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SEMI ME1392-0305 © SEMI 2003, 2005 2 complicate its practical application at l onger wavelengths. Diffraction e ffects can be properly dealt with in scatter measurements, 3 but they are not discussed in this practice. 2.…
SEMI ME1392-0305 © SEMI 2003, 2005 1
SEMI ME1392-0305
GUIDE FOR ANGLE RESOLVED OPTICAL SCATTER
MEASUREMENTS ON SPECULAR OR DIFFUSE SURFACES
This guide was technically approved by the Global Silicon Wafer Committee and is the direct responsibility
of the North American Silicon Wafer Committee. Current edition approved for publication by the North
American Regional Standards Committee on December 10, 2004. Initially available at
www.semi.org
January 2005; to be published March 2005. Original edition published by ASTM International as ASTM E
1392-90. Last previous edition SEMI ME 1392-96 (Reapproved 2002).
1 Purpose
1.1 The microroughness and contamination due to particulates and films on silicon wafers are interrogated with
varying forms of light scattering techniques. The angular distribution of light scattered by semiconductor surfaces is
a generalized basis for most scanning surface inspection systems and as such may be used to cross-correlate various
tools.
1.2 The angular distribution of scatter from optically smooth surfaces, such as polished silicon wafers, can be used
to calculate surface parameters or reveal surface characteristics. For example, the total scatter found by integrating
the bidirectional reflectance distribution function (BRDF) over the hemisphere can be related to surface roughness.
The amount of scatter at a given scatter angle can be associated with a specific surface spatial frequency.
1.3 The angular distribution of scatter is a general property of surfaces that may have direct consequences. Scatter
from mirrors and other components in an optical system can be the limiting factor in resolution or optical signal to
noise level. Scatter can be an important design parameter for telescopes. Scatter measurements are crucial to
correct operation of ring laser gyros. Scatter from a painted surface, such as on automobiles, can influence sales
appeal.
2 Scope
2.1 This guide 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 BRDF, which is a convenient and well
accepted means of expressing optical scatter levels for many purposes.
1
,2
Additional data presentation formats
described in Related Information 1 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 Related Information 2.
2.2 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.
2.3 This guide does not provide a method to extrapolate data for one wavelength from 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 guide. Normally the user must make
measurements at the wavelengths and angles of interest.
2.4 This guide 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, for example, ASTM Practice E 167 and
ASTM Guide E 179).
2.5 The wavelengths for which this guide 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 m. Diffraction effects that start to become important for wavelengths greater than 15 m
1 Nicodemus, Fred E., “Directional Reflectance and Emissivity of an Opaque Object,” Applied Optics 4, 767 (1965).
2 Nicodemus, F. E., Richmond, J. C., and Hsia, J. J., “Geometrical Considerations and Nomenclature for Reflectance,” NBS Monograph 160,
1977.
SEMI ME1392-0305 © SEMI 2003, 2005 2
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.
2.6 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. Related Information 3 gives a suggested
reporting format that is adaptable to varying any of the sample or system parameters.
2.7 This guide 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.
2.8 The apparatus and measurement procedure are generic, so that specific instruments are neither excluded nor
implied in the use of this guide.
NOTICE: This standard does not purport to address safety issues, if any, associated with its use. It is the
responsibility of the users of this standard to establish appropriate safety and health practices and determine the
applicability of regulatory or other limitations prior to use.
3 Referenced Standards
3.1 SEMI Standards
SEMI M20 — Practice for Establishing a Wafer Coordinate System
SEMI MF1048 — Test Method for Measuring the Effective Surface Roughness of Optical Components by Total
Integrated Scattering
3.2 ASTM Standards
E 167 — Practice for Goniophotometry of Objects and Materials
4
E 179 — Guide for Selection of Geometric Conditions for Measurement of Reflection and Transmission Properties
of Materials
4
E 284 — Terminology Relating to Appearance
4
3.3 ANSI Standard
ANSI/ASME B46.1— Surface Texture (Surface Roughness, Waviness, and Lay)
5
NOTICE: Unless otherwise indicated, all documents cited shall be the latest published versions.
4 Terminology
4.1 Definitions of terms not included here will be found in Terminology E 284 or ANSI Standard B 46.1.
Additional graphic information will be found in Figures A1-1 through A1-3 in Appendix 1.
4.2 Definitions
4.2.1 angle of incidence,
I
, — polar angle between the central ray of the incident flux and the ZB axis, normal to
the sample surface.
4.2.2 beam coordinate system, XB YB ZB — a Cartesian coordinate system with the origin on the central ray of the
incident flux at the sample surface, the XB axis in the plane of incidence (PLIN) and the ZB axis normal to the
surface.
