Transcript Surface States of Si(111) Surface

Surface States of Si(111) Surface
Vildana Hodzic
ENEE 697 Project
Spring 1999
Surface States of Si(111) Surface
Introduction
Si(111) surface structure
- Ideal versus real surfaces
- Real surfaces: 7x7 reconstruction of Si(111)7x7
surface
- Dimer-Adatom-Stacking-Fault Model
- Surface density of states and band banding
- Fermi level pinning at Si(111)7x7 surfaces
- Theoretical work on surface states of Si(111)7x7
Preparation of clean Si(111)7x7 surfaces
Theory of observation and experimental data
Introduction
The reliability and stability of all semiconductor devices are closely related to their surface conditions.
Therefore, an understanding of the surface physics is of great importance to device operation.
Investigating surface electronic properties is also very important since with the downscaling of
electronic devices the surface effects become larger as their scale becomes smaller.
The surface of a crystalline solid in vacuum is generally defined as a few (approximately three)
outermost atomic layers of the solid that differ significantly from the bulk. It may be atomically clean
or it may have foreign atoms deposited on it or incorporated on it. A complete characterization of a
solid surface requires knowledge of not only what atoms are present but also where they are. Just as in
the bulk, it is not the atomic coordinates as such that are of much direct interest. We are interested in
electronic and magnetic properties of the surface and it is the geometrical arrangement of the surface
atoms that largely determines the surface charge and spin density.
One can start by thinking of a clean surface in terms of a zero-order approximation, the so-called "ideal
surface". That is an abstraction created by passing a plane through an infinite crystal and separating the
two parts to infinity without perturbing positions of the atoms and the electron density. "Ideal surfaces"
as such do not exist in nature. All surfaces are energetically unfavorable in a sense that they have a
positive free energy of formation. A highly unstable or metastable state occurs when covalent bonds
are broken by cleavage. The surface atoms undergo relaxation and reconstruction in order to reduce the
surface free energy. Both relaxation and reconstruction may occur with clean surfaces in ultrahigh
vacuum, but adsorption of species onto the surface may enhance, alter or even reverse the process.
The differences between the real structure of the clean surface and the ideal structure may be
imperceptibly small (e.g. a very slight surface relaxation) or much more marked and involving a
change in the surface periodicity in one or more of the main symmetry directions (surface
reconstruction).
Ideal versus real surfaces
The ideal surfaces of the diamond lattice each expose hybrid orbitals that “dangle” into the
vacuum. Every such orbital is half-occupied if we imagine that the two bonding electrons/orbital
of the bulk are shared between the two half-crystals formed by cleavage. The (111) surface
contains one dangling hybrid per surface unit cell. From Fig.1a ) we see that the areal density of
dangling hybrids is lowest for the (111) surface. The surface tension of the (111) face is lowest.
This is the natural cleavage plane for Si.
Fig.1 Crystallography of a homopolar semiconductor: a) edge view that illustrates the ideal
termination of the three low-index faces [1]; b) top view of (111) face-decreasing atom size
indicates increasing distance from the surface. Dashes outline the surface unit mesh;
c) surface unit cell and sp3-hybrid lobes which would exist on (111) planes in the perfect bulk
material [2].
1. Harrison,W.A., Electronic Structure and the Properties of Solids, San Francisco: W.H. Freeman, (1980).
2. Ivanov,I., Mazur,A. and Pollmann,J., ”The ideal (111), (110) and (100) surfaces of Si, Ge and GaAs;
a comparison of their structure”, Surf.Sci. 92, 365 (1980).
Real surfaces: 7x7 reconstruction of Si(111) surface
Clean (111)-oriented Si surfaces prepared by
cleavage and subsequent heating to at least
650K in ultra-high vacuum reconstruct into the
famous Si(111)7x7 surface structure.Studies of
the surface crystallography by LEED back in
1959 revealed that this surface exhibits large
surface mesh [3].
Fig.2 Low-energy electron diffraction (LEED)
pattern of the Si(111)7x7 reconstruction [3].
The first comprehensive structure analysis of
the Si(111)7x7 reconstruction was performed
by evaluating intensity distribution of the
spots in the TED patterns [4]. This resulted
in the Dimer-Adatom-Stacking-Fault model.
TED typically uses 100 keV electrons so that
the single-scattering approximation can be
assumed.
Fig.3 Transmission electron diffraction (TED)
pattern of the Si(111)7x7 [4].
3. Schlier,R.E. and Fransworth,H.E.,J.Chem.Phys. 30, 917 (1959).
4. Takayangi,K.,Tanishiro,Y.,Takahashi,S. and Takahashi,M., ”Structure analysis of Si(111)-7x7 reconstructed
surface by transmission electron diffraction”, Surf. Sci. 164, 367 (1985).
Dimer - Adatom - Stacking - Fault Model
DAS model of the Si(111)7x7 reconstruction is
shown schematically in Fig.4 [4]. The nonreconstructed (111) cell corresponding to the 7x7
unit cell contains 49 atoms which are all in the
surface plane.In the DAS model the energy
associated with the dangling bonds is decreased
by reducing their number from 49 to 19. The top
layer contains 12 atoms (the so called adatoms)
while the layer below consists of 42 atoms. Due
to their position, all adatoms are not
electronically equivalent.Because of a stacking
fault in the unit cell, the two triangular halves are
not equivalent and are referred to as faulted and
unfaulted halves.
