For information on some of the terminology I have used here, please
be certain to read my paper RHEED Studies of the Si(111) 7x7 Surface
which follows below. The audience of this paper is the scientific
undergraduate student with no prior knowlege of surface science techniques.
Currently I am working on iron (Fe) / silicon (Si) multilayers grown
on SiO2 (glass) and on MgO (substrates).
Specifically, I am using molecular beam epitaxy (MBE) in a reflection high
energy diffraction (RHEED) chamber operating in the 10-10
Torr regime (ultra high vacuum). Dr. John Carlisle and I are investigating
the properties of these multilayers as a function of Si layer thickness,
substrate, and temperature. We will spend the first full week of
August 1998 at the Advanced
Light Source, beamline 8.0, performing fluorescent spectroscopy on
these multilayers. Specifically of interest to us is the composition
of the Si spacer layers. We would like to be able to control the
diffusion of the Si into the Fe layers by variation of the parameters stated
above. Previous experiments* by Dr. Carlisle and others have been
performed on samples that were created by ion beam sputtering techniques,
instead of MBE, which promises to allow much better control of the Si/Fe
During the spring semester I worked breifly on Fe thin films on Si (111)
7x7 reconstruction. A paper on that subject follows. It is
out intention to study Fe thin films on the Si (100) surface as well, as
*Carlisle, J. A., Chaiken, A., Michel, R. P., and Terminello,
L. J., Phys. Rev. B, Vol. 53, No. 14 (R8824), 1996.
and Chaiken, A., Michel, R.P., and Wall, M. A.,
Phys. Rev. B, Vol. 53, No. 9 (5518), 1996.
RHEED Studies of the Si(111) 7x7 Surface
Raina N. Smith
PHY 450, Senior Physics Lab
Virginia Commonwealth University
May 5, 1998
Abstract: The silicon (111) 7x7 reconstructed surface has been
extensively studied, and it’s characteristics allow for calibration and
verification of data. Reflection High Energy Electron Diffraction
(RHEED) is a useful tool for examining the surface of smooth samples.
The Silicon (111) 7x7 Surface
The structure of a crystal at the surface is not, as one might think, merely
a truncation of its bulk structure, but exhibits phenomenon such as reconstruction.
Reconstruction occurs when the 2-D lattice for the surface differs from
that of the bulk1, as is the case with
silicon (111). Atoms left dangling after the crystal is cleaved move
closer to each other, sometimes forming bonds, to minimize the surface
energy. Semiconductors such as Si tend to form very complex reconstructions.
One of the Si(111) reconstructions is the 7x7, as shown in Figure
1. This is the surface which forms when a commercial Si wafer
is ‘flashed’ briefly up to ~1200°C. I have added to this image
an outline of the unit cell, a diamond shape with seven atoms along each
edge, for two different orientations. The unit cell is repeated throughout
the surface to form the 2-D lattice. Note that there is both a long
axis and a short axis in the unit cell. The length of the unit cell
edge is known as the lattice parameter a, and is a defining property of
Reflection High Energy Electron
Diffraction (RHEED) Imaging
RHEED imaging utilizes a monoenergetic electron beam with primary energies
between 10 and 100keV in an ultra high vacuum (UHV) environment (~ 10-10
Torr). The beam is directed toward the sample surface at an angle
of less than 5°, and the diffracted beam is observed on a fluorescent
screen (see Figures 2 and 3). The image is then captured
using a video camera and transferred to a computer for analysis.
Since the beam is incident at such a low angle RHEED allows for constant
imaging during film growth on a substrate, whereas most imaging methods
require that a film be laid down in one chamber, and imaged in another.
It is easy to see the benefits that RHEED provides by allowing samples
to remain in UHV without requiring multiple chambers for deposition and
|Figure 2: Phosphor Screen on Chamber
||Figure 3: Diffraction Pattern on Screen
There are two types of lattices associated with every crystal: a crystal
lattice and a reciprocal lattice2.
A crystal lattice is a ‘real space’ mapping of the atoms in the lattice,
whereas a reciprocal lattice maps the atoms in ‘reciprocal space.’
