493 29
encountered for an arbitrary orientation of the beam to the
crystal is actually the sum of the contributions of many
planes. Generally, these contributions tend to cancel giving
the amorphous average backscattering except when the
Bragg condition for a certain set of planes dominates the mix,
giving rise to a sharp change in the channeling condition.
What is the magnitude of Bragg angles for typical SEM beam
and target conditions? Consider an incident beam of E0 =
15 keV, where the electron wavelength, λe is given by the de
Broglie equation:
λe=h/p (29.2a)where h is Planck’s constant and p is the momentum (m 0 v). In
terms of beam energy, the wavelength is given by
λe 0.5
0.5
()nm 1.226 ()1+0.979E^6
=/EE−
(29.2b)where E is expressed in eV (Hirsch et al. 1965 ).
At 15 keV, λe = 0.00994 nm. If this 15 keV-beam is directed
at a crystal of silicon, which has a diamond-cubic crystal lat-
tice with a fundamental cube dimension of a = 0.543 nm, the
series of possible “allowed” Bragg angles (expressed in the
“Miller indices” [hkl] which designate the crystal planes) is
given in. Table 29.1.
We can directly image the effects of crystallographic
channeling on the total backscattered electron intensity for
the special case of a large single crystal viewed with a large
scanned area (i.e., low magnification). As shown schemati-
cally in. Fig. 29.2, the act of image scanning not only moves
the beam laterally in x- and y-directions, but at each beam
position the angle of the beam relative to the surface normal
changes. For a 10-mm working distance from the scan rock-
ing point, a scan excursion of 2 mm in width causes the beam
incidence angle to change by ±12° across the field. As seen in
. Table 29.1, the allowed Bragg angles for a 15-keV electron
beam striking Si have values of a fraction of a degree to a few
degrees, so that a scan angle of ±12° will certainly cause the
beam to pass through the Bragg condition for at least some of
the crystal planes. A large area image created at E 0 = 15 keV
by scanning a flat, topographically featureless silicon crys-
tal—prepared with the surface nearly parallel to the (001)
plane—is shown in. Fig. 29.3. The image consists of a pat-
tern of bands, each running parallel to a particular crystal
plane, creating a so-called electron channeling pattern
(Coates 1967 ). The channeling effect appears as this series of
prominent bands that span the crystal because the intersec-
tion of the crystal planes with the surface defines a linear
trace, and the Bragg condition is satisfied along lines parallel
to this trace where the scan angle relative to the planes equals
the Bragg angle, ±θB. “Higher order” Bragg angles (n = 2, 3, 4,
etc., with the specific integers that appear depending on
“allowed reflections”) are satisfied as a series of progressively
fainter lines parallel to the central bands, which can be seen
in. Fig. 29.3 (b) for the family of {220} type bands. Note that
it is appropriate to apply both a dimensional marker and an
angular marker to this image. When the scanned area is
decreased, that is, the magnification is increased, the range of
the angular scan is reduced, and consequently, the bands on
the display appear to widen and the angular extent of the
electron channeling pattern decreases, as shown in. Fig. 29.4a, b. If the magnification is made high enough and
the angular range is sufficiently reduced, the beam will scan
through such a small angle that the observer will see the cen-
ter of the pattern swell to eventually fill the image with a
single gray level. Effectively, the crystal presents a single
atomic density that restricts the channeling effect to a single
intensity value.
. Table 29.1 Bragg angles for Si with E 0 = 15 keV
Planes (hkl) Spacing (nm) θB (degrees)111 0.314 0.908
220 0.192 1.48
311 0.164 1.74
400 0.136 2.10
422 0.111 2.57
511 0.105 2.72- qB qB
. Fig. 29.2 Wide field (“low magnification”) image scanning produces
sufficiently large changes in the scan incidence angle to pass through
the Bragg conditions for the particular set of crystal planes. Note that
the Bragg condition is satisfied in positive and negative going angles,
giving rise to two sharp changes in contrast
29.1 · Imaging Crystalline Materials with Electron Channeling Contrast