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Surface metrology
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1997 Meas. Sci. Technol. 8 955
(http://iopscience.iop.org/0957-0233/8/9/002)
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Meas. Sci. Technol. 8 (1997) 955–972. Printed in the UK
PII: S0957-0233(97)70308-4
REVIEW ARTICLE
Surface metrology
D J Whitehouse
Department of Engineering, University of Warwick, Coventry CV4 7AL, UK
Received 14 October 1996, in final form 21 May 1997, accepted for publication
21 May 1997
Abstract. Some important types of instrumentation for measuring surfaces both
past and present are reviewed. Exhaustive lists of instruments and performance
are not presented; rather more emphasis is placed on the philosophy of
measurement. An attempt is made to classify the surface features and also the
function of surfaces as a pre-requisite to measurement. It is revealed that, as the
push towards miniaturization is being taken beyond the nanometrology scale, some
theoretical restrictions are likely to be encountered.
1. Why measure surfaces?
In recent years surface texture has been recognized as
being significant in many fields. In particular the surface
roughness is an important factor in determining the
satisfactory performance of the workpiece, in tribology for
example or in coatings. Also in engineering applications
the surface roughness has been found useful in machinetool monitoring. These aspects will be discussed presently.
It is, however, pertinent to consider how the importance
of surface roughness is changing with the passage of time
and how the importance of roughness depends on the actual
scale of size of the workpiece and the process used to make
it.
In very general terms the requirements for energy
transfer and information transfer and storage have
dominated the development of technology. This will no
doubt also be true in the future but the factors governing
such transfer depend themselves on size. As objects get
smaller changes emphasizing the importance of the surface
take place. The energy and force equations experience a
change of balance, figure 1(a), as the scale of size of the
moving object decreases.
Information storage in 3D is possible but still very
difficult to achieve; also, data retrieval is a major problem.
On the other hand, storage of data on surfaces is still
actively being extended. This capability is obviously a
function of the surface area. There is no problem with
accessibility of the stored data like there is with volume
storage. Notice that information storage trends tend to have
the opposite trend to the energy equations with respect to
the effect of the scale of size, figure 1(b). In both situations
the critical regime is that of area. Consider figure 1(a). In
the force diagram momentum effects quickly decrease as
the size is reduced, in fact by a factor of L3 . Damping is
proportional to the area and decreases as L2 . Elastic forces
only decrease as a linear factor of L so that they become
progressively more important than the others as the scale of
0957-0233/97/090955+18$19.50
c 1997 IOP Publishing Ltd
Figure 1. The importance of surface properties with scales
of size.
size decreases. In rotational situations the dependence on
scale is even more pronounced. For example the moment
of inertia decreases by a factor of L5 .
Of the above factors, the elastic properties can be
controlled by varying the properties of materials, which
are well understood, and inertial forces can be controlled
by design. This leaves areal or damping forces which
cannot be controlled easily. Energy losses and transfer
and information storage and transfer are all sensitive to
uncontrolled areal properties and the areal property which
is most likely to be influential is the surface roughness.
955
D J Whitehouse
It is also the least understood and manageable. Hence the
greater emphasis being placed on its measurement in recent
years. The pressure to do so is due to the search for a better
quality of goods and also to achieve better manufacturing
control.
Surface metrology is as much concerned with the nature
of the surface and its use as it is with the practical aspects
of measurements, so some clarification of surface use will
be given as a pre-requisite to measurement. Sections 2
and 3 describe some of the uses of surface measurement
and the type of parameter used. There is no description
of parameters as such in that which follows but more a
justification for the measurement. Also topics such as
measurements of roundness and cylindricity have been
left out because these techniques have the same general
problems of data collection as does roughness. They differ
in the way the pick-up is presented, and moved relative
to the surface. They have been described in detail in the
references, for example Whitehouse (1994).
Certain topics have deliberately been left out in this
review. These are points concerned with data processing
such as filtering methods, parameter characterization,
digital data analysis and also methods of calibration. These
omissions should not be taken to indicate their lack of
importance; all of these points are necessary in order to
validate the values of any parameter measured. However,
the emphasis here has been placed on illustrating the reason
for the use of techniques. All the other points have
been covered comprehensively elsewhere, for example by
Whitehouse (1994).
2. Surfaces and their importance in manufacture
There are two basic ingredients involved in manufacturing
a workpiece, the manufacturing process and the machine
tool or production technique.
How they relate to
surface measurement is shown in figure 2. At one
time measurement of the surface was considered largely
irrelevant but it soon became apparent that the finish on
the surface was extremely sensitive to any changes in
the process. Hence it became logical to assume that
measurement of the surface could be used to control the
process of manufacture. The argument was that, if the
surface parameter being measured remained constant from
workpiece to workpiece, then the process must be under
control. Any change in the surface parameter should initiate
a review of the process parameters. In the UK and USA
(Page 1948) the average roughness Ra was used as the
control parameter whereas in Germany and USSR peak
parameters were used (Schlesinger 1942, Schorsch 1958).
The UK approach was pragmatic in the sense that the
parameter specified on the drawing had to be measurable.
In Germany the approach was to use parameters such as
Ry , the maximum peak-to-valley height on the surface, in
an attempt to impose functional constraints on the surface
as well as manufacturing control. The peak parameters,
however, are inherently divergent—they become larger as
the sample size increases. Also, sometimes, the maximum
values of a parameter are difficult to find over a large
area of the surface. Extreme peak–valley measures soon
956
Figure 2. Surface measurement and manufacturing.
degenerated into measurements of average peak–valley
heights RT M , Rz and so on simply in order to make them
reliable.
Although the use of a single parameter of the surface
roughness could be used to indicate a change in the
manufacturing process, it is not sufficiently discriminating
to pinpoint where the changes in the process have occurred.