Scanning Tunneling Microscopy (STM) images as in Figure 1 are of
the crystal lattice, and diffraction patterns such as RHEED (Figures
4 and 5) are images of the reciprocal lattice derived from the 2-D
net of surface atoms3. A Fourier
transform is used to go between points in real space and points in reciprocal
space. Length in the reciprocal lattice has the dimensions of L-1,
where L is the length in the crystal lattice, hence the name reciprocal
|Figure 4: RHEED Image of Si(111) 7x7 along the long axis
||Figure 5: RHEED Image of Si(111) 7x7 along the short axis
Figures 4 and 5 show RHEED images of the Si(111) 7x7 surface
along the two possible axes of the unit cell. In Figure 4,
the electron beam is traveling parallel to the long axis, and perpendicular
to the short axis. In reciprocal space the length of the short axis
becomes larger, and the spots are further apart. In Figure 5,
the beam is traveling perpendicular to the long axis, and the spots in
reciprocal space are closer together.
The Ewald construction is a helpful method of determining where diffraction
spots will occur in the reciprocal lattice (see Figure 7).
A vector k is drawn along the direction of the electron beam a length
of 1/(lambda) where (lambda) is the wavelength of the beam.
Next a sphere (called the Ewald sphere) is drawn about k, and wherever
the Ewald sphere intersects the reciprocal lattice, there will be a diffraction
spot. The 3-D Fourier transform of a 2-D system of periodic points
a distance a apart results in a system of periodic infinite rods
normal to the original plane of points and located a distance 1/a
apart. When the periodicity of the crystal lattice is not perfect,
there are maxima and minima which occur on the rods (the maxima corresponding
to the diffraction spots in Figure 7).
An interesting situation arises when you ‘rock’ the crystal sample in
a direction parallel to the beam. This shifts the Ewald, sphere down,
correspondingly shifting the intersections of the sphere with the reciprocal
lattice down. If you examine the RHEED pattern during the rotation,
the dots will move steadily downward, winking in and out of existence as
the Ewald sphere approaches and passes the diffraction spots.
Deposition of Thin Films of Iron
on Si(111) 7x7 Substrate
Several variables affect the result of deposition of thin films on a substrate
of Si(111). The temperature of the substrate, the thickness and composition
of the film, and other factors determine the resulting structure.
Figure 6 illustrates the findings of Le Thanh Vinh, J.Chevrier, and
J. Derrien4. At substrate
temperatures between 300 and 350°C approximately 3.75 monolayers (ML)
of Fe produced FeSi (a 2x2 reconstructed surface). But only
50° warmer at 400°C, FeSi2 was formed which is a sqrt(3)
x sqrt(3) reconstructed surface.
Figure 6: Phase diagram describing reactive deposition epitaxy (RDE)
growth of iron silicides
Figure 7: Si(111) Reciprocal Lattice
RHEED was used to determine experimentally the lattice parameter of Si(111),
to study the effects of ‘rocking’ the sample on the diffraction pattern
of Si(111), and to survey the effect of molecular beam epitaxy (MBE) of
up to 0.5 monolayers (ML) of Fe with the substrate at room temperature
(RT) and up to 5 ML with the substrate at ~650°C. A schematic
of the setup is shown in Figure 8.
Figure 8: Schematic of RHEED setup
For all experiments, a 10 keV beam of electrons was used, which has
a wavelength lambda of 1.228x10-11 m.
The distance L of the diffracted beam is 191 ± 2 mm.
