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SEMI ME1392-0305 © SEMI 2003, 2005 5 5.2 Source As sembly — containing the source and associ ated optics to produce irradian ce, E e , on the sample over a specified spot area, A . If a broad band source is used, the wav…
SEMI ME1392-0305 © SEMI 2003, 2005 4
furnish the instrument signature when reporting BRDF data so that the user can decide at what scatter direction the
sample BRDF is lost in the signature. Preferably the signature is several decades below the sample data and can be
ignored.
4.2.11 noise equivalent BRDF, NEBRDF — the root mean square (rms) of the noise fluctuation expressed as
equivalent BRDF.
4.2.11.1 Discussion — Measurement precision is limited by the acceptable signal to noise ratio with respect to these
fluctuations. It should be noted that although the detector noise is independent of
s
, the NEBRDF increases at large
values of
s
because of the 1/cos
s
factor. Measurement precision can also be limited by other experimental
parameters as discussed in Section 10. The NEBRDF can be measured by blocking the source light.
4.2.12 plane of incidence, PLIN, — the plane containing the sample normal and central ray of the incident flux.
4.2.13 receiver — a system that generally contains apertures, filters and focusing optics that gathers the scatter
signal over a known solid angle and transmits it to the scatter detector element.
4.2.14 receiver solid angle,
— the solid angle subtended by the receiver aperture stop from the sample origin.
4.2.15 sample coordinate system — a coordinate system fixed to the sample and used to specify position on the
sample surface for the measurement.
4.2.15.1 Discussion — The sample coordinate system is application and sample specific. The Cartesian coordinate
system shown in Figure A1-1 is recommended for flat samples. The origin is at the geometric center of the sample
face with the Z axis normal to the sample. A fiducial mark must be shown at the periphery of the sample; it is most
conveniently placed along either the X or Y axes. For silicon wafers, the fiducial mark is commonly placed on the
periphery of the wafer at the Y-axis as defined in SEMI M20.
4.2.16 sample irradiance, E
e
— the radiant flux incident on the sample surface per unit area.
4.2.16.1 Discussion — In practice, E
e
is an average calculated from the incident power, P
i
, divided by the
illuminated area, A. The incident flux should arrive from a single direction; however, the acceptable degree of
collimation or amount of divergence is application specific and should be reported.
4.2.17 sample radiance, L
e
— a differential quantity that is the reflected radiant flux per unit projected receiver
solid angle per unit sample area.
4.2.17.1 Discussion — In practice, L
e
is an average calculated from the scattered power, P
s
, collected by the
projected receiver solid angle,
·cos
s
, from the illuminated area, A. The receiver aperture and distance from the
sample determines
and the angular resolution of the instrument.
4.2.18 scatter — the radiant flux that has been redirected over a range of angles by interaction with the sample.
4.2.19 scatter azimuth angle,
s
, — angle from the XB axis to the projection of the scatter direction onto the XB-YB
plane.
4.2.20 scatter direction — the central ray of the collection solid angle of the scattered flux specified by
s
and
s
in
the beam coordinate system.
4.2.21 scatter plane — the plane containing the central rays of the incident flux and the scatter direction.
4.2.22 scatter polar angle,
s
, — polar angle between the central ray of the scattered flux and the ZB axis.
4.2.23 specular direction — the central ray of the reflected flux that lies in the PLIN with
s
=
i
and
s
= 0.
5 Apparatus
5.1 General — Non-specular reflectometers or instruments
6
used to measure scattered light utilize some form of the
five components described in this section. These components are described in a general manner so as to not exclude
any particular type of scatter instrument. To achieve (
i
,
i
;
s
,
s
) positioning the instrument design must
incorporate four angular degrees of freedom between the source, sample holder, and receiver assemblies.
6 Hsia, J. J. and Richmond, J. C., “A High Resolution Laser Bidirectional Reflectometer with Results on Several Optical Coatings,” J. Res. NBS-
A. Physics and Chemistry 80A, 189-205 (1976).
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5.2 Source Assembly — containing the source and associated optics to produce irradiance, E
e
, on the sample over a
specified spot area, A. If a broad band source is used, the wavelength selection technique should be specified.
