GB2472302A - An in situ calibrated AFM - Normal and lateral force standards as well as tip radius and sample elasticity standards in scanning atomic force microscopy - Google Patents

Abstract

A system for in-situ calibration of AFM probe tips relies on calibration samples. Exact characterization of the probe tips is not conducted by means of an independent technology, like electron microscopy. Tip pressure is calibrated using phase transitions of material such as of a CaCO3crystal from the calcite to the aragonite structure; or measurements on phospholipid films in the 2-dimensional "gas" to "liquid" phase. Apparent heights as measured by AFM have to be calibrated for sample (substrate) elasticity, which is done here by depositing well defined "hard" e.g. 5nm gold nanospheres as in situ nanometric calibration test objects onto the sample substrate and then recording force versus distance curves on these nanometric test objects. From the slope of these force curves, the substrate elasticity and thus the true heights of deposited objects can be deducted. Nano particles may be adhered electrostatically to the probe tip thus providing a well defined tip. Finally, the effective temperature on the sample surface has to be standardized, for this, the 2-dimensional crystallization of Sio2- (or other) nanoparticles at a certain concentration suspended in water hereby forming 2-dimensional opal crystals shall be exploited.

Description

An in situ calibrated AFM -Normal and lateral force standards as well as tip radius and elasticity standards in scanning atomic force microscopy

Description:

Summary:

A significant problem in scanning force and also scanning probe microscopies in general lies in standardizing/calibrating the actual probing forces and pressures respectively. Closely related is the very problematic exact characterization of the probe tips on the size scale of the (lateral and vertical) resolution expected and the cantilever spring constant on the force scales used in AFM. Here in the present invention, this standardizing shall not be attempted as usual by means of an independent technology, like for instance electron microscopy, since almost any microscopy procedure induces alterations on these minutely small (nanometric) probe tips, but measurement procedures are presented, that are based solely on scanning force microscopy and thus can be employed "in situ" in parallel. The price to pay for this is only a more elaborate sample preparation of the objects of interest on just these suggested force and tip-radius standardizing calibration test samples.

As a tip pressure standard the phase transition of a CaCO3 crystal from the calcite to the aragonite structure form shall be exploited. A similar alternative for this are pressure-induced solvation processes on calcite (or other) crystals, which expresses itself in form of accelerated migration of monoatomic steps in the [under water]-AFM-picture as compared to these atomic steps migration velocities as expected from the solvation statistics (dissolution constant). In order to conclude from the hence obtained pressure-standard to an actual probing force load standard, the tip radius (and thus the approximate effective interaction surface area) has to be known, which is later characterized by well-defined microstructures or which is fabricated "in situ" on the sample using electrochemistry. For all scanning force microscopy measurements especially also the lateral forces have to be independently quantified, also in order to be able to evaluate the forces acting vertically on the sample independently (and more accurately); this is proposed here by means of measurements on phospholipid films in the 2-dimensional "gas" to "liquid" phase. Finally the effective temperature on the sample surface has to be standardized, which is in fact hardly conventionally measurable on the length scale of a few nanometer; for this, the 2-dimensional crystallization of Si02-(or other) nanoparticles at a certain concentration suspended in water hereby forming 2-dimensional opal crystals shall be exploited.

Finally, once an abslout force calibrating "anchor point" of the force versus distance curves is obtained from the above, all apparent heights as measured by AFM have to be calibrated for sample (substrate) elasticity, which is done here by depositing well defined "hard" e.g. Snm gold nanospheres as in situ nanometric calibration test objects onto the sample substrate and then recording force versus distance curves on these nanometric test objects. From the slope of these force curves, the substrate elasticity and thus the true heights of deposited objects can be deducted as well as by simply comparing the spheres known heights with the apparent heights as measured by AFM, even without knowing the exact spring constant of the AFM cantilever, as it can simply be determined using the above force "anchor point" and the point of zero force deflection in a force versus distance curve.

These procedures can of course also be applied to biological materials.

Furthermore, for non-contact AFM, the absolut tip sample distance ought to be calibrated in situ independently of AFM-instrument calibrations, which is done for AFM in water by evaluating the oscillatory solvation forces and liquid molecule packing forces in general.

All these calibration techniques compromise exact quantitative measures, however all of them can be performed in an exact comparing fashion "in situ" (while investigating the sample of interest), where e.g. the to be micrographed molecules simply" will have to be prepared on the same calibration test sample. Other than that, these here proposed calibration techniques still provide quantitative indications for the according (exact) numerical values.

Problem: A severe problem in scanning force microscopy and generally in scanning probe micrsocopy lies in standardizing the actual probing forces and pressures in effect. Closely related is the very problematic exact characterization of the probe tips, sample elasticity and tip-sample separation on the size scale of the (lateral and vertical) resolution expected. Here in the present invention, this standardizing shall not be attempted as usual by means of an independent technology, like for instance electron microscopy, since almost any microscopy procedure induces alterations on these minutely small (nanometric) probe tips, but measurement procedures are presented, that are based solely on scanning force microscopy and thus can be employed "in situ" in parallel. The price to pay for this is only a more elaborate sample preparation of the objects of interest on just these suggested force and tip-radius standardizing calibration test samples.

