Precise three dimensional (3D) profile measurements of vertical sidewalls of concave micro-structures are impossible by conventional profiling techniques. This paper introduces a simple technique which can obtain 3D sidewall geometry by means of laser fluorescent confocal microscopy and an intensity gradient algorithm. The measurement principle is: when a concave micro-structure is filled up with fluorescent solution, the position where the maximum intensity variation lays represents the profile of the micro-structure in the fluorescent 3D volume image. The physical essence behind this measurement principle is analyzed in this paper in detail. The strengths and limitations of this technique are studied by experiments or by illustrations. The factors that are able to improve the measurement accuracy are discussed. This technique has demonstrated the capability for measuring of 3D geometry of various concave features, such as vertical, buried and other micro channels with sub-µm (RMS) measurement accuracy and repeatability.
© 2008 Optical Society of America
The increasing interest in MEMS and micro-component production correspondingly demands the development of surface profilometry tools that can provide fast, accurate and complete information on device geometry [1–3]. However, for many typical micro-structures the recovery of complete information on surface geometry is not practical with conventional profiling techniques. The measurement of sidewall profiles of the concave micro-structures is a significant problem, especially when the sidewall is almost vertical. Profilometry based on conventional confocal microscopy is unable to measure these sidewalls as the reflected light is too weak in this region. Optical interferometry has the issue of interference fringes exceeding the density that can be resolved. Typical stylus profilometers or atomic force microscopy (AFM) systems are unable to measure sidewalls if the sidewall angle is greater than the slant angle of the probe cone. By way of example, Fig. 1 shows the surface profile of an elliptical microchannel obtained by optical interferometry. The red color in the figure represents the higher value, and the blue color represents the lower value. This color definition is effective in all the topographic 3D volume or intensity images in this paper. Almost all of the data in the sidewall region is missing, as indicated by the white regions in the figure. For many practical applications however the sidewall region is very rich in potentially useful information as there is significant geometric variation. Such information could provide valuable feedback to the optimization of production methods for micro devices. The sidewall geometry directly relates to several production parameters such as sidewall angle, edge roundness, and linewidth [2, 3]. Some significant defects on sidewall are also of interest for inspection purposes.
Currently, there are three main techniques used to measure sidewalls. The most common method is to observe a sample’s cross-section with optical microscopy or scanning electron microscopy (SEM) after the sample has been cut. The second technique is critical dimensional SEM (CD-SEM), which can reconstruct a complete 3D profile with an image of the structure of interest obtained at two different beam tilt angles[1, 2], or by analyzing secondary electrons (SE) signal profile . The third approach is CD-AFM or scanning probe microscopy (SPM), which can obtain the sidewall profile by means of specially designed probes [4, 5]. The crosssectional imaging technique is a destructive measurement technique and can observe the geometry at the point of cross-section only. In many cases it is also practically challenging to cut samples without introducing any deformation due to the applied force or the release of residual stresses. The main limitations to the wider application of the CD-SEM, CD-AFM and SPM methods are their high equipment cost, long data acquisition time, demanding sample preparation and environmental requirements. CD-AFM and SPM are also limited in the depth of features that they are able to observe due to the limits on probe length. An additional issue is that polymer-based micro-devices are currently rising in popularity due to their low cost and suitability for high-speed production. Conventional SEM is not able to directly measure polymer-based devices due to serious charging effects. CD-AFM and SPM may also encounter difficulty due to probe interaction with the softer polymer materials. It is necessary to explore a new measurement technique to nondestructively measure sidewall profiles by overcoming the above limitations.