Even using a number of simple parameters rather than just
one fails to provide the necessary discrimination. It is only
recently that surface metrology has become comprehensive
enough to be used as a diagnostic tool. This capability arose
because of the advent of random-process analysis. That is,
the use of autocorrelation, power spectra and probability
density functions.
These are functions rather than numbers such as the Ra
(average roughness) of the profile and so can reveal much
more of the underlying statistics of the surface. They are
more reliable because in the case of autocorrelation and
power spectral density any random phase shifts between the
sinusoidal components making up the profile are eliminated.
The autocorrelation function is particularly useful for
looking at random surfaces and the power spectrum is more
useful for looking at periodic surfaces, as will be seen
shortly. Neither is particularly difficult to generate. The
autocorrelation function is simply a plot of the correlation
coefficient between the surface profile and the same profile
shifted in space by a set amount. The power spectrum
is the Fourier transform of this (see for example Papoulis
(1965)). These were introduced because of the needs of
functional prediction (to be discussed later) but have now
been incorporated into the manufacturing control problem
(Peklenik 1967).
2.1. Autocorrelation and manufacture
These statistical parameters are effective because they
provide a large enhancement of the signal over the noise
introduced into the system. For example, each point on the
autocorrelation function of a profile taken from a surface
is a result of a great deal of averaging. Small changes
between surfaces became significant. As a general rule the
autocorrelation function can best be used to reveal changes
in random processes such as grinding whereas power
Surface metrology
Figure 3. The significance of autocorrelation in manufacturing.
spectral analysis can be used to best advantage in processes
which are fundamentally periodic or repetitive, such as in
turning or milling. Both the autocorrelation function and
the power spectrum hunt for the unit machining event. In
the case of grinding the unit event is the impression left on
the surface by an average grain on the grinding wheel. In
power spectral analysis it is the periodic signal left on the
surface by a clean cutting tool on a perfect machine.
Take grinding, for example, as a case in which
autocorrelation is useful. Figure 3(a) shows the impression
left on the surface by a sharp grain (Whitehouse 1978).
Figure 3(b) is a typical profile and figure 3(c) is the
correlation function. Notice that the correlation length (the
distance over which the correlation drops almost to zero)
is a direct measure of the effective grain hit width. For a
grinding wheel in which the grains are blunt, figure 3(d ),
there is a considerable piling up of material as well as
the formation of a chip. By examining the correlation
function it is apparent that the piling up or ploughing is
revealed by lobing in the autocorrelation function. The
width of the central lobe is a measure of the amount of
material removed. At a glance, therefore, the shape of
the autocorrelation function reveals the efficiency of the
grinding in all its aspects, figure 3(g). Notice that this
would not be revealed by looking at the profile or by using
simple parameters. In figure 3 any longer waves in the
autocorrelation function of the surface show that there are
other problems such as the need to dress the wheel.
2.2. The power spectral density in manufacturing
Another example shows how the power spectrum can be
used to identify problems in turning. As the tool wears and
the machine tool deteriorates significant changes occur in
the spectrum of the surface, as shown in figures 4 and 5.
Figure 4(a) shows a profile of turning produced by
a good tool, together with its spectrum. As would be
expected for good turning, the spectrum shows some line
frequencies, the fundamental corresponding to the feed and
a few harmonics due to the shape of the tool.
As the tool wears the ratio of the harmonic amplitudes
to that of the fundamental increases (see figure 4(c)). This
is due to the imposition on the surface of the wear scars on
the tool. Also, on this right-hand side of the fundamental
spectrum, the base line can rise, due to random effects of
the chip formation and microfracture of the surface. See
figures 4(b)–(e).
957
D J Whitehouse
Figure 4. Power spectral analysis and its use in manufacturing.
To the left-hand side of the fundamental wavelength
there appear periodicities whose wavelengths are much
greater than that of the fundamental. These are due to
machine-tool problems such as bearing wear, slideway error
or even lack of stiffness in the machine tool itself, which
may cause chatter. Identifying these effects by using the
surface texture is an important first step in remedying the
problem.
The spectrum can therefore be split up into two parts,
one to the right-hand side of the fundamental frequency
and one to the left, figures 5(a)–(e). On the right-hand
side there appear process problems and on the left, in
the sub-harmonic region, machine-tool problems. These
advances in machine monitoring and diagnostics stem
from the realization that the surface generated by the
manufacturing process constitutes a very extensive data
bank of information. The surface is in effect a fingerprint
of the manufacturing process.
3. The surface and function
The surface is obviously important in many practical
situations. This has been known for years. The problem
is that of knowing how important it is. For many years
very simple parameters were used to describe the surface
958
and, it was hoped, its properties. These included the
average value Ra , the RMS value Rq and various peak
height estimates. Investigators in Germany and the USSR
used peak measurements rather than average values because
they argued that peak measurements correlated more with
tribological situations than did average values (Perthen
1949). Also the peak measurements of roughness could
be measured equally well with optical and stylus methods.
This philosophy proved to be practically unsound.
The notion of being able to predict the performance
of a workpiece from the geometry of the surface has been
attractive for some time. Early investigators used simple
models of the surface. These usually involved modelling
peaks on the surface as hemispherical spheres scattered on
a plane. Then these hemispheres or ‘bosses’ were assumed
to be distributed in a random Gaussian way in height
(Greenwood and Williamson 1964, Greenwood 1982). This
development was closer to real surfaces than previous ones
had been but it had the disadvantages that two surface
descriptions were needed, one deterministic to describe
the shape and size of the hemispherical ‘peaks’ and one
statistical to describe their distribution in space (Archard
1957).
This confusing model was eventually replaced by the
random-process model mentioned earlier which was based
Surface metrology
Figure 5. Some space–frequency kernels and their
relationship: A, machine; B, process; and C, material
properties.
totally on communication theory (Whitehouse and Archard
1970). This allowed all salient features of the surface to be
described with one model. This random-process model was
and still is considered to be a big breakthrough in surface
characterization.
