surface and interface science physics 627; chemistry 542...
TRANSCRIPT
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References and Resources: Woodruff and Delchar (2nd ed.), pp 105-212
http://venables.asu.edu/grad/lectures.html
http://www.cem.msu.edu/~cem924sg/
http://www.cem.msu.edu/~cem924sg/Topic06.pdf
http://www.chem.qmul.ac.uk/surfaces/scc/
http://philiphofmann.net/surflec3/surflec014.html
http://www.material.tohoku.ac.jp/~kaimenb/B_RHEED.html
Wikipedia (!)
Surface and Interface Science Physics 627; Chemistry 542
Lectures 4 Feb 3, 2013
Determining Surface Structure Diffraction methods: LEED; RHEED
Real Space: STEM
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Electrons in the ~ 20 – 200 eV range have wavelengths
comparable to lattice dimensions
Now, put in numbers!
If we express E in eV:
and in Ǻ:
We get:
Therefore Ekinetic = 36 eV (easy to do!)
gives = 2.1 Ǻ!! Just about right!!!
ph /• (de Broglie Relation)
mpEkinetic 2/2• (Free electron energy-momentum relation)
kineticmEp 2 kineticmEh 2/and
sJ1062.6 34 h gm k1091.9 31
J1060.1eV 1 19
m101Å 1 10
eV)(in /4.12Å)(in kineticE
“Universal Curve”
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Basic idea of LEED: Scattering off a two
dimensional array of atoms.
If d = n, we get constructive interference!
What happens to Θ when is changed?
Why two dimensional, not 3D??
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LEED is an important diffraction technique for the determination of
surface structures. It may be used in one of two ways.
Qualitatively : The diffraction pattern is recorded. An analysis of the
spot positions yields information on the size, symmetry and rotational
alignment of the surface unit cell.
Quantitatively : The intensities of the various diffracted beams are
recorded as a function of the incident electron energy to generate I-V
curves which, by comparison with calculated curves, gives accurate
information on atomic positions.
Low Energy Electron Diffraction (LEED)
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Schematic diagram of a LEED apparatus
Commercial LEED apparatus
LEED apparatus mounted in UHV chamber
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LEED diffraction patterns from W(100) at two different energies
(Which is higher energy???)
(What’s the ratio of energies??)
(01) (01)
(10)
(10)
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Real and reciprocal space
pictures of unit cells
Real Space Reciprocal
Space
kji
kj
iaaa
aaa
2* (i, j, k cycl.)
*
1a
*
2a2a
1a
1a
2a
z
General for 3D
In 2D, use:
za ˆ*
3
zayaaxaa ˆ ; ˆ ; ˆ 32211
Consider:
xaaa
xa
zyaxa
zyaa ˆ
2ˆ2
ˆˆˆ
ˆˆ2
121
2
21
2*
1
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Superstructures
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Interference between
different layers (single
scattering) I-V curve (intensity profile) for Ni(100)
First complication: Scattering from different layers
parallel to the surface can interfere constructively or
destructively
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Second complication: Multiple scattering
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The inspection of the LEED pattern gives a qualitative picture of the
surface periodicity i.e. the size of the surface unit cell and to a certain
degree of surface symmetries. It will give no information about the atomic
arrangement within a surface unit cell or the sites of adsorbed atoms.
A more quantitative analysis of LEED experimental data can be achieved
by analysis of I-V curves (measurements of the intensity versus incident
electron energy). These curves are then compared to computer
calculations based on the assumption of a particular model. The model is
changed in an iterative process until a satisfactory agreement between
experimental and theoretical curves is achieved. A quantitative measure
for this agreement is the so called reliability- or R-factor, for example:
and Voi is the imaginary part of the electron self-energy. In generally is considered as a good agreement, is considered mediocre and is considered a bad agreement. Figure 7 shows examples of the comparison between experimental I-V spectra and theoretical calculations.
where
and Voi is the imaginary part of the electron self-energy
How to get quantitative results from LEED
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Theory vs. experiment (red) for I-V profiles for Al(111)
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Summary
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Reflection High Energy Electron Diffraction
(RHEED)
• High energy electrons (10 – 30 keV)
• Grazing incidence geometry
• Widely used to monitor epitaxial growth
• Not as well understood quantitatively as LEED
• No energy filtering
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MBE apparatus with RHEED
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RHEED experimental geometry
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(Schematic) origin of RHEED
oscillations
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A RHEED pattern from a TiO2 (110)
Streaked RHEED pattern from the
TiO2(110) surface. The sample had
a terraced surface, which caused
noticeable streaking compared to
the RHEED pattern from the flat
TiO2(110) surface shown to the left.
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RHEED summary
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Scanning tunneling microscopy (STM)
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Quantum tunneling
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The STM measures charge density, not directly atomic positions
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STM of Si(111) (7x7) at good (top left) and optimal (right) resolution
Calculated (left) STM pictures for the surface structure at right
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Atomic manipulation
using the STM tip
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The influence of bias: Si(100) (1x2)
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Spectroscopy: Si(111)
adatom sites A,
corner holes B
vacancy sites C
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Atomic force microscopy (AFM)
AFM image of NaCl