1 The principles of Atomic Force Microscopy (AFM) Introduction: Microscopes have historically been tools of great importance in biological science. The atomic force microscopy (AFM) is one of a family of scanning probe microscopes which has grown steadily since the invention of the scanning tunneling microscope by Binning and Rohrer in the early eighties for which they received the Nobel Price for Physics in 1986. There are some significant advantages of AFM as an imaging tool in biology and physics when compared with complementary techniques such as electron microscopy. Not only does AFM achieve molecular resolution but can be performed under fluids permitting samples to be imaged in near native conditions. The fluid may be exchanged or modified during imaging and therefore there is the potential for observing biological processes in real time, something which electron microscopy is not currently able to achieve. There have been many studies of biological materials using AFM in the few years since its conception. Examples include nucleic acids and their complexes with proteins, two dimensional protein crystals and individual isolated proteins, membranes and membrane bound proteins, and living cells. The instrument is also capable of manipulating molecules and measuring the strength of molecular interactions with pico-newton sensitivity. Fig. 1: The AFM. Adjustment of the microscope requires in this case coarse and fine approaches of fiber end and cantilever on the one hand and of cantilever and sample on the other hand. This task is solved by a combination of different piezoelectric actuators involving two concentric piezo tubes for fiber and cantilever positioning, a motor driven by shear piezos for positioning of the probe with respect to the sample, and an arrangement of three piezo tubes for scanning. Since the set-up does not contain any elements which could only be adjusted manually, fine tuning of the interferometer or the probe-sample seperation within a cryostat or UHV(ultrahigh vacuum)-chamber is straightfoward. The piezoelectric walker can move stepwise over a few milimeters exhibiting a single-step precision of 100 nm or less. Since the whole microscope head is made from non-magnetic components, it can be operated under the influence of high magnetic fields.Piezoelectric ceramics are a class of materials that expand or contract in the presence of a voltage gradient or, conversely, create a voltage gradient when forced to expand or contract. Piezoceramics make it possible to create three-dimensional positioning devices of high precision. Most scanned-probe microscopes use tube-shaped piezoceramics because they combine a simple one-piece 2 construction with high stability and large scan range. Four electrodes cover the outer surface of the tube, while a single electrode covers the inner surface. Application of voltages to one or more of the electrodes causes the tube to bend or stretch, moving the sample in three dimensions.

Fig. 2: The tube. If AFM should be performed on liquid / solid interfaces, the sample holder is substituted by an electrochemical cell. Fig. 3: An electrochemical cell. For experiments where youhave to change the fluid during scanning, there is also a cellwith two small plastic tubes for controlled input and output of fluids available. Another kindof fluid cell can be heathen. This device contains a couple of reference electrodes and is chemically largely inert. Sample, cantilever and fiber end are all immersed in the liquid environment. A considerable strength of the fiber interferometer is that no interference between light reflected off the cantilever on the one hand and at the liquid / gas (or liquid / air) interface on the other hand affects the measurement. Ever more complex are set-ups which additionally allow a variable sample temperature involving low and elevated values. The most sophisticated approaches offer the option to additionally apply high magnetic fields. AFM can generally measure the vertical and horizontal deflection of the cantilever with picometer resolution. To achieve this, most AFMs today use the optical lever, a device that achieves resolution comparable to an interferometer while remaining inexpensive and easy to use. The optical lever operates by reflecting a laser beam off the back of the cantilever. Angular deflection of the cantilever causes a twofold larger angular deflection of the laser beam. The reflected laser beam strikes a position-sensitive photodetector consisting of four side-by-side photodiodes. The difference between the four photodiode signals indicates the position of the laser spot on the detector and thus the angular deflection of the cantilever. If the tip is scanned over the sample surface then the deflection of the 3 cantilever can be recorded as an image which represents the three dimensional shape of the sample surface (deflection image).But the AFM not only measures the force on the sample but also regulates it, allowing acquisition of images at very low forces. The feedback loop consists of the tube scanner that controls the height of the entire sample; the cantilever, which measures the local height of the sample; and