This invention relates to an atomic force microscope for profiling the properties of a surface at nanometer resolution and for probing the properties of individual molecules attached to that surface.
The atomic force microscope utilizes a sharp probe which may be precisely positioned above a surface. The probe is attached to a positioning device via a soft (spring-like) cantilever. Interaction with the surface is indicated by motion of the probe end of the tip with respect to the driven end of the cantilever. In its common use for mapping the topography of a surface, this deflection is held constant by adjusting the probe to sample distance as the probe is scanned over the surface.
The interaction between the probe and the surface is of considerable interest in its own right. By sweeping the tip back and forth from the surface and monitoring the deflection of the probe relative to the driven end of the cantilever, so called force curves may be mapped out as taught by Elings et al., U.S. Pat. Nos. 5,224,376; 5,237,859; and 5,329,808. These curves are valuable both for setting the operating point of the microscope and for mapping the elastic properties of a surface.
The scheme for obtaining force curves according to the prior art is set out in FIG. 1A. A piezoelectric actuator 1 is used to sweep the stiff end of a cantilever 2 by some amount (labeled X.sub.D) toward the sample S in FIG. 1A. The flexible cantilever 3 (having a stiffness k.sub.T) bends as the tip 4 indents the sample, represented in FIG. 1A by a spring 5 of stiffness k.sub.s. As a consequence, the displacement of the tip, X.sub.T, is generally less than the displacement of the stiff end of the cantilever, X.sub.D. This situation is represented in FIG. 1B which shows the arrangement of the two springs corresponding to the cantilever (k.sub.T) and the sample (k.sub.S) together with the displacement of the actuator (X.sub.D) and the tip (X.sub.T). In equilibrium, the force, F, along the mechanical path must be equal at all points and, far below resonant frequencies where the cantilever and sample behave as Hookean springs: ##EQU1## Here k.sub.eff is an effective spring constant describing the relationship between displacement and applied force at the point at which the force is applied. From Equation (2) we see that ##EQU2## Thus, in this method for measuring the stiffness, the effective spring constant is equivalent to a series combination of the two springs represented by k.sub.S and k.sub.T. In such a relationship, the weakest spring dominates the spring constant of the combination. Thus, this prior art scheme is of limited use for measuring the stiffness of soft samples, unless a correspondingly soft (i.e., having greater flexibility) cantilever is used. The use of soft cantilevers is often precluded by their increased propensity to jump into contact with the surface.
To make matters worse, the prior art method relies on sweeping either the entire sample up towards the tip, or the entire tip assembly (and scanning tube) down towards the sample. These massive components have a low resonant frequency by virtue of their mass, so this method is intrinsically slow, a disadvantage when it is desirable to obtain force curves rapidly.
A further disadvantage of this method of obtaining force curves lies with the piezoelectric material that is used as the displacement actuator. This material suffers from a considerable hysteresis. On reversing the direction of the applied voltage, the cantilever displacement usually lags the displacement at the same applied voltage but reached by scanning from the opposite direction. This is illustrated in FIG. 2 which shows a typical force curve. This is a plot of cantilever displacement versus distance moved towards or away from the surface. When the tip is far from the surface, the cantilever is not deflected so the plot is a flat horizontal line 6. When the tip is close enough to the surface, it often snaps uncontrollably into the surface (depicted at 7), remaining in contact and being pushed up by the surface (line 8). When the direction of the sweep is reversed, the tip comes down with the surface (line 9), but the scan is displaced by some amount .DELTA.z along the horizontal axis owing to piezoelectric hysteresis. The cantilever tip pulls off the surface again (depicted at 10), further displaced from the original contact point by adhesion between the tip and surface. The amount of the hysteresis depends upon the sweep rate and other characteristics of the piezoelectric actuator and its history. It is a poorly characterized quantity and the source of considerable uncertainty in obtaining force curves.
