Lateral Tip Control Effects in CD-AFM Metrology: The Large Tip Limit

Abstract

Sidewall sensing in critical dimension atomic force microscopes (CD-AFMs) usually involves continuous lateral dithering of the tip or the use of a control algorithm and fast response piezo actuator to position the tip in a manner that resembles touch-triggering of coordinate measuring machine (CMM) probes. All methods of tip position control, however, induce an effective tip width that may deviate from the actual geometrical tip width. Understanding the influence and dependence of the effective tip width on the dither settings and lateral stiffness of the tip can improve the measurement accuracy and uncertainty estimation for CD-AFM measurements.

Since CD-AFM typically uses tips that range from 15 nm to 850 nm in geometrical width, the behavior of effective tip width throughout this range should be understood. The National Institute of Standards and Technology (NIST) has been investigating the dependence of effective tip width on the dither settings and lateral stiffness of the tip, as well as the possibility of material effects due to sample composition. For tip widths of 130 nm and lower, which also have lower lateral stiffness, the response of the effective tip width to lateral dither is greater than for larger tips. However, we have concluded that these effects will not generally result in a residual bias, provided that the tip calibration and sample measurement are performed under the same conditions.

To validate that our prior conclusions about the dependence of effective tip width on lateral stiffness are valid for large CD-tips, we recently performed experiments using a very large non-CD tip with an etched plateau of approximately 2 μm width. The effective lateral stiffness of these tips is at least 20 times greater than typical CD-AFM tips, and these results supported our prior conclusions about the expected behavior for larger tips. The bottom-line importance of these latest observations is that we can now reasonably conclude that a dither slope of 3 nm/V is the baseline response due to the induced motion of the cantilever base.

1. INTRODUCTION

Critical dimension atomic force microscopes (CD-AFMs) use flared tips and two-dimensional sensing and control of the tip-sample interaction to enable scanning of features with near-vertical or even reentrant sidewalls.[1] Features of this sort are commonly encountered in semiconductor manufacturing and other nanotechnology industries. The National Institute of Standards and Technology (NIST) has experience in the calibration and characterization of CD-AFM instruments and in the development of uncertainty budgets for typical measurements in semiconductor manufacturing metrology.[2–5]

Sidewall sensing in CD-AFM usually involves continuous lateral dithering of the tip, and this was the only method available in early instruments. Current instruments can also utilize a control algorithm and fast response piezo actuator to position the tip in a manner that resembles touch-triggering of coordinate measuring machine (CMM) probes. All methods of tip position control, however, induce an effective tip width that may deviate from the actual geometrical tip width.

Since the advent of AFM, a purely geometrical model of tip-surface contact and imaging has often been a viable approximation.[6] Even in intermittent contact mode, there are operating regimes (e.g., large cantilever oscillation and low damping) for which this approximation is often sufficient – even for purposes of dimensional metrology.[7] Indeed, for many applications of CD-AFM metrology, this model can be sufficiently augmented with the assumption of an effective tip width rather than a purely geometrical one.

Nevertheless, as the typical tip diameters and the scale of the relevant application features have decreased well below the 100 nm level, there are circumstances in which a purely geometrical interaction model may not be sufficient. For example, Foucher, et al. first reported observations indicating that the lateral stiffness of a tip could affect the consistency of the tip calibration using a type of sample known as a vertical parallel structure (VPS).[8] This was a surprising observation since it seems to indicate a breakdown in the assumption that for given instrument parameters there is fixed offset between the geometrical tip width and the effective tip width. In practical application terms, their results indicated the presence of a non-geometrical tip contribution that did not completely cancel when performing a tip calibration and subsequent measurement.

NIST has been investigating the dependence of effective tip width on the dither settings and lateral stiffness of the tip [9,10], as well as the possibility of material effects due to sample composition. A more detailed understanding of the dither response for various types of tips fits into a larger picture of modeling the tip-sample interaction in AFM imaging to understand where the assumption of effective tip width and geometrical interaction might break down. A good understanding of effective tip width and its potential sources of variation is important to achieving accurate results for linewidth measurements which is the most important application of CD-AFM.

