surface states to the top of valence bands where they overlap with the lower (occupied) dangling bond band. Fig. 1 shows the calculated density of states in the vicinity of the valence band edge. The lower peak labelled d0~~ is fully occupied, the upper peak (d1~) empty, creating a semiconducting surface. The question about the distribution of the dangling bond electrons in real space on a (2 X 1) reconstructed surface is explored by considering charge density plots. Thus in fig. 2 we present charge density contour plots for electrons occupying the lower peak labelled d0~t(left plot) and *
Supported in part by the National Science Foundation Grant DMR72-03206-A02.
*
Swiss National Science Foundation fellow,
I v,~bands
~
~ \
-
d00~
d~0
-
P
2
-
I
-
E
Iv 0
0.1
I 0.2
I 0.3
0.4
0.5
ENERGY (eV) Fig. 1. Calculated density of states for a 12 layer Si(111) film with (2 X 1) reconstructed surfaces. The energy zero is taken at the bulk valence band edge.
for electrons hypothetically excited into the unoccupied states labelled ~ (right plot). The effect of reconstruction is to transfer about one dangling bond electron from every lowered atom to its raised neighboring atom. This leaves the Si (2 X 1) surface ionic. Conversely, excited electrons are localized around the lowered atoms only. The infrared absorption [3] is therefore described by a charge transfer from raised to lowered atoms. However, the net charge transfer obtained in our calculation is presumably too large and would be decreased by correlation effects. These effects can be considerable for bands of 0.3 eV width, since they are not properly included in our calculation, the results are of more qualitative nature. It can be seen that the electronic charge which is localized around the raised atoms partially leaks Into the back bonds between the first, second and third layers. The origin for this is the lowering in energy of these dangling bond states and the rising of the back 217
Volume 53A, number 3
16 June 1975
PHYSICS LETTERS
a) Si (111) SURFACE, (2x1) RECONSTRUCTED STATES AT 0 eV (d 0~,)
b) Si (111) SURFACE, (2><1) RECONSTRUCTED~ STATES AT 0.35 eV )d1~)
Fig. 2. Charge density plots for states labelled d0~tand din in fig. 1. The plots are shown in a (110) plane intersecting the (111) surface at right angles.
bond states such that overlap occurs. This observation could explain the three-fold rotational pattern of photoelectrons originating from an energy interval between 0 and —1.3 eV observed by angular resolved photoemission [4]. Part of this work was supported by the U.S. Energy Research and Development Administration.
References ~iJ M.L. Cohen,
M. SchlUter, J.R. Chelikowsky and S.G. Louie, to be published; M. SchiUter, J.R. Chelikowsky, S.G. Louie and M.L. Cohen, to be published. [21 A. Taloni and D. Haneman, Surf. Sci. 10 (1968) 215. [3] G. Chiarotti, S. Nannarone, R. Pastore and P. Chiaradia, Phys. Rev. B4 (1971) 3398. [4] J.E. Rowe, M. Traum and N.y. Smith, Phys. Rev. Lett. 33 (1974) 1335.
218