Another method for driving the tip has been described by Lindsay et al., "Scanning Tunneling Microscopy and Atomic Force Microscopy Studies of Biomaterials at a Liquid-Solid Interface," J. Vac. Sci. Technol. 11:808-815 (1993); Lindsay, U.S. Pat. No. 5,513,518; and Lindsay, U.S. Pat. No. 5,515,719; and also by Florin et al., "Atomic Force Microscope with Magnetic Force Modulation," Review of Scientific Instruments 65:639-643 (1993) and O'Shea et al., "Atomic Force Microscopy of Local Compliance at Solid-Liquid Interfaces," Chemical Physics Letters 223:336-340 (1994). In this approach, a force is applied directly to the tip (as opposed to the rigid part of the cantilever holder) by fixing a magnetic particle or film on the tip and using an external magnetic field to drive the tip. This is illustrated schematically in FIG. 3A. Here, the actuator 1 is held in a fixed position, as is the rigid part of the cantilever assembly 2. The magnetic particle or film 12 is acted on by an external magnetic field so to exert a force F on the end of the flexible cantilever 3, pushing the tip 4 into the sample represented by the spring 11 of stiffness k.sub.S. In this case, referring to FIG. 3B, both the stiff end of the cantilever and the sample are fixed so EQU F=(k.sub.S +k.sub.T)X.sub.T =k.sub.ef X.sub.T (4)
where EQU k.sub.eff =k.sub.T +k.sub.S. (5)
So, in this case, the cantilever and sample act as springs in parallel. This method has the advantage that a soft surface (k.sub.S small) does not lower the resonant frequency of the assembly appreciably. Furthermore, because only the tip is being moved, and this has by far the smallest mass of all the microscope components, rapid operation is possible.
There are two methods for driving the tip magnetically. In one (FIG. 4A) a particle of a magnetic material 12 is placed on the end of the cantilever 13 with its magnetic moment M aligned along the direction of desired motion. A magnetic field gradient, dB/dz, 14 is applied along the same direction as the magnetic moment, resulting in a force, F.sub.z along the z direction ##EQU3## A second geometry (FIG. 4B) utilizes a film having its magnetic moment M (15) perpendicular to the direction of desired motion. A magnetic field B is applied in the direction of desired motion 16 so that a torque, n is generated on the cantilever according to EQU n=M.times. (7)
and, in the geometry shown, this is equivalent to a force on the end of the cantilever in the direction of desired motion F.sub.z given by ##EQU4## where l is the length of the cantilever. This latter method of operation has been described by Lindsay, U.S. Pat. No. 5,515,718 and verified by Han et al., "A Magnetically-Driven Oscillating Probe Microscope for Operation in Liquids," Applied Physics Letters 69:4111-4114 (1996). It is more sensitive than the former method which relies on the magnitude of dB/dz. Large magnetic field gradients are difficult to generate. In the second method, where a given B field produces a torque, this is translated into a large force by the shortness of the cantilever, as described by Equation 8.
This method is most sensitive when operated in an AC mode as taught by Lindsay and Han et al, supra, and as demonstrated by the force curves obtained by O'Shea et al., supra. This method of operation is outlined in FIGS. 5A and 5B. When the cantilever 20 is far from the surface 21 (FIG. 5A), the tip is oscillated with an amplitude X.sub.0. If the driving frequency is well below a resonance frequency of the tip, then ##EQU5## whereas, when the cantilever 20 is interacting with surface 21 (FIG. 5B) of stiffness k.sub.S , ##EQU6## As the surface is approached, k.sub.S becomes much bigger than k.sub.T so that the ratio X/X.sub.0 becomes 1/k.sub.S or equal to the compliance of the sample or surface. It should be noted that a relationship similar to Equation 11 can be derived for the ratio X.sub.T /X.sub.D for the case where the stiff end of the cantilever is driven. However, this is not experimentally useful because it is the quantity X.sub.T that is measured (referred to as X in equation 11). Where X.sub.T is far from the surface, it is not simply related to X.sub.D if the tip is driven in a medium such as a fluid, even if far from resonance.
For the case of direct-force driving of the tip near a surface, a plot of the quantity X/X.sub.0 as a function of distance from the surface reflects the relative compliance of the surface, (k.sub.S /k.sub.T).sup.-1. Such a curve might more appropriately be called a compliance curve to differentiate it from a force curve. The inherently greater sensitivity and information content of compliance curves is illustrated by the measurements of O'Shea et al., supra.
Finally, there is presently considerable interest in measuring the stiffness of individual molecules attached between the tip and the surface as illustrated in FIG. 6. Chemical means are used to attach one end of a macromolecule 30 to the tip 4, while the other end is attached to the surface 21 below the tip 4. The prior art has consisted of generating a force curve (like that shown in FIG. 2) as the molecule is stretched or compressed by motion of the piezoelectric actuator 1. An example of such a measurement is the recent work by Reif et al., "Reversible Unfolding of Individual Titin Immunoglobulin Domains by AFM," Science 276:1109-1112 (1997). Dramatic variations in stiffness were observed as particular domains of a protein were unfolded sequentially.
Accordingly, the need still exists in this art to provide an apparatus for measuring the compliance of samples on a nanometer scale as a function of the approach distance of a tip more rapidly and without the hysteresis problems of the prior art. There is also a need to provide a method for setting the operating point of an imaging microscope to a fixed value of surface compliance prior to scanning the tip over the surface.