The Problem

During an STM experiment the tip is less than 1nm above the surface and must be held in position to within 0.001nm. This means that the STM tip can jiggle above the surface by no more than 1/200th the diameter of a single atom! How can we prevent vibrations from travelling into our microscope and jiggling the tip?

To begin with we must ask what causes things to jiggle in the first place. The most obvious culprit is ambient vibrations and noise in the surrounding building. A vibration is a form of energy and the transfer of this energy to the tip can cause it to jiggle. We need to separate our STM from the outside world using a material that absorbs but does not transmit vibrations.

In Introductory Physics, we are often introduced to a study of vibrations in which a single oscillation occurs in a spring, or in a swinging pendulum. In the real world, the sources of oscillations are many, objects can vibrate in more than one way, materials can damp the vibration by converting the energy due to motion into heat, and the oscillations are not always smooth.

In order to treat real world oscillations, then, we must know how to deal with multiple vibrations, and vibrations with sudden changes. When waves are complex, we must know how to determine the most important aspects of the vibration, or the fundamental vibrational modes.

When we know what vibrations our instrument is subject to, we can then treat our main problem, eliminating instrument vibration.