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SEMI M40-0200 © SE MI 2000 6 other noise s o urces, such as background electronic noise and Rayl eigh air scatter, are not issues. 8 Roughness Measurem ent s 8.1 Parameters 8.1.1 R q and R a are generally used f o r s il…
SEMI M40-0200 © SEMI 20005
θ
i
= incidence angle of light.
7.3.2 Corresponding amplitude examples assuming a
limit of 0.1 result in
a ≤ 23 nm for λ = 633 nm, θ
i
= 0° and
a ≤ 51 nm for λ = 488 nm, θ
i
= 70°
7.3.3 The equivalent rms-roughness values for a
sinusoidal profile and for a limit of 0.1 are
R
q
≤ 16 nm for λ = 633 nm, θ
i
= 0° and
R
q
≤ 36 nm for λ = 488 nm, θ
i
= 70°
7.3.4 Light scattering tools can be ap plied to rougher
surfaces than those surfaces identified in equations 1
and 2, but then other mathematical approaches as
compared to PSD curves have to be applied to calculate
roughness or slope values. Also, the slope of the PSD
curve can be important in certain situations (Stover).
7.3.5
There is a basic high spatial fr equency (short
spatial wavelength) limit for light scattering tools which
cannot be exceeded. This limit is:
a) twice the inverse wavelength,
λ
2
, of the light used in
case of grazing incidence (θ
i
= 90°), and
b) one inverse wavelength,
λ
1
, in the case of normal
incidence (θ
i
= 0°).
These conditions follow directly from the one-
dimensional grating equation
λ
θφθ
i
ss
x
f
coscossin −
=
where: θ
s
= scattering angle in the incident plane,
and
φ
s
= scattering angle out of the plane-of-incidence.
NOTE 3: f
x
becomes -1 when the light is scattered back in the
direction of the incoming light in the incident plane (
φ
s
=
180
o
).
7.4 Total Integrating Scatteromete rs (TIS)
7.4.1 These instruments most often use an incidence
angle close to zero. The low and high frequency limits
of the accessible spatial bandwidth are defined by the
design of the optical system. An appropriately
designed system may be able to access a spatial
bandwidth from about 0.8 µm to about 40 µm. These
systems may also be designed so that the scattered
signal can be broken into low spatial frequency (near
specular) and high spatial frequency (large scatter
angle) bands.
7.5 Angle-resolved Light Scatterometers (ARLS)
7.5.1 The high spatial frequency lim it of this technique
is defined by incident and scattering angles and the
illumination wavelength used.
7.5.2
The low spatial frequency limi t is given by
• the above equations (for incidence angle),
•
the diameter of the incident illumination spot at the
wafer surface,
•
the solid collection angle of the optical system, and
• the smallest angular distance allowed by the
instrument between specular reflected light and the
detector.
7.5.3
The roughness may be measur ed by using a
fixed incidence angle and by recording the intensity of
scattered light at various scattering angles in the plane
of incidence. The two-dimensional PSD curve of the
surface can then be calculated from the angular
spectrum of the scattered light (BRDF). R
q
as well as
mq may be calculated from a one-dimensional or
isotropic PSD curve for a given spatial bandwidth as
long as the above mentioned limits are accommodated.
7.5.4
Such tools may be able to access a spatial
bandwidth range of about one-half the wavelength of
the illuminating light up to several hundred µm.
7.6
Scanning Surface Inspection Systems (SSIS)
7.6.1 SSIS measurements are integra ted scatter
measurements similar to those made by TIS systems, in
that they gather light over large solid angles; however,
there are some significant differences. In general, most
SSIS avoid light collection within five to ten degrees of
the specular beam, because in this region the scatter
tends to be dominated by surface roughness scatter
(which becomes background noise) competing with the
signal from laser light scattering events. The early
(older) scanners generally had one detector measuring
light from a very large solid angle collector. Later
systems tend to use several smaller collection angles,
each with their own detector. Whatever the
arrangement, each collection angle can be defined in
terms of its spatial frequency band pass region, and
each detector will have some background haze
component (or threshold) that is caused by surface
roughness. Thus, in the absence of laser light scattering
events, measured haze may be converted to an rms
roughness for the defined spatial frequencies. This
conversion assumes that the surface meets the
necessary (smooth, clean, front surface reflective)
conditions required for roughness calculations, and that
SEMI M40-0200 © SEMI 2000 6
other noise sources, such as background electronic
noise and Rayleigh air scatter, are not issues.
8 Roughness Measurement s
8.1 Parameters
8.1.1 R
q
and R
a
are generally used for silicon wafer
surfaces. Other roughness measurement parameters
may also prove useful. This guideline does not suggest
which parameters to use, rather it suggests how to
incorporate any parameter into a standardized
measurement specification.
