Lateral Resolution and Image Formation in Scanning Ion

Article pubs.acs.org/ac

Lateral Resolution and Image Formation in Scanning Ion Conductance Microscopy Johannes Rheinlaender and Tilman E. Schaff̈ er* Institute of Applied Physics, University of Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany S Supporting Information *

ABSTRACT: The scanning ion conductance microscope (SICM) is a powerful tool for imaging the topography of soft samples in an aqueous environment. Despite the rising popularity of the SICM, the image formation process and the fundamental limit of the lateral resolution are still a matter of debate. Using microfabricated samples, we investigated the imaging of small cylindrical particles, elongated objects, and topography steps and present the first direct comparison of numerical and experimental data. For the lateral resolution we considered two alternative definitions: the distance at which two small particles can clearly be resolved from each other in an image, and the apparent full width at half-maximum of small particles. For both definitions, we found a lateral resolution of about 3 times the inner opening radius of the pipet. We further validated this resolution limit in measurements on supported lipid bilayers and a polycarbonate sample using pipets with opening radii down to 8 nm.

T

free, and estimated the lateral resolution on elongated objects as 2ri (using the edge-to-edge spacing between the objects as their distance). We present the first direct comparison of numerical and experimental data on the SICM imaging process. We experimentally recreate configurations from simulations in previous studies9,10 and thereby validate fundamental theoretical predictions. First, we validate that small cylindrical particles on a planar surface appear bell-shaped or ring-shaped, depending on particle height and scan distance. Second, we validate that the lateral resolution of the SICM, assessed by imaging small, closely spaced particles and v-shaped objects, is approximately 3ri. Third, we demonstrate that the smeared-out image of sharp topography steps is a consequence of the finite lateral resolution of the SICM. Additionally, we present highresolution measurements on supported lipid bilayers and on a polycarbonate sample, thereby extending the validation to small pipets with opening radii down to 8 nm.

he scanning ion conductance microscope (SICM) was introduced in 1989 by Hansma et al.1 and developed further by Korchev et al.2 It is based on a pipet that scans the topography of a sample surface by monitoring the ion current passing through the opening of the pipet. The SICM can image sample topography without mechanical contact and has therefore found many applications on delicate biological samples such as living cells,3,4 proteins,5 and suspended artificial membranes.6 Despite the increasing popularity of the SICM, the image formation process and the fundamental limit of the lateral resolution are still a matter of debate. Recently, Weber and Baker7 used topography trenches to investigate the lateral resolution of the SICM and found that topography trenches can be resolved down to a trench width of 0.5ri, where ri is the pipet inner opening radius. The first numerical approach was presented by Adenle and Fitzgerald,8 who applied a state-space model using the ion current density to mimic the imaging process and predicted that a small object is displayed with a full width at half-maximum (fwhm) of about 1−1.5ri. Rheinlaender and Schäffer9 used finite element modeling (FEM) to predict the distance behavior of the measured ion current and to simulate imaging of small topographical objects. They predicted that small topographical objects appear bell-shaped or ringshaped, depending on their size and the scan distance. Furthermore, they found a lateral resolution, defined as the distance at which two small particles can clearly be resolved from each other in an image (i.e., when a dip is visible between the particles), of about 3ri. Edwards et al.10 simulated imaging topography steps and pits and found that steps appear smeared out to a lateral distance of about 3−4ri and that small pits appear ring-shaped (denoted as “halo artifact”). Del Linz et al.11 simulated imaging of elongated objects, investigated under which conditions a steep topography step is imaged contact© 2015 American Chemical Society

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EXPERIMENTAL SECTION SICM Setup. We used a conventional SICM setup, in which a conical nanopipet was placed in the vicinity of a sample in an electrolytic environment (Figure 1a). The SICM head was home-built and was made compatible with a commercial atomic force microscope (AFM) (MFP3D-BIO, Asylum Research, Santa Barbara, CA) interfaced with an inverted optical microscope (Nikon Ti-S, Nikon Corporation, Kanagawa, Japan). The head was equipped with a fast z-piezo for vertical positioning of the pipet and a home-built linear variable Received: March 6, 2015 Accepted: June 22, 2015 Published: June 22, 2015 7117