However, current thinking indicates that even this
model needs modifying to reflect better the mechanical
situation that occurs, for example, in contact where the
surfaces contact top down on each other. Another problem
which has to be considered is that contact occurs in a
parallel mode rather than a serial one. The conclusion
has been reached that random-process analysis is adequate
for monitoring the manufacturing process, but is rather
inadequate for some cases of functional prediction.
Figure 6 shows classification of function and surface
features (Whitehouse 1994). The classification of function
is achieved using the separation of the surfaces and their
lateral movement. This classification is an essential element
in trying to understand how functional performance is
influenced by the surface geometry.
Identifying very specific parameters of the surface
geometry with areas in the function plot is fraught with
problems. In practice only broad categories can be used, as
shown in figure 6. Perhaps in the future it will be possible
to correlate function and geometry better. However, despite
its complexity figure 6 represents a step in the right
direction.
Figure 6 shows the type of parameter of the surface that
could be useful in various functional situations. The x axis
corresponds to the relative lateral movement between two
surfaces and the y axis to the inverse of their separation.
On the extreme right-hand side is a column indicating
the type of parameter which is most significant. These
are (i) unit event characteristics, (ii) profile parameters,
(iii) areal parameters, (iv) spatially variable characteristics
and extremes of distributions and finally (v) defects. It
is a fact that often combinations of these parameter types
are needed in order to predict the performance of the
surface. Figure 6 shows the requirement for surface
measurement which in turn decides the specification for
the instrumentation in hardware and software. One point
to notice is that it is rarely the individual parameter Ra or
Rq for example which is important but often the type of
parameter. Little or no convincing evidence is available to
link very specific surface parameters to function.
The important point to notice in figure 6 about the
surface geometry characteristics important in function is
their diversity. They fall into two basic sets. One is the
statistical type required, of which there are a number of
options. The questions which have to be asked concern
whether an average value, an extreme value, the presence or
absence of a feature or perhaps even the spatial variability is
required. The other basic issue is that of whether the feature
of importance is basically height orientated, in which case
profile information will often suffice, or areal. It should
be noticed that areal information reveals structure which is
most often important when movement is involved. Under
these circumstances it is often extremes of parameters rather
than averages which are important.
Although profile-height information has been available
for many years with stylus instruments (Reason et al 1944)
it has been only recently that areal information has been
recognized as important. Serious attempts are now being
made to integrate all aspects of areal (sometimes called
3D) measurement (Stout et al 1994). The reason for
this swing to areal measurement is that the possibility of
using surface geometry for functional prediction is now
recognized. Previously, control of manufacture could be
achieved reasonably well with just profile information.
One factor which has been omitted from figure 6
is the importance of physical parameters such as nanohardness and elasticity. Also missing is the presence
of thin chemical films on the surface. These factors
are known to be important.
These non-geometrical
properties of the surface should also be measured and
included in the surface characterization if a true estimate
of the surface performance is to be obtained. There is
evidence that multidisciplinary parameters are now being
incorporated into some instruments (Marti et al 1990).
However, their use is non-standardized and at present
unsatisfactory calibration methods have held back their
general implementation.
It should be emphasized that these non-geometrical
parameters refer not to bulk properties of the materials but
959
D J Whitehouse
Figure 6. Surface geometry and function.
rather to the properties of the outermost skin of the surface,
where the skin thickness is taken to be of the same scale as
the roughness, if not smaller. The reason for this distinction
between bulk and skin properties is primarily that all the
action, that is energy transfer, takes place at the surface
boundary rather than in the bulk of the material (Gant and
Cox 1970).
Whether asperities are crushed or deform elastically
is very dependent on the skin property. Apparently soft
materials such as copper have a considerably harder surface
skin than had previously been thought, which is why stylus
measurement is possible despite having stylus pressures
greater than the nominal hardness of the material. It is when
trying to measure surface parameters which are significant
in fatigue or corrosion that the greatest problems arise
because in these examples of function it is the isolated
deep scratch or defect which often initiates the breakdown.
Finding such cracks over a wide area on the surface is a
real problem, requiring an instrument to cover a wide area
yet with high resolution.
It seems obvious from that which has been reported
above that surfaces can be very important. The question is
that of how to measure the surface most effectively.
960
4. Conventional instrumentation
4.1. Introduction
The earliest ways of measuring surfaces were using the
thumb nail and the eye. Both of these are highly effective
but completely subjective. Demand for quantitative results
led to the development of two parallel branches of
instrumentation: one following the tactile example of the
nail, the other mimicking the eye.
As will be described in that which follows, the two
methods actually evolved to measure different things.
The optical methods looked for lateral structure, namely
spacings and detail in the plane of the surface, whereas the
stylus method examined heights in the plane perpendicular
to the surface. Optical methods were developed to help the
metallurgist or biologist whereas the stylus method was for
engineers’ use.
4.2. Stylus methods
The stylus method essentially uses a caliper, the two arms
of which touch a reference surface and the surface under
test respectively. The arm towards the test piece ends
Surface metrology
Figure 7. The stylus principle.
Figure 8. The measurable surface bandwidth.
with a diamond stylus whose tip dimension is such that it
can penetrate the detailed geometry of the surface (Reason
1970).
The other arm contacts a reference surface, figure 7(a)
and (b) by means of another stylus. All surface-measuring
instruments have this basic configuration in one form or
another. In some cases it is difficult to spot the reference.
One such variant has both caliper arms contacting the
surface, as shown in figure 7(c). Here the ‘skid’ technique
provides an ‘intrinsic’ reference. In other words the surface
itself generates the reference by having one stylus much
blunter than the other. The blunt stylus integrates the
surface. It acts as a mechanical filter having a lower cut-off
than that of the sharp stylus, see figure 8.
