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SEMI M40-0200 © SE MI 2000 3 5.7 Other Documents International Technology Road map for Semico nduct ors 6 Optical Scattering in the Optics, Semiconductor, and Computer Disk In dustries, Second Edition 1995, J C Stover, E…
SEMI M40-0200 © SEMI 2000 2
4.2 Historically a variety of rough ness parameters for
profiling techniques have evolved and have been
standardized, including rms roughness (R
q
) and average
roughness (R
a
). Profiling instruments measure the
surface topography and derive roughness statistics, such
as R
q
, from a series of height data. Light scattering
techniques measure R
q
from the angular dependence of
scattering; some light scattering systems derive other
parameters through interpretation and estimation.
4.3 A roughness value representative of an entire
wafer surface, or a large portion of the surface, cannot
be based on data obtained at a single point. Yet,
specifications often describe a single value for a wafer.
Therefore, this guideline suggests and defines
standardized patterns of scan sites that can be described
and used unambiguously. A model describing the
relationship between several types of roughness
variation, scan patterns, and reported results is included
in the attached Related Information to assist users in
specifying and interpreting these variables.
4.4 A common feature of all roughness measurements
is their dependence on the bandwidth and transfer
function of the tool used. In addition, high or low
spatial frequency software filters are common and
affect reported results. Widely different numbers can
be reported for the same surface by two measurement
instruments. This guideline includes suggestions on
specifying and reporting the instrument bandwidth and
transfer function.
5 Referenced Standards
5.1 SEMI Standards
SEMI M1 — Specifications for Polished
Monocrystalline Silicon Wafers
SEMI M20 — Specification for Establishing a Wafer
Coordinate System
5.2 ASME Standard
1
ASME B46.1 — Surface Texture (Surface Roughness,
Waviness, and Lay)
5.3 ASTM Standards
2
E 1392 — Practice for Angle Resolved Optical Scatter
Measurements on Specular or Diffuse Surfaces
F 1048 — Test Method for Measuring the Effective
Surface Roughness of Optical Components by Total
Integrated Scattering
1 American Society of Mechanical Engineers, United Engineering
Center, 345 East 47th Street, New York, NY 10017
2
American Society for Testing and Materials, 100 Barr Harbor
Drive, West Conshohoken, PA 19428-2959
F 1620 — Practice for Calibrating a Scanning Surface
Inspection System Using Monodisperse Polystyrene
Latex Spheres Deposited on Polished or Epitaxial
Surfaces
F 1811 — Estimating the Power Spectral Density
Function and Related Finish Parameters from Surface
Profile Data
5.4 DIN Standards
3
DIN 4760 — Form Deviation, Waviness, Surface
Roughness; System of Order, Terms and Definitions
DIN 4768 — Determination of Values of Surface
Roughness Parameters Ra, Rz, Rmax by Means of
Electrical Contact (Stylus) Instruments; Terminology,
Measuring Conditions
DIN 4777 — Metrology of Surfaces; Profile Filters for
Electrical Contact Stylus Instruments; Phase-Corrected
Filters
5.5 ISO Standards
4
ISO 468 — Surface Roughness – Parameters, Their
Values and General Rules for Specifying Requirements
ISO 1879 — Instrument for the Measurement of
Surface Roughness by the Profile Method - Vocabulary
ISO 1880 — Instruments for the Measurement of
Surface Roughness by the Profile Method - Contact
(Stylus) Instruments of Progressive Profile
Transformation - Profile Recording Instruments
ISO 3274 — Instruments for the Measurement of
Surface Roughness by the Profile Method – Contact
(Stylus) Instrument of Consecutive Profile
Transformation – Contact Profile Meters, System M
ISO 4287/1 — Surface roughness – Terminology – Part
1: surface and its parameters
ISO 4288 — Rules and Procedures for the
Measurement of Surface Roughness Using Stylus
Instruments
5.6 JIS Standards
5
JIS B 0601 — Surface Roughness - Definitions And
Designation
JIS B 0652 — Instruments For The Measurement Of
Surface Roughness By The Interferometric Method
JIS B 0659 — Roughness Comparison Specimens
3 Deutches Institut für Normung e.V., Beuth Verlag GmbH,
Burggrafenstrasse 4-10, D-10787 Berlin, Germany
4 ISO Central Secretariat, 1, rue de Varembé, Case postale 56, CH-
1211 Genève 20, Switzerland
5
Japanese Standards Association, 1-24, Akasaka, 4-Chome, Minato-
ku, Tokyo 107 Japan
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