Furthermore, one notices that the reconstruction
is accompanied by very large angular distortions.
The dangling bonds saturated by the adatoms,
and the dimer bonds are such examples. These
distortions extend in depth to the third layer
below the surface.
Fig.4. Atom arrangement on Si(111)7x7 surfaces
according to the dimer-adatom-stacking-fault (DAS)
model [4].
A major breakthrough in surface science occurred
after the invention of the Scanning Tunneling
Microscope (STM) in 1982 by Binnig et al. [5],[6].
The first atomically resolved STM imaging of
Si(111)7x7 surface was achieved a year later [7].
Atomically resolved Atomic Force Microscope
(AFM) imaging of Si(111)7x7 surface was the next
powerful tool used for studying this surface [9].
Fig. 5 Topographic image of Si(111)7x7 surface as
recorded using Scanning Tunneling Microscope
(STM) with a bias voltage of + 2 V [8].
Fig. 6 A 3D image of ac-mode Atomic Force
Microscope (AFM) data of the Si(111)7x7
surface [9].
5. Binnig,G., Rohrer,H., Gerber,Ch. And Weibel,E., Physica 107 A&B, 1335 (1982).
6. Binnig,G., Rohrer,H., Gerber,Ch. And Weibel,E., Appl. Phys. Lett. 40, 178 (1982)
7. Binnig,G., Rohrer,H., Gerber,Ch. And Weibel,E.,”7x7 Reconstruction on Si(111) Resolved in Real Space”,
Phys. Rev. Lett. 50, 120 (1983).
8. Wiesendanger,R., Tarrach,G.,Scandella,L. and Gunthererodt,H.-J., Ultramicroscopy 32, 291 (1990).
9. Erlandsson,R. and Olsson,L., Appl. Phys. A 66, S879 (1998).
Surface density of states and band bending
a)
b)
c)
d)
Fig. 7 Difference STM images of occupied surface states on
a Si(111)7x7 surface:a) topographic image;b) adatom states
at -0.35eV;c)dangling bond states at -0.8eV;d)back bond
states at -1.7eV [15].
Electronic properties of Si(111)7x7 surface have been
analyzed using different techniques: photoemission
[10], [11]; electron energy-loss spectroscopies [12],[13];
scanning tunneling microscopy [14],[15].
Angle-resolved photoemission studies have consistently
reported the existence of three surface-state bands. The
two bands closest to the Fermi level EF (S1 and S2) are
interpreted as dangling-bond and the third is associated
with back-bonds. The S1 and S2 bands show only a weak
dispersion [10]. This has been verified in STM studies
[15]. The S1 state, at -0.35eV (relative to EF), is located
on adatoms and S2, at -0.8eV, is located to the rest atom
positions and at the corner-hole atoms. Photoemission
shows significant emission at EF implying that
Si(111)7x7 surface is metallic.
Low-temperature (55K) photoemission study [11]
shows a previously undetected surface-state structure
(S’1) at ~0.5eV below EF. It is assigned to danglingbond states located mainly at the adatoms near the
corner holes.
Fig.8 Angle-resolved spectra
obtained from the Si(111)7x7
surface at three different sample
temperatures.The new surface
state S’1 appears in the lowtemperature spectra at ~0.5eV
below EF [11].
Fig. 9 Photoemission
spectra
obtained for various emission
angles along -M direction of
the 1x1 surface Brillouin zone
(SBZ) [11].
Fig. 10 Dispersion of the S1 ,S’1
and S2 surface states along the
-K and -M symmetry lines of
the 1x1 SBZ [11].
10. Martensson,P.,Ni,W.-X.,Hansson,G.V.,Nicholls,J.M. and Riehl,B., Phys.Rev B 36, 5974 (1987).
11. Uhrberg,R.I.G.,Kaurila,T..Chao,Y.-C.,”Low-temperature photoemission study of the surface electronic
structure of Si(111)7x7”,Phys.Rev.B 58, R1731 (1998)
12. Demuth,J.E.,Persson,B.N.J. and Schell-Sorokin,A.J., Phys.Rev.Lett. 51, 2214 (1983).
13. Demuth,J.E.,Persson,B.N.J. and Schell-Sorokin,A.J., Phys.Rev. B 30, 5968 (1984).
14. Wolkow,R. and Avouris,Ph., Phys.Rev.Lett. 60, 1049 (1988).
15. Hamers,R.J.,Tromp,R.M. and Demuth,J.E., Surf. Sci. 181,346 (1987).
Fig. 11 a) Dispersion of surface states on Si(111)7x7 surfaces. S1 to S4 data for occupied states
from[10] and U1 data for empty states from [16].Shaded areas indicate surface-projected bulk
valance bands; b) Local density of states of restatoms (R), at adatoms near to the corner holes
(Ach) and in the center of the unit mesh (Ac) as well as at corner-hole atoms (C) of the
Si(111)7x7 DAS structure [17].
