3.1.

Tip-on-Tip Imaging

Generally, the major challenges to tip-on-tip imaging are navigation and the transfer of mechanical energy from the imaging tip and cantilever system to the target tip and cantilever. However, these turn out to be less daunting than might be expected.

These challenges are potentially dependent upon the mounting of the target tip for imaging. Initially, elaborate holder designs were considered, but the dimensional variation from cantilever to cantilever ultimately suggested that this would be impractical. The method used in the prior NIST work was to mount the tips on a 200-mm silicon wafer using double-sided carbon tape.⁷ For the current work, an aluminum substrate was also used. This carrier has a recessed slot machined into it with a 3-deg surface slope on the bottom. The function of this slope is to adjust the angle of observation of the tip under imaging. Figure 2 shows a top down photographs of standard AFM tip substrates mounted on both carriers with double-sided carbon tape.

Fig. 2

Top down photographs of standard AFM tip substrates mounted with double-sided carbon tape on (a) the 200-mm Si wafer and (b) the Al carrier with recessed slot machined at 3-deg slope.

The CD-AFM operated by NIST has a tip mount that induces a 3-deg tilt of the cantilever, along its long axis, with respect to the imaged surface. When scanning along this axis, the apparent tip geometry is rotated by this tilt. Partly for this reason, the instrument fast-scan axis normally coincides with the short axis of the cantilever—which is not tilted. Some cantilevers are available with incorporated 3-deg tilt of the tip with respect to the cantilever to compensate for the tip mounting angle in the instrument. Generally, the most effective way to mount nontilt-compensated tips is horizontally on the silicon wafer, and the most appropriate way to mount tilt-compensated tips is using the aluminum carrier. For tilt-compensated tips, it is thus possible to align the axes of both tips with each other and with the $z$-axis of the instrument.

Navigation to achieve tip-on-tip contact is the most challenging for very small tips. The tips must ultimately contact each other at their extrema; if the initial contact between the tips is too far down on their respective shanks, then the available $z$-range of the scanner will not be sufficient to achieve tip overlap using just a single engage. Thus, the probability of success on initial engage is a function of navigation optics, stage accuracy, $z$-axis scanner range, and operator experience. In the case of the NIST experiments, it was not typically possible to achieve tip overlap using just a single engage. However, it was usually possible to readily tune up on the overlap by using a repeated cycle of tip engage, disengage, and adjustment of lateral scanner offsets.

3.2.

Refined Experiments Using a Single Lateral Axis

The prior NIST work involved three types of CD tips: CDR50Cs, CDR300s, and CDR850s. Subsequently, for the present work, experiments have been performed using the following tip types: CDR50S, CDR140, and EBD-CDR25. An experiment was also performed combining a CDR120 and CDR300 and substituting a linewidth standard for the third tip.

CDR50S tips have a shorter effective length than CDR50C tips, and thus have greater lateral stiffness. So it was expected that CDR50S tips would exhibit better self-consistent calibration performance than did CDR50C tips. This was generally the case, but the performance did not reach the level previously observed using CDR300 tips.

An example tip-on-tip image using CDR50S tips is shown in Fig. 3. The image stability is good. For the measurements using CDR50S tips, the instrument was operated using fast dither tube actuation (FDTA) mode. For purposes of this work, a consequence of using FDTA is that this is generally expected to minimize additional lateral tip motion and mechanical coupling between the target and imaging tips.

Fig. 3

Tip-on-tip image using CDR50S tips. The imaging stability is better than previously observed using CDR50C tips. FDTA mode is used.

The results of the self-consistency analysis using the CDR50S data are shown in Table 1. A refinement that has been made to the analysis in the current work is to separately track the “left” and “right” values of the VEH for each tip. As in the prior work, results are included using both the functionality of the native CD-AFM software and an off-line analysis developed at NIST. The offline analysis offers the advantages of not depending on manual or visual analysis of the data and it removes user judgement in identifying the relevant extrema. It is also potentially advantageous for tips that exhibit significantly nonideal shapes—such as those for which the lateral extrema occur in different scan lines. On the other hand, the use of the native software provides very high convenience to an end user. A typical end user working with ordinary CD-AFM tips would probably derive minimal benefit from the additional effort of offline analysis, but it is useful to NIST both as a validating comparison, and it supports the NIST goal of developing a traceable VEH calibration.

