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6.4 CD Measurement Function (Option)
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(3) Measurement Error Caused by Pixel Size or Image Resolution
Described in this section are the measurement errors caused by pixel size or SEM image
resolution. These errors are more conspicuous as the measured dimension becomes smaller.
(a) Measurement Error Caused by Pixel Size
In the CD measurement function, dimensions are measured by counting a number of
pixels included within measurement cursors in the acquired SEM image of 640 × 480
pixels. The minimum dimension for measurement (measurement resolution)
therefore coincides with pixel size in the image.
As shown in Fig. 6.4-8, if the number of pixels included within cursors is N and the
measured dimension is L, the true dimension L0 will be in the following range:
L
N
1
1LL
N
1
1
0
⋅
+<<⋅
− ..............................................(6.4.6)
In other words the measured dimension includes error of ±L/N relative to true value L0.
When the number of pixels within cursors is 10 and measured dimension is 1 µm, for
example, the true value of dimension will be in the range of 0.9 to 1.1 µm. Therefore
the measured dimension includes error of ±10% in this case. However, if
measurement is made by 100 pixels at ten times higher magnification on the same
dimension (1 µm), the true dimensions will be in the range of 0.99 to 1.01 µm and the
error will decrease down to ±1%.
The number of pixels within cursors is dependent on dimensions and image
magnification. Higher magnifications allow more pixels for measuring dimensions,
and therefore the measurement error caused by pixel size decreases at higher
magnifications. But the effect of resolution in SEM image upon measurement error
becomes more important at higher magnifications. The effect of installation
conditions (floor vibration and stray magnetic field), sample damage and
contamination will also be important at higher magnifications. The highest
magnification which is suitable for measuring dimensions is limited for these reasons.
L = L
0
(1 ± 1/N)
L : Measured value
L
P
: Pixel size
L
0
: True dimension (L
1
< L
0
< L
2
)
Fig. 6.4-8 Measurement Error Caused by Pixel Size
Measurement curso
r
Pixel
L = N × L
p
L
1
= (N - 1) × L
p
L
2
= (N + 1) × L
p
L
p