charge-coupled device (CCD, a type of digital sensor) camera using an
objective lens. From this image, ellipsometric data of the sample (including
thickness) can be extracted pixel by pixel, generating a surface topography
map of the sample. Therefore, the ellipsometric data for the entire
sample can be determined quickly, resulting in a 3D image of the sample.
8.7.1.3 Methods for extracting ellipsometric data in imaging ellipsometry
The “pixel-by-pixel” ellipsometric data from an imaging ellipsometer
setup can be determined using one of several methods. A popular method
is to employ “off-null” mode analysis. We recall from our discussion of
ellipsometry in Section 8.3 that conventional ellipsometers are often
operated in null mode. In null mode, the change in the polarization state
of the reflected light is determined by changing the polarizer, compensator, and analyzer so that a null condition is achieved (no light passes
through the analyzer). Depending on the values of the polarizer, compensator, and analyzer used to achieve this null condition, different
ellipsometric parameters may be calculated. In “off-null” mode, the
imaging ellipsometer is “zeroed” by determining the null conditions for
the bare substrate. These conditions are then kept constant as the entire
sample is imaged. Since the sample is generally not of the same thickness
and refractive index as the substrate, light of greater and greater intensity
passes through the analyzer for thicker regions of the sample. Therefore,
the intensity of the light in each pixel can be related to the thickness of the
sample at that point. It should be noted, however, that this type of off-null
mode analysis is substrate-, sample-, and thickness-dependent, so comparisons with a reference material of known thickness and refractive
index are often recommended. For example, for a pure silicon substrate
and a biological sample, the intensity I under an off-null condition has
been reported to be related to the film thickness d by I = kd
2 where k is a
proportionality constant (not the imaginary component of the refractive
index), and this equation is valid with a deviation of approximately 2%
up to d ∼ 5 nm.
An alternative and perhaps more straightforward method for obtaining
the “pixel-by-pixel” ellipsometric parameters is to continually adjust the
polarizer, compensator, and analyzer in order to determine the null
condition for each pixel (or group of pixels) and then extract the
parameters from those null conditions as would be done in conventional
ellipsometry. While this approach is slightly more time-consuming, it
does not require the use of any reference samples or the intensitythickness assumptions employed in “off-null” mode analysis.
IMAGING NANOSTRUCTURES 309
objective lens. From this image, ellipsometric data of the sample (including
thickness) can be extracted pixel by pixel, generating a surface topography
map of the sample. Therefore, the ellipsometric data for the entire
sample can be determined quickly, resulting in a 3D image of the sample.
8.7.1.3 Methods for extracting ellipsometric data in imaging ellipsometry
The “pixel-by-pixel” ellipsometric data from an imaging ellipsometer
setup can be determined using one of several methods. A popular method
is to employ “off-null” mode analysis. We recall from our discussion of
ellipsometry in Section 8.3 that conventional ellipsometers are often
operated in null mode. In null mode, the change in the polarization state
of the reflected light is determined by changing the polarizer, compensator, and analyzer so that a null condition is achieved (no light passes
through the analyzer). Depending on the values of the polarizer, compensator, and analyzer used to achieve this null condition, different
ellipsometric parameters may be calculated. In “off-null” mode, the
imaging ellipsometer is “zeroed” by determining the null conditions for
the bare substrate. These conditions are then kept constant as the entire
sample is imaged. Since the sample is generally not of the same thickness
and refractive index as the substrate, light of greater and greater intensity
passes through the analyzer for thicker regions of the sample. Therefore,
the intensity of the light in each pixel can be related to the thickness of the
sample at that point. It should be noted, however, that this type of off-null
mode analysis is substrate-, sample-, and thickness-dependent, so comparisons with a reference material of known thickness and refractive
index are often recommended. For example, for a pure silicon substrate
and a biological sample, the intensity I under an off-null condition has
been reported to be related to the film thickness d by I = kd
2 where k is a
proportionality constant (not the imaginary component of the refractive
index), and this equation is valid with a deviation of approximately 2%
up to d ∼ 5 nm.
An alternative and perhaps more straightforward method for obtaining
the “pixel-by-pixel” ellipsometric parameters is to continually adjust the
polarizer, compensator, and analyzer in order to determine the null
condition for each pixel (or group of pixels) and then extract the
parameters from those null conditions as would be done in conventional
ellipsometry. While this approach is slightly more time-consuming, it
does not require the use of any reference samples or the intensitythickness assumptions employed in “off-null” mode analysis.
IMAGING NANOSTRUCTURES 309