This document provides an overview of surface characterization techniques using low energy electron diffraction (LEED) and reflection high energy electron diffraction (RHEED). It discusses the instrumentation, principles, and applications of LEED and RHEED. LEED uses elastic scattering of electrons to determine the structure of crystalline surfaces. RHEED similarly uses electron diffraction but is more surface sensitive due to the grazing angle of incidence. Both techniques provide information on surface structure, phase transitions, crystal growth, and more through analysis of diffraction patterns and intensity variations.

1. Surface Characterization by Low Energy Electron
diffraction(LEED) & Reflection High Energy Electron
Diffraction(RHEED)
EEE 6410: Semiconductor Characterization Technology
Course Teacher:
Prof. Dr. Md. Shafiqul Islam, Head, Dept. of EEE, BUET
Dhaka-1205, Bangladesh.
Prepared by :
Name: SAKIB REZA
ID: 0417062299

3. What is LEED [1]

4. History of LEED [1]

5. Instrumentation of LEED [1]

6. Kinematic Theory of LEED [2]
• Crystal surface are elastically scattered only once. In accordance to the De Broglie hypothesis:
• The interaction between the scatterers present in the surface and the incident electrons is most
conveniently described in reciprocal space. In three dimensions the primitive reciprocal
lattice vectors are related to the real space lattice {a, b, c} in the following way:
• Condition for constructive interference given by the Laue condition:
where,
• Only the first few atomic layers contribute to the diffraction. This means that there are no
diffraction conditions in the direction perpendicular to the sample surface. As a consequence the
reciprocal lattice of a surface is a 2D lattice. So equation (1) reduces to

7. Kinematic Theory of LEED (Cont’d) [2]
• where a* and b* are the primitive translation vectors of the 2D reciprocal lattice of
the surface and denote the component of respectively the reflected and
incident wave vector parallel to the sample surface. a* and b*are related to the real
space surface lattice in the following way:
• The Laue condition equation (2) can readily
be visualized using the Ewald's sphere construction.

8. Dynamical Theory of LEED [2]
• Quantitative analysis of LEED experimental data by analysis of I-V curves
(measurements of the intensity versus incident electron energy)
• The I-V curves can be recorded by using a camera connected to computer
controlled data handling or by direct measurement with a movable Faraday cup.
• The experimental curves are then compared to computer calculations based on the
assumption of a particular model system.
• 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.
• It is expressed in terms of the logarithmic derivative of the intensity:
• The R-factor is then given by:

9. LEED Patterns for Super lattice and Stepped Layers [3]
Notice super lattice
have smaller
reciprocal unit cell
than the substrate.

10. LEED Patterns for Domains [3]
Two domains in real space
The diffraction
pattern for both
domains together
When electron beam diameter is larger
than domain size on surface: the presence
of multiple (rotational) domains increases
complexity of diffraction pattern.

11. The Energy of the Electrons in LEED [3]
The short free path length of electrons with 20-200 eV for LEED gives
very high surface sensitivity, however, the electrons still penetrate several
atomic layers. The scattering from the several layers modulates the 2D
Ewald construction toward 3D case. This gives the change of intensity of
each diffracted spots with changing electron energy.
2p/avertical

12. Tensor LEED [4]

13. LEED Animation

15. What is RHEED?

16. Instrumentation of RHEED [5]

17. Principles of RHEED [5]
Ewald Construction

18. Principles of RHEED (Cont’d) [5]
Coherence Length
The spatial resolution in RHEED structure analysis is determined by the coherence length
of electron beam used. The coherence length, in which the scattered waves interfere by
keeping the phase information, is determined by how much monochromatic the energy of
electron beam is and how much parallel the electron beam is. The coherence length l is
defined by the energy speared ∆E and the divergence angle ∆θ of the electron beam by
where λ is the wavelength of electron wave and α is the angle between the incident electron
beam and the direction for measuring l.
when α=0, l= lL (longitudinal coherence length)
when α=90, l= lT (transverse coherence length)

19. Practical Aspects of RHEED [6]

20. Phase Transition of RHEED [7]

21. RHEED Rocking Curve Analysis [8]

22. Weissenberg RHEED [9]

23. RHEED Intensity Oscillation [10]

24. Animated RHEED

25. Comparison of LEED & RHEED [1]

26. References
[1] https://es.scribd.com/document/87969909/Final-Leed-Rheed
[2] https://en.wikipedia.org/wiki/Low-energy_electron_diffraction
[3] https://www.physics.nus.edu.sg/~phygaoxy/6LEED&RHEED.ppt
[4] https://sundoc.bibliothek.uni-halle.de/diss-online/05/05H034/t4.pdf
[5]http://wwwsurface.phys.s.utokyo.ac.jp/papers/2012/CharacteriMat(Hasegawa)201202.pdf
[6] Horio, Y. and Ichimiya, A. 1983. Intensity anomalies of Auger electron signals observed by
incident beam rocking method Physica 117B/118B:792–794.
[7] Hasegawa, S., Nagai, Y., Oonishi, T., and Ino, S. 1993. Hysteresis in phase transitions at clean
and Au-covered Si(111) surfaces. Phys. Rev. B 47:9903–9906.
[8] Hanada, T., Daimon, H., and Ino, S. 1993. Rocking-curve analysis of reflection high-energy
electron diffraction. Phys. Rev. B 51:13320–13325.
[9] Abukawa, T., Yamazaki, T., Yajima, K., and Yoshimura, K.2006. Weissenberg reflection high-
energy electron diffraction for surface crystallography. Phys. Rev. Lett.97:245502.
[10] Fukutani, K., Daimon, H., and Ino, S. 1992. Reflection highenergy electron diffraction study
of the growth of Ge on the Ge(111) surface. Jpn. J. Appl. Phys. 31:3429–3435.

27. Thank You
Q/A