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SEMI ME1392-0305 © SEMI 2003, 2005 14 RELATED INFORMATION 2 MODEL DEPENDENT CAL CULATED PARAMETERS NOTICE : This related information is not an official part of SEMI ME1392 and is not intended to modif y or supercede the …

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SEMI ME1392-0305 © SEMI 2003, 2005 13
R1-3 Reflectance Factor
R1-3.1 A measure of diffuse reflectance in common use is the reflectance factor, R, that is the ratio of flux
propagated from source to receiver in a reflectometer with a specimen, to the flux propagated with a perfectly
reflecting diffuser. Regarding a scatterometer as a very directional bi-directional reflectometer, the following
relationship between R and BRDF is obtained as follows:
BRDF
1/
BRDF
BRDF
BRDF
diffuser
R
(R1-6)
Additional information can be found in ASTM Practice E 167. Note that reflectance factor and specular reflectance
share the same symbol, R, but they are not the same parameter.
SEMI ME1392-0305 © SEMI 2003, 2005 14
RELATED INFORMATION 2
MODEL DEPENDENT CALCULATED PARAMETERS
NOTICE: This related information is not an official part of SEMI ME1392 and is not intended to modify or
supercede the official standard. It was developed during the original approval of this standard by ASTM Committee
E12 in 1996. SEMI approval was by full letter ballot procedures with publication authorized by the NA Regional
Standards Committee on December 10, 2004. Determination of the suitability of the material is solely the
responsibility of the user.
R2-1 Total Integrated Scatter (TIS)
R2-1.1 TIS can be calculated from BRDF by integrating BRDF over the hemisphere.
12
Typically a 5° total angle
“hole” is left around the specular beam since specular light is not included in total integrated scatter (see SEMI
MF1048).
R2-1.1.1 For an isotropic surface, measure in-plane BRDF at
i
= 0 and calculate the expected total integrated
scatter by integrating over the angle limits specified in SEMI MF1048.
70
5.2
1
calculated
dsinBRDFcos2TIS
sss
R
(R2-1)
R2-1.1.2 Sample specular reflectance, R, must be included because total integrated scatter is referenced to reflected
and not incident power. The cos
s
term must be included because BRDF is defined in terms of the projected
receiver aperture. This comparison between total integrated scatter and BRDF may not be exact since the total
integrated scatter detector is less sensitive to light incident on the detector at large angles and if low f (close to
specular) scatter dominates, the 5° hole size is critical. In addition a TIS instrument is not polarization selective.
R2-2 Roughness
R2-2.1 The rms surface roughness,
, is an often quoted number that can be obtained from direct profile
measurements with stylus or optical profilometers. It can also be inferred from total integrated scatter when,
<<
/4
for front surface scatter from a clean, smooth surface,
13
as described in SEMI MF1048.

2/1
TIS
4
(R2-2)
R2-2.1.1 The user must confirm the usefulness of this
calculation based on the particular measurement
circumstances. It may have strong frequency limitations and not agree with surface roughness derived from optical
or mechanical profile instruments (which can have different spatial frequency limits
14
).
R2-3 Power Spectrum
R2-3.1 The surface power spectral density function (PSD) can be calculated from the BRDF through a scatter
model. For example, the grating equation model discussed in §R1-2 shows that high frequency surface
perturbations scatter light far from specular and low frequency perturbations scatter close to specular. The PSD
shows the amount of modulation versus f , that is, the square of the Fourier transform of the surface profile. Since it
is a sample property, the same PSD should be obtained regardless of wavelength and incident angle dependent
differences in the BRDF data.
R2-3.2 Wavelength scaling is another check on system calibration. Smooth, clean, nonabsorbing front surface
reflectors should yield the same PSD for different BRDF measurement wavelengths. If the instrument does not
wavelength scale on appropriate samples, the BRDF measurement may be suspect. Polished molybdenum and
12 Stover, John C., Hourmand, Bahram, and Kahler, Jeffrey, A., “Comparison of Roughness Measurements by Differential Scatter and Total
Integrated Scatter,” Proceedings SPIE 511, 2-6 (1984).
13 Stover, John C., Optical Scattering: Measurement and Analysis, 2nd Edition, (SPIE Optical Engineering Press. Bellingham, WA, 1995)
Chapter 4.
14 Bennet, Jean M., and Mattsson, Lars, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, DC, 1989)
p. 32.
SEMI ME1392-0305 © SEMI 2003, 2005 15
silicon wafers are two examples of surfaces that have been shown to wavelength scale from the visible into the
infrared. Many beryllium mirrors and silicon carbide mirrors have been shown to not wavelength scale because of
anomalous scatter that arises from features other than surface roughness.