4.2.2.1 Discussion — The angle of incidence, scatter angle, and incident and scatter azimuth angles are defined
with respect to the beam coordinate system. This coordinate system is illustrated in Figure A1-1.
3 Smith, Sheldon M., “Reflectance of AMES 24E, Infrablack and Martin Black,” SPIE 967, 251 (1988).
4 Annual Book of ASTM Standards, Vol 06.01, ASTM International, 100 Barr Harbor Drive, West Conshohocken, PA 19428. Telephone: 610-
832-9500, Fax: 610-832-9555, Website:
www.astm.org
.
5 American National Standards Institute, New York Office: 25 West 43rd Street, New York, NY 10036, USA. Telephone: 212-642-4900; Fax:
212-398-0023, Website:
www.ansi.org
.
SEMI ME1392-0305 © SEMI 2003, 2005 3
4.2.3 bidirectional reflectance distribution function, BRDF — the sample radiance divided by the sample
irradiance.
4.2.3.1 Discussion — The procedures given in this practice are correct only if the field of view (FOV) determined
by the receiver field stop is sufficiently large to include the entire illuminated area for all angles of incidence of
interest. BRDF is a differential function dependent on the wavelength, incident direction, scatter direction, and
polarization states of the incident and scattered fluxes. In practice, it is calculated from the average radiance divided
by the average irradiance as follows:
1
cos
sr
cos
BRDF
si
s
A
P
A
P
e
e
P
P
E
L
i
s
s
(1)
The BRDF of a lambertian surface is independent of scatter direction. If a surface scatters nonuniformly from one
position to another then a series of measurements over the sample surface must be averaged to obtain suitable
statistical uncertainty. Nonuniformity may be caused by irregularity of the surface microughness or film, optical
property nonhomogeneity, or subsurface defects.
4.2.4 cosine-corrected BRDF — the BRDF times the cosine of the scatter polar angle.
4.2.4.1 Discussion — The cos
s
in the BRDF definition is a result of the radiometric definition of BRDF. It is
sometimes useful to express the scattered field as normalized scatter intensity [(watts scattered/solid angle)/incident
power] as a function of scatter direction. This is accomplished by multiplying the BRDF by cos
s
.
4.2.5 delta beta,
— the projection of
onto the XB-YB plane, that is, the delta theta angle measured in
direction cosine space.
4.2.5.1 Discussion — For scatter in the PLIN,
= sin
s
sin
i
. For scatter out of the plane of incidence (PLIN),
the calculation of
becomes more complicated (see §R1-2).
4.2.6 delta theta,
— the angle between the specular direction and the scatter direction.
4.2.7 incident azimuth angle,
i
— the fixed 180° angle from the XB axis to the projection of the incident direction
onto the XB-YB plane.
4.2.7.1 Discussion — It is convenient to use a beam coordinate system (refer to Figure A1-2), in which
i
= 180°,
since this makes
s
the correct angle to use directly in the familiar form of the grating equation. Conversion to a
sample coordinate system is straight forward, provided the sample location and rotation are known.
4.2.8 incident direction — the central ray of the incident flux specified by
i
and
i
in the beam coordinate system.
4.2.9 incident power, P
i
— the radiant flux incident on the sample.
4.2.9.1 Discussion — For relative BRDF measurements, the incident power is not measured directly. For absolute
BRDF measurements it is important to verify the linearity, and if necessary correct for the nonlinearity, of the
detector system over the range from the incident power level down to the scatter level which may be as many as 13
to 15 orders of magnitude lower. If the same detector is used to measure the incident power and the scattered flux,
then it is not necessary to correct for the detector responsivity; otherwise, the signal from each detector must be
normalized by its responsivity.
4.2.10 instrument signature — the mean scatter level detected when there is no sample scatter present expressed as
BRDF.
4.2.10.1 Discussion — Since BRDF is defined only for a surface, the instrument signature provides an equivalent
BRDF for the no-sample situation. The limitation on instrument signature is normally stray scatter from instrument
components and out-of-plane aperture position errors for receiver positions near the specular direction. For high
grade electronic detection systems, at large scatter angles, the limitation on instrument signature is normally
Rayleigh scatter from molecules within the volume of the incident light beam that is sampled by the receiver field of
view. As
s
approaches 90°, the accuracy of
s
becomes important because of the l/cos
s
term in BRDF. The
signature can be measured by scanning a very low scatter reference sample in which case the signature is adjusted
by dividing by the reference sample reflectance. The signature is commonly measured by moving the receiver near
the optical axis of the source and making an angle scan with no sample in the sample holder. It is necessary to