State of the art: Probe tip radii for force microscopy are obviously characterized by electron microscopy; however, for doing this, the tips have to electrically conductive or have to be made conductive respectively for instance by metal coating the tips, by which they will have been drastically altered already. This is not true only for a few exceptional cases in which the the probe tips are electrically conductive anyhow already (e.g. boron doped diamond tips). Probing forces are for instance quantified indirectly by calculations using the geometry of the cantilever spring (the AFM-cantilever) and the resonance frequency of this cantilever spring using the formulae [1]: spring constant: k=t3Ew/(4L3) and resonance frequency FR=O.162 (E/p)V2t/L2 where: L...length, w...width, t...thickness of the cantilever; E...elastic modulus, p... density of the cantilever material Since however, the microtechnical fabrication process rarely provides an ideal (rectangular) cantilever geometry and often from reasons of mechanical stability a completely different triangular geometry is chosen/used and also material inhomogenuities are to be expected, the computation results are extremely error-prone and thus direct measurements are needed. A simple possibility is a direct comparative measurement with a precisely fabricated and calculated, i.e. in turn again indirectly characterized "standard spring; the same problem as above will arise: The direct characterization using this "standard spring" will be the more precise though the closer the size of this standard spring is to the size of the cantilever spring to be characterized, but if this standard spring has to be fabricated that small, its initial indirect characterization will be just as inaccurate (as mentioned above). If this standard spring is fabricated larger in size, this very simple direct comparative measurement of the bending of these two coupled cantilever springs will be very inaccurate.

Solution: The AFM shall be accurately calibrated in situ during the actual measurement performed on the actual samples of interest, especially in the vertical (z-) direction, i.e. normal tip loading forces, vertical tip sample separation, vertical (z-) piezo travel, vertical sample elasticities and viscosities and the cantilevers spring constant but also in the lateral dimensions regarding lateral tip loading forces, probe tip radii and lateral (x-y-) piezo scanner calibration. This is realized by using suitable gauge sample substrates, onto which the nanometric objects of interest under investigation are deposited while the gauge substrates and in parallel deposited nanometric gauge objects such as well-defined nanospheres allow all the in situ calibrations/standardizations needed. On the atomic length scale, such gauge substrates can be atomically flat covalent or ionic crystals, where the known lattice periodicity immediately provides the x-y-scanner calibration immediately, on the larger (several nm investigated object sizes) scale, 2-and 3-dimenasional protein crystals or ordered and/or non-periodic lattices of nanoparticles shall serve as gauge samples.

Having performed all these neccessary calibrations/standardizations, many applications are possible through these quantitative data, which only a hence in situ calibrated AFM can provide, regarding absolute (normal and lateral) loading forces, sample elasticities and viscosities, tip radii, accurate x-y-z-calibration of the scanner piezo etc.. This presents an important progress as the manufacturer given calibrations are by no means accurate enough, to support quantitative data, and furthermore change over time of usage of the instrument, and for certain quantitative measures drawn from an AFM measurement, the calibration is variable even from sample to sample, from cantilever spring to cantilever spring and of course from probe tip to probe tip.

As a tip pressure standard the phase transition of a CaCO3 crystal from the calcite to the aragonite structure form shall be exploited. A similar alternative for this are pressure-induced solvation processes on calcite crystals, which expresses itself in form of accelerated migration of monoatomic steps in the under water-AFM-picture as compared to these atomic steps' migration velocities as expected from the solvation statistics (dissolution constant). In order to conclude from the hence obtained pressure-standard to an actual probing force load standard, the tip radius (and thus the approximate effective interaction surface area) has to be known, which is later characterized by well-defined microstructures or which is fabricated "in situ" on the sample using electrochemistry. For all scanning force microscopy measurements especially also the lateral forces have to be independently quantified, also in order to be able to evaluate the forces acting vertically on the sample independently (and more accurately); this is proposed here by means of measurements on phospholipid films in the 2-dimensional "gas" to "liquid" phase. Finally the effective temperature on the sample surface has to be standardized, which is in fact hardly conventionally measurable on the length scale of a few nanometer; for this, the 2-dimensional crystallization of Si02-nanoparticles at a certain concentration suspended in water hereby forming 2-dimensional opal crystals shall be exploited. Tip calibration as well as sample elasticity calibration is performed by in situ depositing well defined nanometric test objects onto the sample substrate, where the latter needs the above pressure standard "anchor point" in the force versus distance curve with an absolut force value at a given cantilever deflection, in order to obtain absolute elasticity values even without knowing the exact spring constant of the AFM-cantilever, but assuming linearity of the cantilever spring (constant) in this small deflection range and thus using the zero deflection point as a second "anchor point" in the force curve, it can simply be determined. Hereby, the point of actual zero total force acting on the front-most tip atoms is the point of inflection (2) in the force versus distance curve on the right hand side of the force curves minimum and serves as a third "anchor point" (Fig.lb). Then one approximation has to be done, which is extrapolating the attractive force component "branch" of the force curve (Fig. lb -right hand dotted line) from the point of inflection (assuming linearity of the attractive force potential for small amplitudes). The intersection (3) of this extrapolated line with the extrapolated repulsive force component "branch" (Fig. lb -left hand dotted line) of the force curve (Fig. lb) is then the actual second anchor point in the force curve needed to derive the cantilever's spring constant, which is approximately the known (repulsive) pressure value of the calcite-aragonite transistion multiplied by the tip surface area divided by the öz (on the horizontal axis of the force curve) between this intersection (3) anchor point and the working point in the force curve where this calcite-aragonite transition is observed. This approximation may be crude, but this is a calibration of the cantilever's spring constant which can be performed in situ when using calcite as a substrate.

All these calibration techniques compromise exact quantitative measures, however all of them can be performed in an exact comparing fashion "in situ" (while investigating the sample of interest), where e.g. the to be micrographed molecules "simply" will have to be prepared on the same calibration test sample (for example calcite/aragonite/rhodochrosite, mica, DLC, lipid films and various others like HOPG, M0S2, Si/Si02). Other than that, these here proposed calibration techniques still provide quantitative indications for the according (exact) numerical values.