The actual position of the reference relative to the test
surface is not important; it is not the position or dimension
which is being measured but rather the deviation from an
intended surface shape. There are three basic trends in
conventional stylus instruments. One is the increasing use
of transducers which have a large range-to-resolution value.
Another is the use of areal scanning and the third is the
coming into being of a generation of hand-held instruments.
Simple statements like the above are not sufficient to
describe the advantages and disadvantages of the various
instruments so various merit criteria have been devised.
One can be considered to be mainly applicable to research
instruments, (figure 9) and the other to industrial uses
(figure 10).
The former wavelength–amplitude method (Stedman
1987) shows the limits of the amplitude which can be
measured and the limits on spatial wavelengths that are
imposed by such features as the physical dimension of
the stylus tip and its angle. The size, shape and position
of the envelope reveal the usefulness and application of
the particular instrument. Obviously the best instruments
on this diagram encompass a wide area. Instruments
suited to nanotechnology work best near the origin
whereas instruments more suitable for general engineering
would cover larger amplitudes and wavelengths and not
necessarily be concentrated near the origin. Figure 9 shows
a typical plot for some nanotechnology instruments. It
shows how, for example, the effect of the stylus can be
taken into account.
The range-to-resolution response due to Whitehouse
takes into account the dynamics of the measuring system,
which is important if fast scanning speeds are to be
achieved. This is required when areal scans are needed
or when the instrument is being considered for in-process
measurement. The horizontal axis is also important because
it determines the types of surface feature which can be
measured with one trace. One example is shown in
figure 11, which shows an arcuate profile. If the range to
resolution of the instrument is high then both the radius
and the roughness can be measured at the same time.
Good modern instruments have values of 106 :1. Table 1
gives some typical values for instruments. The actual
performance values shown in figure 9 and table 1 are
continually changing as the technology develops. It is the
general pattern which remains virtually the same. Other
advances in the dynamics of stylus instruments include the
use of optimum damping.
It has recently been realized that there is a more
realistic way of assessing the performance of instruments.
Conventionally the response of the instrument to sinusoidal
inputs had been measured and recorded as the transfer
function. This method is misleading because most surfaces
have significant random features or sharp edges, both of
which have a broad-band frequency component rather than
a single-wavelength sine wave. It is possible (Whitehouse
1988) to utilize this fact by optimizing what is in effect an
integrated transfer function, the inverse of which is shown
in figure 12. The instrument’s performance can thereby
be optimized over the whole frequency band. Figure 12
shows the relative importance attached to each component
in the signal. It can be seen that all signals can have the
same importance (1.0) right up to the resonant frequency,
at which w/wn = 1 for a damping ratio of 0.59 except for
a small amount which is averaged out near the resonant
frequency.
It also follows that the reaction on the surface caused
by the stylus pressure can be made substantially constant
on average over the total frequency range. This approach
has produced the interesting conclusion that the traditional
damping factor used for instruments is too low and that the
optimum damping should be 0.59, which is close to the
961
D J Whitehouse
Figure 9. Instrument criteria: P, profile; NP, profile; SIP, slope integration; N/T, Talystep; and EM, electron microscope.
Table 1. The range/resolution response for typical methods. (Note that ultrasonic pneumatics are suitable for rougher
surfaces only.)
Method
Spatial
resolution
z
resolution
Range z
Frequency
Comments
Stylus
0.1 µm to 1 mm
0.3 nm
50 µm
20 Hz
Optical probe
0.5 µm
0.1 µm
20 µm
10 Hz to 30 kHz
Heterodyne
2.5–200 µm
TIS
0.6–12 µm
Scatterometer ≃ 10 µm
diffraction
0.2 µm
1 nm
1 nm
0.5 µm
0.1 µm
λ/8
100 nm
10 Hz
Seconds
Seconds
Contacts workpiece; easy to
use; traceable
Non-contacting; less traceable;
with servo drive; range
extended to 50 µm
Requires computer unravelling
TEM
2 µm
100 nm
Minutes
2 nm
0.2 nm
2 µm
100 nm
Minutes
Minutes
Minutes
1 nm
1 nm
50 nm
1 µm
2 kHz
Minutes
2 nm to 1 µm
SEM
STM
Normarsky
Capacitance
Interferometry
10 nm
2.5 nm
> 0.5 µm
2 µm
2 µm
Figure 10. Instrument criteria.
critical damping. This development allows higher speeds
to be obtained without the stylus lifting off the surface.
Another example of modern developments is the use of
962
Resolution depends on
aperture; insensitive to
movement
Replication needed can
destroy surface
Vacuum needed
Vibration-free mounting
Needs interpretation and
certain minimum reflectivity
Needs conductors
neural networks to help in optimum measurement. One
example is the use of neural networks to ‘de-convolute’
the stylus shape from the profile measurement (Wang and
Whitehouse 1995). The result of these advances is that the
stylus technique is moving in a direction which takes in the
advantages of both axes, namely faster measurement yet a
larger range-to-resolution ratio too.
The methods outlined above illustrate advances in
integrated and high-precision measurement using the stylus
technique. Attempts have been made to adapt the stylus
method to in-process measurement or at least to reduce the
measurement cycle time. One example of stylus in-process
measurement is shown in figure 13 (Deutschke et al 1973).
This is comprised of a drum which is forced onto the
workpiece. A single probe projects through the drum wall
to contact the test surface. This probe has a displacement
transducer connected to it within the drum. As the
Surface metrology
is measured. Over many revolutions a picture of the
surface is built up, at the same time that the workpiece
is being machined. Problems with the method such as
debris and surface damage caused by the drum rims limit
its usefulness.
4.3. Other (non-optical) methods
Figure 11. Measurement of curved surfaces.
Figure 12. Optimized damping to improve the speed of
response.
