Since the point resolution of the JEOL 200CX electron microscope is
up = 2.6Å it is not possible to obtain a true
structure image of any of the III-V or elemental semiconductors with this
machine. Since the information resolution limit set by electronic
instability (1) u0 = (2/πλΔ)½ =
1.4Å for Δ = 50Å, it is however possible to obtain, by choice of focus and
thickness, clear lattice images both resembling (see figure 2(b)), and not
resembling, the true crystal structure (see (2) for an example of a Fourier
image which is structurally incorrect). The crucial difficulty in using the
information between Up and u0 is the fractional accuracy with which Af and
Cs must be determined, and these accuracies Δff/4Δf =
(2λu2Δf)-1 and
ΔCS/CS =
(λ3u4Cs)-1
(for a π/4 phase change, Δff the Fourier image period)
are strongly dependent on spatial frequency u. Note that
ΔCs(up)/Cs
≈ 10%, independent of CS and λ. Note also that the
number n of identical high contrast spurious Fourier images within the depth
of field Δz = (αu)-1 (α beam divergence) decreases with
increasing high voltage, since n = 2Δz/Δff = θ/α = λu/α
(θ the scattering angle). Thus image matching becomes easier in
semiconductors at higher voltage because there are fewer high contrast
identical images in any focal series.
Parallel Image Processing Concepts
