Exploring the nanoworld with atomic force microscopy Franz J. Giessibl and Calvin F. Quate Over its 20-year history, the atomic force microscope has gradually evolved into an instrument whose spatial resolution is now fine enough to image subatomic features on the scale of picometers. Franz Giessibl is a professor of physics at the University of Regensburg and the University of Augsburg in Germany. Calvin Quate is a professor of electrical engineering and applied physics at Stanford University in California. In 1985 Gerd Binnig and Christoph Gerber took a original 1986 paper, which ranks it among the 10 most-cited temporary leave from IBM’s Zürich Research Laboratory in articles in Physical Review Letters. This past August the Inter- Rüschlikon, Switzerland, where the excitement created by the national Conference on Nanoscience and Technology in invention of the scanning tunneling microscope (STM) made Basel, Switzerland, celebrated the STM’s 25th anniversary it hard for them to experiment without frequent interruptions. and the AFM’s 20th. The accompanying exhibition hosted After relocating to California, they worked with one of us more than a dozen manufacturers that offer AFMs for use in (Quate) and colleagues at Stanford University and with scien- ambient conditions, liquid environments, ultrahigh vacuum, tists at IBM’s Almaden campus to implement Binnig’s idea of and even outer space (aboard the Phoenix Mars mission), that same year: the atomic force microscope.1 In February 1986, plus light and portable versions powered by batteries. De- Binnig, Quate, and Gerber introduced the first prototype AFM, spite the variety of AFM flavors and applications, in this ar- six months before Binnig and Heinrich Rohrer won the Nobel ticle we will focus on the nature of its atomic-scale imaging. Prize for their STM. The STM records the quantum-mechanical tunneling current that flows between a sharp voltage-biased Path to atomic resolution tip and a conductive surface; from such data one can build a The 1986 Binnig, Quate, and Gerber paper reported experi- three-dimensional atomic-scale map of the surface. An AFM, mental data of a sapphire surface with lateral features spaced in contrast, probes the cumulative forces that act between 3 nm apart—far from atomic resolution. But the authors also atoms in the tip and surface (see figure 1). presented a plethora of visionary ideas on how to improve the Because forces act among insulators as well as conduc- AFM’s resolution, including oscillating-cantilever modes that tors, the idea of force microscopy promised to extend the spa- would later become so successful. Their confidence in the po- tial resolution achieved with an STM. Today, that widespread tential for atomic-scale imaging—the paper’s central claim— applicability is reflected in more than 4700 citations of the arose partly from the observation of forces acting on the STM Box 1. The physics of tip–sample forces In vacuum, the interaction Fts between the Electrostatic forces follow the general =− 2 sample and the tip of an atomic force micro- equation Fe 1/2 U dC/dz, where U is scope is governed by short-range chemical- the voltage between tip and sample and C bonding forces and long-range van der R the capacitance. For a spherical tip and flat = −πε 2 ε Waals, electrostatic, and magnetic-dipole surface, Fe 0RU /z where 0 is the forces. The van der Waals forces originate z permittivity of vacuum. from fluctuations in the electric dipole moment Both van der Waals and electrostatic of atoms and their mutual polarization. For interactions can become quite large com- two atoms separated by a distance z, the pared with chemical-bonding forces. A tip of induced dipole–dipole energy varies as radius 100 nm about 0.5 nm from the sur- 1/z 6. The standard Hamaker approach to 4 face experiences a van der Waals force of calculating the van der Waals energies for 0 about −10 nN and an electrostatic force of − = macroscopic bodies assumes that individual –4 5.5 nN for U 1 volt. As modeled by a atom–atom interactions are additive. That (nN) Morse potential, the chemical bonding –8 ts makes it possible to calculate the forces acting F energy of two atoms decays exponentially –12 in simple geometries. For the case of a spher- Short-range forces with the distance z until it reaches a repulsive ical tip approaching a flat surface, as pic- –16 Long-range forces regime. That makes the bonding contribution tured and plotted here, the van der Waals –20 relevant mainly for tip and surface atoms forces F =−A R/6z2, with R being the 0 0.5 11.5 2 that are closest to each other. The strong vdW H z (nm) tip’s radius, AH the Hamaker