The scanning tunneling microscope (STM) has provided stunning insights into the world of single atoms. However, STM can only image samples with electrical conductivity. The atomic force microscope , introduced in 1986, can image nonconducting surfaces as well. The success of STM was launched with the first image of the Si(111)-(7×7) surface in real space . Will the atomic force microscope ever pass this benchmark test? This question was open for almost a decade after the AFMs introduction until a positive response was achieved with a dynamic technique . Frequency modulation force microscopy  is now a standard technique that allows to image semiconductors, metals and insulators with true atomic resolution [4-6]. In the first successful experiment, a cantilever with a spring constant of 17 N/m, an eigenfrequency of 114 kHz and a quality factor of 28000 was operated in the frequency-modulation mode with a constant amplitude of 34 nm . The tip-sample interaction caused the operating frequency to drop by 70 Hz. The most remarkable issue in this set of empirical parameters is the large oscillation amplitude. The chemical forces responsible for the image contrast have merely a range of a few hundred picometers, and the amplitude is several hundred times greater. Intuitively, it appears sensible to use much smaller amplitudes. However, experiments seemed to show that these extremely large amplitudes were necessary. Parameters of this order are still used today successfully to image surfaces with atomic resolution by AFM. Nevertheless, intuition is right: the use of small amplitudes does yield greater resolution and greater sensitivity to short-range forces.
For stability reasons very stiff cantilevers have to be used in order to minimize the effects of conservative and dissipative tip-sample forces. The motion of the cantilever — a nearly perfect harmonic oscillator in the absence of tip-sample interaction — should only be slightly disturbed by the tip sample forces. The relevant mechanical parameters are the stiffness of the cantilever k, its oscillation amplitude A and its quality factor Q. The most critical state is the point of closest approach of tip and sample. For minimal disturbance, we demand that two stability criteria, involving the retracting force of the cantilever at closest approach and the energy stored in the cantilever are met . Traditional cantilevers require amplitudes of some ten nanometers for stable oscillation. Stable oscillation at sub-nm amplitudes is realized for cantilevers with a stiffness of ≈ kN/m.
Four new developments became possible with the stiff cantilever/small amplitude technique: a) subatomic resolution where features within atoms were attributed to atomic orbitals , b) lateral force microscopy with true atomic resolution , c) imaging of rest atoms within the Si(111)-(7×7) surface at room temperature  and d) subatomic resolution by dynamic STM . The implementation of the small-amplitude / stiff-cantilever method is simplified greatly with the introduction of self-sensing quartz cantilevers.
In summary, atomic force microscopy has matured significantly in four aspects: a) resolution, b) versatility, c) theoretical understanding and d) ease of use. This work is supported by the BMBF (EKM 13N6918).
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