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Introduction
All smooth surfaces possess some degree of roughness, even if only at the atomic
level. For man-made surfaces, this roughness arises from the manufacturing process
which may involve chemical deposition, grinding, polishing, etching or several
other commonly used techniques. Correct function of the fabricated component often
is critically dependent on its degree of roughness. In this technical note we
examine how scatterometers can be used to quantify surface roughness with rapid
and repeatable measurements. We also compare scatterometry and its practical implementation
with other methodologies.
Effects of Surface Roughness
There are numerous problems caused by surface roughness. Although these problems
tend to be application specific, they can be classified into four groups: excess
light scatter, mechanical malfunction, environmental instability, and cosmetic
acceptability.
In optical applications, the primary motivation in measuring surface roughness
is to estimate how much the surface will scatter light at the intended wavelength(s)
of operation. Excess scatter can result in system nonperformance for sensing optics,
imaging optics, laser optics and numerous others. In these instances it is much
better to specify and measure scatter directly, using the scatter definitions
outlined later in this article. For example, if a polished optic is to be used
at 488 nm, then the best specification is the scatter (TIS, BRDF, etc.) measured
at 488nm.
In non-optical applications, excess surface roughness can lead to mechanical
malfunctions. For example, computer hard disks have a narrow tolerance band for
acceptable roughness. If the surface is too smooth, the read/write head may bind
to the surface of the disk. If the surface is too rough, the head may be unable
to fly over the disk surface on its air cushion in the proper manner. Another
example of mechanical malfunction can be found in high performance engine machine
parts which are required to move or rotate at high speed without wear. Excess
surface roughness can lead to unacceptably high levels of frictional heating,
causing damage and even failure.
Rollers used in almost any application from computer printers and plotters
to pressing metals, papers and films in factory environments require careful control
of surface quality to ensure the quality of the finished product. These applications
can benefit from periodic surface testing or in situ surface monitoring to alert
manufacturers of the need to refinish the roller surface before the process degrades
to an unacceptable level. In addition, by testing the surface quality during the
grinding and refinishing process, the roller surface can be brought to the required
smoothness with a minimum amount of processing.
Surface roughness can affect a component's chemical and physical stability.
Surfaces that have to stand up to hostile environments (temperature, humidity,
or hostile chemicals) must be as smooth as possible in order to present the minimum
surface area for attack, and to have as few defects or weak spots as possible.
Cosmetic appearance of a surface can be adversely affected by surface roughness.
Although this may appear to be the most trivial of the problems caused by surface
roughness, it is often important in terms of potential lost revenue. For example,
although a rough paint surface may function perfectly well on an automobile, it
would reduce the customers' perception of quality and value.
How Does Surface Roughness Arise?
Figure 1 shows examples of the common factors contributing to overall surface
roughness. The defects or features which contribute to surface roughness may be
random or regular (periodic). These defects can arise in a number of different
ways.
Figure 1
For surfaces produced by a grinding or polishing process, the most obvious
roughness is the unevenness of the surface itself, i.e. scratches, pits and ridges.
These features can range in size from a step defect in the molecular structure
measuring a few angstroms, up to a visible scratch whose width could be measured
in microns and length measured in millimeters. In the case of nonrandom wear processes
such as diamond turning, these surface imperfections may have an inherent symmetrical
pattern, rather like a smooth version of a phonograph record.
How is Roughness Specified?
The roughness of a surface can be specified by a number of different parameters,
each with its own utility. All these parameters consider roughness in terms of
deviations from the mean surface level. One of the most common parameters in RMS
roughness. Assuming a surface in the horizontal plane, this is the root mean squared
value of all vertical deviations from the mean surface level. Ra roughness, the
arithmetic average roughness, is a term used more for machined surfaces than for
polished optics. It is the arithmetic average of the absolute deviations from
the mean surface level.
