the base line is heat

A famous engineer, Buckminster Fuller, once identified the inability to prevent energy loss in mechanical systems as the foremost inhibitor of technological advancement. The limitation Fuller identified is the fundamental problem faced by micromechanical systems and nanomechanical systems (MEMS and NEMS, respectively) using resonance based detection. Micromechanical resonators are micro or nano sized structures, such as microfabricated cantilevers, plates, and rings used in many applications such as atomic force microscopy [ALBRECHT], fluidic density sensing [ENOKSSON], and bio-substance detection [BURG].

Operated at mechanical resonance, a detected shift in natural frequency is correlated to an applied force such as an acceleration or mass. Critical to the functional accuracy, efficiency, and limit of detection is a very low damping factor (δ), also known as the logarithmic decrement. Low δ results in high signal-to-noise ratio and plays an important role in defining the minimum frequency shift or force that can be resolved with a microcantilver resonator, for given cantilever dimensions and frequency [YASUMURA]. Damping in micromechanical resonators comes from a variety of sources including support loss, viscous damping, clamping losses, internal friction, and thermoelastic damping (TED). The first three mechanisms of damping are extrinsic and may be minimized via design guidelines, as detailed in the next section. Inconveniently, the last two sources are intrinsic and thus establish a damping limit.

Of the intrinsic losses, internal friction is always present and is a difficult form of damping to quantify but can be considered to come from crystallographic or surface defects and the friction at grain boundaries [YANG_2000]. Generally, the use of single-crystal materials such as quartz or semi-conductor grade single-crystal silicon, containing a low density of defects, can reduce this source of damping below that of TED. TED is caused by thermoelastic coupling of an oscillating mechanical stress field to a temperature field and is therefore of great importance for resonance based detection.