Figure 13. In-process measurement of texture.
workpiece rotates the drum is forced to rotate and the probe
makes contact with the surface once per revolution. The
amount by which the probe penetrates into the roughness
Other possible methods for measuring surfaces are
numerous but on the whole they are matched to a particular
process or workpiece shape. One consideration is that, for
the transduction to have a high signal-to-noise ratio, a high
change in energy per unit displacement of the transducer is
required.
One technique which has this high energy is the
pneumatic method (Von Weingraber 1942). In this air is
blown on to the surface via a measuring head and skirt.
The amount of air which escapes can be related to the
surface finish. In practice the leakage is proportional to
the average distance between the skirt lip and the rough
surface. One possibility is to measure the flow of air;
the other is to measure the back pressure. The latter is
most sensitive, but neither is highly sensitive compared
with other methods. Range-to-resolution ratios of about
100:1 are common, which is rather poor. However, they are
cheap and robust. Difficult shapes cause problems because
the shape of the skirt has to match the general shape of the
surface. Also the air supply has to be dry otherwise water
condenses out of the air on to the surface.
Another possibility is the use of capacitance methods
(Perthen 1936). One of these uses an electrode positioned
above the surface. The capacitance between it and the
surface is a measure of the roughness and the average
distance from electrode to surface. Some dielectric such
as air has to be between the two.
If capacitance is to be used in this way there are some
complications because the value of the capacitance is not
simply related to the surface roughness. In fact it follows
an inverse law with nonlinear terms. The capacitance
method can also be used in scanning mode but it is no
real contender.
In general the capacitance method is very sensitive and
can be used effectively in certain applications. However,
it does have problems, one of which is that the signal
from the transducer is susceptible to extraneous noise. So
for high sensitivity shielding has to be used. Also the
electrode shape should follow the general shape of the
workpiece being measured. It should be remembered that
the capacitance method integrates the surface roughness
(Sherwood and Crookall 1968). It has therefore two
attractive features; it measures over an area and it is a
non-contacting method. Scanning methods are currently
being considered but they do not have the same potential
for versatility as do the stylus and optical methods (Matey
and Bland 1985).
A further possible technique for measuring surfaces is
to use ultrasonics (Berry 1973). In this method ultrasonic
waves are projected on to the surface and the scattered
waves picked up. In principle this method has potential
because it is possible to get phase as well as amplitude
963
D J Whitehouse
information, in contrast to optical methods, with which
phase information is lost unless recovered indirectly.
Some snags with this method are that very high
(unrealistic) frequencies are needed to measure the
roughness on fine surfaces and also that ultrasonic waves
only propagate through air with difficulty so that the
attenuation rate is high. The directionality can also be poor.
Another wave technique is that using optics.
Figure 14. The basis of the gloss meter.
4.4. Optical methods
Some optical methods mimic the eye whereas some mimic
the profile produced by a stylus instrument. Such is the
potential of optical methods that the variety of possibilities
is large. In that which follows the simplest method will be
considered first; then the more complicated methods will
follow.
All optical methods involve projecting light on to a
surface. Sometimes the light is focused but often it is
not. Also the light can pass by an obstruction on the
way to the surface or after scattering. In addition the
light can be used coherently or in an incoherent mode and
finally polarization properties can be used (Beckmann and
Spizzichino 1963, Bass and Fuchs 1963, Ogilvy 1991).
More practical assessments by optical means have been
treated thoroughly in the books by Bennett (1994) and
Whitehouse (1996).
Schmaltz in 1927 was the first person to use optical
techniques (Schlesinger 1942, Schmalz 1929). He projected
a collimated beam of light past a knife edge, the shadow
of which was made to intersect the surface at an angle.
When viewed from a different angle a profile of the
surface roughness was apparent. In this method there is
no horizontal magnification. The vertical magnification
is provided by the obliquity angle of the projected edge.
The magnification is only about ×20 so that the method
is restricted to viewing rough surfaces. The roughness
measurement is made by eye using the graticule in the
viewing optics.
The other simple way is to view the scattered light
directly or, more practically, sense the scattered light with
one or more detectors. This is the basis of the gloss meter
or scatterometer (Whitehouse and Bowen 1994, Young et
al 1980).
Two detectors A and B pick up the scattered light
(figure 14). The detector A is positioned at the specular
(reflected) angle. In addition another detector B is used,
which is called the diffuse detector. The surface roughness
can be estimated from the ratio of the scattered light which
hits the two detectors. For a rougher surface whose Ra
of texture is about half the wavelength of light the ratio
is about one half and for very rough surfaces there is no
specular component and the light detected at A is equal
to that at B; that is, the surface number is zero. This
scattering-based number can be used as a basis for surface
quality measurement or quantification. The problem is that
the light-scattering characteristic as a function of roughness
varies with the manufacturing process so that the method
cannot be recommended for general use (Wang and Wolfe
1983). The scattering method can only be used as a
964
Figure 15. The total integrated scattering of an integrating
sphere.
Figure 16. The metrological freak diffractometer. D = λf /d .
comparator. However, if the surface is very fine all the
light scattered can be collected by an integrating sphere.
This total light scattered can be related to the RMS value of
the surface (figure 15) (Beckmann and Spizzichino 1963).
In a more refined version of the scattering method
coherent light is used (figure 16) and the light scattered
from the surface is collected in the Fourier plane of the
collecting lens, namely the back focal plane.
In this method the light source is imaged in the Fourier
(transform) plane (Konczakowski 1983). The image in
the transform plane is modulated principally by the slopes
on the surface. Under certain conditions, for example,
when the surface roughness is small compared with the
wavelength of light, the image in the transform plane can
be taken as the power spectral density of the surface.
This particular configuration has enormous advantages as
a metrological tool. The first is that small detail tends
to scatter over a very wide angle. This produces a
signal on the detector which is far from the centre so
that a large measurement on the detector corresponds to
a small distance on the surface; this is a metrological freak,
figure 16. The situation is usually the other way round; that
is, in the image of the surface, small detail in the object
produces small detail in the image.