Lattice Parameter of Si(111)
The lattice parameter a of a crystal can be calculated based on the distance
xactual (in millimeters) between bulk spots in the RHEED
pattern on the phosphor screen
where (lambda) is the wavelength in meters of the electron beam,
and L is the distance the diffracted beam travels from the sample
to the screen (in millimeters). A ruler is attached to the screen
as a scale of distance, and the distance x in the RHEED image is
adjusted to scale (xactual) before the lattice parameter
Rocking RHEED Analysis
For ‘rocking’ RHEED,
the sample manipulator is placed on low speed setting, and the sample is
moved in one continuous direction parallel to the electron beam (see Figure
6) until the diffraction pattern fades away. A series of images
were taken every 1/3 second during rocking of the sample for a duration
of ~50 seconds (a total of 153 images). The images were then put
into a video format and examined for characteristics of the reciprocal
Molecular Beam Epitaxy of Fe on
A thickness monitor is used to calibrate the Fe evaporator. It is
moved in front of the sample, blocking it, and the evaporator is operated
until it reaches a steady rate. That rate is then recorded, and ideally
checked again after data is taken to assure that it remained constant during
analysis. In our experiment, the rate of deposition was 1 angstrom
/ 64 seconds. Since the thickness of 1 ML of Fe is 1.34 angstroms,
0.1 ML was deposited every 8.6 seconds of continuous operation. 0.2
ML of Fe was first put down on the Si substrate at RT, and then it was
annealed at ~500°C for one minute. Two subsequent annealings
occured at ~600°C for one minute each. 0.3 ML of Fe was added
to the sample with the substrate at RT, and four subsequent annealings
were performed at ~650°C for one minute each. The sample was
then annealed at ~900°C for 15 seconds. Next, approximately 4.5
ML of Fe was deposited onto the sample with the substrate kept at ~650°C.
Images were taken of the RHEED patterns between all annealings and diffractions
Results and Analysis
Lattice Parameter of Si(111)
The measured value for the distance x was 6.4 ± 0.2 mm,
and the lattice parameter a was calculated to be 3.6 ± 0.4 angstroms,
compared to the accepted value of 3.8 angstroms, which is a 5.6% difference
and well within the expected value.
Rocking RHEED Analysis
Although the Si surface was not very smooth and the resulting diffraction
pattern somewhat diffuse, the rocking pattern was exceptionally distinct,
and clearly showed the expected winking in and out of the diffraction spots
as the sample was rocked.
Molecular Beam Epitaxy of Fe on
Images of the RHEED pattern between annealings are shown below. The
negative of the original images has been used to emphasize the pattern.
|  Clean Si(111) sample
|  0.5 ML of Fe after ~5 minutes of annealing
| 0.5 ML of Fe after ~7 minutes of annealing
In Image , the large bulk spots are separated by six smaller
spots evenly spaced (1/7th order) , characteristic of the Si(111) 7x7 surface.
In Images  and , the 1/7th order spots are fading as
Fe is deposited. In Image , weak 1/2 order spots are beginning
to appear, and in Image , the central 1/7th order spots are reappearing.
This could be due to prolonged conditions at 650°C. Silver on
Si(111) forms a 7x7 surface between 600-800°C, so it is reasonable
that Fe on Si(111) would exhibit that reconstruction.
|~3ML of Fe (substrate at 650°C)—weak 2x2
|~5ML of Fe (substrate at 650°C)—weak 7x7
The lattice parameter for the Si(111) 7x7 surface was experimentally determined
to be 3.6 ± 4 angstroms, which is 5.6% difference from the accepted
value of 3.8 angstroms. The rocking RHEED method produced dots which
slowly winked in and out while shifting downward, representing the irregular
sized reciprocal lattice rods of an imperfectly ordered crystal.
Epitaxial layering of Fe on Si(111) 7x7 surface exhibited a weak 1/2
order spots when ~3ML of Fe had been deposited and the substrate was at
~650°C, and a return to a weak 1/7th order reconstruction when ~5ML
of Fe had been applied and the substrate was at ~650°C.
More work is required to develop a complete phase diagram for Fe on
Si(111). We will also be examining Fe-Si multilayers, as well as
Fe on the Si(100) surface. Similar experiments will also be taken
to the Advanced
Light Source in California this August, and results should clarify
our knowledge considerably.
1 Lüth, Hans,
Surfaces and Interfaces of Solid Materials, (Springer-Verlag, Berlin, 1998),
3rd corrected printing, p.88.
Charles, Introduction to Solid State Physics, (John Wiley & Sons, NY,
John Arthur, Geometric and Electronic Structure of Reconstructed Semiconductor
Surfaces: Thesis, Univ. of Illinois at
Urbana-Champaign, (1993), p.11.
Le Thanh, Chevrier, J. , and Derrien, J., Phy. Rev. B Vol. 46, No. 24,
15 946 (1992).
Any comments would be appreciated. I can be reached via Email at email@example.com.
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This page last edited on July 9, 1997.