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SPECIAL ISSUE ON NANOMANUFACTURING

# Exploration of AFM Imaging Artifacts Occurring at Sharp Surface Features When Using Short Carbon Nanotube Probes and Possible Mitigation With Real-Time Force Spectroscopy

[+] Author and Article Information
Santiago D. Solares1

Department of Mechanical Engineering, 2181 Glenn L. Martin Hall, University of Maryland, College Park, MD 20742ssolares@umd.edu

Gaurav Chawla

Department of Mechanical Engineering, 2181 Glenn L. Martin Hall, University of Maryland, College Park, MD 20742

1

Corresponding author.

J. Manuf. Sci. Eng 132(3), 030904 (May 13, 2010) (14 pages) doi:10.1115/1.4001579 History: Received March 31, 2009; Revised April 05, 2010; Published May 13, 2010; Online May 13, 2010

## Abstract

We present an overview of four types of imaging artifacts that can occur during characterization of sharp sample topographies with intermittent contact atomic force microscopy (AFM) when using short nanotube probes ($<100 nm$ in length). We discuss the causes behind these artifacts, as well as their implications in the context of nanomanufacturing, and explore theoretically their mitigation using AFM techniques that can perform simultaneous imaging and spectroscopy. In particular, we focus on the experimentally validated spectral inversion method [Stark, 2002, “Inverting Dynamic Force Microscopy: From Signals to Time-Resolved Interaction Forces,” Proc. Natl. Acad. Sci. U.S.A., 99, pp. 8473–8478; Sahin, 2007, “An Atomic Force Microscope Tip Designed to Measure Time-Varying Nanomechanical Forces,” Nat. Nanotechnol., 2, pp. 507–514] and on a recently proposed dual-frequency-modulation method [Chawla and Solares, 2009, “Single-Cantilever Dual-Frequency-Modulation Atomic Force Microscopy,” Meas. Sci. Technol., 20, p. 015501], which has been demonstrated within computational simulations and is under experimental implementation in our laboratory. We discuss the capabilities and limitations of each of these approaches as well as possible areas of future development.

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## Figures

Figure 1

(a) Atomistic model of a 40,40 SWNT probe (5.4 nm diameter) tilted 15 deg with respect to the surface normal direction imaging a prone 20,20 single-walled carbon nanotube sample (2.2 nm diameter) in tapping-mode AFM; (b) comparison of the image obtained through tapping-mode AFM simulations for the system in (a) to the ideal profilometry scan for a rigid probe and sample of the same dimensions and to the experimental result (reproduced with permission from Ref. 7, copyright ACS 2004)

Figure 2

(a) Tip-sample interaction force curve for scan point 2 (labeled “point 2”) in Fig. 1, where the single-walled carbon nanotube probe and sample slide smoothly past one another (the dashed circle indicates the region where probe and sample first come into contact); (b) tip-sample interaction force curve for scan point 1 (labeled “point 1”) in Fig. 1, where the carbon nanotube probe is imaging the substrate surface (adapted with permission from Ref. 7, copyright ACS 2004)

Figure 3

(a) Illustration of a double-walled carbon nanotube probe approaching a Si(111)-H surface step edge and then snapping around it; (b) typical tip-sample interaction force curve for the approach (notice the discontinuity in the first repulsive region shortly after establishing tip-sample contact); (c) typical tip-sample interaction force curve for the retract after snapping has occurred (reproduced with permission from Ref. 66, copyright Institute of Physics, UK, 2009)

Figure 4

Simulated tapping-mode AFM images of square 2 nm deep (a) and 8 nm deep (b) trenches taken with a double-walled carbon nanotube probe in amplitude-modulation mode, which incorrectly show tilted, asymmetric side walls. The dashed lines show the true topography (reproduced with permission from Ref. 35, copyright Institute of Physics, UK, 2008).