Table 1

Results of conventional tip calibration and self-consistency method for CDR50S tips.

Generally, the level of agreement is significantly better than previously observed using CDR50C tips. With CDR50C tips, TW differences of 6 to 8 nm were observed between the conventional calibration and the self-consistency method. In the present case of CDR50S tips, the TW agreement is generally at the 2- to 4-nm level. The agreement among the VEH values is also generally better, though not dramatically. Despite the better results obtained using CDR50S tips in this experiment, the performance still does not reach the level previously observed using CDR300 tips.

The most successful run thus far was accomplished using CDR140 tips. An example tip-on-tip image is shown in Fig. 4, and the results of the self-consistency experiment are shown in Table 2. As was the case for the CDR50S results shown above, the instrument was operated using the FDTA mode for the CDR140 measurements.

Fig. 4

Tip-on-tip image using CDR140 tips. The imaging stability is good. FDTA mode is used.

Table 2

Results of conventional tip calibration and self-consistency method for CDR140 tips.

There is very good agreement between the self-consistency linewidth results and the conventional method—essentially equivalent or surpassing the prior level using CDR300 tips. The agreement between the offline and native analyses is slightly better. Although the VEH results show more variation and differences, when left/right averages are considered, the VEH results also slightly surpass those for the CDR300 tips.

The previous work of Eves and Green⁸ using conventional AFM tips also substituted a linewidth standard for the third tip. Although a significant benefit of this for their purposes was the reduction of experimental complexity, it does also offer an end user the advantage of calibrating a linewidth standard, which can be retained for subsequent tip calibrations, as part of the self-consistency experiment. For CD-AFM tips, the reduction of complexity comes with a loss of useful information: It is no longer possible to extract a self-consistent value for the VEH of the two CD tips. Despite this limitation, an experimental run of this type was performed using a CDR300 tip, a CDR120 tip, and a linewidth standard.

The tip-on-tip image of a CDR120 tip on a CDR300 tip is shown in Fig. 5. The results of the self-consistency experiment are shown in Table 3. In this case, the linewidth standard was a previously uncalibrated sample from the SCCDRM project. Generally, the results of this run were very good. The analyses of the self-consistency data using the native software and the off-line method are in very good agreement. Additionally, the agreement between the conventional and self-consistency methods is almost within the typical 1 ($k=2$) to 1.3 nm ($k=2$) expanded uncertainty for the conventional method of tip calibration. For circumstances in which the only goal is TW calibration, this modified form of the self-consistency method is probably the best option. However, it is not applicable if there is also a need to determine the tip VEH.

Fig. 5

Tip-on-tip image using a CDR120 tip on a CDR300 tip. The imaging stability is good. FDTA mode is used.

Table 3

Comparison of conventional tip calibration with self-consistency method for CDR300, CDR120, and linewidth sample.

3.3.

Dual Lateral Axis Extension of Technique

The prior NIST work and the experiments described above involved the treatment of tip geometry in only a single lateral axis—the fast scan axis. From the metrology perspective, the fast scan axis is normally more important, and is therefore of primary interest. Additionally, unless cantilevers with tilt compensated tips are used, the profiles along slow scan axis, which is typically aligned with the long axis of the cantilever, will be influenced by tilt-related artifacts. For optimal use of data from both lateral axes, therefore, tilt-compensated tips are desirable.

Tip on tip imaging was further refined using smaller tips made from high-density carbon with cantilever tilt compensation. Prior attempts to use silicon tips $<50\mathrm{nm}$ were not successful, but it seemed plausible that the greater modulus of carbon relative to silicon would partially compensate for smaller size with respect to the resultant lateral stiffness. Nominal 25-nm carbon CD tips are commercially available. These tips are typically designated by the prefix electron beam deposition (EBD) as in: EBD-CDR25. An example of CDR25 on CDR25 tip imaging is shown in Fig. 6. Although noise and scanning instability are observed and present challenges, the image quality is sufficient to work with and to perform a self-consistency experiment.

