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6.4.3
6 - 67
(b) Measurement error Caused by SEM Image Resolution
Image resolution can be regarded as the minimum dimension where sample
information can be reproduced in a form of brightness (contrast) change. Thus there
is no meaningful contrast when a dimension is smaller than the image resolution.
Such an area of no contrast is equivalent to a pixel because there is also no contrast
in a pixel area. Therefore the effect of resolution upon measurement error is similar
to that of pixel size described above, and image resolution finally determines the
measurement error at higher magnifications.
(c) Measurement Error in Consideration of Both Pixel Size and Image Resolution
Measurement errors caused by both pixel size and image resolution are determined by
the effective pixel size.
eff
Px
L which is approximated by the following equation:
2
R
2
P
eff
Px
LLL += ...................................................................(6.4.7)
Here L
P
and L
R
represent pixel size and image resolution, respectively. If image
resolution is 1.5 nm and measured dimension is L at a magnification of 150 k×, for
example, measured dimension L includes error of ±1.95 nm since the effective pixel
size (
eff
Px
L ) is given as 1.95 nm by resolution (1.5 nm) and pixel size (1.25 nm at 150
k×).
Figure 6.4-9 shows the relation between measured dimensions and measurement
error (theoretical value) at various magnifications. Measurement error in the figure is
caused only by pixel size and image resolution (assumed to be 1.5 nm). Other
measurement reproducibility factors are not included. Assuming the upper limit of
measurement magnification is 150 k× and measurement error is suppressed to within
±2%, the minimum theoretical dimension measurable is about 0.1 µm.