On the other hand, fluorescent substances are widely used for examining biological samples and for the 3D imaging of tissues in conjunction with laser confocal microscopy [6, 7]. In the captured images, the fluorescent region appears bright and the non-fluorescent region appears dark. If a concave micro-structure is filled up with fluorescent solution, it should be possible to nondestructively obtain information on the submerged surface profile regardless of its steepness and geometric complexity. Indeed, some researchers [8–10] have observed the 3D interface between two kinds of fluids in microfluidic devices according to the reconstructed 3D fluorescent volume image. Unfortunately, no further work was published to transfer the fluorescent volume image to the geometry profile of the interface, as will be the core of this paper. In some confocal microscopes, such as the Zeiss LSM 510 microscope, there is a “profile” function available. However, such function only displays an intensity variation of one image, rather than the geometric profile of a surface. The Zeiss LSM 510 microscope also incorporates a “topography” function, in which the topographic profile is generated by examining the stack of image for each x-y pixel using the following algorithms: a) finding the maximum intensity value, b) using the first slice coming from the top where the intensity reaches the value defined by a lower intensity threshold, or c) using the center of gravity of all summed up intensities of the stack for a given x-y pixel . Algorithm a) is only effective when there is no fluorescence in the measured samples, while the steep sidewall geometry is impossible to be obtained without the help of fluorescence, as has been pointed out in first paragraph. It can also readily be understood that the output of algorithm c) will have no convincing relationship to the object geometry as the fluorescent solution completely fills the sample features. Algorithm b) is able to produce an output that relates to the surface geometry. However, the result is often inaccurate. By way of example, Fig. 2 shows the cross sectional curves of the surface “profile” of an elliptical microchannel obtained with algorithm b). The microchannel shape and the cross sectional position is to be described in Fig. 5. The lower intensity threshold is set at 30 and 40, respectively for the red and blue lines. Clearly the result is highly dependent on the threshold value, which conflicts with the fact that the geometry of a sample is unrelated to the detection setting. Furthermore the sidewall geometry still is invisible. In fact, the failure of all these algorithms is because they are not related to the physical essence when the laser spot scans through the interface between the fluorescent solution and the profiled micro-structure.
In this paper, we demonstrate the application of laser fluorescent confocal microscopy, in combination with an intensity gradient algorithm, to the measurement of complete sidewall profiles. The algorithm presented in this paper could also be denoted as adaptive threshold algorithm relative to the fixed intensity threshold in the above algorithm b). For comparison, the surface profile produced with the method to be described in this paper is shown as the green line in Fig. 2. The measurement result is independent on the threshold setting, and the complete sidewall profile is evident. The physical essence behind this method will be discussed in detail in section 2. The experimental process will be introduced in section 3. The strengths and limitations of this technique will be discussed in section 4.
2. Theoretical analysis
When a laser spot in fluorescent confocal microscopy scans a sample axially, the interaction of the laser spot with the sample and fluorophore is illustrated in Fig. 3. The ellipsoid represents the effective volume of the laser spot on object. All the light is assumed for the present to focus in this ellipsoid. a, b is denoted as the full width half maximum (FWHM) of the point spread function (PSF) of the laser confocal system in lateral and vertical directions, respectively. Typically, b is about twice a . The confocal plane (CP) under observation coincides with the equatorial plane of the ellipsoid. The region full of fluorescent solution is indicated by the dotted area. Lines AB and CD represent the interfaces between the fluorescent solution and the non-fluorescent sample assuming the solution fully contacts with the surface. The thickness of the fluorescent layer is t. h (l) is the distance between AB and the top (bottom) of the laser spot. d is the scanning step interval.
Now consider the signal variation when the laser spot scans through the profiled surface AB downwards. It is assumed for the present that this surface is planar and normal to the optical axis. The refractive indexes of the fluorescent solution and the measured sample (cover slip) are matched. In case of the refractive index mismatching, special calibration has to be done to obtain accurate results . Three cases are discussed according to the relative dimensions of b and t.
In this case, the laser spot is fully immersed in the fluorescent layer when it starts to contact the interface AB. Assuming the fluorophore is evenly distributed in liquid with density N, the florescence response of each fluorophore to laser intensity is constant Rf, the laser intensity Il in the ellipsoid is uniform, the electrical signal response to fluorescent light intensity is a constant Re, and the sample material is non-porous, the signal value is proportional to the volume with fluorophore inside the ellipsoid. That is 
where h ∊[0,2b], ρ = ReRfNIl.