Fig. 6

Tip-on-tip image using a EBD-CDR25 tip on a EBD-CDR25 tip. The imaging stability is adequate for self-consistency data. A fixed lateral dither mode with 0 V was used.

In the prior work, the FDTA scanning mode was normally used. However, this mode is only available when the instrument $y$-axis, which also corresponds to the short axis of the cantilever, is selected as the fast scan axis. To treat both lateral axes in an equivalent manner, a fixed lateral dither was used instead for the CDR25 tip experiment. The fixed dither input voltage was set to 0 V, corresponding to zero nominal dither, but in most cases the zero-input lateral motion of the tip is sufficient for the scanning control to operate. Using the same fixed input in both lateral axes, the nongeometrical contributions to the effective TW should be equivalent in both lateral axes.

Two complete sets of images for the self-consistency experiment were acquired using the same three CDR25-EBD tips. The conventional tip characterization was also performed. For the $y$-axis fast scans, this involved imaging both a VPS and FSR sample—followed by a width check using the SCCDRM. The $x$-axis fast scans were calibrated directly using the SCCDRM. This reduced experimental steps, but also meant that conventional VEH measurements were not available for the $x$-axis fast scans. Table 4 shows both the conventional and self-consistency results for the $x$-axis fast scan measurements. The y-axis fast scan results are shown in Table 5.

Table 4

Results of conventional tip calibration and self-consistency method for EBD-CDR25 tips using the x-axis as the fast scan. Two self-consistency runs were performed, and each result from the second run is shown below the first.

Table 5

Results of conventional tip calibration and self-consistency method for EBD-CDR25 tips using the y-axis as the fast scan. Two self-consistency runs were performed, and each result from the second run is shown below the first.

As a whole, the results shown in Tables 4 and 5 are favorable, particularly for the TW calibration and are approximately on par with or slightly surpassing the performance observed using CDR50S tips. In most cases, the agreement between the conventional and self-consistency TW values is at the 1- to 2-nm level. There is also usually similarly close agreement between the first and second self-consistency runs. The offline analysis and native analyses show agreement in the 1- to 3-nm range, with the offline results always larger. This is to be expected because the native analysis involves the waterfall function, which requires the selection of one scan line to represent the maximum diameter. If the tip shape in the $x-y$ scan plane is not an ideal circle, this constraint may introduce a small bias. As the offline analysis is based on the lateral extrema of the edges regardless of scan line, it is not subject to this bias. However, it is potentially more sensitive to edge noise, which is not negligible in these scans. A possible strategy for including more data in the analysis and reducing noise sensitivity is considered in the next section.

The VEH results generally show consistency to approximately the level of 5 nm. In particular, the consistency between runs for the offline analysis was about 2 nm. This performance is generally equivalent to or surpasses the results using other tip sizes. However, the goal of using self-consistency results to establish a traceable calibration of VEH would require more stability in the results, and better agreement with both the native and conventional analyses and understanding the origin of any remaining offsets.

3.4.

Toward Planar/Contour Type Analysis

The use of data in both lateral axes for self-consistency calibration is a step toward a complete geometrical representation of CD tips, but most of the information in the images is still not utilized. An additional step toward greater utilization of the images is to estimate a contour of the maximal tip shape in the $x-y$ scan plane.

A basic attempt at such planar analysis of tip shape was made using the “via” analysis function in the native software. This function, which is intended for the analysis of contact holes, allows extraction of the $x-y$ edge position at a certain height all around the perimeter of a feature. In this case, the feature analyzed is the tip-on-tip image, and height selected corresponds to the approximate sum of the VEH values for the two tips.