In the case of real world measurements, it should be understood that each
instrument is limited to a spatial bandwidth of operation. That is, some features
are too wide (or far apart) to be detected and some too narrow (or close). It
is common to give these limits in terms of spatial frequency (i.e., the inverse
of maximum or minimum widths). Therefore, the measured roughness (RMS or Ra) doesn't
include features outside this range. When comparisons between measurements (or
instruments) are made, they must involve identical spatial bandwidths. There are
also limits of operation for measuring the amplitude of surface features. It is
therefore important when expressing roughness to not only specify bandwidth, but
also to state the specific range of surface amplitudes of the instrument.
In the case of machined surfaces it is very useful to know if the surface
has periodic undulations or features. For example, fine sandpaper and a phonograph
record may have the same RMS roughness, but have very different overall characteristics.
The distribution of roughness versus spatial frequency of features is defined
by the Power Spectral Density (PSD) function or Power Spectrum. The sandpaper
would have a rather random distribution of power vs. frequency, where as the phonograph
record would tend to display at least one dominant frequency or a "spike" in a
PSD plot. A similar comparison can be seen in the world of precision optics when
comparing a lapped and polished optic to a diamond turned optic. While RMS or
Ra roughness parameters have evolved as popular numbers to specify, detailed information
about the surface is lost in the "averaged" nature of these numbers.
How is Surface Roughness Obtained from
Light Scatter?
In the case of reflective surfaces, surface roughness causes incident light to
be scattered in directions other than the specular reflection direction (angle
of reflection = angle of incidence), as shown in Figure 2. Clearly, the rougher
the surface, the higher the proportion of incident light that is scattered. For
example, a highly polished aluminum mirror may show little scatter to the naked
eye and is able to form a high quality image in reflection, whereas a sheet of
white paper scatters so much light that any specular reflection becomes indistinguishable
from scatter.
Figure 2
Scattered light is defined by its magnitude and its angular distribution,
both of which may be used to derive important surface roughness data. There are
two commonly accepted measurements used to quantify these functions: TIS (Total
Integrated Scatter) and BRDF (Bi-directional Reflectance Distribution Function).
For a reflective surface, TIS is defined as the ratio of the total scattered
power to the total reflected power. The total scattered power is the sum of all
light scattered outside the specular direction. TIS is related to RMS roughness.
Figure 3
BRDF is determined from the ration of the scatter per unit solid angle to
the incident power, i.e. normalized scatter density. BRDF is commonly presented
as a function of angle. This BRDF function contains valuable information about
the amplitude and width of the surface features (see figure 3).
The amount of scattered light is a result of the amplitude of the scattering
features, whereas the scatter angular distribution is a result of the surface
spatial frequency. TIS can be a very good yardstick by which to measure surface
roughness, but it is the angular distribution, as defined by BRDF, which carries
additional information about the distribution, shape and size of surface imperfections.
Diffraction theory has been used to accurately relate the surface PSD to the BRDF.
These two functions are nearly proportional, which makes determination of surface
parameters from the BRDF straightforward. Additionally, simple integration of
the PSD results in RMS roughness values of the surface over a selected range of
surface wavelengths.
What is a Scatterometer?
Scatterometers consist of a nearly collimated beam of light (often a laser) which
is directed onto the sample surface. Some instruments allow the operator to select
the angle of incidence. The scattered light intensity is measured by an array
of detectors or a single sampling detector which moves in an arc relative to the
surface. The integral microprocessor use measurements of BRDF and TIS to determine
RMS, Ra roughness and PSD, as well as other features for the area illuminated
by the beam. The illuminated spot size may be fixed or variable. Some instruments
allow the spot to be scanned for random testing of several points on a surface
or complete characterization of large surfaces.
How does Scatterometry Compare to Other Methods
for Determining Surface Roughness?