When t>h>2b or h<0, the signal value remains at I max=4/3*πρa2b or Imin = 0. The solid curve with square in Fig.4(a) shows the normalized signal value (I/I max) at different laser point position when t = 2b. The x axis is set as l so that the positive direction of x axis could be consistent with the scanning direction. As there is no refractive index mismatching, l is the same as the piezo stage displacement in the confocal system. “1” is the real position of AB. The signal gradually decreases from the maximum value to zero when the laser spot scans through AB from the fluorescent solution to the non-fluorescent sample.
The signal variation due to the progression over one scanning step (CP moves to C′P′ in Fig. 3) is given by:
By differentiation of Eq. (2), the maximum signal variation is found to happen at h max=b+d/2. That is,
The maximum signal variation, i.e. ΔI min as the intensity decreases gradually, is
Equation 3 indicates the maximum signal variation happens when CP moves from the half of depth interval above the profiled surface to the half of depth interval below the surface. The dashed curve with asterisk in Fig. 4(a) shows the normalized signal variation value ΔI/|ΔI|max at different laser point position. The minimum value is at the place where l/b = 0.95, where d is set as 0.1b in the simulation. It indicates the position of the profiled surface (position “1”) is at the CP position where the signal variation is most significant plus half of scanning step interval when the positive depth direction is the same as the scanning direction. Similarly, when the laser spot scans from the non-fluorescent sample to the fluorescent solution, the position of the profiled surface is at the CP position where the signal variation is most significant minus half of scanning step interval.
In this case, the laser spot is not able to be fully immersed in the fluorescent solution. Still consider the situation where the laser spot goes out of the fluorescent solution through interface AB. During the scanning procedure, the signal variation in unit step still can be presented by Eq.2 when t≥h (the case when point T is immersed in the solution). However, when t<h (T is out of the solution), the signal value becomes
The solid line with square (or dashed line with asterisk) in Fig.4(b) shows the normalized signal (or signal variation) value varies with l when t = 1.5b. Clearly, ΔI is linearly decreased with the increase of l when l≤0.4b. The curve coincides with the curve for t = 2b when l≥0.5b. The position of the global ΔI min remains same as that in section 2.1. The measurement is uncertain when 0.4b<l<0.5b because the point T is changing from the outside of the fluorescent layer to the inside of the fluorescent layer.
Similar to section 2.2, the intensity value is calculated according to Eq. (5) when point T is outside of the fluorescent layer, and calculated according to Eq. (1) when point T is inside of the fluorescent layer. The solid line with square (or dashed line with asterisk) in Fig. 4(c) shows the normalized signal (or signal variation) value when t = 0.5b. The global ΔI min happens when h = 2b-l = 0.5b = t. It means the signal intensity variation is the greatest when T just moves from the outside of the fluorescent layer to the inside of the fluorescent layer. In this case, the measured surface is deeper (greater) than the real surface assuming the positive depth direction is consistent with the scanning direction. Similarly, the measured surface is shallower than the real surface when the laser scans from the non-fluorescent sample to the fluorescent layer. The interface judgment formula Eq. 3 therefore is expired.
In summary, the submerged surface in laser fluorescent confocal microscope system can be found by finding the position where the maximum intensity variation happens according to Eq. (3) as long as the fluorescent solution thickness is greater than the FWHM of the PSF of this system, i.e. a and b. a and b is the measurement resolution of this technique. For an oil immersed objective with N.A. = 1.4, laser wavelength 488nm, and a refractive index of immersion oil of 1.518, a, b is about 160nm and 400nm in lateral and axial directions, respectively. This system is incapable of measuring the concave micro-structures when depth<400nm or width<160nm in theory. The theoretical measurement uncertainty of this technique for each data is ±d/2. The above analysis indicates the technique is actually a general interface measurement technique. However the sidewall interface measurement has been emphasized in this paper as it is particularly difficult to obtain by conventional profiling techniques.