Solution in detail: CaCO3 occurs in 2 different crystal structures which is the well known calcite structure and the lesser known aragonite structure. The (1014)-cleavage planes of calcite exhibit an atomic lattice of oxygen atoms on the "uppermost" surface, which is a rectangular lattice with lattice constants 8.1x5.0 Angstroms, where the Ca-ions and the carbonate-"tri-stars" are arranged in a rhombic lattice of lattice constant 12.82 angströms and an angle of 101.9° [2].

In contrast, the aragonite structure exhibits an hexagonal lattice with lattice constant 5.8 Angstrom on the "uppermost" surface of the (001)-cleavage plane [2].

Fig. la shows an approximately atomically resolved AFM-picture of a calcite crystals cleavage plane, recorded in water at room temperature (here about 20°-23°Celsius). The expected rectangular lattice structure (lattice constant 8.1x5.O Angstrom) of the oxygen atoms [3] is recognizable almost in the whole image, however with an exception: In the lower left quadrant there is a clearly visible hexagonal lattice having a sharp boundary with a lattice constant of 5.0-5.5 Angstrom, which -within the calibration tolerances of scanning force microscopy -corresponds well to the 5.8 Angstrom of the aragonite crystal structure. The tips loading force of the force microscope for this image is roughly of order O(1)x10"N, as is shown in an AFMs so-called force distance curve (Fig. lb): The working point for this image lies just closely on the left side of the minimum of the curve (arrow (1)).

Simply speaking the point of inflection on the right side of the force versus distance curve roughly corresponds to the zero loading force 0x10"N of the front-most tip atoms, whereas closely on the left side besides the minimum (arrow (1)), where stable imaging in feedback mode [3] is possible, the repulsive load on the front-most tip atoms amounts then to roughly 1 to a few 10"N. The latter is explained in detail in [3]. Furthermore, it is known [4], that at a pressure of roughly 6kbar at a temperature of roughly 20°Celsius, the CaCO3 can undergo a phase transition from the calcite to the aragonite structure initiated by the (large) pressure, which has most likely occurred here and was observed in situ, since: At the interaction surface area of size of one tip atom (roughly 1 Angstrom) 6kbar would correspond to a tip loading force of roughly 6x10'2N, at an interaction surface area of a few tip atoms (Si/Si02, roughly loAngstrOm2) which is -as concluded from the lateral resolution obtained -likely here, these 6kbar correspond to a loading force of 6x10"N, hence is of an order of magnitude of O(1)x10"N. This thus means, that the here for the scanning force microscopy used imaging forces correspond coincidentally roughly rather exactly to the pressures, which are neccessary to induce the phase transition of the calcium carbonate from the calcite to the aragonite crystal structures. The value of 6kbar from [4] of course also is only an error prone averaged (dependent on the measurement procedure) measure, but a physical phase transition always occurs at the exact same pressure and temperature, depending on the underlying theory (Landau theory of phase transitions [5]). Often, there is pressure ranges -for interacting gas particles, i.e. real gases, especially for 2-dimensional crystals -across which a phase transition occurs, namely especially if in contaminated systems several/many (re-)crystallization cores originate and the crystal grows or melts slowly across a whole pressure and/or temperature range. Here in Fig. la it is in fact in 2 dimensions looked into a tiny crystallization core (roughly 100 atoms), thus this core most likely has originated instantaneously, because if this core would have slowly originated in turn from (even smaller) single crystallization cores, it could have only been single atoms.

Hence, it is assumed here, that this aragonite core surrounded by a calcite lattice has instantaneously originated at the here present tip loading force of roughly O(1)x10"N at room temperature (roughly 20°Celsius) and thus, this phase transition process represents a pressure standard for the here for this measurement used specific probe tip geometry, which cannot be superceeded in terms of accuracy, just is very difficult to be evaluated quantitatively, but can be perfectly used as a comparative measure (i.e. a pressure standard for AFM).

Since it is very difficult, to "catch" just this phase transition from calcite to aragonite during the force microscopy imaging, an alternative is here furthermore suggested for the standardization of the tip loading forces. This method is less accurate, since 2 processes are mixed, namely the (in the case of calcite very slow) crystal dissolution process of the CaCO3 in water in equilibrium and the here exploited pressure induced abrasive process of single (atomic) crystal steps.

Figs. 2a and 2b show "migrating" monoatomic steplines on the cleavage plane of a calcite crystal, where because of the scan direction from left to right in the force microscopy it can here be clearly concluded (explained in [3]), that an abrasive process is occurring, and thus the lower terraces are spreading/extending. The spreading/extending of the lower terraces, however, could be as well due to a crystal dissolution process in water. Nevertheless, here an abrasive process induced by the probe tip's loading forces is more likely, since even after hours of measurement time, by which a dissolution equilibrium should long have been settled, never any growing" monoatomic steps were observed, always only steps being "wiped away. By means of this in situ imaging of such wiping away of atomic steps a loading force regime is determined (standardized) in a narrow range: The loading force is so small, that monoatomic steps can be imaged at all [with atomic lateral resolution], but already that large such that the bond forces of the atoms/molecules at the step edges can be overcome (the latter mainly by the lateral forces exerted by the imaging tip). Quantifying these forces numerically by means of a measurement is even more difficult than in the above case of calcite-aragonite phase transition, especially since lateral forces are involved (which would have to be also standardized -see below), but nevertheless, the in situ imaging of migrating monoatomic calcite crystal steps again represents a useful comparative measure (i.e. a comparative standard) for the loading forces in scanning force microscopy. As long as no aragonite crystals as in Fig 1 become visible in the images, it can be assumed, that the loading pressures are smaller than the 6kbar (at 20°C), but larger than the now by means of this procedure (Fig. 2) specified threshold value though.

