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SEMI M40-0200 © SE MI 2000 4 NA λ 61 . 0 where NA is the numerical apertu re of the objective lens and λ is the illumination wavelength. 8 6.17 rms area micr oroughness (R q A) — t he root m ea n square of the topog raph…
SEMI M40-0200 © SEMI 20003
5.7 Other Documents
International Technology Roadmap for
Semiconductors
6
Optical Scattering in the Optics, Semiconductor, and
Computer Disk Industries, Second Edition 1995, J C
Stover, Editor
7
NOTE 1: As listed or revised, all documents cited shall be the
latest publications of adopted standards.
6 Terminology
6.1 autocorrelation function — th e Fourier transform
of the Power Spectral Density function. It expresses the
similarity between a surface profile and the same
profile that is slipped, or moved laterally, with respect
to itself.
6.2 autocorrelation length — the l ateral slip required
to reduce the Autocorrelation function to a value equal
to e-1 times its zero slip value. Sometimes 10% or even
0 value definitions are used instead of e-1.
6.3 average roughness (R
a
) — the average of the
surface profile height deviations Z(x) from the mean
line taken within the evaluation length (ASME B46.1).
6.4 bi-directional reflectance distribution function,
BRDF — a description of the distribution of light
scattered by a surface, it is the differential radiance
normalized by the differential irradiance, and is
approximated by the scattered power per unit projected
solid angle divided by the incident power (Stover).
6.5 fixed quality area (FQA) — the central area of a
wafer surface, defined by a nominal edge exclusion, X,
over which the specified values of a parameter apply
(SEMI M1). See also the discussion immediately
following this definition in SEMI M1.
6.6 haze — non-localized light sca ttering resulting
from surface topography (microroughness) or from
dense concentrations of surface or near-surface
imperfections (SEMI M1).
DISCUSSION — Haze due to the existence of a
collection of imperfections is a mass effect; individual
imperfections of the type which result in haze cannot be
readily distinguished by the eye or other optical
detection systems without magnification. In a particle
counter (SSIS), haze results in a background signal and
laser light-scattering events together comprise the
signal due to light-scattering from a wafer surface.
(SEMI M1). It is the total scattered optical flux
6 Semiconductor Industry Association (SIA), 181 Metro Drive, Suite
450, San Jose, CA
7 SPIE, P.O. Box 10, Bellingham, WA 98227-0010
collected by an optical system normalized by the
incident flux.
NOTE 2: Different SSIS instrument types may give
significantly different haze values on a given sample.
6.7 illumination source incidence angle the angle
of the incoming beam, measured from surface normal.
6.8 kurtosis (Rku) — a measure of the sharpness of the
histogram of surface profile height deviations Z(x) from
the mean line within the evaluation length. A complete
random surface will have a Gaussian histogram and Rku
= 3 (ASME B46.1).
6.9 laser light-scattering event — a signal pulse that
exceeds a preset threshold, generated by the interaction
of a laser beam with a discrete scatterer at a wafer
surface as sensed by a detector; see also haze (SEMI
M1). See also the discussion that follows this definition
in SEMI M1.
6.10 lay – the predominant directio n of the surface
pattern, ordinarily determined by the production
method used (ASME B46.1).
6.11 microroughness — surface roughness
components with spacing between irregularities (spatial
wavelength) less than about 100 µm (SEMI M1).
6.12 Nyquist Criterion — the shorte st spatial
wavelength detected. It is twice the sample spacing.
6.13 one-dimensional grating equa tion — in its most
common form, it is an expression that gives the
positions of diffracted orders from a one-dimensional
sinusoidal grating (Stover).
6.14 peak to valley (R
t
) — the highe st to lowest value
of the surface profile height deviations Z(x) from the
mean line taken within the evaluation Length L (ASME
B46.1).
6.15 power spectral density (PSD) function — a
surface characterization function that is proportional to
the square of the modulus of the Fourier transform of
the surface and may be considered as a roughness
power per unit of spatial frequency (ASTM F 1811).
6.16 Rayleigh Criterion (of resolvin g power) — a
condition for distinguishing a pair of diffraction
patterns whereby the maximum of one pattern overlaps
with the minimum of the other.