16. Nicholls,J.M. and Reihl,B., Phys. Rev. B 36, 8071 (1987).
17. Brommer,K.D., Galvan,M., Dal Pino,A. and Joannopoulos,J.D., Surf. Sci. 314, 57 (1994).
Theoretical work on surface states of Si(111)7x7
Theoretical work on Si(111)7x7 surface mainly deals with the details of its reconstruction
geometry and not nearly as much with detailed calculation of the surface band structure. A
detailed analysis of this surface electronic structure is presented in [19]. It is based on the
local density approximation (LDA) [18]. The occupancies of different dangling-bonds
associated with rest atoms,the corner-hole atom, and the adatoms are analyzed. Their
results show that the adatom-dangling bonds control the electron DOS at the Fermi level.
Based on the main results obtained in the LDA calculation a two-dimensional Hamiltonian
is introduced to describe the correlation properties of the electrons localized in the surface
adatom dangling bonds. The results show that the Si(111)7x7 surface has a metallic
character.
A self-consistent method of calculating the electronic structure of crystalline surfaces is
reported in[20]. It has not been tested on the Si(111)7x7 surface yet.
18. Demkov,A.A.,Ortega,J.,Sankey,O.F. and Grumbach,M.P., Phys.Rev. B 52, 1618 (1995).
19. Ortega,J.,Flores,F. and Yeyati,A.L.,”Electron correlation effects in the Si(111)7x7 surface”,
Phys.Rev. B 58, 4584 (1998).
20. Hummel,W. and Bross,H.,”Determining the electronic properties of semi-infinite crystals”,
Phys. Rev. B 58, 1620 (1998).
Fermi level pinning at Si(111)7x7 surfaces
The room-temperature value of the work function of
Si(111)7x7 surfaces is ~4.6eV irrespective of the bulk
doping [21],[22]. The ionization energy is measured to
be 5.3eV [22],[23]. Therefore the surface position of the
Fermi level is at 0.7eV above the valence-band
maximum irrespective of whether the samples are
doped p- or n-type. It is pinned at the surface to within
+or- 20meV (the accuracy of the experiment).
Fig.12 Work function of Si(111)7x7 surfaces as a
function of temperature for samples doped
p-type with Na=4x1013cm-3 and n-type with
Nd=1.5x1016cm-3 [21].
From the given acceptor and donor densities of the
samples in Fig.12, the bulk positions of the Fermi level
are 0.3eV and 0.88eV,respectively, above the valenceband maximum.The identical position of the Fermi
level above the valence band top at both surfaces means
that the bands are bent downward by 0.4eV and upward
by 0.18eV at the surfaces of the sample doped p- and ntype,respectively [22].
The experimental data shown in Fig.12 also shows the
work function of both samples to be rather insensitive
to changes in temperature.
21. Bachmann,R.,Phys.Kondens.Materie 8, 31 (1968).
22. Monch,W.,Semiconductor Surfaces and Interfaces,Springner,1995.
23. Guichar,G.M., Sebenne,C., Garry,G. and Balkanski,M., Le Vide 30, 97 (1975)
Preparation of Clean Si(111)7x7 Surfaces
A n accurate characterization of a surface requires work in ultra high vacuum (UHV).
Since roughly one monolayer per second of the ambient gaseous species impinges on a
surface at a pressure of 10-6 Torr, it is necessary to work at least in the 10-10 Torr range in
order to have sufficient time (~ two hours) to perform an experiment without getting the
surface contaminated.
There are several ways of preparing atomically clean Si(111)7x7 surface :
- Crystal cleavage and subsequent heating to at least 650 K in ultra high vacuum.
- Thermal decomposition of oxide layers on Si substrates.
- Etching of silicon in aqueous HF acid followed by desorbing of hydrogen passivation
layer approximately 850 C.
Theory of observation and experimental data
Progress in surface science has been and still is very
closely correlated with the development of experimental
tools and techniques which are suited for studies of
clean and intentionally modified surfaces.
Some of the most important tools used in studies of
Si(111)7x7 surface have already been mentioned. The
development of the STM has triggered the invention of a
whole family of scanning probe microscopies (SPM).
The information gained by each of these new tools can
be regarded as complementary.
In Fig. 13 AFM image of Si(111)7x7 surface is
compared to STM images of this surface [9].The grey
scales in the images correspond to a height difference of
1 Å. The STM images were recorded with tip voltages
of -2 V and +2.2 V, respectively,and a constant current
of 0.1 nA. The AFM images has been low-pass filtered
using a 3x3 convolution filter while the STM images
show unfiltered data. The cross section through the four
inequivalent adatoms show that the center adatoms
appear 0.13 Å higher than the corner adatoms. The 7x7
unit cell is outlined in the filled-state STM image. The
faulted and unfaulted halves correspond to the left an
right side, respectively.
Fig. 13 A comparison between a) an AFM image and
b) empty- and c) filled-state STM images of
Si(111)7x7 surface [9].