There are a number of alternative methods for deriving surface roughness; the
matrix in Figure 4 shows a condensed comparison of these. The final choice of
methods depends on the type of data that is required, the speed with which the
data must be acquired, the skill level or training time of the operator and the
environment in which the measurements must be made. All of these techniques are
indirect methods of obtaining a surface profile or roughness measurement. That
is to say they "calculate" the surface roughness based on optical or physical
effects measured by the instrument. Also, each method has its own unique and finite
range of heights (RMS roughness) and spatial frequencies. Detailed knowledge of
these techniques and their limitations is critical to properly measuring, understanding,
and interpreting the results from any system.
Scanning Tunneling & Atomic Force
Microscopy
One of the most direct methods of obtaining surface data is to use a scanning
tunneling microscope (STM) or an atomic force microscope (AFM). In these instruments,
a fine probe tip, sometimes only a few atoms in diameter, is brought close to
the surface and rastered across it. The tip is raised and lowered by a feedback
controlled piezomechanism in order to maintain a constant distance above the surface.
STM's and AFM's are capable of surveying large surface areas. In general they
are research instruments which are best suited to high resolution studies of areas
no bigger than a few µm<. They are not well suited for QC or process control tasks.
Stylus Profilometry
A related instrument is the stylus profilometer. As the name suggests, in this
type of instrument a preloaded stylus or needle (usually diamond) is dragged across
the surface. The resultant vertical motion of the stylus compresses a piezoelectric
element which generates a fairly linear voltage response. This is a good method
for looking at small areas or single transacts of very hard surfaces. It is not
suited for soft surfaces such as semiconductor materials or coated and precision
optics, since a heavy preload on the stylus will scratch the surface and a light
preload may not be sufficient to register all surface features. Another related
problem is choice of resolution. Clearly the maximum resolution (i.e. smallest
surface spatial frequency) depends on the sharpness of the stylus tip. In the
simplest case of sinusoidal surface feature, limiting resolution is given by:
d=2(pi)(square root of)ar Where d is spatial wavelength, a is the height (amplitude)
of the feature, and r is the radius of the stylus tip. Although capable of high
resolution, the sharper tips are more likely to scratch the test surface.
Optical Profilometry
Optical profilometry is similar to scatterometry in several ways. The actual surface
shape is computed from an optical measurement. Some optical profilometers use
a monochromatic laser light source whereas others use white light, but the basic
principle of operation is the same in both cases. A collimated beam of light,
coupled to an optical microscope system, is split and focused to a small spot
on both the test surface and a reference surface. Height differences on the test
surface and a reference surface result in optical path differences which are seen
as light and dark fringes on a video camera or diode array detection system. By
precise movement of the reference surface, phase information can be computed for
the interference pattern. Analysis of the intensity and phase of the complex interference
pattern yields information about the shape and roughness of the test surface.
Profilometry and scatterometry also have major differences. In the case of
profilometers, profiles need to be sampled in order to calculate surface roughness
values such as PSD and RMS roughness. The sampling process and subsequent calculations
introduce spatial bandwidths (and small errors) that must be taken into consideration
to create the PSD. Scatterometry, on the other hand, starts with the PSD (which
is directly derived from the BRDF) thus eliminating this source of error. From
the PSD, RMS roughness over required spatial bandwidths is calculated with either
technique. In general, scatterometers can measure to slightly higher spatial frequencies,
while some optical profilometers can measure to slightly lower spatial frequencies.
Advantages of Scatterometry for Quality
Control/Process Control Applications
If the application for the instrument is for use in QC and/or process control,
then speed of measurement and operator training are parameters that directly effect
the cost of the measurement. These factors cause such instruments as optical profilometers,
STM's, and AFM's to be unsuitable when compared to scatterometers. First, it takes
time to align the sample and focus these instruments. Second, they only measure
a relatively small area for each measurement. Some optical profilometers can be
made to focus a larger area of the surface onto the detector pixel array. Unfortunately,
this lowers the resolving power, losing high surface spatial frequency information.
