Aca - Departamento de Física - Universidad Técnica Federico Santa ...

V Encuentro Sud Americano de Colisiones Inelásticas en la Materia
Electron emission by grazing scattering from Be(0001)
C. D. Archubi 1 , M. S. Gravielle 1,2 and V. M. Silkin 3,4
1 Instituto de Astronomía y Física del Espacio, CONICET-UBA, Buenos Aires, Argentina
2 Depto. de Física, Fac. de C. Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
3 Donostia Internacional Physics Center (DIPC), 20018, San Sebastián, Spain
4 IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain
email address corresponding author: archubi@iafe.uba.ar
1. INTRODUCTION
Recently it has been demonstrated that
occupied surface states can modify the dielectric
properties of metal surfaces [1]. Thus, with the
aim of investigating the influence of surface
states on electron emission, we study electron
distributions originated by fast protons colliding
grazing with a Be(0001) surface. Beryllium presents
a technological interest in modern fusion
reactors and it is expected that its surface states
play an important role in inelastic electronic
processes.
To describe the electron emission process
we employ the Band-structure-based (BSB)
model [2], which includes an accurate description
of the electron-surface potential, incorporating
information about the band structure of the
solid. Within the BSB approach the surface interaction
is described by a realistic onedimensional
model potential [3], while the dynamic
response of the medium is derived in consistent
way from the unperturbed electronic
states by using a linear response theory. This
method has been succesfully employed to study
energy loss and electron emission from Al surfaces,
where the effects of the surface states
were found negligible [4].
2. RESULTS
Due to the large mass of the projectile, it
is reasonable to calculate its motion in terms of a
classical trajectory. Within the binary collisional
formalism, the transition probability per unit
path reads
dP 2 π
( x)
= δ ( ∆)
T
dk vs
if
2
(1)
where z is the projectile distance to the surface,
v s is the projectile velocity parallel to the surface
plane, and the Dirac delta expresses the
energy conservation. In Eq (1) T if represents the
T-matrix element, which is evaluated within a
first-order-perturbation theory.
In this work we employ the BSB model
to derive both the unperturbed electronic wave
functions and the surface induced potential. The
differential probability of electron transition to a
given final state with momentum k , is dP dk
, obtained
from Eq (1) by integrating along the classical
projectile trajectory, after adding the contributions
coming from the different initial
states.
10 1
10 0
10 -1
dP/dk (a.u.)
dP/dk (a.u.)
10 -2
10 -3
10 -4
10 1
10 0
10 -1
10 -2
10 -3
10 -4
100 100 keV keV H + H + Be Be (0001)
α = 1
α = 1 ο ο
30 60 90 120 150 180 210 240
30 60 90 120 150 180 210 240
Energy (eV)
Energy (eV)
θ=20 ο
θ=20 ο
θ=30 ο
θ=30 ο
θ=45 ο
θ=45 ο
θ=30 ο Jellium
Figure 1. Differential probability of electron emission
from the valence band, as a function of the electron
energy, for 100 keV protons impinging on a Be
(0001) surface with the angle α=1 o . Three different
electron emission angles, meassured with respect to
the surface plane, are considered: θ =20, 30 and 45
o .
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