LEED and RHEED geometry
2
LEED - angle of incidence 90o
Electron energy ≈ 10 - 100 eV
RHEED - small angle of incidence, below 5o
Electron energy ≈ 10 - 50 keV
∥
In RHEED, due to small angle of incidence, is
the perpendicular component of the electron
wavevector of the same range as in LEED.
1
Ewald construction
Reciprocal lattice rods.
Ewald sphere
Screen
Crystal
∆k1 = k1 − k 0
∆k2 = k2 − k 0
∆k3 = k3 − k 0
Cross section of the Ewald
sphere in electron incidence plane.
k0
∆k1
k1
k2
k3
∆k2
∆k3
0 - th
Laue zone
1 - st
Laue zone
2 - nd
Laue zone
2
Laue Zones - Si(111)-7x7 RHEED pattern example
L0
L0
L1
L2
L1
e beamalongSi 112
e beamalongSi 110
L0
L1
L2
Si(111)-7x7
real space
Si(111)-1x1
reciprocal space
Si(111)-7x7
real space
Si(111)-(1x1)
reciprocal space
Reciprocal lattice reconstruction
from RHEED pattern
screen
, sample
ϕi = 0
θf
θi
, φf
electron beam
∆k x = k0 (cos θf sin φf )
∆k y = k0 (cos θf cos φf − cos θi
∆k z = k0 (sin θi + sinθ f )
)
, To every point of the screen a reciprocal space coordinate may be prescribed
4
RHEED and STM images of Si(557) surface
disordered surface
ordered surface
with Au atomic chains
5
Si(111)-(6x6)Au
RHEED pattern during
Pb film growth at 80K
1 ML Pb
2 ML Pb
4 ML Pb
20 ML Pb
The arrow points
mirror-reflected e-beam
position. Intensity oscillation
of the beam follows layer-by-layer
ultrathin film growth.
6
RHEED oscillations
RHEED mirror-reflected electron beam
intensity oscillations measurd durnig
Pb ultrathin film growing on Si(111)-(6x6)Au
surface in UHV conditions.
This experimental method allows
precise control of the film thickness
and its unformity, thus enables
fabrication of metallic quantum wells.
See more details in:
M. Jałochowski, E. Bauer, Quantum size
and surface effects in the electrical resistivity
and high-energy electron reflectivity
of ultrathin lead films, Phys. Rev. B38, 5272 (1988).
M. Jałochowski, E.Bauer, Reflection high-energy
electron diffraction intensity oscillations during
the growth of Pb on Si(111), J. Appl. Phys. 63, 4501 (1988)