From the power spectral density it is possible to
evaluate the surface roughness and the various moments
of the spectrum leading to slope and curvature information.
Surface metrology
Figure 17. The interferometer method.
Figure 18. The Mireau interferometer for surfaces.
Because this method is essentially a slope-sensitive one, the
scattering pattern is insensitive to movement of the surface.
A point to notice is that, because of this independence
of speed the method lends itself to in-process gauging.
Furthermore, it allows random-process analysis, that is,
power spectral analysis, of the surface geometry to be
carried out (Welford 1977).
In another mode which utilizes the coherent property
of the light the interference between light scattered from
the test surface and that scattered from a reference surface
such as a glass flat (Tolansky 1948) produces fringes. The
reference flat can be positioned as in a Twyman Green
interferometer or a multiple-beam interferometer by laying
it on the surface (figure 17). Fringe contours can then
be examined. The contour pattern when viewed can give
a very clear picture of the general surface geometry. If
the fringes are sharpened up by means of multiple-beam
interferometry it is possible to consider the roughness.
If the reference surface is kept at a small angle
then a set of profiles of the roughness can be produced
(figure 17(b)).
The problem with the conventional
arrangement is that the interpretation of the fringes requires
experience (Young et al 1980). The whole technique
has been automated in a variant which uses the Mireau
interferometer. The reference mirror and the test surface
positioned relative to the objective (figure 18) constitute
the Mireau interferometer.
In this the fringe pattern is viewed by a CCD camera.
The fringe pattern is stored in a computer and then some
subsequent movements are made between the objective
lens (hence the reference) and the test surface (Wyant
1975). The total movement is restricted to about one
wavelength. The form and roughness of the surface are
then computed from the sets of stored data. This is a good
example of how computation can help out in a difficult
metrology situation. There are still problems, however; if
the surface is complicated, the computer can get confused!
For reasonably flat surfaces such as semi-conductor wafers
this method works admirably. Incidentally the instrument
design has to be good so that when the small movements
in the objective position are made there is no twisting or
yawing.
White light can be used in some cases to generate
fringes of equal chromatic order. This technique (FECO)
produces coloured fringes close to any one diffraction order.
This method relies upon multiple reflections and can be
used for very fine surfaces (Hodgkinson 1970). Obviously,
complicated roughness or form cannot be examined by this
method.
One large group of optical methods involves scanning
as part of the technique. The obvious starting point is the
flying-spot microscope (Young and Roberts 1951). In this
very high spatial resolution is obtained by restricting the
illumination on the surface to a very small spot. Light
collected at this time can obviously originate from the
illuminated point on the surface only, which has the effect
of not allowing extraneous light to hit the detector.
A variation on this is the confocal microscope
(Sheppard and Wilson 1978) in which the imaging and
receiving optics are exactly the same. Like in the flyingspot method, the optics is used to produce a spot on the
surface. The reflected light is picked up by a point detector.
The resulting signal is used to modulate the brightness of
a spot on a TV screen. The point detector is in effect a pin
hole which completely blocks out all light from an out-offocus plane which could otherwise mix in with the signal
(figure 19).
As the object is de-focused the light signals fall off
dramatically. This method produces very sharp images.
Resolutions of 1 µm in x and y and 0.1 µm in depth are
possible. The absolute roughness is found by measuring
the axial movement needed to keep the spot focused.
Optical ‘follower’ methods utilize the null technique
outlined above. Essentially the sensor follows the surface
during a scan, maintaining a fixed distance from it. Some
optical means has to be adopted whereby the de-focus of
the optical system is detected and an error signal generated
which corrects the focus. The first attempt at this was due
to Mme Dupuy who used the Foucault knife-edge test as
a basis for the focus-correction mechanism (Dupuy 1968).
In this configuration (figure 20) a knife edge is situated at
the position where the surface spot re-focuses in the image
plane. Further from the objective two photodetectors are
positioned laterally and symmetrically relative to the optical
axis. When, during the scan, the spot on the surface is
higher than the in-focus plane due to a peak, the de-focused
image causes a difference between the signals on the two
detectors. This references the spot via the objective. If a
valley is encountered exactly the opposite occurs.
The movement of the objective lens to maintain
focus is measured and used as the surface profile. The
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D J Whitehouse
Figure 19. A confocal microscope.
Figure 21. A heterodyne follower.
Figure 20. Dupuy’s optical follower.
most successful optical methods are heterodyne techniques
utilizing common-path interference in which two different
types of illumination are projected on to the surface at the
same time.
Invariably the light is split either into two different
wavelengths or into different polarizations, (Sommargren
1981, Simon 1970). The resulting two beams of light
are focused at different axial or transverse positions. It
is possible to follow the surface geometry by observing
how the roughness affects the two positions where focus
occurs for the different rays (figure 21). Some of the
very finest surface measurements have been achieved using
these methods. Differential interference microscopy, such
as by Nomarski methods (figure 22) (Tolansky 1948), is
used to examine fine surfaces but, as the name implies,
the technique is essentially a differentiator. This has
the effect of enhancing edges and generally distorting
heights. Such techniques are best used for visualization
rather than to obtain quantitative information. There are
other optical techniques which have not been examined
in detail here. These include speckle techniques (Erf
1974) and holographic techniques. They have been useful
occasionally for roughness measurement but not generally
so. As versatile tools for metrology they are somewhat
lacking (Whitehouse 1996).
The problem is that the value of the roughness is
obtained indirectly rather than directly as in the stylus
method. In methods such as those using speckle the
roughness value is inferred from the speckle contrast; in
other words some model of the surface has to be assumed
966
Figure 22. The Nomarski technique.
before the roughness value can be obtained; the credibility
of the result can depend heavily on the validity of the
model. For this reason speckle and similar techniques,
particularly those based on scattering, have been restricted
largely to experimental instruments.