To further validate our previous conclusions about the dependence of effective tip width on lateral stiffness, we recently performed experiments using a very large non-CD tip with an etched plateau of approximately 2 μm width. The inherent lateral stiffness of these tips is nearly three orders of magnitude larger than typical CD-AFM tips, but when the effective stiffness due to the torsion of the cantilever itself is considered, these tips only increase the relative stiffness by up to a factor of 50. But most importantly, the experimental results supported our prior conclusions about the expected behavior for larger tips: The observed dependence of effective tip width on input dither, which we refer to as the dither slope, was 2.9 nm/V. This is consistent with our previous observations using normal CD-AFM tips with the highest available lateral stiffness. [9,10]

2. EFFECTIVE TIP WIDTH AND LATERAL DITHER

2.1 Background on CD-AFM lateral tip control

Present generation CD-AFMs can operate with or without the use of fixed amplitude of lateral dithering for sidewall sensing. In first-generation systems, the dither primarily served to generate a periodic and readily detectable modulation of the vertical (z-axis) vibration in order to sense the surface of a near-vertical sidewall.[1] Secondarily, however, the presence of the lateral dither also reduced the tendency of the tip to stick to a sidewall. As typical CD AFM tips have become smaller and more flexible, the importance of minimizing sticking has increased. To mitigate this problem, current generation instruments can be operated in a mode that uses a fast-response piezo to withdraw the tip if sticking occurs. This mode is called the fast dither tube actuation (FDTA) mode.[11] In some general sense, it resembles touch-triggering of CMM probes. The exact details of the FDTA control algorithm are proprietary to the vendor, but the main result of its operation is that the tip is quickly retracted from a sidewall once attraction is detected. Note that this retraction has both lateral and vertical components. During FDTA operation there is no requirement for a fixed value of lateral dither for sidewall detection and scanning. The data discussed in this paper were obtained using both FDTA mode and a fixed lateral dither for various values of the amplitude.

All methods of lateral tip control and surface sensing induce an effective tip width which may deviate from the geometrical tip width. Due to the importance of effective tip width to accurate linewidth metrology, NIST has been investigating the dependence of effective tip width on the dither settings and lateral stiffness of the tip[9,10], as well as the possibility of material effects due to sample composition. Our general conclusion has been that if the tip calibration and sample measurement are performed under the same conditions, there is not a residual bias.

When lateral dithering is used, the effective tip width can be understood as approximately the sum of the geometrical tip width and the dither envelope (i.e., twice the amplitude). Since it is not possible to directly measure the vibration amplitude of the tip in most instruments, it is not trivial to separate the contributions to the effective tip width. Even the motion of the cantilever base is not typically measured. It is possible and typical, however, to measure and control the input voltage applied to the piezo to generate the dither motion.

Over the displacement ranges typically involved and for most instrument designs, the lateral displacement amplitude of the cantilever may be expected to have an approximately linear dependence on the input voltage. Since the effective width is the sum of the geometrical tip width and the dither, it follows that the effective tip width should exhibit a linear dependence on the applied voltage. In our previous investigations into the effects of lateral dither using a range of tip types, we did indeed observe an approximately linear variation with slopes ranging from 3 nm/V for stiffer (larger) tips to 4.5 nm/V for more compliant (smaller) ones.[9]

As we have discussed elsewhere[10], it is possible that in addition to the induced lateral dither, there could be a non-negligible component of the lateral motion that results from the natural vibration of the tip in response to other sources of noise or mechanical excitation. This could be referred to as spontaneous or ‘zero-point’ dither. This means that the effective tip width would be the sum of the geometrical width, the induced dither, and the spontaneous dither. However, there is no straightforward means of routinely separating these contributions. For our purposes in this paper, we will assume that the spontaneous dither is a relatively small offset which is independent of induced dither and may be lumped in with the geometric tip width for purposes of studying the induced dither response.

2.2 Dither slope measurements and the limit of large tips

Prior to the current work, the largest CD type tips we have used were approximately 850 nm in diameter. Among the most common types of CD-AFM tips that are commercially available, those having nominal diameters of 300 nm and 850 nm also have the largest lateral stiffness values–by almost a factor five over the other common types.[9] In our prior investigations, we observed that these two tip types exhibited an apparent dither slope value of approximately 3 nm/V, in contrast with the 4.0 nm/V to 4.5 nm/V that was typically observed for all smaller tips with larger lateral compliance.

Our working hypothesis based on those observations was that 3 nm/V represented the baseline vibration amplitude due to the direct motion of the cantilever base in the tip mount, and that for tips of sufficiently large lateral stiffness, the additional contribution of lateral tip bending was negligible. Due to lateral tip bending, however, the smaller tips exhibited larger dither slopes. To further validate this hypothesis, we decided to measure the dither slope with the largest diameter and highest lateral stiffness tip that we could find.

