Page 414 - Academic Press Encyclopedia of Physical Science and Technology 3rd Analytical Chemistry

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Encyclopedia of Physical Science and Technology EN012C-568 July 26, 2001 15:32

64 Photoelectron Spectroscopy

FIGURE 7 Angle-resolved photoelectron spectroscopy (see text for details).

field in which ARPES is important is the investigation the beginning, it was assumed that it is the inelastic mean
of two- and three-dimensional periodic structures. Two- free path (IMFP) that has to be used in connection with
dimensional periodic structures are found in layer com- these equations. The IMFP is an intrinsic property of a
pounds or in well-ordered adsorbate systems formed at material which can be measured using other techniques,
the surface of a single crystal. Three-dimensional periodic such as electron backscattering. In the mid-1980s it was
structures are found in all crystalline materials. In most found that the appropriate length is not the IMFP but the
cases the application of ARPES asks for single crystals of attenuation length (AL). Powell defined the AL as “a value
at least a few millimeters in the two surface dimensions. resulting from overlayer-film experiments on the basis of
2
With an illuminated area of less than about 1 mm one a model in which elastic electron scattering is assumed to
either loses too much intensity or risks too much radiation be insignificant.” The AL is typically 10 to 25% shorter
damage. than the IMFP because of the contribution of elastic scat-
The important difference between free or space-fixed tering to the IMFP. If the thickness of the overlayer is
single molecules and periodic structures is as follows. In larger than about three times the AL, the substrate is no
the first case, the intensity of the peaks in the PE spec- longer detectable. This limits the applicability of ARPES
trum is angle dependent but the position of the peaks is to overlayers that are not more than a few nanometers
not. In the second case, the energy of the most prominent thick. Some terms concerning electron transport in matter
features in the spectrum of the valence region depends on are defined in Table II.
the angles
, θ, and φ as well as the polarization of the To convert the “composition versus take-off angle”
ionizing radiation. One therefore speaks of energy distri- curves obtained from an angle-resolved XPS (ARXPS)
bution curves instead of PE spectra in such a case. We will
come back to this type of investigation in Section IV.B.
ARPES has become more and more common in the in-
TABLE II Some Definitions with Regard to Electron
vestigation of substrate/overlayer structures. An overlayer Transport in Matter
is a zone of thickness d that differs in chemical composi-
IMFP Inelastic Mean Free Path. The average distance
tion from the substrate as, for example, a metal oxide on
that an electron with a given energy travels
the surface of a metal. In materials science, the knowledge between inelastic collisions.
of d is often very important (see, e.g., Fig. 30 in Section ED Escape Depth. The distance normal to the surface at
IV.E). To determine d, one makes use of the limited es- which the probability of an electron escaping
cape depth of photoelectrons and the difference in binding without significant energy loss due to inelastic
energy that leads to distinguishable peaks for pure metal processes drops to e −1 (38%) of its original value.
and metal oxide. The larger the d, the smaller becomes AL Attenuation Length. The average distance that an
electron with a given energy travels between
the intensity ratio I metal /I metal oxide . Increase of the polar
inelastic collisions as derived from a particular
angle θ increases the effective thickness of the overlayer model in which elastic scattering is assumed to
and leads to characteristic changes in the intensity ratio. be negligible.
Equations that connect the observed θ dependence of the ID Information Depth. The average distance normal to
intensity ratio with d were derived under the following the surface from which a specified percentage of
two assumptions: (1) the surface is atomically flat and the detected electrons originates.
(2) electrons which reach the detector without energy loss Sampling Three times the IMFP corresponding to an ID for
Depth which the percentage of detected electrons is 95%.
have traveled in straight lines (no elastic scattering). In