Certainly, the above theory assumes a uniform energy density of the light in the ellipsoidal laser spot, with nothing outside. In practice, the laser beam is with Gaussian distribution. The energy density at the beam center is the highest, and there is some light outside of the ellipsoidal laser spot. The real signal variation close to the profiled surface should be more evident than the calculated variation in Fig. 4, and the distance from the maximum intensity to the minimum intensity should be greater than 2b. The impact of different intensity distribution on predicted measurement performance and measurement resolution will be analyzed in future work.
3. Measurement and data processing
A “T” shaped elliptical microchannel whose cross sectional geometry is similar to that in Fig. 1 was studied in the experiment. The fluorescent image after the sample was filled up with fluorescent solution is shown in Fig. 5(a). The red region represents the brighter region, and the blue region represents the darker region. The interface between the two colors is the profiled surface. The solution used was the fluorescein F-1300 *reference standard* (Invitrogen), whose excitation wavelength is 494nm, and emission wavelength is 514nm. The sample was made of soft, transparent polymeric Polydimethylsiloxane (PDMS). The measurement was conducted with a Zeiss LSM 510 META confocal microscope. The sample was scanned step by step in the z direction. A series of images were captured and then stacked together to form a 3D volume image. The cross section of the volume image at A-A is shown in Fig. 5(b). The complete geometry of the profiled surface is clearly identified with the help of fluorescence, which is absolutely different from the profile in Fig. 1. The next step, described below, is to extract the surface profile by carrying out the intensity differentiation procedure.
To extract the surface profile, the image stack is treated as a 3D intensity matrix nx×ny×nz, where nx is the pixel number in width (x), ny is the pixel number in length (y), and nz is the frames of the scanned images in depth (z). In the experiment, nx and ny are both 512. The differentiation matrix of the 3D intensity matrix along the z direction is of size nx×ny×(nz-1), whose cross section at A-A is shown in Fig. 5(c). There were two significant interfaces: the positive differentiation peak related to the interface between the solution and the cover slip, and the negative differentiation peak related to the interface between the solution and the profiled surface. After recording the position where the negative differentiation peak lay for each pixel, a 512 × 512 matrix was obtained. The depth value at each pixel was calculated by multiplying the 2D matrix by the scanning step interval plus half of step interval. In the experiment, the step interval was set 0.2µm. The width or length value was calculated by multiplying pixel number by pixel size. The 2D matrix in which the 3D information of the surface is recorded represents the 3D profile of the micro-structure, as shown in Fig. 5(d). The cross section of the 3D profile at A-A is shown in Fig. 5(e). The root mean square (RMS) measurement error is estimated at 0.2µm by comparing the extracted cross section with the reference cross section obtained by a white light confocal microscopy (WLC). The reference cross section could be regarded as the real cross section of the sample in sub-µm measurement resolution. A set of five repeat measurements of the same feature with both a 63x/1.4 and a 100x/1.3 objective were conducted. The resulting cross sections are shown in Fig.5(f). The measurement repeatability (RMS) is also less than 0.2µm. The detailed algorithm is fixed in Table 1.
4.1 Measurement Strengths of this technique
4.1.1 Vertical sidewall measurements
In metrology field, the measurements of vertical or close to vertical sidewalls are a most challenging issue. The technique presented in this paper can easily solve this problem. As an example, Fig. 6(a) shows the cross section of the 3D fluorescent volume image of a trapezoid microchannel. The sidewall angle of the channel is ~80°, width is 100µm, and depth is 10µm.
As the 3D volume image can be regarded as a 3D matrix in image processing software, the intensity differentiation can be conducted along the x direction, i.e. the width direction of the microchannel. By finding the position where the maximum or minimum differentiation value lay, the profiles of the left and right sidewalls were derived. Figure 6(b) shows the 3D profile of the right sidewall. The cross section of the sidewall profile is shown in Fig. 6(c). The blue and green dots indicate the data at the sidewall. The red line is the cross sectional curve of the sample obtained after the sample was carefully cut. The RMS difference between them is 0.15µm in the range of “a”. Figure 6(d) shows the 3D profile when the differentiation was conducted along the z direction. The sidewall angle, edge roundness and linewidth can be calculated from Fig. 6(d), and the geometry variation on sidewall can be quantified from Fig. 6(b).