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Gemini Supra 40, Carl Zeiss GmbH, Oberkochen, Germany). From the SEM images (an example is shown in Figure 1b) the inner and outer opening radii, ri and ro, respectively, were determined (estimated accuracy about 10%). The ratio ro/ri was consistently found to be about 1.5. The average inner half cone angle, α, was estimated as 3.8° ± 10% for the large pipets (Figures 1−6) and as 2.0° ± 10% for the medium (Figure 7, parts a and b) and small pipets (Figure 7, parts c and d). For the pipets used for imaging, ri was estimated from the maximum ion current, I0, measured with the pipet far away from the sample, and from the average α by15

I0 ≅ πσri tan(α)V0

(1)

where σ is the conductivity of the electrolyte. Sample Preparation. For the characterization of the SICM imaging process gold structures on planar glass surfaces were microfabricated using electron-beam lithography. The glass surfaces were first spin-coated with a poly(methyl methacrylate) (PMMA) bilayer resist (200 and 950 K, Allresist, Strausberg, Germany), which was then metallized with a 5 nm thick layer of gold. After electron-beam exposure of the resist and removal of the metallization with diluted potassium hydroxide solution the PMMA masks were developed in methyl isobutyl ketone (MIBK)−isopropyl alcohol (1:3). The gold structures were made by depositing either 290 or 140 nm of gold on top of a 10 nm thick titanium adhesion layer using electron-beam evaporation to achieve zero step coverage. Finally, the masks were removed with acetone. The heights of the structures were chosen to approximately match ri (“high object”) or ri/2 (“low object”) for the pipets used in this study (ri ≅ 300−400 nm). For comparison, the microfabricated samples were also imaged with a commercial AFM (MFP3DBIO, Asylum Research, Santa Barbara, CA) in air using commercial cantilevers (DNP, version from 2005, Veeco, Santa Barbara, CA) with a nominal spring constant of 0.06 N/m and a square pyramidal tip with faces at 35° with respect to the cantilever normal. The AFM was operated in contact mode, scanning at 90° with respect to the cantilever axis. For highresolution SICM measurements on supported lipid bilayers, phospholipids (heart total extract, HTE, 171201, Avanti Polar Lipids, Alabaster, AL) were deposited on a freshly cleaved mica substrate (for details see ref 16). FEM Calculations. FEM calculations were performed as previously described.9 A three-dimensional finite element model of the tip region was designed. The pipet was placed in the vicinity of a flat horizontal sample surface on which small cylindrical particles (Figures 2−4) or topography steps were placed (Figure 6). The pipet and the sample surfaces were modeled as electrically insulating. The ion current was calculated by solving the Poisson equation in the electrolyte domain using commercial FEM software (COMSOL Multiphysics 4.1, COMSOL AB, Stockholm, Sweden). The macroscopic neck of the pipet was included into the model analytically as previously described.9 The imaging process was mimicked by constructing height profiles of constant ion current amplitude.

Figure 1. (a) Schematic of the SICM setup. A voltage V0 between two electrodes induces an ion current I through an electrolyte-filled nanopipet. Topography images of the sample surface are recorded by measuring the ion current while scanning the sample using a controller, which drives the x−y scanner and the z-piezo. For coarse positioning and sample inspection the SICM was mounted on top of an inverted optical microscope. (b) SEM image of the opening of a typical medium-sized nanopipet, with inner and outer opening radius ri and ro, respectively. (c) Ion current as a function of pipet−surface distance for the dc mode and the hopping mode (top) and mean ion current and amplitude for the ac mode (bottom). The data were recorded on a flat glass surface using a nanopipet with ri = (300 ± 30) nm. The red dashed curves show FEM calculations (no fits).

differential transformer (LVDT) as position sensor. The ion current I was measured with a home-built current amplifier and monitored with the controller of the AFM setup. The controller also drove the closed loop x−y scanner and the z scanner (for details see ref 12). SICM topography images were recorded in ac mode,13,14 where the vertical pipet position was modulated with an amplitude (0 to peak) of 100 nm. The amplitude of the ion current was measured using a lock-in amplifier included in the controller and served as the input to a feedback loop controlling the vertical pipet position. The voltage between the electrodes was set to V0 = 100 mV for larger pipets (Figures 1−6) and to 200 mV for smaller pipets (Figure 7). All SICM measurements were performed at room temperature and in phosphate-buffered saline (PBS) with a conductivity of approximately σ = 1.35 S/m at T = 20 °C. Nanopipets. Nanopipets were fabricated from glass capillaries using a CO2-laser-based micropipet puller (P-2000, Sutter Instruments, Novato, CA). Large pipets with an inner opening radius of ri = 200−400 nm (Figures 1c and 2−6) and medium pipets with ri = 50−100 nm (Figures 1b and 7, parts a and b) were fabricated from borosilicate glass (1B100F-4, World Precision Instruments Inc., Sarasota, FL). Small pipets with ri = 5−50 nm (Figure 7, parts c and d) were fabricated from quartz glass (QF100-50-7.5, Sutter Instrument Company, Novato, CA). For tip characterization the pipets were sputter-coated (for high step coverage) with a 10−20 nm thick layer of aluminum and imaged with a scanning electron microscope (SEM) (Zeiss