Figure 5

(a) Illustration of typical amplitude-distance curves on which amplitude-modulation AFM control is based. The user selects an amplitude setpoint (illustrated by the dashed line), which the instrument seeks to maintain by adjusting the cantilever position according to the amplitude-distance curve. Notice the parallel curves (corresponding to different oscillation regimes) that coexist as a consequence of the bistability of the system (discussed in detail in Refs. 5,74). Any transitions between the two coexisting regimes normally occur in a discontinuous manner. (b) Illustration of a typical amplitude-distance curve exhibiting multistability. As in (a), two amplitude-distance curves coexist but the transitions between them are smooth, such that multiple images are possible for a given probe and sample, depending on the imaging parameters (this phenomenon is discussed in Ref. 45).

Figure 6

(a) Illustration of a single-walled carbon nanotube AFM probe tilted 40 deg with respect to normal, which is contacting simultaneously the sample and the substrate, leading to the distorted simulated image shown in (b). The simulated image shown in Fig. 1 (for a probe tilted 15 deg) is provided for comparison purposes (reproduced with permission from Ref. 46, copyright ACS 2005).

Figure 7

Torsional harmonic cantilever (13)

Figure 8

Simulation of force curve acquisition with the torsional harmonic cantilever for a polymer surface with a modulus of elasticity of 2 GPa using a standard silicon tip with a radius of curvature of 10 nm: (a) torsional and flexural tip trajectories, (b) complex Fourier transform magnitude for the torsional oscillation (notice the enhanced response around the fundamental torsional frequency of 850 kHz), (c) reconstructed time-resolved tip-sample force using 256 harmonics, and (d) reconstructed tip-sample interaction force curve for different numbers of harmonics included in the calculations (18, 25, and 256), compared with the actual force curve. The reconstructed force curve labeled “256 harmonics” is a plot of the time-resolved force in (c) with respect to the flexural deflection in (a). Tip-sample dissipation was not considered. The AM-AFM free oscillation amplitude and amplitude setpoints were 100 nm and 70 nm, respectively, the resonance frequencies were 50 kHz (flexural) and 850 kHz (torsional), the force constants were 5 N/m (flexural) and 500 N/m (torsional), and the quality factors were 100 (flexural) and 1000 (torsional). The details of the THC simulation methodology are provided in Ref. 69.

Figure 9

Simulation of force curve acquisition with the torsional harmonic cantilever for a viscoelastic polymer sample with a modulus of elasticity of 2 GPa using similar parameters to the calculation in Fig. 8, except for the inclusion of dissipation. The upper trajectory of each curve (except for the conservative tip-sample interaction force curve) corresponds to the tip approach and the bottom trajectory corresponds to the retract. The “total” force curve corresponds to the sum of the conservative and local dissipative force curves calculated using the model proposed by Gotsmann (78). The “conservative” and “total” force curves are the actual curves while the curves for 18 harmonics and 256 harmonics are the reconstructed curves. The details of the THC simulation methodology are provided in Ref. 69.

Figure 10

Proposed controls scheme for single-cantilever dual-frequency-modulation AFM. The controls scheme for the dual-cantilever case is similar except for the phase of high-frequency excitation, which is 3π/2 instead of π/2(55,66) (reproduced with permission from Ref. 66, copyright Institute of Physics, UK, 2008)

Figure 11

Schematic illustration of the separation of the eigenmode responses in dual-frequency-modulation AFM to perform simultaneous imaging and force spectroscopy (adapted with permission from Ref. 55, copyright Institute of Physics, UK, 2008)