Depending on the bandwidth and selection techniques, the detector assembly may affect the wavelength sensitivity.
If a laser source is used, it is usually sufficient to specify the center wavelength; however, it is sometimes necessary
to be more specific, such as providing the particular line in a CO
2
laser.
5.2.1 A source monitor is used to correct for fluctuations in the source intensity. If it is located at the source output
it only measures variations in the source power and is not sensitive to variations due to angular drift or downstream
transmission. The source monitor should monitor incident power as close to the sample as possible while
minimizing additional system scatter. Attention should be paid to possible laser mode hopping and consequent
wander of the beam on spatial filter pinholes and to fluctuations in source polarization.
5.2.2 Collimated or slightly converging source light can be used to measure BRDF. Most instruments use a
converging beam focused at the receiver. If the convergence angle is small, the uncertainty introduced by a non-
unique angle of incidence is usually negligible. The same considerations apply if a curved sample is measured. It is
the user's responsibility to assure that any spread in
i
does not compromise the results. Normal practice limits
convergence to f/20 or greater with a focus at the receiver to increase the angular resolution of measurements near
the specular beam or diffraction peaks.
5.2.3 Typically the source assembly is fixed in position and variations in
i
are made with the sample holder. Good
reduction of the instrument signature requires baffling around the source assembly and use of a spatial filter to limit
off-axis light. The final mirror (or lens) which directs light to the sample should have low scatter, since it
contributes directly to small angle scatter in the instrument signature.
5.2.4 A means should be provided for controlling the polarization state of the incident flux as this can impact the
measured BRDF. Orthogonal source polarization components (parallel, or p, and perpendicular, or s) are defined
relative to the plane defined by the source direction and the sample surface normal.
5.2.5 Absorbing samples may be heated by the incident flux and may change their scatter characteristics,
mechanically distort or burn. Special care must be taken with IR laser sources on absorbing samples.
5.3 Sample Holder — The sample holder should provide a secure mount for the sample that does not introduce any
warp. The rotation axes of the stages that achieve the (
i
,
i
,
s
s
) positioning must be relative to the sample front
surface; this can be accomplished by orienting the sample holder or the source, or both, and receiver assemblies.
Some sample mounts incorporate positioning stages for a raster scan of the sample surface at fixed incident and
scatter angles. The sample mount must be kept unobtrusive so that it does not contribute stray flux to the signature
or block large
s
scatter.
5.4 Beam Dump — It is important to trap any specular reflection from the sample so that it cannot contribute to the
scatter signal through lab/instrument reflections. Examples of beam dumps are black paper, a razor blade stack,
absorbing glass plates, or a tapered blackened glass tube.
5.5 Receiver Assembly — If the system design includes angular degrees of freedom at the receiver for achieving the
scatter direction, then the receiver assembly should normally have provisions for rotating about an axis on the front
face of the sample in order to vary
s
. If out of the PLIN measurements are required, the receiver assembly may also
rotate out of the PLIN. This capability may also be provided by pitch, yaw, and roll of the sample, but it becomes
more difficult to dump the specularly reflected beam.
5.5.1 The acceptance aperture for the receiver must be well defined, since the solid angle,
, subtended by the
receiver aperture stop from the sample, is used in the BRDF calculation and defines the angular resolution. The
field of view of the detector must include the entire irradiated area, A. There can be an exception to these
requirements if a relative BRDF or relative total reflectance normalization is used. In that case it is the user's
responsibility to ensure that the system parameters remain constant between measurements.
5.5.2 If the acceptance aperture is too small and a coherent source is used to irradiate the sample, speckle may
cause strong, unpredictable variations in the scatter. This is a common problem when measuring diffuse (that is,
rough) samples. It is sometimes desirable to spin a diffuse sample about its normal to average the effects of speckle
while making a measurement. It is the user’s responsibility to ensure that BRDF features are not due to speckle.