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RESULTS Determination of the Scan Distance in SICM Imaging. To obtain the scan distance, which has a profound influence on the SICM imaging process,9,10 we recorded ion current and amplitude versus distance curves on a flat glass surface (Figure 1c). The absolute vertical sample position is initially not 7118

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pointlike particle can be interpreted as the special point spread function (sPSF) of the SICM. The concept of point spread functions is used in optical microscopy, where the image formation can be described by a convolution of the object with the system’s point spread function.23,24 This concept has to be slightly modified for the SICM, because its point spread function depends on scan distance and particle height, leading to the extended concept of special point spread functions.9 When the sPSF for a given configuration is known, it can be used to characterize the imaging process, because the image of extended objects can be approximated by a convolution of the sample topography with the respective sPSF. FEM calculations showed that the SICM image of a small particle for a given pipet can be bell-shaped or ring-shaped, depending on scan distance and object height (see Figure 4 in ref 9). To experimentally validate these predictions, we imaged small gold particles on planar glass surfaces using experimental conditions that matched the previously modeled configurations (see Figure 4 in ref 9). The particles were imaged first with the AFM to determine the particle dimensions (Figure 2, parts a and b). Apart from some small contaminations (diagonal arrows in Figure 2, parts a and b) the top faces of the particles are plane and horizontal. The left and right side walls of the particles appear sloped under an angle of about 55° relative to the surface due to the pyramidal shape of the cantilever tip with a face angle of 35° with respect to the surface normal (“tip artifact”).25 The top and bottom side walls appear asymmetrically sloped, owing to the cantilever being tilted in the AFM setup (by 11° with respect to the sample plane). The tip artifact is more apparent for the high particle (Figure 2a, height h0 = 320 nm) than it is for the low particle (Figure 2b, height h0 = 130 nm). The actual shape of the particles was assumed as cylindrical with vertical side walls, since it is known that electron-beam evaporation offers zero step coverage. The diameter of a particle, 2r, was estimated as the distance between the top edges (defined as the positions where the apparent slope of the topography is ±55°/2). The same particles were subsequently imaged with the SICM. The high particle, imaged with a large scan distance, appears blurred (Figure 2c). The cross section is bell-shaped with a height of 77 nm = 0.24h0 and a fwhm of 920 nm ≅ 3.1ri (Figure 2c′, solid trace). FEM calculations accurately reproduce this profile (Figure 2c′, red dashed trace), predicting a height of 0.23h0 and a fwhm of 3.0ri. We emphasize that no fitting was performed here: all parameters used for the FEM calculations were determined directly from AFM images (r, h0), from SEM images and measured ion current (ri, ro), and from the current− distance behavior (d). The low particle, imaged with a small scan distance, appears ring-shaped (Figure 2d). The cross section shows a height of 26 nm = 0.21h0, a fwhm of 1020 nm ≅ 3.3ri, a peak-to-peak ring diameter 2R of 560 nm ≅ 1.8ri, and a dip at the location of the particle center (Figure 2d′, solid trace). Again, FEM calculations accurately reproduce this profile (Figure 2d′, red dashed trace), predicting a height of 0.21h0, a fwhm of 3.3ri, and a peak-to-peak ring diameter of 1.7ri. A fwhm of approximately 3ri was also found for different pipet geometries, scan distances, and imaging modes (dc, hopping mode) (Supporting Information Figure S-1 and Table S-1). As previously predicted (see Figure 4 in ref 9), the apparent width (fwhm) of the particles is proportional to the pipet inner opening radius (Supporting Information Figure S2) and the shape depends on the scan distance (Supporting Information Figure S-3). For example, for an increasing scan