At the present time, the largest diameter tip type specifically designed for CD-AFM that is commercially available is the Bruker AFM Probes CDR850^†. Note that the meaning of the naming convention for this type of tip is critical dimension round (CDR), followed by the nominal diameter of the tip in nanometers. We also note that while there are some CD AFM tips available with carbon coatings and some that are fabricated entirely of high density carbon (HDC), all of those used in our prior dither studies and in this work were fabricated from silicon. Due the very long effective length of the CDR850 type tip, however, its lateral stiffness is actually lower than that of the CDR300 which is also available from Bruker AFM Probes. Both of these tip types were used in our previous studies of dither response.

The most suitable tip we found to extend the range of lateral tip stiffness covered in our measurements was the Nanosensors PL2-NCHR^†. Although not specifically designed for CD-AFM, the geometry of this tip type is much closer to that of CD tips than most conventional AFM tips. The functional portion of the silicon tip is a slightly tapered cylinder that terminates in a large plateau. In spite of the taper of the tip ‘rod’, the sidewalls are nevertheless relatively steep making these tips potentially applicable for some CD-AFM measurements. For our purposes, the goal was to measure changes in the apparent width of a near-vertical structure as a function of dither voltage, and our expectation was that these tips would be suitable.

According to the manufacturer, the typical width of the tip plateau is 1.8 μm ± 0.5μm and the typical height of the functional ‘rod’ is approximately 2.0 μm. Using a cylindrical approximation, we estimated the expected lateral stiffness of these tips to be about 2.9 × 10⁴ N/m. This exceeds the estimated lateral stiffness of the CDR850 tips by about three orders of magnitude.

An important point to underscore here is that we have generally ignored the contribution of the cantilever torsion in our analysis of tip bending. All of the cantilevers we used were silicon and had approximately the same geometrical specifications. Consequently, the torsional stiffness values for the cantilevers themselves would all be comparable. To verify that the contribution is negligible for our purposes, we converted the torsional stiffness values into an effective bending stiffness for lateral displacement of the tip. This approach was previously used by Watanabe, et al. [12]

The results of these estimates are that for tip sizes up to the CDR850, the effective lateral stiffness of the cantilever is at least an order of magnitude larger than the lateral stiffness of the tip. In the case of the PL2-NCHR tip, however, the stiffness of plateau ‘rod’ itself exceeds the estimated effective torsional stiffness of the cantilever by at least a factor of 20 and possibly up to a factor of 50. We will take this into account when discussion the results given in section 2.4.

2.3 Tip characterizers for CD-AFM tips

Current generation CD-AFM instruments typically employ two types of tip characterizer samples during routine operation: The first type is a structure that has very nearly vertical sidewalls – often described as a vertical parallel structure (VPS), and the second type is an undercut structure having a sharp overhang – commonly referred to as a flared silicon ridge (FSR). Dahlen et al., have published a detailed discussion of CD-AFM tip characterization and image reconstruction.[13]

The VPS type of characterizer is very useful for measuring the CD tip width – which is typically defined as the lateral distance between the flare apices in the fast scan axis. Due to the vertical sidewalls of the VPS, the apparent width of a given tip is largely independent of the specific flare geometry or even whether or not the tip still has any reentrant capability. In contrast, the FSR type of characterizer is used to estimate the shape of the tip flares since the sharp overhangs of the FSR effectively ‘image’ the tip. In our previous work on the interaction of lateral dither and higher order tip effects, we presented more details on these samples and how they are typically utilized.[10]

For nearly two decades, both the VPS and FSR types of samples have played an important role in CD-AFM metrology and tip characterization. However, there have been multiple commercial and non-commercial implementations of these general sample types in actual tip characterization standards. At the present time, the IVPS100^† (Improved Vertical Parallel Structure 100) and the IVPS100A^† are the most commonly used VPS type of tip characterizer.

The IVPS100 differs from prior VPS designs in two important respects: (1) each target area contains an array of five VPS features with approximately 500 nm pitch, and (2) these features are approximately 100 nm in width – which is much smaller than previous designs. This design is well suited to the majority of CD-AFM tips – which are 300 nm or less in width. In fact, the majority of CD tips in common use are now 50 nm or less. However, tips much larger than the CDR300 are too large to fit into the space between the VPS features in the array. The IVPS100A version of the characterizer solves this problem with the inclusion of an isolated VPS feature that is offset from the array by approximately 2.5 μm.