An example of the planar contour extracted from the run 2 tip B on tip A images (i.e., both $x$- and $y$-axis fast scan) is shown in Fig. 7. The noise and outliers in edge location are significant, but are generally comparable with what is intuitively observed in the images as shown in Fig. 6. As expected, the performance using each axis as the fast scan is the worst near alignment with the orthogonal axis. This is true with respect to both the sampling density and the edge noise. In this example, the performance was surprisingly good and the edge outliers are less noticeable. In this case, none of the points is unambiguously excludable or clearly unphysical. But in some cases, points are observed that lie well outside the main “cluster” of results. When closely examined, however, these points are usually associated with bad scan lines—especially those containing tip “jumps.” For most analysis purposes, it is thus reasonable to exclude such points from the contour. At the present stage of development, the exclusion process is performed manually by inspection, but it should be possible to develop a more automated analysis.

Fig. 7

Planar contour extracted from the run 2 images of tip B on tip A. Results obtained from both the $X$- and $Y$-fast scan images are included.

The extracted contours from both runs of tip C on tip B are shown in Fig. 8. In this plot, the $x$- and $y$-axes fast scan results are included together for each run. It shows the overall reproducibility of the tip-on-tip contour. The most significant and unphysical outliers are easily identified and do not repeat between the two runs. However, there is still a nonnegligible level of edge detection noise—at about the 5-nm level. This is large enough that it must be considered in analysis and interpretation of the data.

Fig. 8

Planar contours extracted from the run 1 and run 2 images of tip C on tip B. Results obtained from four images (both the $X$- and $Y$-fast scan from two runs) are included.

The noise and variability of the tip-on-tip contour illustrate the challenging nature of the data. The analyses discussed in prior sections are based on finding the edge extrema along the fast scan axis. Conceptually, this is only strictly correct for sidewalls aligned with the slow scan axis or areas where the surface normal of the tip-sample contact area is aligned with the fast scan axis.

Additionally, the accuracy of the calculation also depends on the assumption that the extrema are representative of the effective tip geometry rather than noise or jumps in the scan line. However, even after the clear outliers are excluded, the tip-on-tip contour in Fig. 8 shows that this assumption becomes questionable below the level of a few nanometers.

The question then arises as to how to best utilize the tip-on-tip contour data. The self-consistency method is based on simple algebraic equations for three unknowns. However, it is only strictly applicable under certain conditions. The existence of a single well-defined TW metric, such as the radius of an ideal spherical tip, meets these conditions. A more general understanding of the constraints, however, requires some consideration of mathematical morphology.

The geometrical interaction of an AFM tip with a surface or in this case another tip is described by operations in mathematical morphology.^11–13 Specifically, the geometry of the imaging tip dilates the features of the surface or target tip. As this operation is not always information preserving, the self-consistency method may no longer be analytically exact, and the entire tip geometry may not be extractable. In terms of morphological operators, the requirement for the self-consistency method to be applicable to the tip-on-tip contours is that the tip contours are closed to each other. This means, for example, that a dilation of tip A by tip B, followed by an erosion of tip B, will result in recovery of the original tip A contour. A detailed discussion of the implications of this constraint for allowable tip contour geometries is outside the scope of this paper. In qualitative terms, it generally requires that the tip contours do not have asperities or notches with a radius of curvature significantly smaller than the overall radius of the tip contours. The analysis of tip on tip contours will be further investigated by NIST, but for purposes of this paper, the treatment will be restricted to the highly simplified cases of ideal circles and ellipses.

If a CD tip exhibited perfect rotational symmetry, its planar contour would be circular, and thus a single radius metric would be sufficient to characterize the tip shape in the $x-y$ scan plane. For CDR tips that are good condition, this assumption is often a reasonable approximation. This can be observed by comparing the conventionally calibrated TW values as shown in Tables 4 and 5, respectively. For tips B and C, the observed difference in TW between the $x$ and $y$ axes is negligible and well under the 1 nm level of uncertainty. This is consistent with approximate rotational symmetry. Tip $A$, however, does exhibit a nonnegligible difference of 3 nm between the observed TW in $x$ and $y$ axes, respectively.

