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Spatial origin of photoelectrons appears in photoemission angular distributions |
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Does a detected photoelectrom stem from the atoms and bonds of interest?
In the past there was no method to deal with such questions. Now they
can be answered with an analysis of theoretical photocurrents.
We quantitatively investigate the influence of
the initial state and its charge distribution on the angular
distribution of intensity in angle resolved ultraviolet photoemission.
The access to
both electronic and spatial structure actually opens a new perspective for
photoemission.
Photoelectron spectroscopy shows to be sensitive to different
spatial parts of the initial state, depending on the kinetic
energy. Ultraviolet photoemission detects the wave function
in the bonding region outside the core, and the origin of
photoelectrons is traced for the first time into single bonds. For the investigations, azimuthal scans of the photocurrent from the GaAs(110) surface are chosen. GaAs(110) is a well-understood test case and azimuthal scans allow a high accuracy in the visualization of the angular distribution. The new measurements and new calculations show a very good agreement. Because of the combination of several aspects of the photoemission process, one has to deal carefully with a lot of details to get the whole picture correctly. The influences of energy resolution, of the incident light and of the density of states were studied. This allows to separate their influence on the intensities from other effects. E.g., the surface density of states (SDOS) was shown to control the number and the azimuthal positions of the lobes. In Fig. 1 (a) the four lobes, two large and two small ones, correspond to the structure of the SDOS. Since this is a very sensitive dependence, it allows an accurate determination of the band structure by comparing experimental with theoretical scans.
Fig. 1: Photocurrent for -0.75 eV and k|| = 0.6 Å-1 and charge density: (a) measured (dark blue) and calculated (green) current with radius representing the intensity in the polar plot; (b)+(c) contour plots of the charge density for k|| belonging to the lower left lobe in (a), (b) in the xy plane with the cut located as indicated by the line in (c), (c) in the yz plane located as indicated by the line in (b).
The comparison with the SDOS cannot explain the differences in the intensities
of the photocurrent between the lobes at positive and negative y direction.
The wave function of the initial state has to be taken into account. With the
approximation of a free final plane wave the photocurrent is given by the
square modulus of the Fourier tranformation of the initial state. For very
simple cases this has the same angular distribution as the initial charge
density. This is the case for the dangling bond which is localized at one
site and has a simple angular momentum composition. Fig. 1 illustrates this
connection. Contour plots of the charge density are shown in Fig.1 (b)+(c)
for a state, which gives a strong intensity in the current. The charge
exhibits the same asymmetry between positive and negative y direction.
It has been known for long that this simple connection of the intensity
distribution
with the charge density does not hold for less trivial cases.
Fig. 2: Photocurrent for -4.0 eV and k|| = 0.6 Å-1 and charge density: (a) measured (green) and calculated (magenta) current with radius representing the intensity in the polar plot; (b)+(c) partial currents emerging from the middle (b), and the outer (c) area ; (d) contour plot of the charge density in a plane through the the uppermost As and Ga atoms for the initial state belonging to the upper right lobe at 15° as indicated by the black line in (a). The current in (b) is magnified by 100 relative to that in (a) and (c). The middle region is the spherical volume between radii of 0.08 Å and 0.29 Å around the As cores and 0.09 Å and 0.3 Å around Ga as depicted in (d). The outer region is the space outside these spheres. This separation appears as the natural choice for the charge distributions in the given case, cf. also Fig. 1 (c).
For a more powerfull interpretation we adopted
the XPD picture generalized to delocalized valence states. The
amplitude of the initial state appears as the local emissivity for
the spatially distributed source of the electrons to be scattered.
This is a rigorous approach which can be cast into the simple question:
Where do the electrons come from? As will be shown below, the
simplicity of this interpretation is a success.
To achieve insight into the influence of the initial state from this
point of view,
the importance of different parts of the emitting volume
is investigated in a novel way. Apart from the charge density maxima in
the bonding region the initial wave functions also have charge
peaks closer to the cores, as shown in Fig. 1 (c),
Fig. 2 (d), and Fig. 3 (b). In the present case, three areas are
separated by almost spherical nodal surfaces. The separate
contributions to the current from each of these regions are
calculated.
Contributions for the emissions from
-4.0 eV are shown in Figs. 2 (b)+(c). From the
localized middle region arises less than 1% of the total
current for both studied binding energies. Contributions from the
innermost area are even smaller and completely negligible.
This changes drastically with increasing kinetic energy towards dominating
contributions from the middle area.
The dependence of the spatial distribution
on kinetic energy gives an additional feature of ARUPS
from valence states and its relation to XPD. The importance of smaller
spatial scales with increasing energy might be understood as a
localization of an effective emitting source. At high
energies this coincides with the observation that the
XPD patterns from valence bands are nearly identical to those from
the localized core states.
Contrarily, at low kinetic energies valence states may contribute from regions
where the localized core states vanish. These delocalized regions are the
most important for cases studied here. Whereas with the effective
localization at the core the XPD patterns reflect the geometry, ARUPS probes
the bonding region with an intensity distribution showing information
about the bonds. This is a new aspect for the interpretation of ARUPS data.
Fig. 3: Iso-surfaces of the charge densities of inital and final states for -4.0 eV and k|| = 0.6 Å-1: the final charges (a)+(c) belong to the photocurrent of Fig. 2 at 195° (a) and 15° (c), the charge density in (b) is that of the initial state for both of these peaks. The frames indicate the vertical position of the topmost ideal atomic planes.
To further investigate the influence the bonding charge,
we trace the origin of the intensity into one direction. The peak at
15° in Fig. 2 (a) is chosen. Although its
initial state extends over 4 atomic layers as shown in Fig. 3 (b), 80% of the
electrons are excited from the density around the
uppermost As atom and from the bonds towards the next Ga atoms. This bond is
depicted in Fig. 2 (d). An easy understanding of such a selection
give the charge densities of final and initial states in Fig. 3.
Iso-srufaces of the final states for the peaks at 195° and at
15° in Fig. 2 (a) shown. Differences in their charge distributions
are obvious. The related initial states have the same
charge distribution which is shown in Fig. 3 (b). In the golden rule
formulation of photoemission the wave functions of the initial and the final
state appear in the integral. Clearly, large contributions can be expected
from spatial regions where these wave functions are simultaneously
large. Therefore, one might look at the final state as a tool which
probes selected parts of the initial state. Ultraviolet photoemission
not only detects the bonding region but also is sensitive to single
bonds.
See also:
Acknowledgments:
This work was supported in part by the Bundesministerium für Bildung,
Wissenschaft, Forschung und Technologie and by the Materials Sciences
Division of the U.S. Department of Energy, Contract No. DE-AC03-76SF0009.
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