In our instrument, due to our significant usage of larger tips for these and other experiments, we decided to install an additional VPS type tip characterizer. The sample we selected was a prior IVPS design, now considered obsolete by the manufacturer, which has a single and relatively wide (approximately 800 nm) VPS feature in each target area. In addition to accommodating much wider tips, the features on this IVPS sample are also extremely robust against damage during scanning due to the large feature width. Our previously published results involving CDR850 tips used this IVPS characterizer.[9] This characterizer was also used for our current experiments using PL2-NCHR tips.

2.4 Observed dither slope of PL2-NCHR tips using large feature VPS

The IVPS was used for characterization of the PL2-NCHR particular tips that we tested for dither slope. A typical raw CD-AFM profile of the IVPS using a PL2-NCHR tip is shown in Figure 1. Using our internal master standard at NIST, the actual width of the VPS feature was independently calibrated as having a width and expanded uncertainty [14,15] of 709.8 nm ± 1.5 nm (k = 2). The much larger apparent width is due to the tip contribution – which can be estimated as approximately 2.1 μm near the plateau. The apparent corner rounding near the top is due primarily to the tip, and the taper of the tip ‘rod’ exhibits an effective sidewall angle of approximately 10°. Some dither slope results for this tip are shown in Figures 2 and 3.

Figure 1.

Raw CD-AFM profile of large-width VPS feature using PL2-NCHR. The tip width is approximately 2.1 μm near the plateau, and the taper of the rod has approximately 10° sidewalls.

Figure 2.

Apparent middle width of tip calibration structure as a function of lateral dither voltage. The value shown at 0 V (with square marker instead of diamond) is the average of six ‘no dither’ results obtained using FDTA (fast dither tube actuation) mode. The standard deviation of those six results is 0.8 nm and error bars are just visible outside the marker. Note that the linear fit is only to the active dither results, but the extrapolation to zero agrees well with the FDTA result.

Figure 3.

Apparent bottom width of tip calibration structure as a function of lateral dither voltage. The value shown at 0 V (with square marker instead of diamond) is the average of six ‘no dither’ results obtained using FDTA (fast dither tube actuation) mode. The standard deviation of those six results is 0.2 nm but is too small to be visible on the scale. Note that the linear fit is only to the active dither results, but the extrapolation to zero agrees well with the FDTA result.

The dither slope plots show the apparent middle (Figure 2) and bottom (Figure 3) widths of the VPS structure as a function of dither voltage. Since the stability of the apparent top width may be impacted by the corner rounding, we emphasized the middle and bottom width results. The general method used is the same as in our previous work with smaller tips.[9] The measurements at non-zero voltages were taken using a fixed value of induced lateral dither. The values shown at zero dither are the averages of six results using FDTA mode – which was mentioned in section 2.1.

The two most important observations to be gleaned from these data are that: (1) the dither response follows the same general, approximately linear behavior as for much smaller tips, and (2) that the slope of the dither curve is approximately 3 nm/V. The type A standard uncertainty[9,10] (k = 1) of a typical dither slope estimate is at least 0.1 nm/V. In our previously reported experiments involving CDR300 and CDR850 tips, the typical dither slopes observed were 2.9 nm/V and 3.1 nm/V. In other words, the dither slopes of 300 nm, 850 nm, and 2100 nm tips are all consistent.

Another interesting observation revealed in Figures 2 and 3 is the close agreement between the FDTA value and the zero-dither intercept of the fixed-dither data. In our previous work we noted that the sign and magnitude of this offset varied from tip to tip.[9] Although there was no consistent trend in this offset with respect to tip type, the stiffer tips usually exhibited smaller offsets. The offset observed using the 2.1 μm plateau tip was less than 1 nm – less than typically observed for smaller tips. This is generally a secondary issue since a tip width calibration and measurement steps should be carried out using the same mode and instrument parameters. In this case the FDTA-zero-dither intercept offset would cancel out. However, we are working to better understand the relationship between the two imaging modes and to determine if there are conditions under which the offset might matter or if it could be tuned out through adjustment of the imaging parameters.

This agreement of the large tip dither slopes is illustrated graphically in Figure 4. The plot shows the typical observed dither slope, using the y-axis as the fast scan direction, as a function of the lateral stiffness scaling parameter for all the tip types that we have experimented with. This graph is an extension of Figure 7 from our previous work. [9] The additional data is the point representing the PL2-NCHR tip. Note, however, that the lateral stiffness scaling is now shown using a logarithmic scale – due to the three orders of magnitude greater lateral stiffness of the PL2-NCHR tip relative to the CDR850 and CDR300.