Figure 2. Experimental characterization of the special point spread function by imaging of small cylindrical gold particles on a planar glass surface. (a and b) AFM topography images of the particles and (a′ and b′) corresponding cross sections through the particle centers. These images give a particle radius r = 140 nm ≅ 0.5ri and height h0 = 330 nm ≅ 1.1ri (“high particle”, left column) and r = 190 nm ≅ 0.6ri and h0 = 130 nm ≅ 0.4ri (“low particle”, right column). (c) SICM topography image of the high particle using a pipet with ri = (300 ± 30) nm and a large scan distance of d = 530 nm ≅ 1.7ri. (d) SICM topography image of the low particle using a pipet with ri = (310 ± 30) nm and a small scan distance of d = 170 nm ≅ 0.54ri. The pipets’ tip openings are outlined as dashed circles in panels c and d. (c′ and d′) Corresponding cross sections through the particle centers and FEM calculations (no fits). The schematics above the images show the to-scale geometries of the particles, the AFM tip, and the pipets; the dashed line denotes a height profile (not to scale).

accessible from these data. We therefore calculated FEM curves (in which the absolute vertical sample position obviously is known) and determined the absolute vertical sample position in the experiment by laterally shifting the experimental curves to match the calculated curves. We thereby used that the ion current curve (relevant for the dc mode,1,2 for the hopping/ backstep mode,17−20 and for the bias/phase modulation mode21,22) (Figure 1c, top) and the mean ion current and amplitude curves (relevant for the ac mode13,14) (Figure 1c, bottom) perfectly match the respective FEM calculations (red dashed curves). We defined the scan distance as the pipet− surface distance in the case of a flat sample and determined it from a current−distance curve (e.g., Figure 1c) for the applied imaging setpoint. For the ac mode, we defined the pipet− surface distance as the distance between the surface and the lower reversal point of the modulation. Imaging of Small Particles. As shown by our previous study based on FEM calculations,9 an image of a small, 7119

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Figure 3. Imaging of two high cylindrical particles with a varying particle distance x0 on a planar surface. (a−d) AFM topography images and (a′−d′) corresponding cross sections through the particle centers. These images give a particle radius r = 170 nm ≅ 0.55ri and height h0 = 320 nm ≅ 1.1ri. (e−h) SICM topography images recorded using a pipet with ri = (300 ± 30) nm and a large scan distance of d = 530 nm ≅ 1.8ri. (e′−h′) Corresponding cross sections through the particle centers and FEM calculations (no fits). For a large particle distance the particles are displayed as individual bell shapes (e and e′). They start to overlap for x0 = 1.2 μm ≅ 4ri (f and f′) and cannot be resolved from each other for x0 = 0.6 μm ≅ 2ri (g and g′) and x0 = 0.3 μm ≅ 1ri (h and h′). The schematics on the left show the to-scale geometries of the particles, the AFM tip, and the pipet.

Figure 4. Imaging of two low cylindrical particles with a varying particle distance x0 on a planar surface. (a−d) AFM topography images and (a′−d′) corresponding cross sections through the particle centers. These images give a particle radius r = 170 nm ≅ 0.55ri and height h0 = 170 nm ≅ 0.55ri. (e−h) SICM topography images recorded using a pipet with ri = (310 ± 30) nm and a small scan distance of d = 180 nm ≅ 0.6ri. (e′−h′) Corresponding cross sections through the particle centers and FEM calculations (no fits). For a large particle distance the particles are displayed as individual rings (e and e′). They start to overlap for x0 = 1.2 μm ≅ 4ri (f and f′) and cannot be resolved from each other for x0 = 0.6 μm ≅ 2ri (g and g′). For an even smaller distance of x0 = 0.3 μm ≅ 1ri (h and h′), the ring shapes overlap above and below the particles and the image appears as if the two particles were rotated by 90°. The schematics on the left show the to-scale geometries of the particles, the AFM tip, and the pipet.