The user may wish to employ a variable aperture stop to trade sensitivity for angular resolution when measuring
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specular surfaces, since best angular resolution is needed near specular where BRDF has a steep slope. Best
sensitivity is needed at larger angles where BRDF might approach the NEBRDF.
5.5.3 It may be necessary to use an optical bandpass filter on the detector to minimize acceptance of background
light. This can also be accomplished by modulating the amplitude (with a mechanical chopper) of the source light,
and using a synchronized, phase sensitive (lock-in) amplifier with the detector.
5.5.4 Since depolarization can occur in scattering, complete characterization of scatter requires measurements with
a polarization analyzer at the receiver. The scatter reflux can be broken into perpendicular and parallel components
that are respectively perpendicular and parallel to the scatter plane (see Figure A1-2).
6 Calibration and Normalization
6.1 General — Instrument calibration is often confused with measurement of P
i
. Calibration of a BRDF instrument
involves systematic standardization and verification of its quantitative results. Incident power must be measured for
correct normalization of the scattered power. Absolute measurement of powers is not required as long as the P
s
/P
i
ratio is correctly measured. Alternatively, a reference sample can be used as a normalization reference.
6.2 Calibration — A leading cause of inaccuracy in BRDF measurement is a lack of instrument calibration. An
error analysis of the four quantities defining the BRDF (P
i
, P
s
,
,
s
) can help to accomplish a calibration.
7
Each of
these four independent variables is a function of system parameters. For example, P
s
depends on receiver linearity,
electrical noise and system alignment parameters. The total error is also a function of incidence angle and scatter
angle. It is reasonable to expect errors in the 3 to 10% range for measurements taken a few degrees from specular to
about
s
= 85°. System nonlinearity is a major contributor to error in this central region. At either end of this
central region errors rise dramatically. Near specular, this is caused by out of plane receiver position error, and near
the grazing angle the increase is due to uncertainty in
s
. Error is also a function of the type of sample being
measured. For example, larger errors are expected in the relatively steep BRDF associated with specular samples
than for the flatter response of a diffuse surface.
6.2.1 The receiver and preamplifier must be calibrated together over their useful operating range. The final result is
a calibration curve showing relative optical power versus voltage for each preamplifier gain setting. Operating
regimes are selected for each gain setting to avoid saturating the detector while remaining on a low gain setting. The
source monitor must also be calibrated in the same way.
6.2.2 There are several ways to vary the optical power and make this calibration curve. Optical filters with a known
attenuation can be used, but multiple reflections and coherent effects (interference between the two filter faces) can
change the attenuation. An excellent method of changing the optical power at the receiver is by moving away from
a diffuse source for 1/r
2
attenuation. Other methods include crossed polarizers or changing the duty cycle of a
chopper. The user must select an attenuation method with suitable reproducibility to perform the calibration.
6.2.3 The receiver and preamplifier each have a maximum output voltage to avoid saturation, but there is also a
minimum electronic noise level which should be kept in mind to avoid reporting noise as BRDF. When electronic
noise is expressed as NEBRDF, note that although the noise may be constant, NEBRDF depends on the receiver
solid angle, , the incident power, P
i
, and cos
s
. This means NEBRDF can be lowered by changing these system
parameters.
6.2.4 A full system calibration is not required on a daily basis, but the system should be checked daily. This check
can be accomplished by measuring the instrument signature and a stable reference sample that provides data over
several decades. Changes from past results are an indication of calibration problems and the cause of the change
must be determined. It is good operating practice to maintain a reference sample at the scatter facility for this
calibration check. Recalibration must be accomplished when components are changed, repaired, or realigned.
Include a data file number for the most recent reference sample measurement with every set of BRDF data as a
record of instrument response in case the data set is questioned at a later time.
6.3 Normalization — There are four acceptable methods for normalizing the scattered power to the incident power.
Each method is dependent on different measured parameters.
7 Cady, F. M., Bjork, D. R., Rifkin, J., and Stover, J.C., “BRDF Error Analysis,” Proceedings SPIE 1165, 154-164 (1989).