4.1.2 Sidewall measurements when sidewall angle> 90°
As the laser confocal microscopy is capable of obtaining the 3D volume image of a randomly shaped sample as long as the sample is optical transparent, this technique is capable of measuring the sidewall even when the sidewall angle>90°. To confirm this capability, a piece of PDMS sample was tilted cut with a sharp blade. By inverting the sample, it can simulate the situation when the sidewall angle> 90°. Figure 7(a) shows the cross section of the 3D volume image. By conducting differentiation along the x direction, the sidewall shape is obtained as shown in Fig.7(b). Certainly, the measurement result needs calibration if the refractive index of the sample is different from that of the design refractive index of the objective and the fluorescent solution .
4.1.3 Subsurface measurements and volume calculation of an enclosed feature
In the experiments, all the samples filled up with fluorescent solution had to be covered with a piece of cover slip. So strictly speaking, all the measurements described above are the subsurface measurements. In practice, other transparent plates could replace the cover slip as long as the refractive index and thickness of the plates is in the designed range of the objective. The capability of measuring the profiles of buried features is unique relative to standard methods such as CD-SEM or CD-AFM. This capability is important for the study of the geometry variation after bonding in multi-layer microfluidic devices. Furthermore, the enclosed volume between the cover layer and the micro-structure can be calculated accurately. By way of example, Figure 8 shows the 3D geometry of both the cover slip and the microstructure in Fig.5. The inside hollow region represents the volume of the buried feature.
Besides the above advantages, this technique exhibits other distinguishing characters relative to its counterparts such as CD-SEM or CD-AFM. No demanding environmental requirements are needed, measurement area is larger, data acquisition time is shorter, and the equipment cost is lower. There is no depth limitation of features as long as the measured depth is in the working distance of the objective. It is easy to measure the polymer or soft material as long as the wetting property of the material is not evident and the material is not very porous. Compared to the current algorithms, the algorithm in this paper is intensity threshold independent and the complete 3D geometry can be obtained.
4.2 Limitations of this technique
Like any other techniques, this technique is not universal. The main limitation of this technique is that the minor geometry variation may not be evident due to the wetting property of the samples. The theoretical analysis in this paper is based on the assumption that the fluorescent solution fully contacts with the profiled surface. However, this assumption may be expired if the fluorescent solution is highly hydrophobic to the sample material. The second limitation is that it is sensitive to the signal intensity which is also a common limitation of other optical based techniques. The profile tends to be noisy if the intensity variation at the profiled surface is less than the measurement noise. The noise in the profile seriously limits the measurement accuracy of this technique. The third is that the measurement resolution of this technique is not as good as that of the SEM or AFM. Also the sample may be polluted if the solution can not be cleaned thoroughly afterwards. However, the first two limitations can be possibly overcome, or at least be suppressed. The first limitation may be overcome by choosing specific solution which is highly hydrophilic to the specific samples to ensure the liquid could fully contact with the measured sample at any regions. The followings will mainly discuss on how to improve the measurement accuracy by enhancing the signal variation at the profiled surface and by decreasing the signal noise at other regions.
4.2.1 Image contrast
The influence of image contrast on the profile quality is easily understandable. In the 3D volume image, there is signal variation noise ΔI noise, which may result from the nonuniform fluorophore distribution, non-constant florescence response, nonuniform or unstable laser intensity, or non-constant electrical signal response. When the image contrast becomes smaller, ΔI becomes smaller. The profile will become noisy when |ΔI| max<ΔI noise. The black line in Fig.9 shows the cross section of the microchannel in Fig.6(d) when the image contrast is low. After the image contrast was enhanced, the profile became clearer and more accurate, as shown as the red line.