a feedback circuit that attempts to keep the cantilever deflection constant by adjusting the voltage applied to the scanner. The faster the feedback loop can correct deviations of the cantilever deflection, the faster the AFM can acquire images; therefore, a well-constructed feedback loop is essential to microscope performance. a c b Fig. 4a, b: The laser spot is focussed on the back of the cantilever and the angle of the reflected laser is detected by a PSD (photosensitive detector). c: The principles of the feedback loop. The tips: In order to detect local forces or closely related physical quantities the sharp probe scanning the sample surface at same distance has to be liked to some sort of force sensor. A convenient way to precisely measure forces is to convert them into deflections of a spring according to Hookes law:Fig. 5:a: A pyramidal tip.It can bemodified by chemical reactions. b: The kind of cantilever which is used in our lab. Each of the cantilever has a characteristic spring constant, thetip iself is positioned at the end ofthe Vs and the bar (*). There aremagnetic and non-magneticcantilevers of this geometryavailable. They are called (from the left to the right) F (not shown), E, C, D, B. * * * *BCDEba ckFz= , where the deflection z is determinated by the acting force F and the spring constant kc. 4 bca Fig. 6: a: Scheme of the tips spring constant. b: Other kinds of tips. Today a variety of cantilevers with different geometries (mainly bar- and V-shaped) and with pyramidal as well as conical tips is commercially available. The resonant frequency of a spring with spring constant kc and lumped effecteve mass m is given by mkc=0 . Because of the Hooks law it is desirable to have a low spring constant in order to achieve maximum force sensitivity. This is contadicted by three aspects:The spring constant should be a maximum in order to achieve a maximum resonant frequency, and thus, a minimum vibrational sensitivity and a maximum scan rate.The ultimate sensitivity of the force measurement is restricted by thermal excitation of the cantilever. The latter quantity can be determined from the equipartition theorem ( )cBrmskT kz = , where is the rms displacement amplitude of the end of the cantilever due to thermal excitation.( )rmsz If the cantilever is subject to a long-range attractive force, and this will almost always be the case upon probe-sample approach, its position becomes unstable if the magnitude of the force gradient equals the cantilevers spring constant. Thus, a certain minimum spring constant is needed in order to approach the sample sufficiently closely without a jump to contact. In order to estimate the order of magnitude which the spring constant of the cantilever could have, it is straightforward to match kc to the respective constant of interatomic coupling in solids.Taking m = 10-25 kg and 0 = 1013 Hz for atomic masses and vibrational frequencies are arrives atkc = 10 N/m. Even smaller spring constants can be easily obtained by minimizing the cantilevers mass. Commercialcantilevers have a typical spring constant in the range of 10-2 N/m kc 102 N/m, typical resonant frequencies in the range of 1 kHz 0 500 kHz, a radius of curvature of the probing tip as small as 10 nm, and are usually fabricated of Si, SiO2 or Si3N4. If one again takes the above estimate for the interatomic couplig (c = 10 N/m) for a rough estimate of the resulting deflection of a cantilever which is subject to an interatomic interaction, one finds that a force of 1 nN causes a deflection of 1, while thermal rms raise amounts to above 20% of this value. Thus, the task is to precisely measure cantilever deflections being smaller than 1. The resolution of AFM depends mainly on the sharpness of the tip which can currently be manufactured with an end radius of a few nanometers. A close enough inspection of any AFM tip reveals that it is rounded off. Therefore force microscopists generally evaluate tips by determining 5 their end radius. In combination with tip-sample interaction effects, this end radius generally limits the resolution of AFM. As such, the development of sharper tips, p. e. nano-tubes, is currently a major concern. Atomic resolution is easily obtained on relatively robust and periodic samples. Soft samples particularly biological samples provide a more difficult surface to image because the forces exerted by the tip during imaging can cause deformation of the sample. The problem involved with imaging soft samples have been overcome to a large extent by the introduction of tapping mode AFM imaging. Instead of maintaining a constant tip-sample distance of a nanometer or so, the cantilever is oscillated in a direction normal to the sample resulting in only intermittent contact with the surface. This greatly reduces the lateral forces being applied in the plane of the sample which are responsible for most of the damage as the tip is scanned. The AFM is capable of better than 1 nm lateral resolution on ideal samples and of 0.01 nm resolution in height measurement. Fig. 7: The principle of scanning: protrusions appear wider, depressions narrower than they are in reality. If the interaction decay length