The smallest repulsive loading force is then reached, if a monoatomic stepline can be scanned imaged in feedback mode [3] multiple times (Fig. 2c).

The lateral forces in scanning force microscopy can be normalized/narrowed down by the following measurement: Fig 3a shows an AFM-image of a phospholipid film (DMPC) transferred onto mica via Langmuir-Blodgett technique in the 2-dimensional gaseous to Iquid phase (at about 5mN/m 1-dimensional "pressure"). Holes and scratches are visible in the thin film and a few crystalline elevated islands. Figs. 3b now show the pure lateral force image of the same sample location of the lipid film transferred onto mica, in the left image the fast scan direction is from left to right and in the right image it is from right to left, exactly as in Figs. 3a; the contrast reversal can be clearly recognized in the lateral force images. Since any "height-plateaus" are feedback-controlled away optimally here, this means, that these two lateral force images are pure true friction force images, lateral deflections of the cantilever's probe tip caused by elevated "height" structures on the sample are most largely eliminated. In the friction force images the (elevated) islands are visible only in form of very faint edges. Fig. 3c now represents a force microscopic crossection cycle ("forward" and "backward" traces) of the friction scan of these images (Fig. 3b), which was quantitatively measured after elaborate calibration using the cantilever's torsion elastic modulus. Hence, it can be concluded from Fig. 3c, that the difference between the AFM-friction signals between mica (in the holes) and the lipid film amounts to roughly 0,024 Volts, which after elaborate calibration of the instrument (0.1V detector signal corresponded to 1.7x103° tilt or torsion of the cantilever spring respectively) leads to a friction force difference of roughly 1.9x107N; hereby used was the formula M=x=2/3L2k4, where M...torsion momentum, L...cantilever length, k...spring constant for the vertical deflection, ...torsion angle, X...torsion stiffness of the cantilever spring, and the formula F= x(ctilh), where h...height of the probe tip. Differences in the friction force between the gas/liquid phase (before the transfer onto the mica surface, afterwards the phase state is fixed/"frozen" on the solid substrate) lipid film and the crystalline islands was practically not measurable. The friction forces on the lipid film itself can also be approximately quantified, because the difference between the fast forward and backward scan amounts to roughly 0.Ol6Volts, which means that the absolute friction force signal is approximately 0.OO8Volts, which -according to above formulae -leads to a friction force of roughly 0.6x107N. Accordingly, the friction force on the mica surface itself comes up to 2.5x107N.

This method for measuring frictional forces on lipid films provides multiple information, since different phase states of those lipid films -which have been extensively studied in the literature -are present here as well as the mostly significantly higher friction on the solid substrate, which eventually provides several control data for the correct procedure for the here proposed friction force quantification. This relatively simple measurement method in the present invention is, however, generally applicable to every other sample as well, important for the friction quantification is only the presence of plateau structures.

For all quantitative measurements in AFM, the precise characterization of the physical and chemical properties of the probe tip is furthermore essential. The primary issue in the normal cases for high but not yet true atomic resolution is of course the tip radius. The latter will be not only quantitatively determined in the following measurements but can also be (crudely) adjusted for instance electrochemically. Fig. 4 shows a calibration sample comprising Snm Au-nanoparticles, whose apparent size in the AFM image allows to conclude to the tip radius of the probe tip. Furthermore, often one (or a few) of these nanoparticles stick to the probing tip and thus forms a very good (since very small) effective imaging tip. Fig. 5 shows a series of images, in which a small 500nm wide gold conducting lead is imaged using a Si/Si02 tip. This probe tip consists of electrically conducting (doped) crystalline silicon, and only at the "untouched" tip surface there is still insulating Si02. After short time of scanning this tip across a hard (here for example Si02-) surface, this frontmost Si02-layer at the very end of that silicon tip will be "milled" away and the electrically conductive Si touches the sample surface. Now, if roughly -12V is applied to the probe tip (cantilever spring and probe tip consist of conducting silicon, they are only oxydation-coated by 5i02), it can be recognized, that the tip gradually gets longer and longer from image to image (the still SOOnm wide gold lead appears narrower and narrower and its edges' appearance becomes sharper and sharper). Upon a sudden polarity reversal to +12V, the whole process immediately reverses and the grown tip disappears at once. Due to the size of the step, the tip radius in the "sharp state" can be approximated to roughly <lOnm. The conducting lead was connected to OVolt during the entire measurement, while the lower end of the lead was connected to earth ground, i.e. it was connected to the IVC -hence, on the probe tip supposedly gold had grown, electrochemically in the water film which is always present on samples in ambient air.

For many processes, which can be imaged by AFM in situ, the temperature on the immediate sample surface during the measurement is an important issue. An attempt for obtaining a comparative measure for this temperature in situ is presented in Fig. 6. Here, Snm-5i02-nanoparticles suspended in water were prepared in water on a mica or 5i02-surface respectively. At a concentration of typically a few llGramms per milliliter and at room temperature (about 23°C) these quartz nanoparticles form a 2-dimensional crystal, a 2-dimensional opal so to speak. This crystallization process could serve as a temperature standard, depending how perfectly these crystals form and how sudden this crystallization occurs -here in Fig. 6 preliminary experiments are shown, which prove the principle; however, more accurate measurements are of course needed, in order to determine the parameters exactly.