4.2.2 Background noise
When the laser spot scans the region without fluorophore, the signal value is the background noise. The obtained profile therefore is noisy. For example, the signal outside of the microchannel in Fig. 5 is the background value. The original cross sectional curve at A-A is shown as the black line in Fig.10. To decrease the background noise, a suitable threshold just above the background intensity was set. All the data less than the threshold were set to null in the 3D volume matrix (nx×ny×nz). The curve is shown as the red line in Fig.10 after the data less than the background threshold were removed.
4.2.3 Differentiation direction
When the differentiation direction is not normal to the profiled surface, ΔI will become smaller, as illustrated in Fig. 11. Assuming the differentiation is conducted along the scanning direction, and the included angle between the surface AB and the scanning direction is α, ΔI is found to be proportional to sinα. If α is too small, then |ΔI|max<ΔI noise, the profile becomes noisy. Obviously, differentiation along the normal or close to normal direction of the profiled surface could effectively improve the measurement accuracy.
4.2.4 Optical objective
In order to obtain a clear 3D topographic image, the maximum signal value in the 3D volume image often is set close to the saturation value Isat. When the laser spot is full of fluorescent solution, ρ has to be less than 3I sat/4πa 2 b according to Eq.1. The maximum signal variation is
according to Eq. (4). Equation (6) indicates the larger of b, the smaller the |ΔI|max is, when assuming d is small enough. The profile tends to be noisy with the lower N.A. objective as b is greater for the lower N.A. objective. Figure 12 shows the comparison of the extracted profile of the micro structure in Fig. 5 with 40x/0.6 and 63x/1.4 objectives, respectively. Clearer and more accurate profile was obtained with the 63x/1.4 objective.
4.2.5 Differentiation step interval
In practice, the differentiation step interval in data processing procedure does not necessarily equal to the scanning step interval in measurement procedure. By differentiation of Eq. (6), it can be found that the |ΔI|max is the largest when d≥2b. It represents the fact that the signal variation is the largest when the laser spot scans from the position where the laser spot is full of fluorescent solution to the next position where there is no fluorescence in the laser spot assuming the laser still scans from the fluorescent solution to the non-fluorescent sample. Figure 13 shows the relationship of the normalized |ΔI|max with d according to Eq. (6). The greater of d, the greater the |ΔI|max is. The profile therefore tends to be clearer. However the theoretical measurement uncertainty for each data ±d/2 will become greater. To balance the measurement uncertainty to the profile clearance degree, the authors used the following measurement and data processing method in the experiments: The samples were first scanned with the step interval almost equal to the axial resolution of the confocal system. Then check the 3D profile by doing differentiation with the unit scanning step interval. If the profile is too rough to do any further analysis, enlarge the differentiation interval till the profile becomes clear enough. Similarly if the original 3D profile is very clear, try to decrease the differentiation interval by interpolating the scanning step interval till the profile is not only clear, but also with lower measurement uncertainty. Figure 14 shows the comparison of the cross sectional profile of a triangular microchannel when choosing the different differentiation intervals d = 2, 4µm, respectively. The channel depth is ~200µm, and width is ~900µm. There is some measurement noise in the profile, as indicated as the points inside the channel. Evidently, there are less data points inside the channel when d = 4µm which means the measurement noise is lower when d is greater.
Another de-noising method was also applied in the experiment. According to the common knowledge, the height (assuming differentiation direction is z) between any two adjacent points is impossible to vary too abruptly. The greatest height variation between adjacent points can be estimated by observing the initial 3D profile of the feature. Set the greatest height variation as the height variation threshold. The height of the next point was set null if the height variation between two adjacent points is greater than this threshold.
In general, the measurement accuracy (the noise in the profile) is mainly affected by whether the signal variation at the profiled surface is much more evident than the signal noise at other regions. The measurement accuracy can be improved by adopting higher N.A. objective, capturing the image with higher contrast and lower background noise, setting a suitable background threshold and height (width) variation threshold in the data set, choosing the normal or close to normal differentiation direction to the profiled surface, and choosing a suitable differentiation step interval. The accurate profile is the clear profile without measurement noise. The measurement accuracy in Fig. 5, 6 is the value after the profile became clear by adopting the above methods.