The potential applicability of the single radius model to tip on tip imaging and self-consistency calibration was tested for this overall dataset. These evaluations are shown in Table 6. A potential advantage of using a circular fit to the tip-on-tip contours would be reduced sensitivity to noise in the detected edges. However, to the extent that the effective planar tip geometry deviates from ideal, a circular fit would be less accurate than locating the edge extrema. Based on the results shown in Table 6, it appears that the single radius model probably oversimplifies too much in most cases.

Table 6

Results of self-consistency analysis for EBD-CDR25 tips obtained using circular fits applied to the tip on tip contour data. Results using data from both runs are included, as well as values obtained using just the x- or y-fast scan data and the x/y data together.

The reproducibility of the circular fit results is at approximately the same level as the edge extrema method. It is better in some cases but not in others. The level of consistency with the conventional TW calibration also varies but is not dramatically better. As tip A exhibits a detectable difference in the $x$- and $y$-axes TWs using the conventional method, this is not surprising. Although tips B and C are closer to ideal, these results are influenced by the tip A results. Only in the case of three nearly ideal tips would the single radius approach be potentially applicable.

One interesting observation from Table 6 is a comparison of the third and fourth results columns on the right side. These columns show the results using circular fits to both the $x$ fast scan and $y$ fast scan data for each tip on tip combination. But as was seen in Fig. 8, there are usually unphysical outliers present in these contours. The calculations in Table 6, however, suggest that the influence of such outliers on circular fits is often not significant and is thus manageable. In most cases, the difference between the results with and without the outliers is 1 nm or less.

In the general case, as most CDR tips are expected to deviate from ideal, a circular fit is probably not a suitable approximation. The next logical step would be an elliptical fit, so this approach was also evaluated, and these results are shown in Table 7. Unfortunately, the general results of using elliptical fits are disappointing. At least for this dataset, the overall level agreement and consistency using elliptical fits are worse than using circular fits.

Table 7

Results of self-consistency analysis for EBD-CDR25 tips obtained using elliptical fits applied to the tip-on-tip contour data. Results using data from both runs are included, and the major and minor axes of the ellipse are used to determine the x- and y-axes TWs. For this analysis, the x- and y-fast scan data were always combined.

As can be seen in Table 7, perhaps the most disappointing observation is that the use of elliptical fits did not correctly capture the $x/y$ asymmetry of tip A that was observed using the conventional method. Additionally, the analysis introduced apparent asymmetry for tips B and C that was not observed using the conventional method. The level of agreement between run 1 and run 2 was not any better than with using circular fits. More surprisingly, the general consistency of the results seems to deteriorate when more outliers are excluded from the tip-on-tip contours.

The overall conclusion from this analysis is that neither elliptical nor circular fits to the CDR25 tip-on-tip contours demonstrated better performance than the prior method based on line-by-line analysis of the images. This is true both with respect to consistency with the conventional method and the apparent run-to-run reproducibility. Furthermore, the elliptical analysis was unable to correctly capture the $x/y$ tip asymmetry (or lack thereof), which was observed using the conventional method.

It thus seems that circular and elliptical fits are likely to be of minimal utility in the most general case due to edge detection noise and to geometrical deviations that are not well represented by either circles or ellipses. Specifically, for tips that exhibit nearly the same width in each axis—as tips B and C did in this work—the elliptical fit is not an improvement because a circular fit would be sufficient. In the presence of edge noise, the elliptical fit becomes slightly worse. Overall, the edge noise and deviations from idealized geometries were likely the primary reasons for the performance of the circular and elliptical fits relative to the line-by-line method. Further evaluation of fitting tip-on-tip contours is warranted, however, as these fits may be applicable in cases for which the $x$ and $y$ widths are in agreement or for which the contours are well described by ellipses.

Whether analysis using the tip-on-tip contours could have value in applications (e.g., measurement of in-plane corner radius) that require consideration of the tip geometry in the $x/y$ scan plane remains an open question. But for applications involving linear-type features, which require data using only a single fast-scan axis, there is no compelling reason to consider the tip-on-tip contours.