This includes the accurate prediction of a “height artifact”9 (reduced apparent height of small features). Lateral Resolution for Small Particles. In our previous study,9 the lateral resolution of the SICM was defined as the smallest distance at which two small particles on a planar surface can clearly be resolved from each other in an image, i.e., when a dip is visible between the particles. This distance was determined by FEM calculations as approximately 3ri. To experimentally validate this finding, we imaged two cylindrical gold particles on a planar glass surface, spaced apart by a

distance, the ring shape becomes less pronounced (see Supporting Information Figure S-1, Table S-1, and Figure S-3). In summary, these results validate the predictions from the FEM calculations that the SICM image of a small particle can be bell-shaped or ring-shaped, depending on the scan distance and on the object height. The close match between experiment and theory, both in functional form and in scale, provides a quantitative, parameter-free validation of the theory within the estimated accuracy of about 10% from the determination of ri. 7120

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Analytical Chemistry varying distance x0, measured from between the particle centers, as was done in our previous numerical study (see Figure 6 in ref 9). As shown in AFM images of the high (Figure 3a−d) and low (Figure 4a−d) particles the particle distance was varied between x0 = 1.8 and 0.3 μm. As in Figure 2, the top faces of the particles are plane and horizontal, and “tip artifacts” occur at the particles’ edges. In the corresponding SICM images (Figures 3e−h and 4e−h) the particles appear as individual objects when the particle distance is large (x0 = 1.8 μm ≅ 6ri, Figures 3e and 4e). For a decreasing distance (x0 = 1.2 μm ≅ 4ri) the particles start to overlap (arrow in Figures 3, parts f and f′, and 4, parts f and f′). When the dip between the particles has disappeared (arrow in Figures 3, parts g and g′, and 4, parts g and g′), the particles cannot be resolved from each other anymore. For low particles and a small particle distance (at about x0 = 0.6 μm ≅ 2ri), two peaks appear, one above and one below the particles, where the two ring shapes overlap (arrows in Figure 4h). This was predicted in our previous study (ref 9, Figure 6l). FEM calculations accurately reproduce the experimental profiles (Figures 3 and 4, red dashed traces). Again, no fitting to the data was performed: all parameters used in the calculations were determined directly from AFM images, SEM images, ion current, and current−distance behavior. In summary, these data show that the FEM calculations accurately match the experimental data. The smallest distance above which the two particles in Figures 3 and 4 can clearly be resolved from each other is smaller than 4ri but larger than 2ri, which gives an upper and lower limit, respectively, of the lateral resolution. Lateral Resolution for Two Stripes. In order to quantify the lateral resolution more precisely, samples consisting of two stripes in a v-shaped arrangement were designed. AFM images show two straight, narrow stripes of height h0 = 320 nm (high stripes, Figure 5a) and of height h0 = 170 nm (low stripes,

Figure 5b) hitting at an acute angle. In the corresponding SICM image of the high stripes recorded with a large scan distance (d = 530 nm ≅ 1.7ri, Figure 5c), each stripe appears blurred with a fwhm of 1.1 μm ≅ 3.7ri, owing to the bell-shaped sPSF (see, for example, Figure 2c). The fwhm is larger than it was in Figures 2−4 since here the objects are elongated and wider rather than pointlike. The apparent height of a single stripe is 150 nm, only 47% of the actual height (320 nm). To measure the lateral distance at which the two stripes can be resolved from each other, the height profile along the x-axis on the centerline between the stripes (indicated by the solid line in Figure 5c) is considered (Figure 5c′, solid trace). At a position of x = 5.6 μm (arrow in Figure 5c′), the height profile equals the apparent height of a single stripe (dashed line). At this position, the stripe distance is 1.03 μm ≅ 3.4ri (arrows in Figure 5c), which is consistent with the theoretical prediction9 for the fundamental limit of the lateral resolution of approximately 3ri, within the estimated accuracy of about 10% from the determination of ri. The low stripes recorded with a small scan distance (d = 230 nm ≅ 0.5ri, Figure 5d) are displayed as double stripes owing to the ring-shaped sPSF (see Figure 2d) and can be resolved at a stripe distance larger than 1.38 μm ≅ 3.1ri (arrows in Figure 5d). Imaging of Topography Steps. FEM calculations predict that topography steps are displayed smeared out in SICM images due to the finite lateral resolution of the SICM.9−11 To validate this prediction, topography steps were imaged with the AFM and the SICM (Figure 6). In the AFM images (Figure 6, parts a and b), the substrate and the gold surface appear relatively plane. Some contaminations can be identified (arrows in Figure 6, parts a and b). In the SICM images (Figure 6, parts c and d) and in the respective cross sections (Figure 6, parts e and f) the topography steps appear smeared out over a lateral distance of about 1 μm ≈ 3ri. The steps are displayed with their full height (vertical arrows in Figure 6, parts e and f), unlike the small particles (Figures 2−4) or the narrow stripes (Figure 5). FEM calculations accurately reproduce the profiles (Figure 6, parts e and f, red dashed traces). Again, no fitting was performed: all parameters used for the calculations were determined experimentally. In the cross section of the low step a wavy substructure can be identified (diagonal arrows in Figure 6f), which is also reproduced in the calculated height profile. This substructure can be understood as a result of the ringshaped form of the sPSF (see Figure 2d) and was already observed in a previous study.10 In summary, we validate that topography steps appear smeared out, owing to the finite lateral resolution of the SICM, in agreement with the predictions from the FEM calculations.9−11 Application to High-Resolution Imaging. The measurements above were performed using pipets with inner opening radii of about 200−400 nm, to match the lateral dimensions of the microfabricated sample structures. To investigate the SICM imaging process also for smaller pipets, high-resolution measurements were performed. As a first example, we imaged supported lipid bilayers on a mica substrate with a borosilicate glass pipet, which had an inner opening radius of ri = (74 ± 7) nm. In the overview SICM image (Figure 7a), several bilayer fragments can be seen. Three larger fragments are shown in the zoom-in image (Figure 7b). This image also shows numerous ring-shaped features from small objects on the substrate (arrows) owing to the small scan distance used here (d = 20 nm ≅ 0.3ri). The fwhm of the ring-shaped features was about 220 nm, and their peak-to-peak