Eventually, all AFM results have to be corrected for sample elasticity concerning the heights of the imaged structural details. For instance the Snm Au spheres imaged on the soft and elastic polyimide in Fig. 4 appear too high by a factor of 2-4, imaged with overall attractive force setting of the AFM. It is noted that convolution of the tip over the nanospheres makes the spheres also appear larger in diameter laterally, but there, only the true height of the spheres goes in, the apparent height (i.e. the portion artificially increased by substrate elasticity) does not contribute to the apparent enlarged lateral sphere diameter in the AFM images. In order to obtain absolute values -at least comparative standards -for the substrate and sample elasticity, the calcite aragonite transition pressure standard "anchor point" in the force versus distance curve is needed, which can be achieved by simply depositing small (Snm) "hard" nanospheres onto a calcite substrate; hereby it is of course a challenging effort, to measure the apparent heights of the deposited nanospheres simultaneously with observing the calcite aragonite lattice transition on the true atomic scale. But if successful, the force versus distance curves can be quantitatively calibrated even without known the exact spring constant of the AFM cantilever, as it can simply be determined using the above force "anchor point" and the point of zero force deflection in a force versus distance curve, since the measured slope in the force versus distance curve gets two anchor points, the above force standard and the zero force deflection point -always assuming linearity of the cantilever spring and the elastic sample deformation in this small amplitude regime.

Generally, in a constant force SFM-image, a small spot on the sample, which is flat but much softer than the surroundings will obviously appear as a hole at overall repulsive AFM-setpoint (as in Fig. 8) and as a bump if the AFM cantilever is being pulled (overall attractive setpoint). Usually, the feedback polarity allows stable imaging obviously only up to the minimum in the force curve (Fig. lb) of the there (attractive) interaction force. Now, the harder the effective "combined" spring constant keff of lever and sample keff = k](1+ kIksiocai) -at maximum keffm= min(kL, k5iocai) -the more closely the force setpoint of the AFM can be adjusted from the left towards that minimum and still allow stable imaging, i.e. inspite of thermal noise or acoustic perturbation of the lever or variations of k5iocai during scanning of the tip. Thus, a stiffer lever's minimized force setting can be pulling back the tip more strongly on average and the artificial heights will increase, roughly scaling with keff and proportional to 1/k'iocai: A z-"offset" originating solely from long-range attractive forces elastically deforming the sample surface is added to the usual topography map, which changes abruptly here when the large' (20 nm curvature radius) probing tip is moving on top of the small' (2.5 nm radius) sphere accompanied by an abrupt change (decrease) in effective local sample spring constant k5iocai (1/65 of the effective contact area I). Regarding this contact area, also the asymmetry (mica, Figs. 7 and 8) between substrate expansion and indentation should be noted. Since the sample is compressed and expanded simultaneously (overall atrractive force setting while tip's front end is still pressing -Fig. 7c), k5iocai is a very complicated function of the elastic tensor of the substrate material, and is most likely not constant at all at the sample deformations relevant here. However, a slight "lift-off" of the spheres or the tip at maximum attractive force setting cannot be ruled out completely.

The table in reference [6] further lists the observed values for h (height) and OD (outer diameter) of the 5 nm Au-spheres, now deposited on mica recorded in distilled water also with three different AFM cantilevers (force setpoint "overall attractive" as usual). h is found too large by up to about a factor of two for the hardest (kL=0.SN/m) lever (note the dependence on the tip radius) scaling down to approximately the correct [7,8] value for the softest lever (kL=0.03N/m). Fig. 7 shows representative force curves on the spheres and on the mica in between. Note also here the "kink" in the force curve on the spheres, most likely reflecting the transition from the "soft" local spring constant of the sample, when the "small" 5 nm Au-sphere is determining the substrate deformation to the indentation caused by the "large" 20 nm tip, when the Snm Au-spheres are completely pressed into the mica substrate. From two single force curves k5iocai0.05 N/m (for the 0.5 N/m lever) and k5[ocaI0.06 N/m (for the 0.1N/m lever), shown in the Fig. 7, can be extracted for the case of the indentation with the Snm spheres, disregarding statistical variations. It is noted that a kink in the force curves can also be observed, if a tip is contaminated for instance when used twice in liquid, i.e. the tip has dried up once; however, in that case, the force curve does not vary significantly while scanning laterally and the adhesion forces (jump-in-jump-out hysteresis) is about one order of magnitude larger than shown here. Repeated rehydrating of the samples was possible though.

Hence, small (5 nm) objects can appear significantly too high in AFM images, if the tip radius is larger (here about 20 nm) and if the working point for imaging with not too soft levers (kL�=0.1 N/rn) was always kept on the "overall attractive side" (illustration in Fig. 7c). The measured apparent heights h were found to systematically decrease with the lever's spring constant kL, ranging here from 0.03-0.5N/m.

Fig. 8 shows the same 5 nm-spheres on mica as before, however now, the longer-range attractive forces between tip and sample were found to be literally switched off by adding aqueous 2.5-5 mM NiCI2 as an imaging liquid. The absence of an attractive portion in the force curves on the bare mica surface next to the spheres requires a force setpoint for stable AFM imaging in the overall repulsive regime. Much stronger adhesion of the spheres to the substrate in NiCI2 environment as compared to pure H20 is observed, the spheres hardly ever detached during imaging. At minimum force load, all three levers now show practically the same correct [7,8] sphere height of about 4.1-4.4 nm (table in reference [6]). These measured heights reduce (reversibly I) with increasing repulsive load (about + 4 nN above minimum in Fig. 8a II) as expected. The force curves on as compared to off the spheres show again a jump in local sample elasticity from "hard" to "softer" (kSiocai 5.8 N/rn) when simply indenting the surface via the 5 nm-spheres instead of the 20 nm tip directly. Finally, on a "hard" substrate (oxydized Si-wafer), the sphere heights (table) were again measured roughly correctly [7,8].