For form and vibration measurements these methods
have had more success (Ribbins 1974, Jones and Wykes
1983).
There are some problems, one of which is
that follower methods tend to be relatively slow. More
Surface metrology
importantly, problems can arise because the surface reacts
to different polarizations in different ways which do not
correspond to the geometrical features of the surface.
This problem is common. In principle the mechanical
stylus and optical methods need not agree when measuring
fine surfaces. The former measures mechanical geometry
whereas the optical methods measure the optical path length
or the optical path difference. If any thin films are present
they will contribute to the value of the roughness measured
optically. Such films can be ignored by stylus instruments.
Another problem with optical methods is that sharp edges
in the surface can produce misleading diffraction spikes
which can be mistaken for real peaks. This effect can be
troublesome in calibration. Hence the practical situation
is that optical methods tend to enhance the noise whereas
stylus instruments tend to reduce the signal (the fine detail
of the geometry is integrated). The best result is somewhere
in between. For a given signal-to-noise ratio the stylus
reduces the signal, and the optics increase the noise.
Figure 23. A diagrammatic representation of a SEM.
5. Unconventional methods
The natural constraints apparently governing the resolution
of surface measurement have been the wavelength of light
and the rather blunt stylus used in tactile instruments.
Recent advances in scanning microscopy have largely
removed these restrictions.
Before examining these
methods their forerunner the scanning electron microscope
(SEM) will be considered.
5.1. The SEM
The basic idea of the SEM is simple (figure 23). Electrons
from a filament are accelerated by a high voltage between
two or three magnetic lenses. These cause the electron
beam to strike the surface in a raster scan. The incident
electrons produce amongst other things secondary electrons
which are detected. The detected signal is synchronized
with the scan to produce an image of the surface on a
cathode-ray tube (CRT). The SEM has no imaging lenses
in the true sense of the word. The image magnification
is determined solely by the ratio of the CRT scan to the
surface scan. This invariably means that low magnifications
are more difficult to produce than are high magnifications
because of the large scanning area in the former case.
One of the big advantages of the SEM is the large depth
of imaging available because of the very low numerical
aperture of the electron beam and the small equivalent
wavelength of the electron beam. Despite the various
options in display the SEM has its drawbacks. One is its
rather poor lateral and vertical resolution and there is also
some distortion produced by sharp edges in the object. This
makes calibration a problem.
It is also ironic that its large depth of focus can cause
ambiguities, as can be seen in figure 24. The large depth of
focus allows large features to be measured. The secondary
electron output is influenced not only by the slope but
also by the curvature. As a result of this, edges become
enhanced. Although this sometimes clarifies the picture
and makes visualization easier, it is qualitative in nature
Figure 24. The emission provoked from surfaces.
and does not help the calibration. In fact a trace taken
through a SEM picture correlates better with the differential
of a profile taken by a stylus instrument than it does with
the profile itself! Nevertheless the SEM has been and is
extremely useful as a surface tool. It constitutes sound
metrology philosophy in the sense that, for measuring
to nanometres and below, a metrology unit, namely the
electron wavelength, is of the same order of size as the
features being measured (Suganuma 1985).
Various methods have been tried to quantify the picture.
One such method is to use more than one detector to get a
stereoscopic view of the surface. Another variant is to look
at back-scattered electrons at the specular angle. There are
many options for measuring surfaces using scattering of
electrons or other particles and waves (figure 25). Most of
these have been used to highlight different aspects of the
surface, see for example Whitehouse (1996).
5.2. The TEM
Transmission electron microscopes (TEM) are not as
important in surface examination because most engineering
surfaces are opaque. However, information can be obtained
if replicas are used. One such application is in measuring
diamond styli. In this the stylus is indented into glass which
is coated with carbon and shadowed with platinum at an
angle. Asperities on surfaces can be highlighted in the
same way. Other replication materials are plastics such
as cellulose acetates which are pressed on to a surface
previously coated with a solvent such as acetone.
967
D J Whitehouse
Figure 25. SEM distortion.
5.3. The STM and the AFM
The routine study of atomic and molecular scale structure
has become possible with the development of the scanning
tunnelling microscope (STM) and the atomic force
microscope (AFM) (Binning et al 1982, 1986, Gehtz et al
1988, Binning 1992). These are similar to the conventional
tactile surface instrument in that there is a stylus.
The difference is that contact with the surface is not
a pre-requisite. In fact gaps of the order of nanometres
have been claimed. These techniques do not measure the
topography necessarily; other features such as the charge
density are revealed in the case of STM and forces in the
case of AFM. In all these cases the information is obtained
via a stylus. The great advance in technology is that these
instruments are not bounded by conventional restrictions
such as diffraction caused by the relatively large wavelength
of light. The limit is imposed by the geometrical size of
the stylus probe.
These can now be made extremely small in tip
dimension. Values of a few nanometres are not uncommon.
The other big difference between the scanning probe
microscopes (SPM) and conventional instruments is that
they rely for their signal on quantum-mechanical effects
(tunnelling currents in the STM, for example). This
probabilistic nature of the new instruments is inevitable
when exploring surfaces on the atomic scale. Differences
between these methods and the more conventional ones are
to be expected (Bhushan 1990).
A typical configuration is shown in figure 26. It is
basically a very simple device comprising of a pick-up and
a translation stage. There are two modes of operation,
open loop (figure 26(a)) and closed loop (figure 26(b)).
In the latter the signal current is kept constant throughout
the traverse by means of a servo system. The other
mode simply moves the probe in a fixed horizontal plane.
Figure 27 is an atomic eye view of what the stylus records
in the cases mentioned above.
In the AFM there is an added advantage in that the
surface being measured does not have to be a conductor. It
simply responds to atomic-scale forces by the deflection of
a simple cantilever. The movement of the cantilever was
968
Figure 26. The mode of scanning.
measured originally by a STM (figure 28) but is now usually
measured optically. The method whereby the deflection is
converted into an electrical signal is not at issue here.