Figure 5. Estimation of the lateral resolution of the SICM by imaging a v-shaped object. (a and b) AFM topography images give a stripe width of 200 nm and height h0 = 320 nm ≅ 1.1ri (“high stripes”, left column) and h0 = 170 nm ≅ 0.4ri (“low stripes”, right column). (c) SICM topography image of the high stripes recorded using a pipet with ri = (300 ± 30) nm and a large scan distance of d = 530 nm ≅ 1.7ri. (c′) Height profile along the centerline between the stripes (indicated by the solid line in panel c). (d) SICM topography image of the low stripes recorded using a pipet with ri = (440 ± 40) nm and a small scan distance of d = 230 nm ≅ 0.5ri. (d′) Height profile along the centerline between the stripes (indicated by the solid line in panel d). 7121

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As a second example, we imaged a polycarbonate surface (compact disc, reflecting layer removed) with a quartz glass pipet, which had an inner opening radius of ri = (8 ± 1) nm. This value for ri is comparable to the estimated ri of the pipets used in a previous SICM study for high-resolution imaging of single proteins.5 In the overview image (Figure 7c) and in the zoom-in image (Figure 7d), numerous small particles can be seen. The smallest particles appeared approximately bellshaped, owing to the large scan distance used here (d = 10 nm ≅ 1.3ri), and had a fwhm of 25 nm (Figure 7d′). This corresponds to approximately 3.0ri, which is in well agreement with the measurement using larger pipets (Figure 2c) and the prediction from the calculations (Figure 4a in ref 9). These results show that the predictions for the imaging process made above for large pipets can be extended to small pipets with inner opening radii down to 8 nm.

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DISCUSSION AND CONCLUSION In this study the imaging process of the SICM was experimentally investigated. Important findings from numerical calculations were validated. An excellent agreement between experimental and FEM data was found, showing that FEM is an accurate tool for characterizing the SICM imaging process. Measurements on small particles validated the predictions from simulations: A high particle imaged with a large scan distance is displayed bell-shaped with a fwhm of about 3ri. A low particle imaged with a small scan distance appears ringshaped with a fwhm of also about 3ri and with a peak-to-peak diameter of about 2ri. Vice versa, the diameter of such a ring shape can be used as a rough estimate for the pipet inner opening diameter. However, the diameter of ring shapes depends on several other parameters such as particle shape, pipet wall thickness, and scan distance (see Figure 4 in ref 9). The lateral resolution of the SICM, here defined as the smallest distance at which two small features can clearly be resolved from each other in an image, was assessed by imaging small, closely spaced particles and v-shaped objects. We found an excellent agreement between experimental and FEM data and showed that the fundamental limit for the lateral resolution is approximately 3ri. Further numerical calculations suggest that

Figure 6. Imaging of topography steps. (a and b) AFM topography images give a step height h0 = 320 nm ≅ 1.1ri (“high step”, left column) and h0 = 170 nm ≅ 0.4ri (“low step”, right column). (c) SICM topography image of the high step recorded using a pipet with ri = (300 ± 30) nm and a large scan distance of d = 530 nm ≅ 1.7ri. (d) SICM topography image of the low step recorded using a pipet with ri = (440 ± 40) nm and a small scan distance of d = 230 nm ≅ 0.5ri. (e and f) Cross sections across the steps at the locations marked with horizontal lines in the images and FEM calculations (no fits). The schematics above the images show the to-scale geometry of the topography steps, the AFM tip, and the pipets.

diameter was about 150 nm (Figure 7b′). This corresponds to approximately 3.0ri and 2.0ri, respectively, which is in well agreement with the measurement using larger pipets (Figure 2d) and the prediction from the calculation (Figure 4e in ref 9).

