Optical profilers are mature instruments used in research and industry to study surface topography features. Although the corresponding standards are based on simple step height measurements, in practical applications these instruments are often used to study the fidelity of surface topography.
In this context it is well-known that in certain situations a surface profile obtained by an optical profiler will differ from the real profile. With respect to practical applications such deviations often occur in the vicinity of steep walls and in cases of high aspect ratio.
In this contribution we compare the transfer characteristics of different 3D optical profiler principles, namely white-light interferometry, focus sensing, and confocal microscopy. Experimental results demonstrate that the transfer characteristics do not only depend on the parameters of the optical measurement system (e. g. wavelength and coherence of light, numerical aperture, evaluated signal feature, polarization) but also on the properties of the measuring object such as step height, aspect ratio, material properties and homogeneity, rounding and steepness of the edges, surface roughness. As a result, typical artefacts such as batwings occur for certain parameter combinations, particularly at certain height-to-wavelength ratio (HWR) values. Understanding of the mechanisms behind these phenomena enables to reduce them by an appropriate parameter adaption. However, it is not only the edge artefacts, but also the position of an edge that may be changed due to the properties of the measuring object.
In order to investigate the relevant effects theoretically, several models are introduced. These are based on either an extension of Richards-Wolf modeling or rigorous coupled wave analysis (RCWA). Although these models explain the experimental effects quite well they suffer from different limitations, so that a quantitative correspondence of theoretical modeling and experimental results is hard to achieve.
Nevertheless, these models are used to study the characteristics of the measured signals occurring at edges of different step height compared to signals occurring at plateaus. Moreover, a special calibration sample with continuous step height variation was developed to reduce the impact of unknown sample properties. We analyzed the signals in both, the spatial and the spatial frequency domain, and found systematic signal changes that will be discussed. As a consequence, these simulations will help to interpret measurement results appropriately and to improve them by proper parameter settings and calibration and finally to increase the edge detection accuracy.
Optical measurement techniques are widely applied in high-resolution contour, topography and roughness measurement. In this context vertical scanning white-light interferometers and confocal microscopes have become mature instruments over the last decades. The accuracy of measurement results is highly related not only to the type and physical properties of the measuring instruments, but also to the measurement object itself. This contribution focuses on measurement eﬀects occurring at edges and height steps using white-light interferometers of diﬀerent numerical apertures. If the edge is perfectly perpendicular, batwing eﬀects appear at height steps. These batwings show maximum height if the height-to-wavelength-ratio (HWR) is about one forth or three forth, and they disappear if the HWR value is about an integer multiple of one half. The wavelength that is relevant in this context is the eﬀective wavelength, i.e. the center wavelength of the illuminating light multiplied by a correction factor known as the numerical aperture correction. However, in practice the edges are usually not perfectly perpendicular. In this case, the measurement results depend also on the derivative of the surface height function and they may diﬀer from theory and the prediction according to the HWR value. Measurements of such steps show systematical eﬀects depending on the lateral resolution of the instrument. In this context, a Linnik interferometer with a magniﬁcation of 100x and NA = 0.9 is used to characterize the three dimensional topography of more or less rectangular calibration specimens and quasi-perpendicular structures produced by the nanoimprint technology. The Linnik interferometer is equipped with LED light sources emitting at diﬀerent wavelengths, so that the HWR value can be changed. This is possible since the high NA objective lenses show a rather limited depth of focus such that the temporal coherence gating may be replaced by focal gating in this particular instrument. In addition, measurement results are compared with those achieved by a Mirau interferometer of NA = 0.55. A commercial confocal microscope with NA of 0.95 serves as a reference instrument for further comparison. Numerical simulations considering diﬀraction eﬀects are carried out in order to explain the experimental results obtained by the diﬀerent white and colored light interferometers
Increasing capabilities in precision manufacturing and micro technology are accompanied by increasing demands for high precision industrial metrology systems. With respect to optical metrology especially the lateral resolution capabilities of an optical profiler gains in importance. If, in addition, nanometer height resolution is needed interferometers seem to be the most promising instruments. This contribution focuses on interference microscopes using objective lenses of high numerical apertures in order to reach high lateral resolution. Increasing the numerical aperture influences both, the envelope as well as the phase of interference signals obtained by a so-called depth scan, i. e. changing the distance between the measuring object and the interference microscope. The depth of focus of a high numerical aperture objective limits the width of the signal envelope simultaneously increasing the fringe spacing which results in a longer effective wavelength. We demonstrate the practical consequences of these effects using a self-assembled Linnik interferometer of 0.9 numerical aperture. Phenomena resulting from concrete measuring objects will be discussed: Step height structures may lead to a further change of the effective wavelength as a consequence of changes in the signal spectrum due to interference phenomena within a single Airy disk. This may influence the lateral resolution of an interference microscope for a specific measurement task. In addition, a strong dependence of the measurement results on either TE or TM polarization occurs if step height structures are measured. Modeling the polarization dependence requires to consider the angle dependence of Fresnel reflection coefficients and edge diffraction phenomena. Although the maximum measurable surface slope of a tilted surface can be increased by increasing the numerical aperture there is a limitation due to the fringe density compared to the optical resolution of the microscope as it will be demonstrated by measurement results obtained from a chirp-shaped surface standard.
