1.1 Introduction

This chapter is an introduction to the main aspects encountered in modeling and designing mechanical microresonators.

Aside from the technological reasons for realizing systems that integrate the mechanical structure and the associated silicon/semiconductor electronic circuitry, the drive toward smaller-scale, nano-domain mechanical resonators is motivated by the need for pushing the limits to the resonant frequencies in the gigahertz domain. It is known that the stiffness of a mechanical resonator varies with the inverse of the length (because the basic definition of stiffness is force divided by length):

and that the resonant frequency is proportional to the square root of the stiffness:

As a consequence, increasing the resonant frequency of a mechanical device implies miniaturization, and therefore very high frequencies are achieved by very small resonator dimensions. In addition, as this chapter discusses, higher resonant frequencies (which are achieved with small-dimension resonators) also contribute to increasing the quality factor of a system, which is a measure of its resonant performance. Smaller is also better, as Chap. 6 will demonstrate, in detecting minute amounts of deposited substances as the capacity of capturing the effects of mass at the cell level is inversely proportional to the geometric dimensions of a mechanical resonator.

Constructively, the mechanical microresonators can be cantilevers, as sketched in Fig. 1.1a; bridges, as in Fig. 1.1b; tuning forks, as shown in Fig. 1.2a, b, and c. Or they can be of a more complex geometry, such as the lateral resonator design with folded-beam suspensions illustrated...