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Surface Measurement Errors using Commercial Scanning White
Light Interferometers
F Gao
1
, R K Leach
2
, J Petzing
1
and J M Coupland
1
1
Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University,
Loughborough, Leicestershire LE11 3TU, UK
2
Industry & Innovation Division, National Physical Laboratory, Hampton Road, Teddington,
Middlesex TW11 0LW, UK
F.Gao@lboro.ac.uk
Abstract:
This paper examines the performance of commercial scanning white light interferometers in a
range of measurement tasks. A step height artefact is used to investigate the response of the
instruments at a discontinuity, while gratings with sinusoidal and rectangular profiles are used
to investigate the effects of surface gradient and spatial frequency. Results are compared with
measurements made with tapping mode atomic force microscopy and discrepancies are
discussed with reference to error mechanisms put forward in the published literature. As
expected it is found that most instruments report errors when used in regions close to a
discontinuity or those with a surface gradient that is large compared to the acceptance angle
of the objective lens. Amongst other findings, however, we report systematic errors that are
observed when the surface gradient is considerably smaller. Although these errors are
typically less than the mean wavelength they are significant compared to the instrument
resolution and indicate that current scanning white light interferometers should be used with
some caution if sub-wavelength accuracy is required.
Key words: White light interferometry, measurement errors, surface roughness measurement,
multiple scattering effect.
PACS code: 42.25.Kb (Coherence), 42.25.Fx (Diffraction and scattering) 42.25.Hz
(Interference), 47.50.Ef (Measurements)
1. Introduction
Scanning white light interferometry (SWLI) is now an established method to measure
precision surfaces [1-5]. In comparison with stylus profilometry and scanning probe
microscopy, SWLI presents significant advantages. It is an optical, non-contacting technique
and as such can be used to measure the profile of delicate membranes or soft materials
without risk of damage. It is also significantly faster than confocal or near field microscopes
since SWLI only requires a scan in a single (vertical) direction. SWLI shares many
characteristics with its close relative, phase shifting interferometry (PSI), but differs
essentially in the use of an extended polychromatic source that allows the fringe order to be
identified unambiguously and results in a virtually unbounded measurement range. As an
interferometric technique, the vertical resolution of SWLI is limited by the precision to which
the phase of the reflected signal can be identified and is typically around one thousandth of
the mean wavelength (ie sub-nanometre). As a high power microscope, SWLI promises
lateral resolution up to the Rayleigh diffraction limit, which is typically around 0.5 µm for
objectives of large numerical aperture (NA).
In contrast with PSI, a stable source is not exploited in most SWLI instrumentation and
calibration of the scanning mechanism is required to ensure accuracy. For the measurement of
constrained surfaces such as step heights and gauge blocks this is sufficient to provide
traceability. However, the popularity of SWLI has led to its use in circumstances that are far
removed from traditional gauge block interferometry and SWLI manufacturers have been
quick to cater for these demands by including, for example, specialised software to estimate
areal surface texture parameters and film thickness [6,7]. In these cases, the accuracy of
SWLI is much more difficult to define.
In 1990, Hillmann questioned the accuracy of surface measurements obtained by optical
methods [8]. He reported that the results measured on a roughness standard by optical
methods present significant deviations with reference to the results from stylus profilometry.
This work was of great concern to practicing experimentalists and has provoked many more
to document problems encountered with SWLI in surface measurement [8-13]. It is fair to
point out that most of the problems cited in the literature have been observed when a surface
gradient is large compared to the NA. Most samples, however, will have regions where
geometry, surface roughness or debris means that this is not the case, and anomalous
measurements can result. We briefly summarise the errors that are observed in the following
paragraphs.
The batwing effect is a well known example of an error that is observed around a step
discontinuity especially for the case of a step height that is less than the coherence length of
the light source [10,11]. This problem is called the batwing effect, because of the shape of the
error (see for example Figure 15) and it is usually explained as the interference between
reflections of waves normally incident on the top and bottom surfaces following diffraction
from the edge. Interestingly, an SWLI does not give the correct surface height at the positions
close to the step even if the step height is significantly greater than the coherence length. This
can be thought of as a phase change caused purely by the way the optical field interacts
(diffracts) around the discontinuity. In this case the measurement error is small but still
significant compared to the instrument resolution.
On some early SWLI systems, stepped artefacts have been reported when measuring
perfectly flat objects [12]. Errors of this kind are commonly referred to as ghost steps. These
usually correspond to a 2π phase jump or a surface height error of around half the mean
wavelength. More generally phase jumps of this magnitude are referred to as 2π errors and
can be thought of as a misclassification of fringe order [13,14]. In this case the error is due to
a field dependent dispersion that is due to the geometry of Mirau interference objectives [12].
If spatial phase unwrapping algorithms are implemented the effect can be minimised and the
use of matched objectives in reference and object arms of a Twyman-Green interferometer is
also reported to reduce the effect.
A similar dispersive effect makes SWLI instrumentation sensitive to surface gradient [15].
Tilt dependent dispersion is often the cause of 2π errors in SWLI measurements even when
the tilt is small compared to the NA of the objective. If errors of this kind are present then 2π
errors can appear, for example, at regular intervals on regular sinusoidal profiles (see for
example Figure 10a). A combination of field and tilt dependent dispersion is also responsible
for errors of similar appearance to the batwing effect and was recently reported by Lehmann
[16]. In contrast with regular batwing errors, the presence of these phase jumps depends
systematically on position and generally increases in severity toward the edge of the field of
view. This effect also depends strongly on the polarity of the discontinuity. It is noted that
(depending on the height retrieval algorithm used) in extreme cases the dispersive batwing
effect can result in errors that propagate and result in a corresponding error in step height
measurement (see for example Figure 5).