DISCUSSION — When a lens is free from aberrations,
the images of point objects appear as diffraction
patterns. When the principle maximum of one pattern
strikes the first minimum of another, the images are
described as being resolved. With respect to circular
optics, this criterion applies when the distance between
resolvable point objects, viewed from the objective lens
of the instrument, is
SEMI M40-0200 © SEMI 2000 4
NA
λ
61.0
where NA is the numerical aperture of the objective lens
and λ is the illumination wavelength.
8
6.17 rms area microroughness (R
q
A) — the root mean
square of the topographic deviations of a surface Z(x,y)
from the mean surface taken within the evaluation Area
(=L
x
L
y
) (SEMI M1). See also the extended discussion
that follows this definition in SEMI M1.
6.18
rms microroughness (R
q
) — th e root mean square
of the surface profile height deviations Z(x) from the
mean line taken within the evaluation Length L (SEMI
M1). See also the extended discussion that follows this
definition in SEMI M1.
6.19
rms slope (mq) — the root-mean-square value of
the rate of change of profile departures within the
evaluation length (Adapted from ISO 4271/1).
6.20 roughness — the more narrowly spaced
components of surface texture (SEMI M1). Compare
with waviness.
6.21
skewness (Rsk) — a measure o f the asymmetry of
the surface topographic deviations of a surface Z(x,y)
about the mean line. A perfect random surface will
have Rsk = 0 (ASME B46.1).
6.22
spatial bandwidth — the range of wavelengths in
which a given instrument operates (Stover).
6.23 spatial frequency — spatial frequency (F
spatial
) is
the inverse of spatial wavelength (λ
spatial
).
6.24 spatial wavelength — the spac ing between
adjacent peaks of a purely sinusoidal profile (ASME
B46.1).
6.25 ten point roughness height (R
z
) — the average
value of the absolute values of the heights of the five
highest profile peaks and the depths of the five lowest
profile valleys from the mean line taken within the
evaluation length. (Adapted from ISO 4281/1.)
6.26
transfer function — the response of an instrument
over all measured spatial wavelengths.
DISCUSSION — A perfect instrument would have a
100% response over all spatial wavelengths. Every
measuring instrument will have some deviation from a
perfect response especially at the low spatial frequency
limit (the traversing length) and at the high spatial
frequency limit. The power spectrum can be used to
examine this limit near the high spatial frequency
8 Optics, Eugene Hecht, et al; 3rd edition (August 1997); Addison-
Wesley Publishing Co; ISBN: 0201838877
response. Contact the instrument supplier for this
information.
6.27 traversing length — the maximum distance
sampled in a given direction. The maximum
measurable spatial wavelength is always less then the
traversing length.
6.28
wavelength scaling — a surfac e is said to
wavelength scale if the scatter measurements at one
wavelength may be used to predict scatter
measurements at another wavelength (Stover).
6.29
waviness — the more widely spaced (spatial
wavelength) components of surface texture (SEMI M1).
Compare with roughness.
7 Instruments and Capabilities
7.1 Profilometers
7.1.1 The high spatial frequency limit of AFM,
mechanical and optical profilers can be approximated
by the radius of the mechanical tip or by the diameter
and intensity profile of the laser spot, respectively.
Their response functions are complicated, and in some
cases are a combined effect of the probe and the
measured surface. The high spatial frequency limit of
such tools has to be set or selected reasonably removed
from that limit in order to achieve reasonable,
comparable, and repeatable measurements.
7.2
Interference Microscope
7.2.1 The high spatial frequency lim it of these
instruments is defined by the focusing optics or in some
cases by the pixel spacing of the detector array. The
high spatial frequency limit of such tools has to be set
or selected reasonably removed from that limit in order
to achieve reasonable, comparable, and repeatable
measurements.
7.3
Scattering Instruments
7.3.1 A straightforward relation between scattered
light intensity and roughness exists only for sufficiently
smooth surfaces. The Rayleigh smooth-surface
criterion, given below, is frequently used for estimating
the smooth-surface limit (Stover).
1
cos4
2
1
2
<<
ö
ç
ç
è
æ
λ
θπ
i
a
(1)
1<<m (2)
where: m = profile slope,
λ = wavelength of incident light,
a = amplitude of sample profile (half of the peak-to-
valley height), and
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