Chapter 11

Report
XI. Reflection high energy electron diffraction
Surface reconstruction studied by RHEED
--- used in MBE (molecular beam epitaxy)
Schematic of a
RHEED setup
The distance from sample to screen, L, and the
energy of the electron beam must be known to
derive the lattice spacing of the crystal.
Streaky RHEED pattern
(1) Streaky pattern
t  L  tan( 2 )
2d hk sin   
a
 2 2
sin     a   small
h  k2
t
sin  
 t  L  tan( 2 )  2 L
2L
a
t
  2
h2  k 2 2L
a
L h 2  k 2
t
Higher accuracy at longer L since t is longer.
(2) Sensitivity of RHEED
(2-1) Coherence zone
The electron beam can be treated an in-phase
source only within a coherence zone.
The finite coherence zone is due to both
finite convergence and finite energy spread
of the electron beam.
(a) Energy spread ∆E of incident electrons gives
time incoherent
 2k 2
 2 2kk
E
 E 
2m
2m
E 2k
kE

 k 
E
k
2E
k  2k sin  s
t
||
Resolved parallel to surface, for small s
kE
kE
k  2
sin  s 
s
2E
E
t
||
(b) Spread in arrival angle over 2s gives spatial
incoherence,
k||s  k sin  s  ( k sin  s )
 k  2 s
(c) Combine uncertainties and define
coherence zone diameter X
t 2
s 2
Xk||  2
k||  ( k|| )  ( k|| )
k||  ( k||t ) 2  ( k||s ) 2  ( kE s / E ) 2  ( 2k   s ) 2
k||  2k s 1  ( E / 2 E )
2
2
2

X 


k|| 2k s 1  ( E / 2 E ) 2 2  s 1  ( E / 2 E ) 2
-Typical RHEED, E = 100 keV, E = 0.5 eV, and
s = 10-5 rad  X  200 nm!
-Typical LEED, E = 50-200 eV, E = 0.5 eV, and
s = 10-2 rad  X  5-10 nm!
RHEED&LEED are sensitive to the order of
surface atoms inside the area defined by
coherence zone (area within the radius of X)!
(2-2) Island growth
3. Surface reconstruction of GaAs(001)2x4
http://newton.ex.ac.uk/research/qsystems/people/jenkins/smg/
gaas/gaas_001_beta2_2x4_top.gif
RHEED patterns of As-stabized GaAs(2x4)
(30 KeV)
(a) Along [ 1 1 0]
(b) Along [1 1 0]
Explanation:
(1) Reciprocal lattice structure of
GaAs(100)2x4
(2) RHEED patterns along two perpendicular
directions
4. RHEED oscillation (adapted from Wiki)
With RHEED oscillation, the epitaxial growth of
a film within a precision less than a monolayer
can be achieved.
Mechanisms of
RHEED
intensity
oscillations
during growth
of a monolayer.
5. A/B tilted superlattice ( Petroff)

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