Physics 9826b Lecture 3, January 21, 2013 1 1 Lecture 3 Surface Structure, continued: Low Energy Electron Diffraction and Microscopy References: 1) Zangwill, Chapter 3 2) Woodruff & Delchar, Chapter 2 and pp. 449-460 3) Attard and Barnes, pp,25-28, 47-62 4) Kolasinski, pp.84-91 5) LEEM: http://www.research.ibm.com/leem/#item2 How to determine surface structure: - Theoretical background - Low Energy Electron Diffraction (LEED) - Reflection High-Energy Electron Diffraction (RHEED) - Low Energy Electron Microscopy (LEEM) Additional: Scanning Electron Microscopy Lecture 3 2 Electron Backscattering: concepts of diffraction Short inelastic mean free path for electrons means that elastic scattering of electrons is very surface sensitive e Electron diffraction and microscopy: Elastic backscattered e - , ~ few % at 100eV “Universal curve” for electrons
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Lecture 3 Surface Structure, continued: Low Energy Electron … · 2013. 1. 21. · Physics 9826b Lecture 3, January 21, 2013 1 Lecture 3 1 Lecture 3 Surface Structure, continued:
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Physics 9826b
Lecture 3, January 21, 2013 1
Lecture 3 1
Lecture 3
Surface Structure, continued:
Low Energy Electron Diffraction and Microscopy
References:
1) Zangwill, Chapter 3
2) Woodruff & Delchar, Chapter 2 and pp. 449-460
3) Attard and Barnes, pp,25-28, 47-62
4) Kolasinski, pp.84-91
5) LEEM: http://www.research.ibm.com/leem/#item2
How to determine surface structure:
- Theoretical background
- Low Energy Electron Diffraction (LEED)
- Reflection High-Energy Electron Diffraction (RHEED)
- Low Energy Electron Microscopy (LEEM)
Additional: Scanning Electron Microscopy
Lecture 3 2
Electron Backscattering: concepts of diffraction
Short inelastic mean free path for
electrons means that elastic scattering
of electrons is very surface sensitive
e
Electron diffraction and microscopy:
Elastic backscattered e-, ~ few % at 100eV
“Universal curve” for electrons
Physics 9826b
Lecture 3, January 21, 2013 2
Lecture 3 3
3.1 Real Space and Reciprocal Space Lattices
- Given a unit cell with basis vectors
- There is a complementary reciprocal lattice
) ,( 21 aa
*) *,( 21 aa
1221 * and * )2 ,1,( * aaaajiaa ijji
a
1a
2a
a*
*1a
*2a
Area of unit cell A
AA
aaA
aaA
1*
*sin|* ||*|*
sin| |||
21
21
a
a
Rectangular Lattice
*1a
*2a
real space
reciprocal space
Non-rectangular lattice
*1a
*2a
real space
reciprocal space
Lecture 3 4
Substrate and Overlayer Structures
Suppose overlayer (or reconstructed surface layer) lattice different from substrate
21
21
bmbnT
amanT
B
A
a
1a
2a
b
1b
2b
2221212
2121111
aGaGb
aGaGb
Overlayer real space lattice:
*det
*
*det
*
matrix) d transpose(inverse ~
*
*****
*****
1
2221212
2121111
G
GG
G
GG
GGwhere
aGaGb
aGaGb
ji
ij
jj
ii
Overlayer reciprocal lattice:
Physics 9826b
Lecture 3, January 21, 2013 3
Lecture 3 5
3.2 Reciprocal Lattice and Diffraction
Recall the de Broglie relation:
Constructive interference when path length difference = n l