Dispersive effects of the kind mentioned are clearly a function of the quality of the optical
system (they are artefacts of chromatic aberration), however, the optical properties of the
surface to be measured are also a potential source of error. It is well known that different
materials exhibit different phase changes on reflection, and depending on the processing
algorithms used, these will affect the surface height measurement [13,17]. Phase changes are
typically less than 45 degrees (corresponding to surface height errors of less than 30 nm) but
can combine with dispersive effects to give 2π errors as discussed previously. Clearly, this
type of error is only a problem when two or more materials with different optical properties
are present in a sample.
Finally it is important to note that surface roughness plays a significant role in
measurement quality when using SWLI instrumentation. Many researchers have found that
estimates of surface roughness derived from SWLI measurements differ significantly from
other measurement techniques [8,18-21]. The surface roughness is generally over estimated
by SWLI and this can be attributed to multiple scattering. Although it may be argued that the
local gradients of rough surfaces exceed the limit dictated by the NA of the objective and,
therefore, would be classified as beyond the capability of SWLI instrumentation, measured
values with high signal to noise ratio are often reported in practice. If for example, a silicon
V-groove (with an internal angle of 70.52 degrees) is measured, a clear peak is observed at
the bottom of the profile due to multiple reflections (scattering) [22]. Although this example
is specific to a highly polished V-groove fabricated in silicon it is believed to be the cause for
over estimation of surface roughness since a roughened surface can be considered to be made
up of randomly oriented grooves with varying internal angles.
The error mechanisms described in the preceding paragraphs and references therein, have
either been discussed with reference to a specific instrument or a generic model of SWLI.
Although commercial SWLI hardware is very similar, the instruments differ quite
significantly in the way that they record and process fringe data. It is clear that the
identification of fringe order and the inference of surface topography from fringe data is a
highly non-linear process and consequently has a large bearing on the final measurements.
Although the basic processing methods used by the manufacturers are outlined in patent and
other literature [23-25] the actual algorithms that are used remain uncertain. In this paper we
provide a comparison of the performance of commercial SWLI instrumentation for a number
of measurement tasks. A step artefact is used to investigate the step response of the
instruments, while gratings with sinusoidal and rectangular profiles are used to investigate the
effects of surface gradient and spatial frequency. The performance is discussed with reference
to the error sources outlined above.
It is noted that the intention of this work was not to appraise the relative performance of
commercial SWLI instrumentation, indeed the measurements presented are neither
sufficiently controlled nor suitably comprehensive for this task. The aim of our work is to
demonstrate and discuss the errors that are frequently observed when commercial
instrumentation is applied to the measurement of small scale artefacts. To avoid any attempt
form an appraisal from the information presented here, we refer to the instruments by a
simple alphabetic label.
2. Instrumentation
Tests were made on commercial SWLI instruments provided by commercial SWLI
instrument manufactures, and with the areal profilometry equipment within the metrology
laboratory at Loughborough University. Measurements made by the commercial instruments
were performed by measurement engineers at the company or on the premises of their UK
representatives. The commercial SWLI instruments involved are labeled Instrument B,
Instrument C and Instrument D. At Loughborough University measurements were made using
a SWLI labeled Instrument A which was made by the same manufacture as Instrument B and
an atomic force microscope (AFM) in a controlled environment (20 °C, 45% relative
humidity). The manufacturer’s specifications of these instruments are listed in Table 1.
.
Objective
lens
NA
Vertical
resolution
(nm)
Rayleigh
resolution
λ = 600nm
(µm)
Pixel
resolution
2
(µm)
Repeatability
10X
0.30
0.1
1.0
2.15
0.55
Instrument A
50X
0.55
0.1
0.55
0.43
0.11
Instrument B
50X
0.55
0.1
0.55
0.43
0.11
RMS < 0.01 nm
Step height < 0.1%
5X
0.12
0.1
2.31
0.98
0.85
Instrument C
50X
0.55
0.1
0.55
0.38
0.09
RMS < 0.01 nm
Instrument D
50X
0.55
0.01
0.55
0.36
RMS < 0.003 nm
Step height < 0.1 nm
AFM
1
-
-
0.1
-
-
-
1
Resolution is tip dependent. It is cited for a tapping mode tip with 10 nm radius, resolution is
listed in the table.
2
The pixel resolution listed on the top line for each objectives were used in the tests. The
bottom lines are the maximum achievable pixel resolution.
Table 1. Instruments used in the comparison and their specifications
Most commercial SWLI instrumentation includes a means to remove spurious data. For
example Instrument A prompts the user to define a minimum fringe modulation below which
measurements are not reported. In addition the user can elect to remove spikes to post-process
the data. In all cases the minimum modulation was set as low as possible (1% on Instrument
A) and spike removal and other filtering operations were requested to be turned off.
For Instrument A, Instrument B and Instrument D, the algorithm used in the instruments to
detect the position of the envelop peak involves both intensity and phase fitting. Therefore the
working mode for these instruments are combined vertical scanning interferometry (VSI)
mode and PSI mode. For Instrument C, only VSI mode was available for the instrument we
used in the test.
3. Measurement Artefacts and Evaluation Methods
Three types of measurement artefacts were used in this study; a calibrated step height and
two sets of grooves with approximately sinusoidal and rectangular profiles respectively.
The step artefact is a 1.844 µm step (manufactured by VLSI Standard Inc) that was
supplied by the manufacture for calibration of Instrument A. In the study this artefact was
used to calibrate the Instrument A used at Loughborough whilst the other instruments were