For scatterometers, sample alignment is comparatively trivial and the resolutions
less dependent on the size of the sampling area, thus ensuring fast repeatable,
highly accurate measurement.
Operator skill is another important factor. Although optical profilometers,
STM's and AFM's can be powerful tools in the hands of a skilled operator, it requires
experience and skill to correctly focus and align these instruments on the sample.
Consequently, operators must be trained to a high proficiency level to avoid making
erroneous measurements. Scatterometers require less skill to operate, especially
for the repetitive measurements generally associated with QC operations.
Vibration sensitivity is another important difference between these techniques.
Optical profilometry depends on precision interferometry and the instrument must
be mounted on some type of vibration isolation table. STM's, AFM's and stylus
profilometers can be ultra sensitive to vibrations, erroneously interpreting them
as roughness on the surface. Scatterometers are relatively insensitive to vibration.
This has lead to the development of portable and hand held devices which can be
operated on the factory floor. In a machining process, parts can actually be tested
in situ, i.e. without removing from the machine.
Finally, when testing large surfaces (e.g. magnetic disks or large mirrors)
the best way to reduce testing time and increase statistical validity is to test
the roughness of several small areas at a variety of locations on the surface.
Since the alignment is critical for optical profilometers, STM's and AFM's, this
can be a very slow process. Stylus profilometers measure only a very fine line,
typically 1mm in length, which is an exceptionally small area relative to the
entire surface. In the case of scatterometry, the inspection spot can be quickly
and automatically rastered over the entire surface.
The differences between scatterometers and other optical techniques (i.e.
STM's, AFM's and optical profilometers) can be summarized as follows. STM's, AFM's
and optical profilometers require the intervention of a skilled operator and perform
measurements relatively slowly, whereas the scatterometer is much simpler and,
consequently, can make measurements more rapidly while still maintaining excellent
repeatability and accuracy.
Stylus profilometers, like scatterometers, are simpler devices which require
less skilled operators. However, there are a number limitations that effect a
stylus type system. For example, measurements must be conducted under vibration
isolation conditions, and large areas require numerous scans. While these instruments
are well suited to single measurements of hard materials, such as machined surfaces
and parts, they are generally destructive to soft materials such as most coated
optics. Furthermore, as they are very sensitive to vibration, they are not well
suited for QC or process control applications.
Conclusions
Making quantitative measurements of surface roughness can be important in a wide
range of diverse applications. When the requirement is to detect variations in
a process or part, commercial or custom scatterometers, which are relatively simple
to operate, offer a very cost competitive option for making accurate and repeatable
measurements.
| Instrument |
Features |
Comments |
Applications |
| |
| Scatterometer |
Derives surface roughness and spatial frequency data from scattered
light distribution. |
Insensitive to ambient vibration. Can quickly locate defects
on large surfaces. |
Optical components Materials & Process R & D
QC/QA testing Machined Parts Automated,
volume testing
|
| |
| Hand Held Scatterometer |
Derives surface roughness and spatial frequency data from scattered
light distribution. |
Portable for use in process control and production line environments. |
in process testing
in situ testing |
| |
| Optical Profilometer |
Derives surface roughness by interferometric comparison to a
reference surface. |
Sensitive to ambient vibrations.
Not suitable for large surfaces.
|
Optical components
Materials & Process R & D
Low volume QC |
| |
| Stylus Profilometer |
Measures surface profile along a line using a contact stylus. |
Tip size limits measurement's bandwidth. Can damage soft samples. |
Materials & Process R & D
Low volume QC |
| |
| STM/AFM |
Measures surface profile along a line using a non contact stylus. |
Capable of atomic resolution. Cannot measure surfaces larger
than a few |
Materials & Process R & D |
If you would like more information or if you have a question we have not covered
please fill out our online question form or e-mail
our measurement services manager, Danny Hanley, at dhanley@schmitt-ind.com.
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