One advantage of this new generation of microscopes
is their ability to measure more than one feature. For
example, by varying the voltage between the specimen
and the probe in the STM different physical phenomena of
various substances can be investigated on the atomic scale.
The instrument can in effect be used both as a spectroscope
and as a topographer. The STM provides spectroscopic data
by utilizing its sensitivity to the electron energy states of
the sample. Measurements of the tunnelling current made
under conditions of changed bias voltage can provide data
on the local density of states.
In another mode (figure 26) changing the height of the
tip and measuring the tunnelling current can give information about the local work function. The STM in spectroscopic mode has a considerable advantage over conventional spectroscope techniques in that the results are not averaged. Figure 29 is a schematic diagram of a typical STM.
The versatility of instruments like the STM has
allowed many different surface experiments to be carried
out. These include the measurement and detection of
growth in biological specimens, the initiation of some
chemical reactions, the machining of substrates and the
microfabrication and movement of material around the
Surface metrology
Figure 27. The atomic view of a signal from STM.
6. Trends in metrology
Figure 28. An AFM.
surface. Also other physical properties can now be
examined using this basic technique. (Wickramasinghe
1989). The techniques are:
(i) magnetic force microscopy (MFM), in which the
probe is magnetized;
(ii) electrostatic force microscopy (EFM), in which the
probe has an electrostatic charge;
(iii) scanning thermal microscopy (STM), in which the
probe is designed as a thermocouple;
(iv) scanning conductance microscopy (SICM), in
which a micropipette probe containing an electrode is used;
and
(v) near-field scanning optical microscopy (NSOM), in
which the probe is in fact a submicrometre aperture (Guerra
1990).
5.4. X-rays
The trend towards atomic measurements and in particular
various atomic measurements on the surface has pointed
towards the use of x-rays (Hogrete and Kunz 1987,
Wormington et al 1994). This makes sense because the
wavelength of x-rays is about the same as the atomic lattice
spacing. Recent work has shown that by varying the angle
of incidence, the surface interface can be assessed, at least
crudely (figure 30). In the same measurement an estimation
of crystal flaws and residual stress is also possible. It is in
effect an extension of the optical scattering methods.
Figure 31 shows the trends in surface metrology in
recent years. The z axis shows the scale of size under
consideration in terms of resolution. The x axis refers to
the lateral information on the surface and the y axis to the
height information. Both x and y are scaled chronologically
with the origin at 1950. The scale of size in z is the
resolution of a typical instrument.
There are three curves in figure 31 each representing
a family of instruments. The left-hand curve refers to
stylus instruments; its position to the left-hand side of
the graph reflects the fact that, during the early stages of
development, stylus instruments measured height almost
exclusively. Optical methods, shown by the right-hand
curve, on the other hand, were almost completely concerned
with lateral structure and spacings. The middle curve
represents the other, newer, techniques such as those
involving the scanning microscopes.
This graph has been described as showing the ‘horns of
metrology’ (Whitehouse 1988, 1991). The ‘horns’ are the
curves of the stylus and optical methods which have been
converging in their measurement philosophy: both are now
attempting to measure height as well as lateral structure.
Other changes in the philosophy have to be recognized.
These changes are concerned with the physical basis of
the measurement. At the normal engineering scale of size,
called macro in figure 31, measurement is deterministic;
distances rely on readings of scales, fringes and so on. At
the sub-micrometre level that which is measured in positioning, for example, relies on statistical averaging to produce very high resolution; distance is the separation of two
planes, each determined by the average position of millions
of atoms. This regime is called here statistical mechanics. Measurement to sub-nanometre accuracy in two dimensions is possible using statistical mechanics. Problems
arise, however, when atomic accuracy in all three dimensions is required. This accuracy can only be achieved with
a closed-loop system; there has to be evidence of proximity
between the two points in space for which this accuracy is
required. (Notice that this type of measurement cannot refer
to planes or lines.) However, because of the limited number
969
D J Whitehouse
Figure 29. A schematic diagram of a STM.
Figure 30. The scattering of x-rays by a rough surface.
Figure 31. The probability problem—the horns of metrology.
of atoms involved in the points, it is difficult to get a signal
between them. Quantum mechanics does not readily allow
it! The loop closure is not possible on a continuous basis.
970
The only way to achieve a measurable signal strength
is to reduce the measurement bandwidth; that is, the signal
has to build up in time. The actual value of the signal
Surface metrology
is determined by quantum mechanics which determine the
point-to-point tunnelling. The probabilities only convert to
a measurable signal after a considerable time lapse; hence
all effects of external vibration and environment will be
included in the measurement, so the signal-to-noise ratio
will increase rather than decrease with time. This effect
constitutes an uncertainty principle in metrology between
time and spatial 3D discrimination, which has yet to be
solved! Compare this restriction with that of signal to noise
in the stylus and optical methods mentioned earlier.
7. Summary
Measurement techniques for surfaces have progressed
rapidly during the last decade. Traditional complementary
techniques such as the stylus and optical methods are
converging to satisfy areal and vertical measurement
requirements. This is not to say that they are competing
against each other. Contact and non-contact methods both
have advantages.
Contacting methods clear unwanted debris away. Also,
there is the possibility of measuring the nano-hardness
and even the friction at the nano-scale with tactile stylus
methods.
Optical and ultrasonic methods can be quicker because
they do not contact the surface. Also, neither does stylus
damage to the surface occur nor is there a change in
resolution due to stylus damage. Optical techniques are
still plagued by the lack of suitable standards but these are
now being introduced by standardization committees.
Calibration is still a problem with the newer generation
of scanning microscopes. At the same time as making
atoms visible the new technology has revealed a challenge
to metrology in terms of achievable signal levels.
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