8.2
Measurement Sites
8.2.1 Roughness can vary considerably across a wafer
surface. It may also have a preferential direction or
anisotropy, often called “lay” (ASME B46.1). Many
measurement techniques are limited to a very small
measurement area and to one or two scan directions.
Therefore specific measurement patterns must be
defined to obtain representative and reproducible
results. These patterns should correspond to effects
observed on wafers in different manufacturing steps.
These processing steps can generate features on a wafer
surface with rotational symmetries ranging from mirror
to infinite. The wafer slicing process may produce low
symmetry, while single-wafer polishing can produce
high symmetry.
8.2.2
In cases where only a small nu mber of spots is
measured, the spot pattern and the scan orientation have
to be identified. See Figure 1 for some patterns and
orientations; others may be agreed upon between
interested parties.
8.3
Site Patterns
8.3.1 One-point — This can be usef ul for rapidly
reviewing results of a quantity of wafers. This is often
at the wafer centerpoint.
8.3.2
In applications where only a small number of
locations are to be measured, the pattern and orientation
of the local scans have to be identified. Measurements
are performed at locations as outlined in Figure 1. For
each local scan, a representative roughness is
calculated. The wafer’s representative roughness is
then a function of the n individual representative scan
values. The roughness variation can be calculated by
the average, the standard deviation, the maximum or the
range (Max-Min) of the individual scan values. Other
statistical approaches may be employed.
8.3.3
Standard patterns include:
a. 1-point Wafer center,
b. 5-point Wafer Center plus four points at 2r/3
from the wafer center, and
c.
9-point Wafer Center plus four points at 2r/5
and four at 4r/5 from the wafer center.
NOTE 4: These patterns have been shown to be useful with a
range of symmetries and values. See Related Information.
8.3.4 Standard measurement orientation patterns
include:
a.
Type A - linear scans parallel and perpendicular
to the fiducial bisector, and
b. Type B - linear scans at 45
o
relative to the
fiducial bisector.
NOTE 5: Type A is generally used for all surfaces. Type B
has been reported to be useful for some surface conditions on
(111) wafers.
8.4 Bandwidth
8.4.1
Two issues affect the bandwidth of the
roughness results. The first is the bandwidth of the
roughness measuring tool, which is discussed in Section
7. The second bandwidth effect is from the analysis
software, which is user selected to emphasize certain
spatial frequencies. Both long and short spatial
wavelength (or frequency) limits must be defined in µm
(or µm
-1
). When entering this information into a
measurement, specification wavelength units shall be
used. Profiling instruments should have scan length
and bandwidth adjusted according to DIN 4768 and
4777 or ASME B46.1.
8.5
Precision
8.5.1 The precision of the roughness measuring
instrument (P) is important. The relationship between
P and the tolerance of the parts to be characterized (T)
is often called the P/T Ratio. SEMI M27 describes how
to determine and interpret the factors: “A test
instrument is usually deemed to be suitable for the
purpose if P/T lies below 10%. If P/T is greater than
30%, the test instrument is not likely to be suitable for
the purpose. Cases for which P/T lies between 10%
and 30% must be judged on an individual basis,
depending on the requirements being placed on the
measurement system.”
9 Roughness Measurement Specifications
9.1 The process of defining the me asurements to be
taken involves several distinct steps. The definition
sequence below represents one logical sequence; others
may be equally useful. See Table 1 for measurement
abbreviations.
9.2
First, select the type of instrument to be used,
including ALL of the following:
9.2.1 Generic instrument type
SEMI M40-0200 © SEMI 20007
9.2.1.1 Interferometer
a. Interference microscope
9.2.1.2
Profilometer
a. AFM
b. Other scanning probe microscopes
c. Optical profilometer
d. Mechanical stylus
9.2.1.3
Scatterometer
a. Total Integrating (TIS)
b. Angle-resolved light (ARLS)
c. Scanning Surface Inspection System (SSIS)
9.3
Next, select the roughness para meter to by
calculated.
9.4 Select the measurement pattern (Figure 1):
a. Center point
b. 5-point
c. 9-point
d. Full-FQA raster scan
e. Full-FQA R-theta scan
9.5
Select the pattern orientation ( Figure 1)
a. Type A
b. Type B
9.6
Select the local measuring condition
a. Point
b. Line
c. Area
9.7
Specify the measurement calculations to be
reported
a. Average (A)
b. Range (R)
c. Maximum (M)
d. Standard Deviation, 1 sigma (S
n-1
)
9.8 Specify the bandwidth and sca n length limits
within which data is to be gathered.
9.9 Lastly, record the abbreviations describing these
selections (see Appendix 1 for examples), separating
adjacent abbreviations with a comma and using periods
for decimal notation. This creates a seven-field
abbreviation. The field sequence described above
follows the order of elements in Table 1.
10 Measurement Reporting S equence
10.1 In general, one value is reported for a wafer.
Where more than one pattern is specified the calculated
values are reported in the order in which they are listed
in Table 1.