Figure 12

Simulated dual-frequency-modulation instantaneous frequency of the high-frequency response as a function of time for a complete cycle of the low-frequency response (a) and calculated tip-sample force gradient as a function of the low-frequency response tip position (b) for a conventional 15 nm diameter silicon tip tapping on a flat Si(100)–OH surface. The results in graph (a) came from the data acquired during the AFM raster scan and the results in graph (b) were calculated using Eq. 4. This type of data could be collected for any low-frequency oscillation at any horizontal position on the sample as the topographical image is acquired. The imaging (v1−o) and spectroscopy (v2−o) frequencies were 10 kHz and 1.5 MHz, respectively; the corresponding force constants were 50 N/m and 1000 N/m, respectively; the corresponding quality factors were 100 and 500, respectively; and the corresponding oscillation amplitudes were 5 nm and 0.1 nm, respectively, (reproduced with permission from Ref. 55, copyright Institute of Physics, UK, 2008)

Figure 13

Comparison of the tip-sample force curves acquired within simulations of the dual-frequency-modulation method to the actual force curves for a 15 nm diameter silicon tip (a) and a 5.4 nm diameter carbon nanotube tip (b) tapping on flat Si(100)–OH. The “actual” curves correspond to molecular dynamics calculations. The blue curve in (a) (closest to the actual curve) is the numerical integral of the data shown in Fig. 1. The other two curves on the same graph were constructed using the same AFM parameters, except for the indicated values of the spectroscopy frequency (“freq,” v2−o) and oscillation amplitude (A2). (reproduced with permission from Ref. 55, copyright Institute of Physics, UK, 2008)

Figure 14

(a) atomistic model of a 1.5 nm diameter double-walled carbon nanotube AFM tip imaging a hypothetical 5.5 nm wide and 1.37 nm deep surface trench on a Si(111)–H surface with graphite bottom, (b) simulated dual-frequency-modulation topography using parameters similar to those listed in the caption of Fig. 1 and a scan speed of 200 nm/s; (c)–(e) comparison of the tip-sample force curves acquired at various locations along the scan (horizontal position, x=1 nm, 5 nm, and 7.25 nm) to the actual force curves (calculated with molecular dynamics). For clarity, Fig. 1 (force curve obtained while tapping on the step edge) shows only the approach force curves (the retract curves are different, similar to that illustrated in Fig. 3). Notice that even when the force curve exhibits snapping discontinuities, one can find the approximate locations where the force vanishes near the surface skin, suggesting that it is possible to obtain faithful topographical images from the tip-sample force data (reproduced with permission from Ref. 66, copyright Institute of Physics, UK, 2008)

Figure 15

Simulation of force curve acquisition with the torsional harmonic cantilever for a snapping tip-sample interaction force curve and different numbers of harmonics included in the calculation (18, 60, and 256), analogous to the result shown in Fig. 1 for the dual-frequency-modulation method. The simulation parameters are similar to those used to construct Fig. 8, except for the force curve shape.

Figure 16

Experimental dual-frequency results using the fundamental eigenmode to acquire the sample topography in AM-AFM operation and the third eigenmode to obtain frequency shift contrast in PLL operation. The frequency shift contrast is shown as the color superimposed on the topography. This image was acquired using the first and third eigenmodes (frequencies are 73.47 kHz and 1.184 MHz, respectively) of an Olympus AC240TS cantilever (82) and a phase calibration standard sample (electron microscopy sciences PT-1 block copolymer specimen (83)). The free oscillation amplitude and amplitude setpoint of the fundamental eigenmode were 100 nm and 60 nm, respectively, and the oscillation amplitude of the third eigenmode was ∼12.5 nm. The scan speed was 3 μm/s.

Figure 17

Comparison of the topography calculated for the atomistic model shown in Fig. 1 from the 3D tip-sample force data (post-processed topography) to that obtained from the low-frequency cantilever vibration signal using the FAM-AFM algorithm (Fig. 1), to the true sample skin, and to the rigid probe-rigid sample (classical profilometry) result. The post-processed topography was approximated from the molecular dynamics tip-sample interaction forces, assuming that the dual-frequency-modulation method underestimates the repulsive forces by ∼1 nN. The dashed circles highlight topography errors that occur due to a decrease in the stiffness of the tip-sample contact when the probe is only partially tapping on the trench edge (see the leftmost atomistic model in Fig. 3).

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