Instead of metallic nanospheres also biological particles like viruses, bacteria and cells can be deposited on -in comparison to them -harder solid substrates or mounted otherwise and their intrinsic elasticity itself can be evaluated using the method decribed above, i.e. recording force scans on such particles, all measured values calibrated for absolute values or for comparative standards with the methods suggested above. Figs. 9 show vaccinia (cow pox) virus particles on a 5i02 substrate (from [9, 10]), and just like on the Au-nano spheres, force versus distance curves can be recorded and from their slope and curvature in the contact regime the elastic constants of these virus particles can be derived. Just here, the situation is having a "hard" substrate and softer and elastic (biological) deposited nanoparticles instead of vice versa in the above, where the substrate is elastic and the metallic nanospheres are hard. The same holds for bacteriae, where a high resolution scan (showing the protein lattice) is shown in Fig.10 on the surface of a (cigar shaped) bacillus coagulans (from [9]), on whose surface force scans as well as frequency spectra can easily be recorded. Fig. 10-I shows a same cell of bacillus coagulans, but now here antibodies against the cell wall proteins of the bacillus coagulans were added to the imaging liquid. It is clearly visible that a molecular "contamination layer1' is attaching to the regular periodic lattice of the cell surface, which by increasing the AFM's repulsive imaging force (at the front end of the tip) gets wiped away again. From the hereby arising lateral forces, which can be calibrated as described above, the binding forces of the antibodies can be estimated to be about 109-10'°N. Fig. 10-lI ([9,13]) shows a fragment of the bacterial surface layer (S-layer) of bacillus coagulans, where also antibodies were added to the imaging buffer solution and the attaching molecular aggregates are also visible. Fig. 10-Ill ([9,13]) shows for comparison this bacterial S-layer fragment in high (molecular to submolecular) resolution.

Through these measurements, antibody binding forces can be quantitatively estimated but simultaneously, the proteins to which these monoclonal antibodies are attaching can be identified and/or labelled on the viral, bacterial or cellular surface, since they are imaged at the same time while approximately measuring these forces. Monoclonal antibodies can be prepared with attached flurescence marker molecules or nanoparticles attached, such that specific proteins for instance on a viral or bacterial or cellular surface can be labelled for further e.g. spectroscopic or optical microscopy investigation.

Fig. 11 now shows a frequency spectrum of the AFM-cantilever in the acoustic regime as measured with the probe tip in contact with the surface of a monkey kidney cell held by a micro pipette (from [9, 10]), where Fig. lib shows the frequency spectrum of the mere pipette and Fig. ha the complete spectrum with the cell mounted to the tip of the pipette; two mechanical resonances that can thus be relatively clearly attributed to the cell only are well visible. Such frequency modulation techniques can also be used for imaging as is shown in Fig. 12 (from [9,10]. The cell is vibrated with 2 kHz at an amplitude of about 2nm and the lockin signals of amplitude and phase (respectively the lockin signals in phase and 90° out of phase with the reference driving signal) are displayed in the images as a function of lateral tip position (Fig. 12 b,c), while Fig. 12a is showing the mere averaged constant force signal while modulating. Both "amplitude" and "phase" (in phase and 90° out of phase of the driving signal) lockin signals approximately are a measure of the local elasticity and viscosity of the cellular surface. These elasticity data of biological specimen and organelles can be used to characterize and classify various cells, bacteriae and viruses, distinguish healthy from sick cells and perhaps even, e.g. using ultrasound therapy to distroy for instance viruses in the blood stream or other physiological fluids and environments, similar to blood-washing in the case of kidney insufficience. The technique of holding a biological cell for successful AFM imaging by a micropipette has first been described in [11].

Finally, for non-contact AFM, it is very imprtant to be able to quantify the exact tip sample separation in the non-contact regime before the tip ever gets in contact with the sample, as even by a first touch, the sharp tip end might already be destroyed. Usually, the tip sample distance is calibrated via the z-piezo calibration by recording a force versus distance curve well into the repulsive regime, but as mentioned, this might already destroy a high quality probe tip, at least might contaminate it already. Thus, in a liquid, a new method is here presented using the oscillatory solvation forces and generally liquid molecule packing forces always present in a liquid. Fig. 13 now shows a force versus distance curve recorded by AFM in water on a calcite crystal. The (horizontal) non-contact part of this force curves show clear oscillations with a periodicity of roughly 3.2 Angstroms, which originate from packing effects of the liquid, here a very dilute solution of calcium carbonate. So the the tip-sample distance can simply independently of AFM-instrument calibrations and in absolute values be calibrated by counting these oscillations like an atomic ruler for the z-position of the tip. Their periodicity will simply depend on the size of the dissolved ions or in pure water, it will simply be approximately the size of the water molecules (about 0.1 nm) in direction of their dipole moment plus the hydrogen bond length (0.l8nm). Of course, to avoid tip damage, these force curves then have to be gently driven into to the oscillatory solvation force regime just before the tip gets in contact with the sample. The same holds for hydrophobic liquids, where also oscillatory packing forces will arise between tip and sample upon tip sample approach. Oscillatory packing and solvation forces are well described in [12].

Figures: Fig. la: Pressure induced calcite-aragonite crystal phase transition imaged by AFM in water at room temperature.

Fig. ib: (while scanning across a calcite cleavage plane) averaged force versus distance curve in scanning force microscopy in water at room temperature.

Fig. 2a and b: "Migrating" crystal steps [on calcite] (Crystal dissolution process versus pressure induced wiping away of the steps) in water at room temperature.