constant, rough- covalent bonds, such as those in silicon, for ly an electron volt for solids, and z the tip–sample distance. example, reach maximal attractive forces of about −4 nN. 44 December 2006 Physics Today © 2006 American Institute of Physics, S-0031-9228-0612-020-7 Downloaded 07 Nov 2012 to 131.215.16.11. Redistribution subject to AIP license or copyright; see http://www.physicstoday.org/about_us/terms tip. But other researchers remained skep- Z tical. Experimental challenges are greater Y in force microscopy than in tunneling mi- Concept Realization X croscopy. Indeed, the STM produced k spectacular atomic-scale images shortly after its development (see Quate’s article in PHYSICS TODAY, August 1986, page 26, m and Tien Tsong’s article in March 2006, k page 31), but it took a decade for force ts microscopy to mature into a true atomic- scale tool.2 Figure 1. Like the gentle touch of a tiny finger, the atomic force microscope (AFM) The reason lies in the complicated feels the force of atoms on a surface to create an image of the local topography. nature of the surface forces that can act on Mounted on a cantilever having a spring constant k, the tip can be drawn along the a tip (see box 1) and the instrumental so- surface, while computer-controlled feedback maintains a constant deflection. Or the phistication required to deal with them tip can be deliberately vibrated up and down as it scans a surface. In that dynamic (see boxes 2 and 3), compared with the = mode, the derivative of the tip–sample force, kts dFts/dz, is measured. As the tip simplicity of electron tunneling. The ex- approaches the surface, the AFM senses the shift in the cantilever’s resonance fre- ponential drop-off in current that tunnels √ π √ + π quency from (k/m)/2 to ([k kts]/m)/2 , where m is the cantilever’s mass. across the gap between tip and surface in (Adapted from G. Binnig, H. Rohrer, Rev. Mod. Phys. 71, S324, 1999.) an STM ensures that the current is spa- tially confined to the frontmost atom of the tip and surface. That distance dependence is also mono- keep a cantilever stable near an attractive sample so that tonic, which makes a simple feedback scheme possible. The chemical bonds can influence deflection, it turns out that one feedback loop withdraws the tip when the current is larger must either vibrate a soft cantilever with large amplitude or than some setpoint and advances the tip otherwise. Currents use a stiff cantilever. in the nanoampere range can be measured with modest ex- Nevertheless, soon after the AFM’s introduction, atomic perimental means and an excellent signal-to-noise ratio. contrast became apparent in images recorded under ambient In an AFM, the cumulative force—a mixture of short- conditions. Those images showed periodic lattices without and long-range interactions—is much less tractable as a point defects or steps. It soon became clear that the contact feedback signal. It is not monotonic with distance, nor is area between tip and sample in those experiments must have measuring forces on the order of nanonewtons with high been much larger than a single atom, and an averaging signal-to-noise ratios an easy task. In vacuum, the force is process was taking place that mimicked true atomic resolu- dominated by attractive van der Waals forces for distances tion as many tip atoms interacted with many surface atoms. larger than about half a nanometer. Chemical-bonding The situation was akin to one egg crate profiling another one. forces, initially attractive as the tip approaches the surface, The key task in achieving true atomic resolution is to sin- turn repulsive as the gap closes. gle out the chemical-bonding forces of surface atoms on the Forces are usually measured indirectly by determining front atom of the tip from the various other forces at play and the deflection of a spring with stiffness k. A force F deflects exploit its signal for distance feedback. Binnig and Gerber the cantilever by a distance F/k, and one would think that to realized that reaching that goal would require a controlled obtain a large signal and a good signal-to-noise ratio, soft can- environment—ultrahigh vacuum and low temperature—to tilevers would be best suited. The problem is that large cope with the instability problems inherent in the AFM. One van der Waals forces cause the tip to jump uncontrollably to of us (Giessibl) joined the project in the newly founded IBM the surface as the soft, springy cantilever approaches it. To physics group at the University of Munich. After a few years a b c 100 nm 5nm 1nm 2nm Figure 2. A gallery of atomic-resolution images, made using the AFM’s frequency-modulation mode of operation.