ASTM E1392-96

Standard Practice for Angle Resolved Optical Scatter Measurements on Specular or Diffuse Surfaces

SCOPE
1.1 This practice explains a procedure for the determination of the amount and angular distribution of optical scatter from an opaque surface. In particular it focuses on measurement of the bidirectional reflectance distribution function (BRDF). BRDF is a convenient and well accepted means of expressing optical scatter levels for many purposes (1,2).  Additional data presentation formats described in Appendix X1 have advantages for certain applications. Surface parameters can be calculated from optical scatter data when assumptions are made about model relationships. Some of these extrapolated parameters are described in Appendix X2.
1.2 Optical scatter from an opaque surface results from surface topography, surface contamination, and subsurface effects. It is the user's responsibility to be certain that measured scatter levels are ascribed to the correct mechanism. Scatter from small amounts of contamination can easily dominate the scatter from a smooth surface. Likewise, subsurface effects may play a more important scatter role than typically realized when surfaces are superpolished.
1.3 This practice does not provide a method to extrapolate from data for one wavelength to data for any other wavelength. Data taken at particular incident and scatter directions are not extrapolated to other directions. In other words, no wavelength or angle scaling is to be inferred from this practice. Normally the user must make measurements at the wavelengths and angles of interest.
1.4 This practice applies only to BRDF measurements on opaque samples. It does not apply to scatter from translucent or transparent materials. There are subtle complications which affect measurement of translucent or transparent materials that are best addressed in separate standards (see Practice E167 and Guide E179).
1.5 The wavelengths for which this practice applies include the ultraviolet, visible, and infrared regions. Difficulty in obtaining appropriate sources, detectors, and low scatter optics complicate its practical application at wavelengths less than about 0.25 [mu]m. Diffraction effects that start to become important for wavelengths greater than 15 [mu]m complicate its practical application at longer wavelengths. Diffraction effects can be properly dealt with in scatter measurements (3), but they are not discussed in this practice.
1.6 Any experimental parameter is a possible variable. Parameters that remain constant during a measurement sequence are reported as header information for the tabular data set. Appendix X3 gives a recommended reporting format that is adaptable to varying any of the sample or system parameters.
1.7 This practice applies to flat or curved samples of arbitrary shape. However, only a flat, circular sample is addressed in the discussion and examples. It is the user's responsibility to define an appropriate sample coordinate system to specify the measurement location on the sample surface for samples that are not flat.
1.8 The apparatus and measurement procedure are generic, so that specific instruments are neither excluded nor implied in the use of this practice.
1.9 This standard does not purport to address the safety concerns if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.

General Information

• Status: Historical
• Publication Date: 09-Dec-1996
• Technical Committee: F01 - Electronics

Relations

• Replaced By: ASTM E1392-96(2002) - Standard Practice for Angle Resolved Optical Scatter Measurements on Specular or Diffuse Surfaces (Withdrawn 2003)
• Effective Date: 10-Dec-1996

Standards Content (Sample)

NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
Designation: E 1392 – 96
Standard Practice for
Angle Resolved Optical Scatter Measurements on Specular
or Diffuse Surfaces
This standard is issued under the fixed designation E 1392; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
This standard has been approved for use by agencies of the Department of Defense.
1. Scope obtaining appropriate sources, detectors, and low scatter optics
complicate its practical application at wavelengths less than
1.1 This practice explains a procedure for the determination
about 0.25 μm. Diffraction effects that start to become impor-
of the amount and angular distribution of optical scatter from
tant for wavelengths greater than 15 μm complicate its practical
an opaque surface. In particular it focuses on measurement of
application at longer wavelengths. Diffraction effects can be
the bidirectional reflectance distribution function (BRDF).
properly dealt with in scatter measurements (3), but they are
BRDF is a convenient and well accepted means of expressing
2 not discussed in this practice.
optical scatter levels for many purposes (1,2). Additional data
1.6 Any experimental parameter is a possible variable.
presentation formats described in Appendix X1 have advan-
Parameters that remain constant during a measurement se-
tages for certain applications. Surface parameters can be
quence are reported as header information for the tabular data
calculated from optical scatter data when assumptions are
set. Appendix X3 gives a recommended reporting format that is
made about model relationships. Some of these extrapolated
adaptable to varying any of the sample or system parameters.
parameters are described in Appendix X2.
1.7 This practice applies to flat or curved samples of
1.2 Optical scatter from an opaque surface results from
arbitrary shape. However, only a flat, circular sample is
surface topography, surface contamination, and subsurface
addressed in the discussion and examples. It is the user’s
effects. It is the user’s responsibility to be certain that measured
responsibility to define an appropriate sample coordinate
scatter levels are ascribed to the correct mechanism. Scatter
system to specify the measurement location on the sample
from small amounts of contamination can easily dominate the
surface for samples that are not flat.
scatter from a smooth surface. Likewise, subsurface effects
1.8 The apparatus and measurement procedure are generic,
may play a more important scatter role than typically realized
so that specific instruments are neither excluded nor implied in
when surfaces are superpolished.
the use of this practice.
1.3 This practice does not provide a method to extrapolate
1.9 This standard does not purport to address the safety
data for one wavelength from data for any other wavelength.
concerns, if any, associated with its use. It is the responsibility
Data taken at particular incident and scatter directions are not
of the user of this standard to establish appropriate safety and
extrapolated to other directions. In other words, no wavelength
health practices and determine the applicability of regulatory
or angle scaling is to be inferred from this practice. Normally
limitations prior to use.
the user must make measurements at the wavelengths and
angles of interest.
2. Referenced Documents
1.4 This practice applies only to BRDF measurements on
2.1 ASTM Standards:
opaque samples. It does not apply to scatter from translucent or
E 167 Practice for Goniophotometry of Objects and Mate-
transparent materials. There are subtle complications which
rials
affect measurement of translucent or transparent materials that
E 179 Guide for Selection of Geometric Conditions for
are best addressed in separate standards (see Practice E 167
Measurement of Reflection and Transmission Properties of
and Guide E 179).
Materials
1.5 The wavelengths for which this practice applies include
E 284 Terminology Relating to Appearance
the ultraviolet, visible, and infrared regions. Difficulty in
F 1048 Test Method for Measuring the Effective Surface
Roughness of Optical Components by Total Integrated
This practice is under the jurisdiction of ASTM Committee F01 on Electronics 4
Scattering
and is the direct responsibility of Subcommittee F01.06 on Silicon Materials and
2.2 ANSI Standard:
Process Control.
Current edition approved Dec. 10, 1996. Published December 1997. Originally
published as E 1392 - 90. Last previous edition E 1392 – 90.
2 3
The boldface numbers in parentheses refer to a list of references at the end of Annual Book of ASTM Standards, Vol 06.01.
the text. Annual Book of ASTM Standards, Vol 10.05.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
E 1392
ANSI/ASME B46.1, Surface Texture (Surface Roughness, the XB axis to the projection of the incident direction onto the
Waviness, and Lay) XB-YB plane.
3.2.7.1 Discussion—It is convenient to use a beam coordi-
3. Terminology
nate system (refer to Fig. A1.2) in which f = 180°, since this
i
3.1 Definitions:
makes f the correct angle to use directly in the familiar form
s
3.1.1 Definitions of terms not included here will be found in
of the grating equation. Conversion to a sample coordinate
Terminology E 284 or ANSI Standard B 46.1. Additional
system is straight forward, provided the sample location and
graphic information will be found in Figs. A1.1-A1.3 in Annex
rotation are known.
A1.
3.2.8 incident direction—the central ray of the incident flux
3.2 Definitions of Terms Specific to This Standard:
specified by u and f in the beam coordinate system.
i i
3.2.1 angle of incidence, u —polar angle between the cen-
i
3.2.9 incident power, P —the radiant flux incident on the
i
tral ray of the incident flux and the ZB axis.
sample.
3.2.2 beam coordinate system, XB YB ZB—a cartesian
3.2.9.1 Discussion—For relative BRDF measurements, the
coordinate system with the origin on the central ray of the
incident power is not measured directly. For absolute BRDF
incident flux at the sample surface, the XB axis in the plane of
measurements it is important to verify the linearity, and if
incidence (PLIN) and the ZB axis normal to the surface as
necessary correct for the nonlinearity, of the detector system
shown in Fig. A1.1.
over the range from the incident power level down to the
3.2.2.1 Discussion—The angle of incidence, scatter angle,
scatter level which may be as many as 13 to 15 orders of
and incident and scatter azimuth angles are defined with
magnitude lower. If the same detector is used to measure the
respect to the beam coordinate system.
incident power and the scattered flux, then it is not necessary to
3.2.3 bidirectional reflectance distribution function,
correct for the detector responsivity; otherwise, the signal from
BRDF—the sample radiance divided by the sample irradiance.
each detector must be normalized by its responsivity.
The procedures given in this practice are correct only if the
3.2.10 instrument signature—the mean scatter level de-
field of view (FOV) determined by the receiver field stop is
