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SEMI ME1392-0305 © SEMI 2003, 2005 15 silicon wafers are two ex amples of surfaces that hav e be en shown to wavelength scale from the visible in to the infrared. Many beryllium mirrors and silicon carbide mirrors have b…

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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.
SEMI ME1392-0305 © SEMI 2003, 2005 16
RELATED INFORMATION 3
SUGGESTED REPORTING FORMAT
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.
R3-1 There is a considerable amount of information that should accompany BRDF measurements. This suggested
data file format (see Table R3-1) divides the information into descriptive headers followed by a data sequence of
variables. The headers consist of laboratory information, system information, sample information and measurement
parameters. These are simply generic labels that help to organize the fields under the headers. Any of the header
fields can be a variable in the data sequence; however, variables are normally limited to measurement parameters.
R3-2 The data files are stored as ASCII text fields. Each set of data taken is stored as a separate data file. Each
field in the headers and each data point in the data sequence begins on a new line (carriage return–line feed pair
terminates each line). Multiple items under each field in the headers and multiple variables per data point field in
the data sequence are separated by commas. Each field in the headers has a unique one word name preceding the
field contents on the same line. This name identifies the contents of the field. The first character of a name must be
an alpha character.
R3-3 The data sequence must come at the end of the file. Each line in the data sequence represents a single data
point. It must begin with a numeric character, the “+” character or the “” character. Multiple variables for each
data point are on the same line but separated by commas. This permits the data sequence to be printed as a set of
columns. Each variable must remain in the same column throughout a file. The VARS field specifies which
variable is in each column.
R3-4 Because of the name tag, there is no position dependence for information in the headers. The number of
header fields can vary from one data file to another. If a certain field is not in the file it means that information was
not recorded or does not apply to that measurement. Every user should supply a format template for their header
and data sequence in order to expedite conversion from site to site and avoid confusion over units and field size.
Fields can easily be added to the headers if sufficient descriptive text is provided in the field or on the template.
Fields can be added or deleted from old data sets without obsoleting the data file. This is a suggested list of fields in
a recommended grouping and order. Additional fields can be defined by users, and they can be added to this guide
as they become accepted by the scatter community.
Table R3-1 Suggested Data Format
L
ABORATORY INFORMATIO
N
LAB_NAME text field with the name of the facility
LAB_ADD street address of the facility
LAB_CITY city the facility is located in
LAB_STATE state the facility is located in
LAB_ZIP zip code
LAB_PHONE phone number of the laboratory
LAB_OPERATOR name of the operator
LAB_COMMENTS comments that pertain to the laboratory in open format
SYSTEM INFORMATION
SYSTEM_NAME name of the instrument the data was measured with; many facilities have more than one
scatter instrument
SOURCE_KW key words describing the source assembly such as laser, coherent, broad band, blackbody, or
vendor
RX_KW key words describing the receiver assembly such as cooled, silicon, array, HgCdTe