348
11 Surfaces
Fig. 11.14 Schematic
wavefunction versus
coordinate for a bulk state
in the vicinity of the surface
(its position indicated by
the vertical dashed line), b
surface state and c surface
resonance state
(a)
(b)
(c)
Fig. 11.15 Surface band
structure of
Si(100)-(2 × 1), lines
denote a theoretical
quasi-particle calculation,
symbols represent
experimental data. The grey
areas indicate the projected
bulk band structure.
Adapted from [1079]
2.0
1.0
0
-1.0
Energy (eV)
J
M
J ‘
Si(100)-(2 1)
Surface wave vector
the bulk and the outside (Fig. 11.14b). A third type of states is a surface resonance which is oscillatory
in the bulk and has enhanced probability at the surface, of course also decaying towards the outside
(Fig. 11.14c); such states are surface related but energetically degenerate with states of the bulk band
structure.
Surface states for Si(100) in 2 × 1 reconstruction are shown in Fig. 11.15. The surface bands arise
from (filled and unfilled) π- and π
∗ -orbitals from the dangling bonds on the threefold-coordinated
surface atoms [1079]. A calculation for the ideal (unreconstructed) (100), (110) and (111) surfaces
of Si, Ge and GaAs can be found in [1080]. Further work on silicon surface states (clean and with
adsorbates) is compiled in [1081].
For a conventional insulating material (with gap) the states of conduction and valence band have
defined s- and p-type symmetry (cmp. Fig. 2.5) and the surface states can be populated with spin up
and down electrons as is schematically drawn in Fig. 11.16a. Such ‘normal’ surface states are thus not
spin-polarized. This has been shown, e.g., for the well-known surface states of Si(111)-(7 × 7) [1082]
in [1083].
In a so-called topological insulator [464], a band inversion is present (cf. Sect. 6.2.6). In HgTe-like
materials, s- and p-type bands are inverted at the point (cmp. Sect. 6.11). In layered (orthorhombic)
Bi 2 Se 3 -like tri-chalcogenide materials two p z -orbitals with opposite parity are inverted at the point.
Reasons for the band inversion are spin-orbit interaction but also scalar relativistic effects and lattice
distortions [1084]. The spin-orbit interaction is responsible for opening a gap; the associated surface
11 Surfaces
Fig. 11.14 Schematic
wavefunction versus
coordinate for a bulk state
in the vicinity of the surface
(its position indicated by
the vertical dashed line), b
surface state and c surface
resonance state
(a)
(b)
(c)
Fig. 11.15 Surface band
structure of
Si(100)-(2 × 1), lines
denote a theoretical
quasi-particle calculation,
symbols represent
experimental data. The grey
areas indicate the projected
bulk band structure.
Adapted from [1079]
2.0
1.0
0
-1.0
Energy (eV)
J
M
J ‘
Si(100)-(2 1)
Surface wave vector
the bulk and the outside (Fig. 11.14b). A third type of states is a surface resonance which is oscillatory
in the bulk and has enhanced probability at the surface, of course also decaying towards the outside
(Fig. 11.14c); such states are surface related but energetically degenerate with states of the bulk band
structure.
Surface states for Si(100) in 2 × 1 reconstruction are shown in Fig. 11.15. The surface bands arise
from (filled and unfilled) π- and π
∗ -orbitals from the dangling bonds on the threefold-coordinated
surface atoms [1079]. A calculation for the ideal (unreconstructed) (100), (110) and (111) surfaces
of Si, Ge and GaAs can be found in [1080]. Further work on silicon surface states (clean and with
adsorbates) is compiled in [1081].
For a conventional insulating material (with gap) the states of conduction and valence band have
defined s- and p-type symmetry (cmp. Fig. 2.5) and the surface states can be populated with spin up
and down electrons as is schematically drawn in Fig. 11.16a. Such ‘normal’ surface states are thus not
spin-polarized. This has been shown, e.g., for the well-known surface states of Si(111)-(7 × 7) [1082]
in [1083].
In a so-called topological insulator [464], a band inversion is present (cf. Sect. 6.2.6). In HgTe-like
materials, s- and p-type bands are inverted at the point (cmp. Sect. 6.11). In layered (orthorhombic)
Bi 2 Se 3 -like tri-chalcogenide materials two p z -orbitals with opposite parity are inverted at the point.
Reasons for the band inversion are spin-orbit interaction but also scalar relativistic effects and lattice
distortions [1084]. The spin-orbit interaction is responsible for opening a gap; the associated surface