3.5.

Assessing Relative Performance of Different Tip Types

In the present work, three different tip types were evaluated: CDR50S, CDR140, and EBD-CDR25. A multitype and linewidth sample combination using a CDR120 and CDR300 tip along with a linewidth sample was also implemented. The prior NIST work⁷ involved three different tip types: CDR50C, CDR300, and CDR850. Additionally, the EBD-CDR25 tips permitted a separate implementation for both lateral scan axes. Taken all together, this amounts to eight independent self-consistency experiments for TW, and seven for VEH as the implementation involving a linewidth sample does not allow for VEH extraction.

A cursory inspection of all the tip-on-tip images and the tables of self-consistency results reveals that the performance varies for different tip types. To be more quantitative than that, however, some form of performance metric is required, and different approaches are possible. For purposes of this discussion, a variability metric was defined by the following method: first, the difference between the observed maximum and minimum values of TW or VEH was calculated for each tip of each type. The second step was to average these values over all three tips (or LW sample) for each implementation. Note that the first step included all available values from both the conventional method and the self-consistency method using both the offline and native software analysis. It also included multiple runs that were available for the EBD-CDR25 tips. Consequently, this value is a hybrid metric that includes reproducibility contributions, computational effects resulting from the analysis software, and any average offset between the self-consistency and conventional methods. Although other metrics are possible, the author regards this metric as a useful representation of the overall performance for purposes of comparing the implementations.

In Fig. 9, the width performance is shown as a function of tip type. The results shown include both those from the present and prior NIST work. Additionally, the performance among the implementations can be compared in two ways: the first is by the absolute value of the variability metric in nanometers, and the second is by a relative variability in which the variability metric is divided by the average value of the width for that implementation. This is potentially useful because comparing only the absolute values potentially understates the relative performance of larger tip sizes in the self-consistency implementation.

Fig. 9

Width variability metric as a function of tip type—including results from both present and prior NIST work.

The visual representation of Fig. 9 is interesting, but there are ultimately few surprises to be found in comparing the performance of the different tip types. The results are consistent with the qualitative assessments given in the preceding sections. Optimum performance of the self-consistency width results is found in the range around CDR140 and CDR300 tips—with the linewidth sample run comparing very favorably. The figure also shows that the EBD-CDR25 tips, despite being half the width, able to perform around the same level as the CDR50S tips. This is consistent with intuitive observation from the images, and it is probably due to the carbon composition and resultant lateral stiffness of these tips.

An analogous plot of performance for tip VEH as a function of tip type is shown in Fig. 10. Because the implementation using a CDR300, CDR120, and a linewidth sample does not yield a result for VEH, this run is not included in Fig. 10. As was the case for Fig. 9, the VEH performance among the implementations can be compared in two ways: the first is by the absolute value of the VEH variability metric in nanometers, and the second is by a relative variability in which the variability metric is divided by the average value of the VEH for that implementation. This is potentially useful because comparing only the absolute values potentially understates the relative performance of tips with larger values of VEH, and it also clearly emphasizes the challenges remaining with very small tips.

Fig. 10

VEH variability metric as a function of tip type—including results from both present and prior NIST work.

The visual representation of VEH performance shown in Fig. 10 is also interesting, but as was the case for the width performance there are ultimately few surprises to be found in comparing the VEH performance of the different tip types. The results are consistent with the qualitative assessments given in the preceding sections. Optimum performance of the self-consistency VEH results is found for CDR140 tips. The figure also emphasizes that the EBD-CDR25 tips perform well with respect to absolute VEH variability. However, because these tips tend to have smaller values of VEH in general, the figure also underscores the point that the relative VEH variability of the EBD-CDR25 tips is larger.

Ultimately, the quantitative variability analysis shown in Figs. 9 and 10 provides a foundation for the qualitative and intuitive inferences made from the tip-on-tip images and from a cursory inspection of the results in tables. There are no surprises, but the graphs clearly emphasize which tips have exhibited the optimum performance in self-consistency calibrations and for which tips there is room for more progress.