The sidewall profile of concave micro-features was successfully measured by the use of laser fluorescent confocal microscopy and an intensity gradient algorithm in this paper. The technique provided a new non-destructive method for the measurement of 3D sidewall profiles of particular value when the sidewall angle is close to or greater than 90° or the surface is buried. In comparison to its counterparts, CD-SEM or CD-AFM, that are widely used to measure the sidewall profile, this technique is convenient and fast. It is applicable to measurement over large sample areas and imposes no additional constraints on the measurement environment. Unlike CD-AFM, the measurement depth is only limited by the working distance of the objective and unlike the CD-SEM, it does not need special material preparation. The enclosed volume between two surfaces also can be calculated accurately, which is valuable for microfluidic applications. The ability to resolve interfaces of this technique is the same as the measurement resolution of the laser confocal microscopy. The preliminary experimental results showed the measurement accuracy and repeatability (RMS) is 0.2µm when using large N.A. objectives.
The authors would also like to thank Dr. Ge Ning, Dr. Li Hoi Yeung, Cecilia Yang Caixia, and Prof Alex Law Sai-Ki at School of Biological Sciences (SBS) of Singapore Technological University (NTU) for their great assistance in the experiments. Thanks to Dr. Samuel Ko of Carl Zeiss Office in Singapore for the technical support. Thanks to Dr. Zhao Liping at Singapore Institute of Manufacturing Technology (SIMTech) and Dr. Li Hoi Yeung at SBS of NTU for suggesting the original idea in this paper. Thanks to Pooja Chaturvedi at SIMTech for providing the fluorescent solution and cover slips.
References and links
1. T. Marschner, G. Eytan, and O. Dror, “Determination of best focus and exposure dose using CD-SEM side-wall imaging,” Proc. SPIE 4344, 355–365 (2001). [CrossRef]
2. B. M. Rathsack, S. G. Bushman, F. G. Celii, S. F. Ayres, and R. Kris, “Inline Sidewall Angle Monitoring of Memory Capacitor Profiles,” Proc. SPIE 5752, 1237–1247 (2005). [CrossRef]
3. C. G. Frase, E. Buhr, and K. Dirscherl, “CD characterization of nanostructures in SEM metrology,” Meas. Sci. Technol. 18, 510–519 (2007). [CrossRef]
4. K. Miller, V. Geiszler, and D. Dawson, “Characterization and control of sub-100-nm etch and lithography processes using atomic force metrology,” Proc. SPIE 5375, 1325–1330 (2004). [CrossRef]
5. Meyyappan, M. Klos, and S. Muckenhirn, “Foot (bottom corner) measurement of a structure with SPM,” Proc. SPIE 4344, 733–738 (2001). [CrossRef]
8. D. L. Hitt, “Optical Considerations for Accurate Volumetric Reconstructions from 3-D Confocal Imaging,” in Science, Technology & Education of Microscopy: an Overview, Vol. II, A. Mendez-Vilas, ed. (Formatex, Badajoz, Spain, 2004).
9. D. L. Hitt, “Confocal Imaging of Fluidic Interfaces in Microchannel Geometries,” in Science, Technology & Education of Microscopy: an Overview, Vol.1, A. Mendez-Vilas, ed. (Formatex, Badajoz, Spain, 2003).
10. D. L. Hitt and N. Macken, “A simplified model for determining interfacial position in convergent microchannel flows,” J. Fluids Eng. 126, 758–767 (2004). [CrossRef]
11. LSM 510 and LSM 510 META Laser Scanning Microscopes, Operating Manual, Carl Zeiss, 2002
13. G. B. Thomas and R. L. Finney, Calculus and Analytic Geometry, 8th ed., (Addison-Wesley, 1992) 328. [PubMed]