Figure 7. High-resolution SICM imaging on supported HTE lipid bilayers (top row) and on a polycarbonate sample (bottom row). (a) Overview image and (b) higher-magnification image of the region marked with a box in panel a. Small particles on the substrate are displayed as rings (arrows in panel b). (b′) Cross section through one ring along the white line in panel b. (c) Overview image and (d) higher-magnification image of the region marked with a box in panel c. (d′) Cross section through one object along the white line in panel d. The estimated pipets’ tip openings with ri = 74 nm and ri = 8 nm are outlined as dashed circles in panels b and d, respectively. 7122

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this result also applies to objects much higher (in z-direction) than the ones used here (data not shown). As the SICM imaging process can be approximately described by convolution,9 there is the possibility to resolve objects even below the fundamental resolution limit of 3ri by using deconvolutionbased image processing algorithms. In a previous study, the lateral resolution of the SICM was estimated from a 2D Fourier transform of an image of periodic sample structures as about 0.5−1ri.5 However, an estimation based on spectral information is problematic, because spatial frequencies can be detected on periodic samples even beyond the fundamental resolution limit, given a sufficient instrumental signal-to-noise level.9 In another study, the lateral resolution was estimated from the width of hair cell stereocilia links as about 1ri.18 But such an estimation is somewhat arbitrary, because the apparent width of single, free-standing objects depends on the imaging setpoint and can, in principle, be arbitrarily reduced by using a different setpoint. In a recent theoretical study,11 the lateral resolution of the SICM on larger, elongated objects was stated as 2ri. In another recent experimental study,7 it was found that topography trenches of widths down to 0.5ri can be detected. However, both studies used the separation between the closest edges and not between the centers of objects as a measure of their distance. The separation between object edges, however, is not a meaningful measure for the (fundamental) lateral resolution since even the narrowest gap between two objects could be detected, given a sufficiently high signal-to-noise ratio. When using the more meaningful distance between the centers (consistent with the Rayleigh criterion in optical microscopy26), the results in ref 11 correspond to a minimum resolvable object distance of 4ri. This is slightly larger than 3ri, because the objects in ref 11 were quite wide. A more convenient measure for the lateral resolution is the fwhm of the microscope’s PSF, a method routinely used in optical microscopy.27 Here, for experimentally realistic pipet geometries, we determined a fwhm of the sPSF of approximately 3ri, regardless of the imaging mode (ac, dc, or hopping mode) and for different scan distances and pipet geometries (Supporting Information Figure S-1 and Table S-1). We found that applying this definition to the data in the other studies5,7,11 also leads to a lateral resolution of approximately 3ri. In summary, we showed that 3ri is a meaningful and robust value for the fundamental limit of the lateral resolution of the SICM.

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The authors declare no competing financial interest.

ACKNOWLEDGMENTS

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REFERENCES

We thank Stefan Ballmann from the University of ErlangenNuremberg for assistance in the design of the microfabricated samples and in the operation of the SEM. We thank Asylum Research for technical support. We are grateful to Nicholas A. Geisse for the preparation of the lipid bilayer samples.

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ASSOCIATED CONTENT

S Supporting Information *

Additional information as noted in the text: numerical data showing the influence of particle height, scan distance, and pipet wall thickness and experimental data showing the influence of pipet inner opening radius and scan distance. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.analchem.5b00900.

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*E-mail: tilman.schaeff[email protected]. Phone: +49 7071 29 76030. Fax: +49 7071 29 5093. 7123

DOI: 10.1021/acs.analchem.5b00900 Anal. Chem. 2015, 87, 7117−7124

Article

Analytical Chemistry (27) Cole, R. W.; Jinadasa, T.; Brown, C. M. Nat. Protoc. 2011, 6, 1929−1941.

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DOI: 10.1021/acs.analchem.5b00900 Anal. Chem. 2015, 87, 7117−7124