Fig. 2c: Calcite crystal steps at imaging conditions optimal for the repulsive feedback mode, i.e. with calibrated heights in the [pseudo-] 3D-image in water at room temperature.

Fig. 3a: Normal force image of DMPC (islands and holes, "gaseous" to "fluid" 2-dimensional phase), both horizontal scan directions in air at room temperature.

Fig. 3b: Lateral force image of DMPC (islands and holes, "gaseous" to "fluid" 2-dimensional phase), both horizontal scan directions in air at room temperature.

Fig. 3c: Cross section of the images in Fig. 3b with quantified friction forces/lateral pressure forces Fig. 4: Snm Au-nanoparticles on poly-imide (from [6]), AFM image recorded in water at room temperature.

Fig. 5: Voltage induced tip radius shaping via electrodeposition in ambient conditions.

Fig. 6: 2-dimensional crystallites of opal as a temperature and concentration standard for nanoparticles, imaged in water at room temperature.

Fig. 7: a: 5 nm Au-spheres [7,8] on mica, in water (kL=0. iN/rn), force setpoint overall attractive. b: Force vs. distance curves on and off the spheres (kL=O.i N/in). ); I denotes the jump-out point, II the jump-into contact point. At III, the slope of the force curves switches". Above that force, most likely only the tip-radius itself deterrnines the spring constant for the indentation, and not the delicate track geometry anymore. III is the transition of kSiocai from defonnation through the small 5nrn sphere (soft) to that through the larger (2Onm) tip (stiffer) i.e. at III, the sphere has most likely been "pressed into" the substrate completely. C: Illustration for sample deformation at overall attractive force setpoint, while the tip's front end is still being pressed against the sample surface. (from [6]).

Fig.8: a: 5 nm Au-spheres [7,8] on mica, in 2.5-5 mJVI NiC12 (kL=O.1 N/rn). I) at mninirnurn repulsive force setpoint. II) at repulsive force setpoint increased by about 4 nN. Heights reduce and increase reversibly when cycling the force setting. b: Force vs. distance curves on and off the spheres (kL=O.5 N/rn). Characteristic points I, II, III as in the Figs. above, however, III is now clearly on the overall repulsive side (sample indentation) whereas in the Figs. I e and 3, III was located close to the transition from overall attractive to overall repulsive force setting (from [6]).

Fig. 9: Vaccinia virus particles on a Si02 substrate imaged by AFM in various magnifications up to almost submolecular resolution (ring like molecules denoted by the arrows) (from [9,10]).

Fig. 9a: high resolution (molecular to even submolecular resolution) frames c and d of Fig.9, enlarged and with the viral envelope proteins indicated with dotted lines.

Fig. 10: a: Surface of a bacterial cell (bacillus coagulans) imaged by AFM in water at molecular resolution, the protein lattice is clearly visible, even a wedge dislocation (Fig. lOb) as would be expected on the cigar shaped cellular particle. (from [9]). The lower frames are the same as the upper frames, just with the (short range) imperfect cell wall protein ordering indicated with lines.

Fig. 10-I: As in Fig. 10, but now under addition of polyclonal antibodies to the imaging liquid. Images a-x again show the periodic protein lattice of the bacetrial cell wall in the background; now in image frame y the scan area was shifted by about half an image area to the bottom, such that in the upper image half a region becomes visible, which the probing tip had not touched before and there, clearly a deposited contamination layer is visible, which through continuous scanning at imaging forces of about 109-10'°N gets wiped away again and the underlying protein lattice of the bacterial envelope becomes visible again, as demonstrated in image frame z. From this, also the binding forces of the antibodies can be roughly estimated to be of this same order of magnitude (from [9]).

Fig.1O-II: As Fig. 10-I, but instead of whole bacteria cells (bacillus coagulans), only S-layer sheets of the same bacteriae are imaged by AFM in buffer solution under addition of antibodies, where again slight increase of the tips loading force begins to wipe away the attached molecular aggregates (from [9,13]).

Fig. 10-Ill: as Fig. 10-Il, S-layer sheets of bacillus coagulans, but without addition of antibodies to the imaging solution, the ordered protein lattice is clearly visible in high (molecular to even submolecular) resolution (from [9,13])..

Fig. 11: a) (II) Frequency spectrum (average of 100 spectra) of the cantilever when the probe tip is in contact with the monkey kidney cell which is held by a micropipette in aqueous solution, while this pipette had been excited by a white noise signal of an rms amplitude of about 6 nm. b) (I) same as a) but with the tip in contact with the end of the pipette directly (from [9,10]).

Fig.12: AFM images on the surface of a monkey kidney cell in aqueous solution, while the pipette is driven in the z-direction with 2 kHz at an amplitude of about 2nm. A) constant force image (averaging out the 2nm drive amplitude in a very slow scan); B) amplitude signal from the lockin amplifier (in phase with the drive signal) displayed as a function of the x-y scan -corresponding to local elasticity; C) as B) just the phase signal (900 phase shifted with respect to the drive signal) from the lockin amplifier is displayed corresponding to local viscosity.

Fig. 13: Oscillatory solvation forces as shown in an AFM-force versus distance curve, here recorded on a calcite crystal in an extremely dilute calcium carbonate solution (from [9]) at room temperature.

Legend: (1) Working point of the scanning force microscopy in repulsive feedback-mode, at which roughly a repulsive force of O(1)x10"N is acting on the front-most tip atoms.

(2) Point of inflection in the force versus distance curve during an AFM-imaging of calcite, at which the front-most tip atoms are sensing roughly the zero force, i.e. 0x10"N.