Figure 4.

Observed values of y-axis dither slope as a function of tip lateral stiffness scaling parameter. (a represents the tip radius and L represents the tip length). Two points are shown for the PL2-NCHR tips – since the stiffness of the tip ‘rod’ itself is nearly two orders of magnitude greater than the effective lateral stiffness due to cantilever torsion.

As mentioned in section 2.2, however, for the case of the PL2-NCHR tip, our previous assumption that the cantilever torsion represented a negligible contribution to the effective lateral compliance of the tip is no longer valid. In fact, the opposite is true: The compliance of the tip is now a negligible contribution relative to the torsional compliance of cantilever–which is between 20 and 50 times as large. While the ratio in effective stiffness between the plateau tip and other CD tips is thus not as large as we had originally hoped, it nevertheless represents an increase of more than an order of magnitude in the effective stiffness range that is covered by our experiments. This situation is emphasized in Figure 4 by the inclusion of the dither slope result at two different points on the stiffness scaling axis. The larger value represents where the range would extend if compliance were due only to the tip, and the lower value indicates approximately where our range really extends, due to the limitation of cantilever torsion.

The bottom-line importance of the observations shown in Figure 4 is that we can now reasonably conclude that a dither slope of 3 nm/V is, indeed, the baseline response due to the induced motion of the cantilever base. At the present time, we do not have a model that fully explains the larger dither slopes observed for smaller tips. Although large slope is correlated with lower lateral stiffness, the free dynamic response of the tips in response to the driving lateral dither does not explain the behavior. Our previous work discussed this in more detail. [9] We suspect that attractive forces and snap-in behavior are involved, as is the case for the sidewall scanning behavior of some carbon nanotube (CNT) tips [16], but we do not yet have a quantitative model to explain the observed dither slopes.

3. SUMMARY AND CONCLUSIONS

NIST has been investigating the dependence of effective tip width on the dither settings and lateral stiffness of the tip, as well as the possibility of material effects due to sample composition. Generally, we have concluded that these effects will not result in a residual bias, provided that the tip calibration and sample measurement are performed under the same conditions.

Previously, we had observed a dependence of dither slope observations on the lateral stiffness of the tips. Five common types of smaller CD-AFM tips having diameters of 130 nm or less exhibited typical slopes of 4.0 nm/V to 4.5 nm/V. Two larger tip types of diameters 300 nm and 850 nm, which also have lateral stiffness values a factor of five larger than those of the smaller tips, exhibited dither slopes of approximately 3 nm/V. Our prior hypothesis was that this result represented a baseline value due to the motion of the cantilever base.

In the current work, we have now validated this hypothesis using a plateau type tip with a diameter of approximately 2.1 μm and an effective lateral stiffness value more than an order of magnitude larger than the 300 nm and 850 nm tips. The observed dither slope using this plateau tip was consistent with the 300 nm and 850 nm tips at 3 nm/V. This generally suggests that for tips of 300 nm and larger diameters, the effective tip width is influenced only by lateral dither and not by lateral tip bending. We are continuing to investigate tip and dither effects in CD-AFM metrology and hope to develop a more quantitative model of the behavior of the high compliance tips and larger dither slopes.

Biographies

Ronald Dixson is a physicist in the Physical Measurement Laboratory (PML) of the National Institute of Standards and Technology (NIST). His current research interests are calibration methods, traceability, and uncertainty analysis in atomic force microscope (AFM) dimensional metrology – including the NIST traceable AFM (T-AFM) project and metrology applications of critical dimension AFM (CD-AFM). He holds a Ph.D. in Physics from Yale University and is a member of SPIE and the American Physical Society.

Ndubuisi G. Orji is a mechanical engineer in the Physical Measurement Laboratory of the National Institute of Standards and Technology (NIST). His research interests are in atomic force microscopy, surface metrology, nano-scale dimensional metrology, and optical metrology. He holds a PhD in mechanical engineering from the University of North Carolina at Charlotte. He is a member of the American Society for Precision Engineering.

Ryan S. Goldband is an undergraduate Computer Engineering student at Binghamton University, State University of New York, Watson School of Engineering and Applied Science. He has internship experience working for a government research lab, a large defense contractor and a utilities company. He was participant in the NIST Summer Undergraduate Research Fellowship (SURF) program during 2015. Upon completion of his bachelor’s degree he plans to begin graduate work studying Electrical and Computer Engineering.