Increasing capabilities in precision manufacturing and micro technology are accompanied by increasing demands of high
precision industrial metrology systems. Especially for measuring functional surfaces, areal optical principles are widely
used. If, in addition, nanometer height resolution is needed interferometers seem to be the most promising instruments.
First, this contribution focuses on the transfer characteristics of white-light interferometers with microscopic field of
view. In general, microscopic instruments suffer from their limited lateral resolution capabilities. Hence, the transfer
function of these instruments is typically assumed to show a linear low-pass characteristic. We studied the transfer
characteristics of white-light interferometers by theoretical simulations and experimental investigations. Our results show
that in most practical cases these instruments behave nonlinear, i.e. the output surface profile cannot be obtained from the
input profile by a simple linear filter operation.
Although they are well-established, there are some further limitations of white-light interferometers if they are used to
measure micro or even sub-microstructures. If edges, steeper slopes or abrupt slope changes are present on a measuring
object characteristic errors such as batwings occur. Furthermore, a high effort concerning the correction of chromatic
aberration is necessary in order to avoid dispersion effects. Otherwise, there will be systematic discrepancies between
profiles obtained from evaluation of the coherence peak and those resulting from the phase of the interference signals.
These may lead to 2π phase jumps if the fringe order is obtained from the position of the coherence peak. Finally,
measurement artifacts may also result if the measured micro-structure shows discontinuities of the surface slope.
This contribution analyses the different phenomena and discusses approaches to overcome existing limitations.
Scanning white-light interferometry (SWLI) provides the capability of fast and high-precision three-dimensional
measurement of surface topography. Nevertheless, it is well-known that white-light interferometers more than imaging
microscopes suffer from chromatic aberration caused by the influence of dispersion. In this paper several interferometric
measurement systems are used for surface topography measurement. A Linnik interferometer and two Michelson
interferometers of different aberration correction are compared. A correction system designed using the ray tracing
software “Zemax” aims at an optimization the modulation transfer function (MTF). Although the MTF is optimized the
resulting spot diagrams are blurred due to chromatic aberration. Finally, a doubly corrected Michelson interferometer
will be presented. For this interferometer a nearly optimal MTF as well as minimized spot diagrams are achieved.
Due to its outstanding depth resolution capabilities vertical scanning low-coherence or white-light interferometry is one
of the most used optical techniques in the field of 3D micro-metrology. Unfortunately, step height structures often lead to
disturbing effects known as batwings in SWLI measurement that overlay the real profile heights of a rectangular
structure. As a consequence, the lateral resolution capabilities and the transfer characteristics of white-light interference
microscopes are difficult to characterize. In general, the lateral resolution of such instruments is assumed to agree with
the lateral resolution of a conventional light microscope for 2D imaging and the measurement process of an optical
profiler is assumed to be linear similar to a microscopic imaging process.
Our results show that there are significant discrepancies between the instrument transfer function of a white-light
interferometer and the optical transfer function of a conventional microscope. In this paper we analyze the transfer
characteristics of current white-light interferometers based on theoretical considerations, simulation studies, and
experimental investigations. It turns out that under certain conditions a correct measurement of a rectangular profile is
possible even if only the first order diffraction component is captured by an objective lens with a given numerical
In addition to the discussion of current instruments new approaches to overcome existing limits will be introduced: In
order to reduce the batwing effect we combine a Mirau white-light interferometer with a confocal illumination system.
Furthermore, it is shown that proper adaption of the evaluation wavelength of the low-coherent light can improve the
measurement accuracy significantly if rectangular profiles are obtained from the phase information inherent in WLI