(3) Intersection of the extrapolated lines of the attractive and repulsive force component "branches" of the force versus distance curve, which can be considered as an approximated (virtual) zero-point for the repulsive force component acting on the front most tip atoms.

(I) "jump out of contact-point of an AFM force scan (II) "jump into contact-point of an AFM force scan (III) is the transition of kSiocai from deformation through the small 5nm sphere (soft) to that through the larger (2Onm) tip (stiffer) i.e. at III, the sphere has most likely been "pressed into" the substrate completely, represented by the steeper slope. The shallower slope represents the elasticity of the indentation of the substrate by the 5nm sphere.

Abbreviations: AFM -atomic force microscopy HOPG -highly oriented pyrolytic graphite DLC -diamond like carbon SFM -scanning force microscopy kL -spring constant of the AFM-cantilever spring k5iocai -local (with respect to the AFM's lateral resolution capability) spring constant of the sample substrate References: [1] A. Heuberger (Ed.) "Mikromechanik", Springer 1989.

[2] R.W.G. Wycoff, "Crystal structures" (Wiley, NY 1964).

[3] F. Ohnesorge, G. Binnig, Science 260, 1451 (1993); F. Ohnesorge, Dissertation, LMU Munich 1994.

[4] W. Kleber, "Einfuhrung in die Kristallographie", 11. edition (1971), VEB Verlag Technik Berlin, pp. 185.

[5] Landau Theory of phase transitions.

[6] F. Ohnesorge, R. Neumann, Europhys. Lett. 50(6), 742-748 (2000) [7] In all cases where the correct sphere heights should be measured (soft lever, hard substrate, switched-off long-range attraction), instead of the manufacturer given expected average of 5.2 nm [8], a 20 % smaller average is found. One reason for this additional systematic error may simply be, that during preparation and imaging, smaller spheres have a higher probability of adhering sufficiently strongly to the surface.

[8] Ted Pella Corp, Redding, CA, USA: mean diameter of Au-spheres: 5.22nm +1-0.9 nm.

[9] F. Ohnesorge, Dissertation, LMU München, (1993) [10] F.M. Ohnesorge et a!, Biophysical Journal 73, 2183 (1997).

[11] W. Häberle et al., Ultramicroscopy 42-44, 1161(1992).

[12] J. lsraelachvili, Surface and Intermolecular Forces, 2nd ed., Academic Press, London 1992.

[13] F.Ohnesorge et. al., Ultramicroscopy 42-44, 1236-1242 (1992).

An in situ calibrated AFM -Normal and lateral force standards as well as tip radius and sample elasticity standards in scanning atomic force microscopy Summary: A significant problem in scanning force and also scanning probe microscopies in general lies in standardizing/calibrating the actual probing forces and pressures respectively. Closely related is the very problematic exact characterization of the probe tips on the size scale of the lateral and vertical resolution expected. Here in the present invention, this standardizing shall not be attempted as usual by means of an independent technology, like for instance electron microscopy, since almost any microscopy procedure induces alterations on these minutely small nanometric probe tips, but measurement procedures are presented, that are based solely on scanning force microscopy and thus can be employed "in situ" in parallel. The price to pay for this is only" a more elaborate sample preparation of the objects of interest on just these suggested force and tip-radius standardizing calibration test samples. As a tip pressure standard the phase transition of a CaCO3 crystal from the calcite to the aragonite structure form shall be exploited. A similar alternative for this are pressure-induced solvation processes on calcite (or other) crystals, which expresses itself in form of accelerated migration of monoatomic steps in the under water-AFM-picture as compared to these atomic steps' migration velocities as expected from the solvation statistics (dissolution constant). In order to conclude from the hence obtained pressure-standard to an actual probing force load standard, the tip radius (and thus the approximate effective interaction surface area) has to be known, which is later characterized by well-defined microstructures or which is fabricated "in situ" on the sample using electrochemistry. For all scanning force microscopy measurements especially also the lateral forces have to be independently quantified, also in order to be able to evaluate the forces acting vertically on the sample independently and more accurately; this is proposed here by means of measurements on phospholipid films in the 2-dimensional "gas" to "liquid" phase. Finally the effective temperature on the sample surface has to be standardized, which is in fact hardly conventionally measurable on the length scale of a few nanometer; for this, the 2-dimensional crystallization of Si02-(or other) nanoparticles at a certain concentration suspended in water hereby forming 2-dimensional opal crystals shall be exploited. Finally, once an absolute force calibrating "anchor point" of the force curves is obtained from the above, all apparent heights as measured by AFM have to be calibrated for sample (substrate) elasticity, which is done here by depositing well defined "hard" e.g. Snm gold nanospheres as in situ nanometric calibration test objects onto the sample substrate and then recording force versus distance curves on these nanometric test objects.

From the slope of these force curves, the substrate elasticity and thus the true heights of deposited objects can be deducted as well as by simply comparing the spheres known heights with the apparent heights as measured by AFM, even without knowing the exact spring constant of the AFM cantilever if combined with the force calibration methods above, as it can then be derived independently. These procedures of course can also be applied to biological materials. Furthermore, for non-contact AFM, the absolut tip sample distance ought to be calibrated in situ independently of AFM-instrument calibrations, which is done for AFM under liquid by evaluating the oscillatory solvation forces and liquid molecule packing forces in general. All these calibration techniques compromise exact quantitative measures, however all of them can be performed in an exact comparing fashion "in situ" (while investigating the sample of interest), where e.g. the to be micrographed molecules "simply" will have to be prepared on the same calibration test sample.

Other than that, these here proposed calibration techniques still provide quantitative indications for the according (exact) numerical values.