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
Fig. 1. Plan view of the surface profile of a “┛” shaped elliptical microchannel obtained with optical interferometry (Model: Veeco NT3000). Color represents height value. Unit: µm. The inset is the schematic of the cross section of the microchannel
Cross sectional profile comparison at A-A in Fig.5
conducted between the adaptive threshold method in this paper and the fixed threshold method in the commercial laser confocal microscope.
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
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]
], or by analyzing secondary electrons (SE) signal profile [3
3. C. G. Frase, E. Buhr, and K. Dirscherl, “CD characterization of nanostructures in SEM metrology,” Meas. Sci. Technol. 18, 510–519 (2007). [CrossRef]
]. The third approach is CD-AFM or scanning probe microscopy (SPM), which can obtain the sidewall profile by means of specially designed probes [4
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]
]. 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.
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
Fig. 3. Model of signal intensity variation when laser spot scans through a profiled surface with laser fluorescent confocal microscopy
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 [8
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).
]. Three cases are discussed according to the relative dimensions of b
∊[0,2b], ρ = ReRfNIl.
<0, the signal value remains at I
= 0. The solid curve with square in Fig.4(a)
shows the normalized signal value (I/I
) at different laser point position when t
. 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
/2. That is,
The maximum signal variation, i.e. ΔI
min as the intensity decreases gradually, is
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
at different laser point position. The minimum value is at the place where l
= 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.
Normalized signal intensity I
and intensity variation over one scanning step ΔI
in plots) varied with laser point position l
when (a) t
, (b) t
, and (c) t
is normalized with the depth resolution of the objective, b
. Position “1” represents the profiled surface position. The intensity gradually decreases from the maximum intensity to the minimum in Fig. 4(a)
. The profiled surface is at the ΔI
position plus half of step interval. The intensity cannot reach the peak during scanning in Fig. 4(b)
, however the profiled surface still can be found with the same rule in Fig. 4(a)
. There is no fixed relationship between the profiled surface and ΔI
position in Fig. 4(c)
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
(the case when point T
is immersed in the solution). However, when 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
. Clearly, ΔI
is linearly decreased with the increase of l
. The curve coincides with the curve for t
. The position of the global ΔI
remains same as that in section 2.1. The measurement is uncertain when 0.4b
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
. The global ΔI
happens when h
. 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
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
is about 160nm and 400nm in lateral and axial directions, respectively[12
]. 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) The fluorescent image of a “T” shaped elliptical channel. Color represents the signal intensity value. A-A is the cross sectional position in Fig. 2
, and Fig. 5 (b, c, e, f)
. (b) Cross sectional image of the 3D image stack. (c) Cross section of the 3D differentiation stack nx
-1). (d) Extracted 3D profile of the microchannel. (e) Comparison between the cross sectional curve of the extracted profile with the reference cross section. (f) Cross sectional curves measured for 5 times for the same feature.
Table 1. Detailed algorithm to extract sidewall profile
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 100µ
m, and depth is 10µ
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 0.15µ
m 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)
Fig. 6. (a) Cross section of the 3D volume image of a trapezoid channel. (b) 3D profile of the right sidewall of the microchannel. (c) Comparison of the extracted sidewall profile with the cross sectional curve obtained after the sample was cut. (d) 3D profile of the microchannel when the differentiation was conducted along the z direction.
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 [8
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).
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.
Fig. 7. (a) Cross section of the 3D volume image of an edge whose sidewall angle >90°. (b) Extracted sidewall profile
The enclosed volume between the cover slip and the microchanel in Fig. 5
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
, 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
. 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.
Comparison before and after image contrast adjustment for the microchannel in Fig. 6 (a)
Comparison before and after the background noise is removed for the microchannel in Fig. 5
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
). 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
is found to be proportional to sinα
. If α
is too small, then |ΔI
, 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
according to Eq.1
. The maximum signal variation is
according to Eq. (4
). Equation (6
) indicates the larger of b
, the smaller the |ΔI
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.
Fig. 11. Illustration on signal intensity variation when the scanning direction tilts to the profiled surface
Fig. 12. Profile comparison when using different N.A. objectives
4.2.5 Differentiation step interval
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
is the value after the profile became clear by adopting the above methods.
Fig. 13. Variation of |ΔI|max with the differentiation step interval
Fig. 14. Measured cross sectional profiles of a triangular microchannel when choosing different differentiation intervals. The data points inside the channel profile are noise points.
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.
References and links
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]
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]
C. G. Frase, E. Buhr, and K. Dirscherl, “CD characterization of nanostructures in SEM metrology,” Meas. Sci. Technol. 18, 510–519 (2007). [CrossRef]
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]
Meyyappan, M. Klos, and S. Muckenhirn, “Foot (bottom corner) measurement of a structure with SPM,” Proc. SPIE 4344, 733–738 (2001). [CrossRef]
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).
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).
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]
LSM 510 and LSM 510 META Laser Scanning Microscopes, Operating Manual, Carl Zeiss, 2002
G. B. Thomas and R. L. Finney, Calculus and Analytic Geometry, 8th ed., (Addison-Wesley, 1992) 328. [PubMed]
(100.5010) Image processing : Pattern recognition
(100.6890) Image processing : Three-dimensional image processing
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.2830) Instrumentation, measurement, and metrology : Height measurements
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure
Instrumentation, Measurement, and Metrology
Original Manuscript: November 16, 2007
Revised Manuscript: February 10, 2008
Manuscript Accepted: February 26, 2008
Published: March 11, 2008
Vol. 3, Iss. 4 Virtual Journal for Biomedical Optics
Shiguang Li, Zhiguang Xu, Ivan Reading, Soon Fatt Yoon, Zhong Ping Fang, and Jianhong Zhao, "Three dimensional sidewall measurements by
laser fluorescent confocal microscopy," Opt. Express 16, 4001-4014 (2008)