tected when there is no sample scatter present expressed as
sufficiently large to include the entire illuminated area for all
BRDF.
angles of incidence of interest.
3.2.10.1 Discussion—Since BRDF is defined only for a
L ~P /VA cos u ! P
e s s s 21
surface, the instrument signature provides an equivalent BRDF
BRDF 5 5 5 @sr # (1)
E P V cos u
~P /A!
e i s
i
for the no-sample situation. The limitation on instrument
3.2.3.1 Discussion—BRDF is a differential function depen-
signature is normally stray scatter from instrument components
dent on the wavelength, incident direction, scatter direction,
and out-of-plane aperture position errors for receiver positions
and polarization states of the incident and scattered fluxes. In
near the specular direction. For high grade electronic detection
practice, it is calculated from the average radiance divided by
systems, at large scatter angles, the limitation on instrument
the average irradiance. The BRDF of a lambertian surface is
signature is normally Rayleigh scatter from molecules within
independent of scatter direction. If a surface scatters nonuni-
the volume of the incident light beam that is sampled by the
formly from one position to another then a series of measure-
receiver field of view. As u approaches 90°, the accuracy of u
s s
ments over the sample surface must be averaged to obtain
becomes important because of the l/cos u term in BRDF. The
s
suitable statistical uncertainty. Nonuniformity may be caused
signature can be measured by scanning a very low scatter
by irregularity of the surface microughness or film, optical
reference sample in which case the signature is adjusted by
property nonhomogeneity, or subsurface defects.
dividing by the reference sample reflectance. The signature is
3.2.4 cosine-corrected BRDF—the BRDF times the cosine
commonly measured by moving the receiver near the optical
of the scatter polar angle.
axis of the source and making an angle scan with no sample in
3.2.4.1 Discussion—The cos u in the BRDF definition is a
the sample holder. It is necessary to furnish the instrument
s
result of the radiometric definition of BRDF. It is sometimes
signature when reporting BRDF data so that the user can
useful to express the scattered field as normalized scatter
decide at what scatter direction the sample BRDF is lost in the
intensity [(watts scattered/solid angle)/incident power] as a
signature. Preferably the signature is several decades below
function of scatter direction. This is accomplished by multi-
the sample data and can be ignored.
plying the BRDF by cos u .
3.2.11 noise equivalent BRDF, NEBRDF—the root mean
s
3.2.5 delta beta, Db—the projection of Db onto the XB-YB
square (r/min) of the noise fluctuation expressed as equivalent
plane, that is, the delta theta angle measured in direction cosine
BRDF.
space. For scatter in the PLIN, Db = sin u − sin u . For scatter
s i
3.2.11.1 Discussion—Measurement precision is limited by
out of the plan of incidence (PLIN), the calculation of Db
the acceptable signal to noise ratio with respect to these
becomes more complicated (see Appendix X1.2).
fluctuations. It should be noted that although the detector noise
3.2.6 delta theta, Du—the angle between the specular direc-
is independent of u , the NEBRDF will increase at large values
s
tion and the scatter direction.
of u because of the 1/cos u factor. Measurement precision can
s s
3.2.7 incident azimuth angle, f —the fixed 180° angle from
i
also be limited by other experimental parameters as discussed
in Section 10. The NEBRDF can be measured by blocking the
source light.
Available from American National Standards Institute, 1430 Broadway, NY,
NY 10018. 3.2.12 plane of incidence, PLIN—the plane containing the
NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
E 1392
sample normal and central ray of the incident flux. found by integrating the BRDF over the hemisphere can be
3.2.13 receiver—a system that generally contains apertures, related to surface roughness. The amount of scatter at a given
filters and focussing optics that gathers the scatter signal over scatter angle can be associated with a specific surface spatial
a known solid angle and transmits it to the scatter detector frequency.
element.
4.3 The microroughness and contamination due to particu-
3.2.14 receiver solid angle, V— the solid angle subtended
lates and films on silicon wafers are interrogated with varying
by the receiver aperture stop from the sample origin.
forms of light scattering techniques. The angular distribution of
3.2.15 sample coordinate system—a coordinate system
light scattered by semiconductor surfaces is a generalized basis
fixed to the sample and used to specify position on the sample
for most scanning surface inspection systems and as such may
surface for the measurement.
be used to cross-correlate various tools.
3.2.15.1 Discussion—The sample coordinate system is ap-
plication and sample specific. The cartesian coordinate system
5. Apparatus
shown in Fig. A1.1 is recommended for flat samples. The
5.1 General—Non-specular reflectometers or instruments
origin is at the geometric center of the sample face with the Z
(4) used to measure scattered light utilizes some form of the
axis normal to the sample. A fiducial mark must be shown at
five components described in this section. These components
the periphery of the sample; it is most conveniently placed
are described in a general manner so as to not exclude any
along either the X or Y axes. For silicon wafers, the fiducial
particular type of scatter instrument. To achieve (u , f ; u , f )
i i s s
mark is commonly placed on the y-axis.
positioning the instrument design must incorporate four df
3.2.16 sample irradiance, E —the radiant flux incident on
e
between the source, sample holder, and receiver assemblies.
the sample surface per unit area.
5.2 Source Assembly— containing the source and associated
3.2.16.1 Discussion—In practice, E is an average calcu-
e
optics to produce irradiance, E , on the sample over a specified
e
lated from the incident power, P , divided by the illuminated
i
spot area, A. If a broad band source is used, the wavelength
area, A. The incident flux should arrive from a single direction;
selection technique should be specified. Depending on the
however, the acceptable degree of collimation or amount of
bandwidth and selection techniques, the detector assembly may
divergence is application specific and should be reported.
affect the wavelength sensitivity. If a laser source is used, it is
3.2.17 sample radiance, L —a differential quantity that is
e
usually sufficient to specify the center wavelength; however, it
the reflected radiant flux per unit projected receiver solid angle
is sometimes necessary to be more specific such as providing
per unit sample area.
the particular line in a CO laser.
3.2.17.1 Discussion—In practice, L is an average calcu-
e
5.2.1 A source monitor is used to correct for fluctutions in
lated from the scattered power, P , collected by the projected
s
the source intensity. If it is located at the source output it only
receiver solid angle, V cos u , fr
...